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Mathematics

Welcome to the mathematics section of the Norwalk Public Schools website.  Our mathematics program aims to provide all students with the mathematical concepts and skills needed to be productive members of society. Our instructional goal and philosophy is to infuse Jo Boaler's mathematical mindset into our practices for teaching and learning. In addition, we aim to provide all students with the ability to move from concrete, visual, and abstract understandings of mathematics to communicate their thoughts and ideas.

The curriculum and instruction in elementary, middle and high school math is focused on computational thinking/problem solving using number talks, collaborative sharing of multiple strategies, and synthesis to allow students the ability to reflect on the process of why and how. Our curriculum frame follows Larry Anisworth's Rigorous Curriculum Design Model and is written by Norwalk Public School teachers. The curriculum is rooted in the Common Core State Standards and blends the 8 Mathematical Practices Standards

Parent Guides to the Math Curricula

Please see below for a parent guide to each math curriculum from kindergarten to high school.

  • Parent Guide to the Math Curriculum - Grade 1

    Unit 1: Adding, Subtracting and Working with Data

    Essential Questions

    Unit 1 Overview

    • How is adding and subtracting like counting?
    • What is the best way to represent data I collect in a survey so that it is clear?
    • How does data help me to explain or describe real life situations?
    • What does it mean to be a member of a mathematical community?

    In this unit, students in grade 1 deepen their understanding of addition and subtraction within 10 and extend what they know about organizing objects into categories and representing quantities.  Activities in this unit reinforce kindergarten understandings of addition and subtraction word problems and initiate the year-long work of developing fluency with sums and differences within 10.  Students also extend their understanding of engaging in data by using drawings, symbols, tally marks, and numbers to represent data, as well as ask and answer questions about the data.

    Unit 2: Addition and Subtraction Story Problems

    Essential Questions Unit 2 Overview
    • How can I use addition or subtraction to show how to solve a story problem where I can add to/take from a total or where I need to figure out the change?
    • How can I use equations to show different ways to make a total amount?
    • How can I show “how many more” and “how many fewer” using addition and subtraction equations?
    • How can I write and solve story problems using drawings, pictures, words, or equations?

    Students expand on their understanding of story problem types that were established in Kindergarten and work to solve the majority of story problem types.  The focus in this unit is for students to interpret and understand the meaning of the story problem and build their fluency of addition and subtraction within 10.  A large focus of this unit is for students to represent story problems with multiple equations, deepening their understanding of addition and subtraction, and to explain the relationship between their equations and the story problem.

    Parent video: Modeling with tape diagrams

    Unit 3: Adding and Subtracting Within 20

    Essential Questions Unit 3 Overview
    • How can I use what I know about tens and ones to add and subtract two-digit numbers?
    • How do I recognize what strategy to use for a specific problem?
    • How can using number relationships help me solve addition and subtraction problems?

    In this unit, students develop an understanding of 10 ones as a unit called “a ten” and use the structure to add and subtract within 20.  Students decompose and recompose addends to find the sum of two or three numbers, for example to find the value of 6 plus 9, they may decompose 6 into 1 and 5, compose the 1 and 9 into 10, and find 5 plus 10.  Students work on subtraction by using their knowledge of addition to find the difference of two numbers and learn two new story problems through the unit.

    Unit 4: Numbers to 99

    Essential Questions Unit 4 Overview
    • How can we find the total when we join two quantities?
    • How can we find what is left when we take one quantity from another?
    • How can we represent a number using tens and ones?
    • What do less than, greater than, and equal to mean?
    • What is estimating and when can you use it?

    Students develop an understanding of place value for numbers up to 99 as well as an understanding of the structure of numbers in our base ten system, allowing them to see that two digits of a two-digit number represent how many tens and ones there are.  As they develop their understanding of tens and ones, they will learn to transition from counting by one to counting by ten and then counting on for numbers greater than 10.  Students will use drawings and mathematical tools to represent numbers up to 99 and will compare two-digit numbers.

    Unit 5: Adding Within 100

    Essential Questions Unit 5 Overview
    • How can I estimate the answers for operations involving two-digit numbers?
    • How can I use what I know about tens and ones to add two-digit numbers?
    • What strategies do I use to compute sums mentally?

    Students use place value and properties of addition to add within 100.  They make sense of methods for adding, like composing a ten when adding ones and ones, and work with a variety of representations- connecting cubes, drawings, expressions, and equations.  The focus for students is to make sense of the numbers and ways of adding rather than applying an algorithm.

    Unit 6: Length Measurements Within 120 Units

    Essential Questions Unit 6 Overview
    • How do I measure length using non-standard units of measure?
    • How do I choose the appropriate tool and unit when measuring?
    • How can objects be measured, compared, and ordered by length?

    In this unit, students extend their knowledge of linear measurement while continuing to develop their understanding of operations, algebraic thinking, and place value.  Students compare the length of objects by lining them up at their endpoints and explore ways to compare lengths of two objects that cannot be lined up.  Students develop precision with different measuring tools, solve story problems and are introduced to new story problem types, and reason how to count and represent groups of objects over 99 up to 120.

    Unit 7: Geometry and Time

    Essential Questions Unit 7 Overview
    • How can I tell time on an analog and digital clock?
    • How can we break shapes into equal shares and what these shares are called?
    • How do I distinguish shapes between defining and non-defining attributes?

    In this unit, students focus on geometry and time, expanding their knowledge of two and three-dimensional shapes, partition shapes into halves and fourths, and tell time to the hour and half an hour.  Students extend the foundation they build about shapes in Kindergarten to develop more precise vocabulary to sort shapes into categories and use shapes to begin to learn the language of fractions.  Students also learn to use the circle as a clock and how hour and minute hands partition the clock to the hour and to “half past” or __:30.

    Unit 8: Putting it All Together

    Essential Questions Unit 8 Overview

    How can using number relationships help me solve addition and subtraction problems?

    How can I use an addition or subtraction equation to show how to solve a story problem where I can add to/take from a total or where I need to figure out the change?

    How can I use numbers to 120?

    In this last unit for Grade 1 math, students will work on solidifying their understanding of the major concepts and skills for the year to prepare them for Grade 2.  The sections in this unit include adding and subtracting within 20, and fluently within 10.  Students will also practice solving story problems they were introduced to during the year.  Additionally, they will count and represent numbers within 120.

     

  • Parent Guide to the Math Curriculum - Grade 2

    Unit 1: Adding, Subtracting, and Working with Data

    Essential Questions

    Unit 1 Overview

    • How can the number 10 help me to add and subtract quickly with larger numbers?
    • How do picture and bar graphs help me to organize my data?
    • How does knowing ‘how many more’ and ‘how many less’ help me determine quantities between two groups?

    In this first grade 2 unit, students build on concepts of addition and subtraction from grade 1 and begin the year-long work to develop fluency with sums and differences within 20.  Students work with new ways to represent data, picture graphs and bar graphs and ask and answer questions described by the data.  This unit also focuses on introduction to mathematical routines and structures for centers, and developing a shared understanding of what it means to do math and to be part of a mathematical community.

    Parent video: Tape diagrams for modeling addition and subtraction

    Unit 2: Adding and Subtracting Within 100

    Essential Questions

    Unit 2 Overview

    • How can I use base-ten blocks to help me add and subtract?
    • Why do you have to decompose a ten sometimes when you subtract?
    • How does using a diagram help me make sense of story problems?

    Students in this unit build onto their understanding of adding within 100 from grade 1 by using strategies based on place value, properties of operations, and relationship between addition and subtraction.  Students use mathematical tools such as base-ten blocks and work to understand composing and decomposing tens to flexibly add and subtract.  They apply this knowledge to solve one- and two-step story problems using a variety of mathematical tools.

    Unit 3: Measuring Length

    Essential Questions

    Unit 3 Overview

    • How can different tools be used to estimate and measure different lengths
    • How can we solve one- and two- step story problems involving addition and subtraction of lengths?
    • How does the structure of a line plot relate to the tools we used to measure lengths?

    In this unit, students learn about standard units of length (centimeters, meter, inches, and feet).  They learn how to measure with different length units as well as how to estimate the length of objects. Through the unit, students continue to solve one- and two- step story problems using addition and subtraction of lengths.  This unit also has students creating and interpreting line plots that show measurement data and use them to answer questions about the data.

    Unit 4: Addition and Subtraction on the Number Line

    Essential Questions

    Unit 4 Overview

    • How can number lines help us solve addition and subtraction problems?
    • How do we represent an equation on a number line?

    Students are introduced to essential representation of the number line.  In this unit, they learn to use the number line to represent whole numbers, sums, and differences.  Students will use the number line for representing addition and subtraction, decomposing a number to get to a ten, and estimate on the number line without having each labeled with a numeral.

    Unit 5: Numbers to 1000

    Essential Questions

    Unit 5 Overview

    • How can we show a number using different tools?
    • What strategies can we use to order numbers on a number line?
    • What is the difference between a one-digit number, a two-digit number, and a three-digit number?

    Students extend their knowledge of the base-ten system to include hundreds.  They learn that a hundred is a unit made up of 10 tens, and three-digit numbers are formed using units of hundreds, tens, and ones.  Students build their flexibility in reasoning with a variety of representations (base-ten blocks, base-ten diagrams or drawings, number lines, expressions, and equations).  

    Parent video: Number forms

    Unit 6: Geometry, Time, and Money

    Essential Questions

    Unit 6 Overview

    • What strategies do you use to count groups of pennies, nickels, dimes, and quarters to find the total value?
    • How do you read and write time to 5-minute intervals using a clock?
    • How can I partition a circle or a rectangle?

    Students spend time in this unit to reason with shapes and partition them into equal shares (halves, fourths, and thirds) to set the foundation for fractions.  They look at attributes of shapes to see that shapes can be identified by the number of sides and vertices (corners). Using their understanding of halves and fourths, students extend it to their understanding of time (“quarter past” and “quarter to”) and skip-count to tell time in 5-minute intervals.  The last part of this unit includes money, building on the fluency of addition and subtraction within 100 by skip-counting, adding and subtracting to find the value of a set of coins, and solving one- and two-step money story problems.

    Unit 7: Adding and Subtracting Within 1,000

    Essential Questions

    Unit 7 Overview

    • What are the ways to add and subtract three-digit numbers?
    • How do we understand place value and use properties of operations to add and subtract?

    In this unit, students add and subtract within 1,000 by applying methods they have learned previously as well as their understanding of place value and three-digit numbers.  Students progress to composing and decomposing one or more units in a two- to three-digit number.  Students learn to recognize when composition or decomposition is a useful strategy when adding or subtracting by place and are encouraged to think flexibly to use strategies that make sense to them.

     

    Parent video: Regrouping to subtract (place value disks)

    Unit 8: Equal Groups

    Essential Questions

    Unit 8 Overview

    • How can you work with equal groups of objects to understand multiplication?
    • How can you use the array model to explain multiplication?
    • How can you show even and odd numbers?

    This unit has students developing an understanding of equal groups, to gain foundation for multiplication and division in grade 3 and beyond.  Students use visual patterns to identify whether numbers of objects are even or odd, describe rectangular arrays as rows and columns, and see the total number of objects as a sum of the objects in each row and the sum of the objects in each column.  They write equations with equal addends to describe arrays (4 + 4 + 4) as well as build arrays.  

    Parent video: Foundation of Multiplication & Division

    Unit 9: Putting It All Together

    Essential Questions

    Unit 9 Overview

    • How can the number 10 help me to add and subtract quickly with larger numbers?
    • Why do you have to decompose a ten sometimes when you subtract?
    • How do we understand place value and use properties of operations to add and subtract?

    In this unit, students revisit the major work and fluency goals of grade 2, applying their learning of the year.  They solidify their fluency with addition and subtraction within 20, add and subtract numbers within 100, and compose and decompose three-digit numbers in different ways, using methods based on place value to work with numbers within 1,000.  Students also interpret, solve, and write story problems with numbers within 100, furthering their fluency of addition and subtraction of two-digit numbers.

     

     

  • Parent Guide to the Math Curriculum - Grade 3

    Unit 1: Introducing Multiplication

    Essential Questions

    Unit 1 Overview

    • What are different meanings for multiplication?
    • How are multiplication and addition related?
    • How do graphs and arrays relate to multiplication?

    Students expand on their grade 2 knowledge of representing data with graphs as they are introduced to multiplication with one picture in a picture graph equaling 2 or 5 units.  As students expand on their understanding of equal size groups and multiplication, they relate the idea of a x b through both groups of objects and amount in each group as well as rows and columns of arrays.  Students also make sense of the meaning of multiplication expressions before solving them.

    Unit 2: Area and Multiplication

    Essential Questions

    Unit 2 Overview

    • How can we find the area of a shape?
    • How does finding the area of a rectangle relate to multiplication?
    • How can I find the missing side lengths of shapes composed of rectangles?

    In this unit, students focus on area as the measure of how much a shape covers.  They explore rectangles and connect the understanding of area of rectangles to multiplication- a product of the number of rows and squares per row.  Through the unit, students develop the understanding of abstract representations of area and learn how to use what they know of area and multiplication to find missing side lengths of figures.

    Unit 3: Wrapping up Adding and Subtraction Within 1,000

    Essential Questions

    Unit 3 Overview

    • How can I use place value to round whole numbers?
    • How are different ways that we add and subtract similar and different?
    • How can I represent and solve two-step word problems with addition and subtraction?

    This unit progresses students toward a third grade goal of fluently adding and subtracting within 1,000.  Students build on their knowledge of addition and subtraction strategies that they learned in second grade.  Students will use place value understanding to round, estimate, and build their fluency in adding and subtracting whole numbers.  They also use expanded form to add and subtract within 1,000 as they move toward the standard algorithm.

    Parent video: Regrouping to subtract (place value disks)

    Parent video: Rounding to the nearest 10 or 100

    Unit 4: Relating Multiplication to Division

    Essential Questions

    Unit 4 Overview

    • What is Division?
    • How can we describe the relationship between Multiplication and Division?
    • How can I use Multiplication to Divide?
    • How do I Multiply a larger number?

    In this unit, students learn about and use the relationship between multiplication and division, place value, and properties of operations to multiply and divide whole numbers within 100.  Previously, students used equal-sized groups to form the basis for their sense of multiplication; this unit has them also use equal-sized groups to make sense of division. Students work toward a grade level goal of fluency in multiplication and division throughout the unit, and learn to decompose numbers greater than 10 into tens and ones to help them multiply.

    Unit 5: Fractions as Numbers

    Essential Questions

    Unit 5 Overview

    • What is a fraction?
    • How are fractions used in our daily lives?
    • What are equivalent fractions?
    • How do we know if one fraction is larger or smaller than another fraction?

    In this unit, students work to make sense of fractions, with a focus in modeling and using diagrams to represent and compare fractions and relate them to whole numbers.  Students use different representations to identify 1 whole and reason about the size of fractional parts.  Later in the unit, students compare fractions with the same denominator as well as those with the same numerator to recognize that as the numerator gets larger, more parts are being counted and as the denominator gets larger, the size of each part in a whole gets smaller.

    Parent video: Fractions on a number line

    Unit 6: Measuring Length, Time, Liquid Volume, and Weight

    Essential Questions

    Unit 6 Overview

    • How can length of time be measured and found?  
    • What are the customary units for measuring capacity and weight?  
    • What are the metric units for measuring capacity and weight?  
    • What is mass and how does it relate to weight?

    Students measure length, weight, liquid volume and time in this unit.  They begin with length measurement, building on their previous units' work of fractions, by exploring length in halves and fourths of an inch on a ruler, learning about mixed numbers and equivalent fractions as they work.  Next, students learn about standard units for measuring weight (kilograms and grams) and liquid volume (liters), finishing the unit by measuring time to the minute.  In the final section of the unit, they solve problems related to all of the measurements learned through the unit.

    Unit 7: Two-dimensional Shapes and Perimeter

    Essential Questions

    Unit 7 Overview

    • How do you find the perimeter of a 2-dimensional shape? 
    • How is geometry apparent in everyday life? 
    • How can two-dimensional shapes be described, analyzed and classified?

    In this unit, students reason about attributes of two-dimensional shapes and learn about perimeter, building on their previously built geometric knowledge from earlier grades.  Students learn to classify geometric shapes into sub-categories based on their attributes (rhombuses, rectangles, squares, quadrilaterals, triangles), while learning the meaning of perimeter and finding the perimeter of shapes.  As the unit progresses, the focus is for students to distinguish situations that involve perimeter and those that involve area (commonly confused) and apply what they have learned to design concepts.

    Unit 8: Putting it All Together

    Essential Questions

    Unit 8 Overview

    • How are fractions used in our daily lives?   
    • How can we find the area of a shape?  
    • How do you find the perimeter of a 2-dimensional shape?  
    • Describe the relationship between Multiplication and Division?

    In this unit, students revisit major work and fluency goals of 3rd grade, applying their learning from the year.  This includes fraction size and location (number lines), perimeter, area, and solving problems about measurement and data through graphs, and multiplication and division fluency.  The last section of the unit prepares them for the major work they will do in 4th grade with comparing, adding, and subtracting fractions, multiplying and dividing within 1,000, and using the standard algorithm to add and subtract within 1 million.

  • Parent Guide to the Math Curriculum - Grade 5

    Unit 1: Finding Volume

    Essential Questions

    Unit 1 Overview

    • What is volume and how is it used in the world around me?
    • How do you determine the volume of a cube or a rectangular prism?
    • How can three-dimensional shapes be represented and analyzed?
    • How do you solve problems related to volume?

    The first 5th grade math unit introduces students to the concept of volume by building on their understanding of area and multiplication.  Students first measure volume by counting unit cubes in a solid shape, then move onto looking at and building right rectangular prisms, paying attention to structure and volume as the prisms become more abstract and less concrete.  They represent their prisms with numerical expressions and, discovering the rules for finding volume.  Toward the end of the unit, students apply their understanding of volume to find the volume of complex shapes as well as apply their knowledge to real-world problems.

    Unit 2: Fractions as Quotients and Fraction Multiplication

    Essential Questions

    Unit 2 Overview

    • How can an even number of objects be divided amongst an odd number of people, places or things? 
    • What does dividing a numerator by a denominator tell me about their relationship? 
    • How does knowing properties in math (commutative, associative and distributive) help me reason with fraction multiplication and division?

    In this unit, students learn to interpret a fraction as a quotient and extend their understanding of multiplication of a whole number and a fraction.  They learn that improper fractions represent division (4 objects shared by 3 people) or multiplication (a third of a group of 4 objects).

    Unit 3: Multiplying and Dividing Fractions

    Essential Questions

    Unit 3 Overview

    • How can drawing, interpreting and analyzing diagrams help us to understand the relationship between multiplication and division of fractions and whole numbers?  
    • How can you multiply a fraction by a fraction? 
    • How can you model division of a unit fraction by a whole OR a whole by a unit fraction with manipulatives and diagrams?

    Students extend multiplication and division of whole numbers to multiply fractions by fractions and divide a whole number and a unit fraction. Students find the product of two fractions, divide a whole number by a unit fraction, and divide a unit fraction by a whole number.

    Unit 4: Wrapping up Multiplication and Division with Multi-Digit Numbers

    Essential Questions

    Unit 4 Overview

    • What strategies can we use to efficiently solve multiplication and division problems? 
    • How can I apply my learning of products and quotients to understand the world around me and solve real world problems? 
    • How can estimating help us when solving multiplication and division problems?  
    • What strategies can we use to efficiently solve division problems and why?

    In this unit, students multiply multi-digit whole numbers using the standard algorithm and begin working toward end-of-grade expectation for fluency. They also find whole-number quotients with up to four-digit dividends and two-digit divisors.

    Unit 5: Place Value Patterns and Decimal Operations

    Essential Questions

    Unit 5 Overview

    • What patterns occur in our number systems? 
    • How do we compare decimals? 
    • How do we solve problems with whole numbers and decimals?

    In this unit, students expand their knowledge of decimals to read, write, compare, and round decimals to the thousandths. They also extend their understanding of place value and numbers in base ten by performing operations on decimals to the hundredth.

    Unit 6: More Decimal and Fraction Operations

    Essential Questions

    Unit 6 Overview

    • How can you use place value concepts to make measurement conversions in the metric system? 
    • What is an example of a real-world fraction problem with unlike denominators that can be solved using different strategies? 
    • How can scaling help me predict and compare products?

    In this unit, students deepen their understanding of place-value relationships of numbers in base ten, unit conversion, operations on fractions with unlike denominators, and multiplicative comparison. The work here builds on several important ideas from grade 4.

    Unit 7: Shapes on the Coordinate Plane

    Essential Questions

    Unit 7 Overview

    • How can coordinates be used to navigate? 
    • How can patterns be displayed on a coordinate grid? 
    • How can the relationship between sets of numbers be used to solve problems?

    In this unit, students learn about the coordinate grid, deepen their knowledge of two-dimensional shapes, and use the coordinate grid to study relationships of pairs of numbers in various situations. 

    Here, students learn about grids that are numbered in two directions. They see that the structure of a coordinate grid allows us to precisely communicate the location of points and shapes.

    Unit 8: Putting it All Together

    Essential Questions

    Unit 8 Overview

    • How can I apply what I have learned in fifth grade?  
    • How can I create a Which One Doesn’t Belong activity to show my learning?

    In this unit, students revisit major work and fluency goals of the grade, applying their learning from the year.  Students deepen their understanding of the standard algorithm for multiplication and practice using it to find the value of products, solve real-world problems about volume and have opportunities to model with mathematics, and revisit work with operations with decimals and fractions.

  • Parent Guide to the Math Curriculum - Kindergarten

    Unit 1: Math in Our World
    Essential Questions Unit 1 Overview
    • How do math tools help me understand mathematics
    • How can I tell how many or how much is in a group?
    • How can I tell if there are enough objects needed for a situation?
    • What does it mean to be a member of a mathematical community?

    Students explore and use mathematical tools while teachers gather information through observations and questions about students’ counting knowledge and skills.  Students also have opportunities to work with math tools and topics related to geometry, measurement, and data through a variety of centers.  In the last section of the unit, students are expected to count up to 10 using various mathematical tools as support.

    Unit 2: Numbers 1-10

    Essential Questions

    Unit 2 Overview
    • How do numbers and quantities relate to each other?
    • How do I write numbers 1-10?
    • How do I know if a number is less than another number?

    Students continue to develop counting concepts and skills, including comparing, while learning how to write numbers.  Students use fingers and five frames as well as familiar activity structures to build their counting skills and concepts.  Students build their math vocabulary as they start to use the terms “fewer” and “more” when comparing the numbers of objects or images.

    Unit 3: Flat Shapes All Around Us

    Essential Questions Unit 3 Overview
    • What shapes are in my environment?
    • How can shapes connect to make different changes?

    In this unit, students will be introduced to the foundational concept of geometry, with a focus on flat (two-dimensional) shapes.  Students will explore differences in shapes and use informal language to describe, compare, and sort them.  Students reinforce counting and comparison skills by using pattern blocks to make larger shapes as well as positional words (above, below, next to, beside) to describe the shapes they compose.

    Unit 4: Understanding Addition and Subtraction

    Essential Questions Unit 4 Overview
    • Why do I need to add?
    • Why do I need to subtract?
    • How can I represent and solve problem situations using objects, pictures, words and numbers?

    Students develop their understanding of addition and subtraction as they represent and solve story problems within 10.  They relate counting to either putting objects together or taking objects away.  Students develop understanding of mathematical expressions and connect expressions to pictures and story problems and find the value of addition and subtraction expressions within 10.

    Unit 5: Composing and Decomposing Numbers to 10

    Essential Questions Unit 5 Overview
    • How can I use place value to decompose numbers to find sums or differences?
    • How do I take apart and recombine numbers in a variety of ways for finding sums and differences?

    Students will explore different ways to compose and decompose numbers within 10 and how to represent the compositions and decompositions.  Students link 10 frames and their fingers as tools to think about pairs of numbers that make 10.  Students will also practice writing numbers and develop the understanding of balanced equations, “5 is 3 plus 2”.

    Unit 6: Numbers 11-20

    Essential Questions Unit 6 Overview
    • How can you know a quantity without counting each object?
    • How do you know how many objects you have?
    • What is an efficient way to count an amount greater than ten?

    In this unit, students count and represent collections of objects and images within 20.  They use the 10-frame as a tool to see teen numbers as 10 ones and some more ones, with emphasis on the structure of the numbers 11-19.  Students practice tracing and writing numbers 11-20 and practice equations with the addend first, using mathematical tools to reinforce understanding.

    Unit 7: Solid Shapes All Around Us

    Essential Questions Unit 7 Overview
    • How can shapes help us count and compare numbers?
    • What shapes are around us?
    • How can we compose shapes using smaller shapes?

    Students explore solid shapes (three-dimensional) while reinforcing their knowledge of counting, number writing and comparison, as well as flat shapes.  They compose figures with pattern blocks and continue to count up to 20 objects, write and compare numbers, and solve story problems.  Students use their own language to describe attributes of solid shapes as they identify, sort, compare, and build them, while also learning the names for cubes, cones, spheres, and cylinders.

    Unit 8: Putting it All Together

    Essential Questions Unit 8 Overview
    • How do numbers and quantities relate to each other?
    • What does it mean to be a member of a mathematical community?
    • How do I take apart and recombine numbers in a variety of ways for finding sums and differences?
    • How can I represent and solve problem situations using objects, pictures, words and numbers?

    In this culminating unit, Kindergarten students revisit major work and fluency goals of the grade, applying their learning from the year.  They revisit concepts of counting and comparing, math in the community, practice composing and decomposing within 5 as well as within 10.  This unit lays the foundation for grade 1, where students add and subtract fluently within 10 and count and compare larger quantities.

  • Parent Guide to the Math Curriculum - Grade 7

    Unit 1: Scale Drawings

    Essential Questions

    Unit 1 Overview

    • How can I decide if two images are scaled copies?
    • How can I use scale factor to understand lengths in scaled drawings?

    In this unit, students study scaled copies of pictures and plane figures, then apply what they have learned to scale drawings (maps and floor plans).  Through the unit, students learn that all lengths in scaled copies are multiplied by scale factor while measure of angles stays the same.  Students work with scale drawings to discover principles and strategies to reason about scale, and learn to express scales in units (1 cm represents 10 km) as well as non-units (the scale is 1 to 100).  The culminating activity for this unit is for students to apply what they have learned and create a floor plan.

    Unit 2: Introducing Proportional Relationships

    Essential Questions

    Unit 2 Overview

    • How can I use tables, graphs, and descriptions to identify proportional relationships? 
    • How can I find and use scale factor with rational number lengths and areas?

    In this unit, students learn to understand and use proportional relationship terms and recognize when a relationship is or is not proportional.  They represent proportional relationships with tables, equations, and graphs and use terms and representations in reasoning about situations that involve constant speed, unit pricing, and measurement conversions.

    Unit 3: Measuring Circles

    Essential Questions

    Unit 3 Overview

    • How can one part of a circle determine the measure of another part? 
    • How are circumference and area connected?

    In this unit, students extend their knowledge of circles and geometric measurement, applying their knowledge of proportional relationships to the study of circles. They extend their grade 6 work with perimeters of polygons to circumferences of circles, and recognize that the circumference of a circle is proportional to its diameter, with constant of proportionality. They encounter informal derivations of the relationship between area, circumference, and radius.

    Unit 4: Proportional Relationships & Percentages

    Essential Questions

    Unit 4 Overview

    • How can we use equations with fractions, decimals, and percentages to represent increase and decrease? 
    • How can we calculate important quantities, such as sales tax, tips, and discounts? 
    • How can we use information about increases and decreases to find original amounts?

    In this unit, students deepen their understanding of ratios, scale factors, unit rates (also called constants of proportionality), and proportional relationships, using them to solve multi-step problems that are set in a wide variety of contexts that involve fractions and percentages.

    Unit 5: Rational Number Arithmetic

    Essential Questions

    Unit 5 Overview

    • How are signed numbers used to represent quantities, opposites, and absolute value? 
    • What concrete and pictorial models can be used to represent operations with integers? 
    • What strategies can be used to predict that the sum of two integers is positive, negative or zero?  
    • What strategies can be used to determine if the product or quotient of two integers is positive or negative?

    In this unit, students interpret signed numbers (all rational numbers in either decimal or fractional form) in context together with their sums, differences, products, and quotients.

    Unit 6: Expressions, Equations, and Inequalities

    Essential Questions

    Unit 6 Overview

    • How can we use representations to model equations? 
    • How do mathematicians use symbols to represent greater than/equal to/less than situations? 
    • What methods can we use to find unknown solutions of equations and inequalities?

    In this unit, students solve equations of the forms px + q = r and p(x + q) = r, and solve related inequalities, e.g., those of the form px + q > r and px + q ≥ r, where p, q and r are rational numbers.

    Unit 7: Angles, Triangles, and Prisms

    Essential Questions

    Unit 7 Overview

    • What are the characteristics of angles and sides that will create geometric shapes, especially triangles? 
    • How can the special angle relationships – supplementary, complementary, vertical, and adjacent – be used to write and solve equations for multi-step problems? 
    • What measurements and calculations can be used to tell how much space is in three-dimensional objects and how much area is needed to cover their surfaces?

    In this unit, students investigate whether sets of angle and side length measurements determine unique triangles or multiple triangles, or fail to determine triangles. Students also study and apply angle relationships, learning to understand and use the terms “complementary,” “supplementary,” “vertical angles,” and “unique” (MP6). The work gives them practice working with rational numbers and equations for angle relationships. Students analyze and describe cross-sections of prisms, pyramids, and polyhedra. They understand and use the formula for the volume of a right rectangular prism, and solve problems involving area, surface area, and volume.

    Unit 8: Probability and Sampling

    Essential Questions

    Unit 8 Overview

    • What influences the probability that a given event will occur? 
    • What tools can we use to model probabilities with real data? 
    • How can predictions be made based on data?

    In this unit, students understand and use the terms “event,” “sample space,” “outcome,” “chance experiment,” “probability,” “simulation,” “random,” “sample,” “random sample,” “representative sample,” “overrepresented,” “underrepresented,” “population,” and “proportion.” They design and use simulations to estimate probabilities of outcomes of chance experiments and understand the probability of an outcome as its long-run relative frequency.

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    Parent Guide to the Math Curriculum - Grade 4

    Unit 1: Factors and Multiples

    Essential Questions

    Unit 1 Overview

    • What does it mean to be a factor or multiple of a whole number?
    • What does it mean to be a prime or composite number?
    • How does knowing factors and multiples better help me multiply and divide whole numbers?

    The first fourth grade math unit has students extending their knowledge of multiplication, division, and area of a rectangle to deepen their understanding of factors and to learn about multiples.  Students expand on their knowledge of area from third grade to make sense of factors and multiples.  They use rectangle areas and side lengths to build understanding of factor pairs and multiples and learn about prime and composite numbers using factor pairs.

    Unit 2: Fraction Equivalence and Comparison

    Essential Questions

    Unit 2 Overview

    • How do we show and create equivalent fractions? 
    • How does finding equivalent fractions help you compare? 
    • What tools are available to help determine equivalent fractions?

    In this unit, students expand on their fractional understanding.  They use fraction strips, tape diagrams, and number lines to make sense of the size of fractions, generate equivalent fractions, and compare and order fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.  Students generalize that a fraction’s equivalency can be represented with expressions and the concepts that link the mathematical models to the mathematical expressions.

    Unit 3: Extending Operations to Fractions

    Essential Questions

    Unit 3 Overview

    • What are different ways we can use visual models to demonstrate multiplication between a whole number and a fraction? 
    • How can decomposing fractions help add and subtract fractions with like denominators including mixed numbers? 
    • How can equivalent fractions help you add tenths (1/10) and hundredths (1/100)?

    In this unit, students deepen their understanding of how fractions can be composed and decomposed, and learn about operations on fractions.  Students multiply fractions by whole numbers, add and subtract fractions with the same denominators, and add tenths and hundredths, using familiar concepts and representations (ex: tape diagrams and number lines).  Students will then apply these skills in the context of measurement and data by analyzing line plots with fractional lengths, answering questions about data.

    Parent video: Decomposing fractions

    Unit 4: From Hundredths to Hundred-Thousands

    Essential Questions

    Unit 4 Overview

    • What is the relationship between fractions and decimals? 
    • How does our base ten number system work? 
    • What effect does the location of a digit have on the value of the digit? 
    • Why is it important for me to be able to compare numbers?

    In this unit, students learn to express both small and large numbers in base ten, extending their understanding to include numbers from hundredths to hundred-thousands.  Students take a closer look at the relationship between tenths and hundredths and learn to express them in decimal notation, reason about the size of tenths and hundredths written as decimals, locate decimals on a number line, and compare and order them.  Students also explore large numbers beyond 1,000 and find the place value relationships while comparing, rounding, and ordering numbers through 1 million as well as add and subtract using the standard algorithm.

    Unit 5: Multiplicative Comparison and Measurement

    Essential Questions

    Unit 5 Overview

    • How can I use multiplication and division fact families to show the relationship between multiplication and division? 
    • How do you determine which operation to use when converting measurements in a measurement word problem? 
    • How can I apply what I have learned about measurement? 
    • Can I construct, model, or illustrate forms of the same multiplication equation?

    In this unit, students make sense of multiplication as a way to compare quantities. They use this understanding to solve problems about measurement. They use the key question, “How many times as many” to help them with this concept of multiplication comparison.  Through this unit, they use their new knowledge to apply their learning to various units of length, mass, capacity, and time to convert units within the same system of measurement.

    Parent video: Units of measure

    Unit 6: Multiplying and Dividing Multi-Digit Numbers

    Essential Questions

    Unit 6 Overview

    • How can multiplication and division help me to solve multi-step problems? 
    • How can I show models to represent multiplication and division? 
    • How can I use different algorithms to solve math problems and generate a pattern?

    In this unit, Students multiply and divide multi-digit whole numbers using partial products and partial quotients strategies, and apply this understanding to solve multi-step problems using the four operations.  Students multiply up to four digits by single-digit numbers, and to multiply a pair of two-digit numbers, transitioning from using diagrams to using algorithms to record partial products.  In division, students see that it helps to decompose a dividend into smaller numbers and find partial quotients, relying on place value application and understanding.  Students apply their knowledge to solve multi-step problems about measurement in various contexts.  

    Parent video: Area model for multiplication

    Parent video: Partial product multiplication

    Parent video: Solving 2 step word problems

    Unit 7: Angles and Angle Measurement

    Essential Questions

    Unit 7 Overview

    • How can I reason about geometric figures? 
    • How are triangles classified by their angles and sides? 
    • How can geometric shapes be described and classified?  
    • How can I solve problems about missing angle measurements?

    In this unit, students deepen and refine students’ understanding of geometric figures and measurement. Students learn to draw and identify points, rays, segments, angles, and lines, including parallel and perpendicular lines. Students also learn how to use a protractor to measure angles and draw angles of given measurements, and identify acute, obtuse, right, and straight angles in two-dimensional figures.

    Unit 8: Properties of Two-Dimensional Shapes

    Essential Questions

    Unit 8 Overview

    • What are the attributes of two-dimensional shapes? 
    • How do properties of geometric shapes help me solve problems?

    In this unit, students deepen their understanding of the attributes and measurement of two-dimensional shapes. Students classify triangles and quadrilaterals based on the properties of their side lengths and angles, and learn about lines of symmetry in two-dimensional figures. They use their understanding of these attributes to solve problems, including problems involving perimeter and area.

    Unit 9: Putting it All Together

    Essential Questions

    Unit 9 Overview

    • How can I apply what I have learned in fourth grade? 
    • How can I create warm-up activities that show my learning?

    In this unit, students revisit major work and fluency goals of the grade, applying their learning from the year. Students consolidate and solidify their understanding of various concepts and skills related to major work of the grade. They also continue to work toward fluency goals of the grade: fractions (comparison, adding and subtracting, and multiplying by whole numbers), whole number addition and subtraction with standard algorithm, multiply and divide using place value strategies, and reasoning with multiplication and division.

    Parent video: Solving 2 step word problems

  • Parent Guide to the Math Curriculum - Grade 8

    Unit 1: Rigid Transformations and Congruence

    Essential Questions

    Unit 1 Overview

    • How are figures affected by various transformations?
    • How can we prove congruence using a variety of methods?
    • What is the relationship between reflections, rotations, and transformations?

    In this unit, students expand on their knowledge of geometric figures to include rotations and mirror orientations.  Students progress through learning of transformations on the plane, to transformations of an object while learning about rigid transformations (translations, reflections, and rotations).  They learn about the properties related to plane figures, and how to reason using these properties.

    Unit 2: Dilation, Similarity, Introducing Slope

    Essential Questions

    Unit 2 Overview

    • How can I use tables, graphs, and descriptions to identify proportional relationships? 
    • How can I find and use scale factor with rational number lengths and areas?

    In grade 8, students study pairs of scaled copies that have different rotation or mirror orientations, examining how one member of the pair can be transformed into the other, and describing these transformations. Initially, they view transformations as moving one figure in the plane onto another figure in the plane. As the unit progresses, they come to view transformations as moving the entire plane.

    Unit 3: Linear Relationships

    Essential Questions

    Unit 3 Overview

    • How can we recognize and model proportional relationships? 
    • What is a linear relationship and how is it represented on a graph? 
    • How do we calculate slope, and what does it mean if the slope is positive, negative, zero or undefined? 
    • What does it mean to be a solution to a linear equation in two variables?

    In this unit, students gain experience with linear relationships and their representations as graphs, tables, and equations through activities designed and sequenced to allow them to make sense of problems and persevere in solving them (MP1).  Students will have opportunities to use language to interpret situations involving proportional relationships, interpret graphs using different scales, interpret slopes and intercepts of linear graphs, justify reasoning about linear relationships, justify correspondences between different representations, and justify which equations correspond to graphs of horizontal and vertical lines.

    Unit 4: Linear Equations and Linear Systems

    Essential Questions Unit 4 Overview
    • What does it mean to say an equation has no solution? One solution? Infinitely many solutions? 
    • What methods can you use to solve a system of equations? 
    • What is the meaning of a “solution” to a system of linear equations?

    In this unit, students build on their grades 6 and 7 work with equivalent expressions and equations with one occurrence of one variable, learning algebraic methods to solve linear equations with multiple occurrences of one variable. Students learn to use algebraic methods to solve systems of linear equations in two variables, building on their grades 7 and 8 work with graphs and equations of linear relationships. Understanding of linear relationships is, in turn, built on the understanding of proportional relationships developed in grade 7 that connected ratios and rates with lines and triangles.

    Unit 5: Functions and Volume

    Essential Questions

    Unit 5 Overview

    • What is a function? 
    • How do the terms “independent variable” and “dependent variable” connect to the inputs and outputs of a function? 
    • What is the difference between a linear function and a piecewise function? 
    • How can you derive the formula for the volume of a cone from the formula for the volume of a cylinder?

    In this unit, students are introduced to the concept of a function as a relationship between “inputs” and “outputs” in which each allowable input determines exactly one output. In the first three sections of the unit, students work with relationships that are familiar from previous grades or units (perimeter formulas, proportional relationships, linear relationships), expressing them as functions. In the remaining three sections of the unit, students build on their knowledge of the formula for the volume of a right rectangular prism from grade 7, learning formulas for volumes of cylinders, cones, and spheres.

    Unit 6: Associations in Data

    Essential Questions

    Unit 6 Overview

    • How does a scatterplot help us make predictions about trends in data? 
    • What does it mean when we say that data in a scatterplot has a positive association, a negative association, or neither? 
    • How do we create a relative frequency table from a two-way table?

    In this unit, students analyze bivariate data—using scatter plots and fitted lines to analyze numerical data, and using two-way tables, bar graphs, and segmented bar graphs to analyze categorical data.

    Unit 7: Exponents and Scientific Notation

    Essential Questions

    Unit 7 Overview

    • How can you use inductive reasoning to observe patterns and write general rules involving properties of exponents? 
    • How can you evaluate a nonzero number with an exponent of zero? How can you evaluate a nonzero number with a negative integer exponent? 
    • How can you perform operations with numbers written in scientific notation? 
    • How can you estimate how many times larger (or smaller) one number written in scientific notation is than another?

    In grade 6, students studied whole-number exponents. In this unit, they extend the definition of exponents to include all integers, and in the process codify the properties of exponents. They apply these concepts to the base-ten system, and learn about orders of magnitude and scientific notation in order to represent and compute with very large and very small quantities.

    Unit 8: Pythagorean Theorem

    Essential Questions

    Unit 8 Overview

    • What is the meaning of the “square root” of a number? 
    • How do you use the Pythagorean Theorem in two and three dimensions, e.g., to determine lengths of diagonals of rectangles and right rectangular prisms? 
    • How do you use the Pythagorean Theorem to estimate distances between points in the coordinate plane? 
    • How do you make decimal approximations of irrational numbers?

    Work in this unit is designed to build on and connect students’ understanding of geometry and numerical expressions. The unit begins by foreshadowing algebraic and geometric aspects of the Pythagorean Theorem and strategies for proving it. In the second section, students work with figures shown on grids, using the grids to estimate lengths and areas in terms of grid units.  In the third section, students work with edge lengths and volumes of cubes and other rectangular prisms.  In the fourth section, students work with decimal representations of rational numbers and decimal approximations of irrational numbers.

    Unit 9: Putting it All Together

    Essential Questions

    Unit 9 Overview

    • How can shapes create patterns called tessellations
    • How can scatterplots and lines of best fit help to organize and understand data?

    In these lessons, students solve complex problems. In the first several lessons, they consider tessellations of the plane, understanding and using the terms “tessellation” and “regular tessellation” in their work, and using properties of shapes to make inferences about regular tessellations. In the later lessons, they investigate relationships of temperature and latitude, climate, season, cloud cover, or time of day. In particular, they use scatter plots and lines of best fit to investigate the question of modeling temperature as a function of latitude.

  • Parent Guide to the Math Curriculum - Algebra 1

    Unit 1: One Variable Statistics

    Essential Questions

    Unit 1 Overview

    • How can the representations and analysis of data inform and influence decisions?
    • How can you collect, organize, and display data?
    • What is the most appropriate way to display a given set of data?

    In this first unit of Algebra, students are building upon their knowledge of summarizing data and data displays that were formed in middle school mathematics.  The students represent and interpret data using different data displays such as box plots, histograms, and dot plots.  Data vocabulary is developed through the unit and students use technology to create data displays and calculate summary statistics.  Students progress through the unit to explore measures of variability and analyze values of data.

    Unit 2: Linear Equations, Inequalities and Systems

    Essential Questions

    Unit 2 Overview

    • What can we do with a system of equations/inequalities that we cannot do with a single equation/inequality?  
    • What types of relationships can be modeled by linear graphs? 
    • How can we utilize equations to solve problems?

    In this unit, students further develop their capacity to create, manipulate, interpret, and connect these representations (algebraic, verbal, tabular, and graphical) and to use them for modeling. Through this unit, students see that graphs of equations can help us make sense of constraints and identify values that satisfy them, investigate different ways to express the same relationship or constraint—by analyzing and writing equivalent equations, and realize that some equations are more helpful than others, depending on what we want to know.  Students see that a solution to an inequality (in one or two variables) is a value or a pair of values that makes the inequality true, and a solution to a system of inequalities in two variables is any pair of values that make both inequalities in the system true. The solution set of a system of inequalities, they learn, can be best represented by graphing.

    Unit 3: Two Variable Statistics

    Essential Questions

    Unit 3 Overview

    • How can you determine if there is an association between two variables? 
    • How do statisticians make predictions based on data?

    In grade 8, students informally constructed scatter plots and lines of fit, noticed linear patterns, and observed associations in categorical data using two-way tables. In this unit, students build on this previous knowledge by assessing how well a linear model matches the data using residuals as well as the correlation coefficient for best-fit lines (found using technology). The unit also revisits two-way tables to find associations in categorical data using relative frequencies.

    Unit 4: Functions

    Essential Questions

    Unit 4 Overview

    • What are some types of mathematical relationships that can be modeled as functions? 
    • How can you represent and describe functions? 
    • How can we use functions to model data and make predictions?

    In grade 8, students learned that a function is a rule that assigns exactly one output to each input. They represented functions in different ways—with verbal descriptions, algebraic expressions, graphs, and tables—and used functions to model relationships between quantities, linear relationships in particular.  

    In this unit, students expand and deepen their understanding of functions. They develop new knowledge and skills for communicating about functions clearly and precisely, investigate different kinds of functions, and hone their ability to interpret functions. Students also use functions to model a wider variety of mathematical and real-world situations.

    Unit 5: Introduction to Exponential Functions

    Essential Questions

    Unit 5 Overview

    • How do I use different representations to analyze exponential functions? 
    • How do I build an exponential function that models a relationship between two quantities? 
    • How can we use real-world situations to construct and compare exponential models and solve problems?

    In this unit, students are introduced to exponential relationships. Students learn that exponential relationships are characterized by a constant quotient over equal intervals, and compare it to linear relationships which are characterized by a constant difference over equal intervals. They encounter contexts that change exponentially. These contexts are presented verbally and with tables and graphs. They construct equations and use them to model situations and solve problems. Students investigate these exponential relationships without using function notation and language so that they can focus on gaining an appreciation for critical properties and characteristics of exponential relationships.

    Unit 6: Introduction to Quadratic Functions

    Essential Questions

    Unit 6 Overview

    • What are the characteristics of quadratic functions and what can they tell you about real-world relationships? 
    • How can you use different forms of quadratic functions to represent conditions in real world situations?

    Prior to this unit, students have studied what it means for a relationship to be a function, used function notation, and investigated linear and exponential functions. In this unit, they begin by looking at some patterns that grow quadratically. They contrast this growth with linear and exponential growth. They further observe that eventually these quadratic patterns grow more quickly than linear patterns but more slowly than exponential patterns.

    Unit 7: Quadratic Equations

    Essential Questions

    Unit 7 Overview

    • How do you decide which method is best when solving quadratic equations? 
    • How can solving a quadratic equation connect to real-world situations?

    In this unit, students interpret, write, and solve quadratic equations. They see that writing and solving quadratic equations enables them to find input values that produce certain output values.

  • Parent Guide to the Math Curriculum - Algebra 2

    Unit 1: Sequences and Functions

    Essential Questions

    Unit 1 Overview

    • What are the different ways to represent sequences and functions?
    • How do sequences and series model real-world problems and their solutions?
    • How can function describe real-world situations,model predictions and solve problems?

    In this uit, students are given an opportunity to revisit representations of functions, using the example of sequence as a particular type of function.  Students learnt that sequences are a type of function in which the input variable is the position, and the output variable is the term at that position.  Students learn how expressing regulation in repeated reasoning is present in linear and exponential functions.  At the end of the unit, students use mathematical modeling to represent mathematical situations.

    Unit 2: Polynomials and Rational Functions

    Essential Questions

    Unit 2 Overview

    • What is the relationship between the zeros and factors of polynomials? 
    • What is the relationship between polynomial functions and rational functions?

    In previous courses, students learned about linear and quadratic functions. They rewrote expressions for these functions in different forms to reveal structure and identified key features of their graphs, such as intercepts. In this unit, students will expand their earlier work as they investigate polynomials of higher degree and the features that all polynomial functions have in common. They will engage in practice to establish the Remainder Theorem, and transition to working with rational functions and solve rational equations, and hone skills to manipulate polynomials expressions while proving or disproving that two expressions are equivalent.

    Unit 3: Complex Numbers and Rational Exponents

    Essential Questions

    Unit 3 Overview

    • How can we use exponents to compare sizes of real-life objects? 
    • How are expressions involving radicals and exponents related? 
    • Why are complex numbers needed to supplement the real number system?

    In this unit, students use what they know about exponents and radicals to extend exponent rules to include rational exponents, solve various equations involving squares and square roots, develop the concept of complex numbers by defining a new number i whose square is -1, and use complex numbers to find solutions to quadratic equations.

    Unit 4: Exponential Functions and Equations

    Essential Questions

    Unit 4 Overview

    • How can we use logarithms to generalize patterns in real-life measurements? 
    • How do you model a quantity that changes regularly over time by a percentage?

    This unit begins by activating students’ prior knowledge.  Students recall that an exponential function involves a change by equal factors over equal intervals and can be expressed as f(x)=a࣪bx, where a is the initial value of the function (the value when x is 0), and b is the growth factor.  They review the use of verbal descriptions, tables, and graphs to represent exponential functions.

    Unit 5: Transformations and Functions

    Essential Questions

    Unit 5 Overview

    • How can we use transformations of functions to model real-life situations? 
    • How can transformations of functions help make predictions?

    Prior to this unit, students have worked with a variety of function types, such as polynomial, radical, and exponential. The purpose of this unit is for students to consider functions as a whole and understand how they can be transformed to fit the needs of a situation, which is an aspect of modeling with mathematics (MP4). An important takeaway of the unit is that we can transform functions in a predictable manner using translations, reflections, scale factors, and by combining multiple functions. Throughout the unit students analyze graphs, tables, equations, and contexts as they work to connect representations and understand the structure of different transformations (MP7).

    Unit 6: Trigonometric Functions

    Essential Questions

    Unit 6 Overview

    • How do trigonometric and circular functions model real-world data? 
    • How can we adjust trigonometric models using transformations to resemble real-life situations and make predictions?

    In this unit, students are introduced to trigonometric functions. While they have previously studied a variety of function types with different key features, this is the first time students are asked to consider periodic functions, that is, functions whose output values repeat at regular intervals. This unit also builds directly on the work of the previous unit by having students apply their knowledge of transformations to trigonometric functions and use these functions to model periodic situations.

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  • Parent Guide to the Math Curriculum Grade 6

    Unit 1: Area and Surface Area

    Essential Questions

    Unit 1 Overview

    • How does the level of precision affect accuracy in mathematics?
    • How do geometric relationships and the application of measurement help us solve life problems?

    In the first grade 6 math unit, students extend on their previous understanding of shapes to reason and make sense of area that are not composed of rectangles.  They learn strategies for finding area of parallelograms and triangles and develop formulas, use those formulas to solve area problems, and justify their use and application. Students also learn how to find surface area of polyhedra, drawing on their understanding of triangles.  Students begin to transition to mathematical representations more appropriate for algebraic expressions, learning to represent multiplication with a dot instead of the letter x, which will be later used to represent variables.

    Unit 2: Introducing Ratios

    Essential Questions

    Unit 2 Overview

    • What is the connection between ratios and rates?
    • When in life will you want to be able to relate one quantity to another?
    • How would the world be different without ratios and rates?

    In this unit, students learn that a ratio is an association between two quantities, e.g., “1 teaspoon of drink mix to 2 cups of water.”

    Students analyze contexts that are often expressed in terms of ratios, such as recipes, mixtures of different paint colors, constant speed (an association of time measurements with distance measurements), and uniform pricing (an association of item amounts with prices).

    Unit 3: Unit Rates and Percentages

    Essential Questions

    Unit 3 Overview

    • Why are percentages an important tool to compare and measure two different quantities? 
    • How can you use charts and diagrams to easily compute different percentages of numbers? 
    • How can ratio thinking be used to convert different units of measurement? 
    • How are unit rates used to solve different types of problems such as distance, speed, and cost?  
    • How are ratios related to percentages?

    In this unit, students build upon their understandings from the previous unit.  They find two values ab and ba that are associated with the ratio a:b, and interpret them as rates per 1. Tables and double number line diagrams help students connect percentages with equivalent ratios.

    Unit 4: Dividing Fractions

    Essential Questions

    Unit 4 Overview

    • How does the relative sizes of a numerator and a denominator affect the size of the quotient? 
    • How can you divide to get a quotient that is larger than the dividend? 
    • How can you relate multiplying and dividing fractions?

    In this unit, students examine how the relative sizes of numerator and denominator affect the size of their quotient when numerator or denominator (or both) is a fraction.  They develop the understanding that dividing by ab has the same outcome as multiplying by b, then by 1a

    Unit 5: Arithmetic in Base 10

    Essential Questions

    Unit 5 Overview

    • Why is understanding division important for real-world settings? 
    • How can you use decimals to explain the magnitude of numbers? 
    • How can you efficiently compute with decimals? 
    • Why is place value important when dividing decimals?

    In this unit, students compute sums, differences, products, and quotients of multi-digit whole numbers and decimals, using efficient algorithms.  They use calculations with whole numbers and decimals to solve problems set in real-world contexts.

    Unit 6: Expressions and Equations

    Essential Questions

    Unit 6 Overview

    How can variables be used to represent and solve equations in real-world problems? 

     

    Why is equivalency important when solving problems? 

     

    Why are operations important in evaluating expressions?

    In this unit, students learn to understand and use the terms, “variable,” “coefficient,” “solution,” “equivalent expressions,” “exponent,” “independent variable,” and “dependent variable.”  They begin to write coefficients next to variables without a multiplication symbol and learn when that symbol can be omitted.  They work with expressions that have positive whole-number exponents and whole-number, fraction, or variable bases and solve for linear equations that include exponents.

    Unit 7: Rational Numbers

    Essential Questions

    Unit 7 Overview

    • How does the number line help determine the magnitude of the number? 
    • How can plotting points on a coordinate plane help us determine specific locations? 
    • Why is it important to use the correct symbol in an equation or inequality?

    In this unit, students are introduced to signed numbers and plot points in all four quadrants of the coordinate plane for the first time. They work with simple inequalities in one variable and learn to understand and use “common factor,” “greatest common factor,” “common multiple,” and “least common multiple.”

    Unit 8: Data Sets and Distributions

    Essential Questions

    Unit 8 Overview

    • What are different ways you can collect, sort and represent data? 
    • How do measures of center and variability help us make sense of the world around us?  
    • How can you determine which type of graphical display is appropriate to a particular data set? 
    • What is a statistical question and what are the steps for solving it?

    In this unit, students learn about populations and study variables associated with a population. They understand and use the terms “numerical data,” “categorical data,” “survey”, “statistical question,” “variability,” “distribution,” and “frequency.” They make and interpret histograms, bar graphs, tables of frequencies, and box plots. They describe graphical distributions using terms such as “symmetrical,” "peaks," “gaps,” and “clusters.” They work with measures of center—understanding and using the terms “mean,” “average,” and “median.” They work with measures of variability—understanding and using the terms “range,”” mean absolute deviation” or MAD, “quartile,” and “interquartile range” or IQR. They interpret measurements of center and variability in contexts.

    Unit 9: Putting it All Together

    Essential Questions

    Unit 9 Overview

    • What role does mathematics have in elections? 
    • How does making an estimation help me when measuring? 
    • How does determining the greatest common factor support fraction work? 
    • How are ratios and percentages related?

    In this unit, students use concepts and skills from previous units.  They use measurement conversions with their knowledge of volumes or surface areas of right rectangular prisms or the relationship of distance, rate, and time.  They work with percentages, answer questions about geometric figures, and use their knowledge of ratios, percentages, and unit rates.

Science

The curriculum and instruction in elementary, middle and high school is hands-on and centered around the process of science. Each unit or course follows a storyline leading with a real world phenomena to unravel disciplinary core ideas covering physical, earth & space, life, and engineering, technology & applications of science each year.

Parent Guide to the Science Curriculum

Please see below for a parent guide to each science curriculum from kindergarten to high school.

  • Parent Guide to the Science Curriculum - Kindergarten

    Unit 1: Mystery Class Pet

    Essential Questions

    Unit 1 Overview

    • How do plant and animal needs help us pick an appropriate class pet?
    • What are living and nonliving things?
    • What do plants need to survive?
    • What do animals need to survive?
    • How do plants and animals get what they need from their habitat?
    • How do plants, animals, and humans impact their environment?
    • What does our class pet need to survive and thrive?

    Through the engagement of a mystery (real or virtual) class pet, students learn what animals and plants need to live and grow.  They also investigate how living things change and are impacted by their environment.

    Unit 2: Waiting for Weather

    Essential Questions

    Unit 2 Overview

    • How does weather affect our everyday choices?
    • How does weather help me know what to wear each day?
    • How do we know what the weather will be each day?
    • How does the sun affect our lives?

    Through this year-long unit, kindergarteners learn about how weather affects and impacts their lives using observational skills and data collection. The overall focus for students is how weather affects what we wear and what we do. Students will also understand that some weather can be considered severe and how scientists follow weather patterns to help communities to prepare.

    Unit 3: Push, Pull Play!

    Essential Questions

    Unit 3 Overview

    • How do we use pushes and pulls during play?
    • What happens when you change the force of a push or pull during play
    • What happens when play objects crash into one another
    • How can weather make things move?  Why do some play objects (toys) fly in the wind better than others?

    In this unit, students investigate the direction of motion in pushes and pulls through their bodies at play as well as how their motion and force affects objects.  As play engineers, students will design and test a flying toy and observe its interaction with weather.

  • Parent Guide to the Science Curriculum - Grade 1

    Unit 1: Playground Shadows

    Essential Questions

    Unit 1 Overview

    • What causes a shadow’s length and position to change?
    • What do you need to make a shadow?
    • How can we change the direction of light?  If we change the direction of light, what happens to our shadow?
    • Why doesn’t the moon’s appearance change?
    • How does the amount and intensity of daylight change with the seasons?

    In this first unit, students investigate and learn about how light interacts with objects.  They begin by exploring their own shadows and investigate how shadows change in length and location relative to the position of the sun.  They use data recording to examine patterns of sunlight and shadow throughout the day.

    Unit 2: Film Animation

    Essential Questions

    Unit 2 Overview

    • How do sound and light communicate information
    • What causes sound?
    • How can light be used to communicate a message?
    • How can we use shadows to tell a story?
    • How are light and sound used to communicate across a distance?
    • Is light necessary to see?  How can we see in the dark?

    Students spend this unit investigating how light and sound to understand how they can be used to communicate a message.  They investigate what is needed to produce sound, what mediums allow light to pass through them to varying degrees (or not at all), and what people use to communicate over long distances.  To end the unit, students become engineers of sound and light to create a soundtrack for a simple animation to share with their class.

    Unit 3: Senses in Nature

    Essential Questions

    Unit 3 Overview

    • How do the external parts of the Venus flytrap, star nosed mole, and tulip help them grow and survive?
    • How do external parts and sunlight help living things grow and survive?
    • How do plant parts help the plant meet its needs?
    • How do animal body structures help it meet its needs for growth and survival?
    • How have humans used nature to solve their problems?  How can I mimic nature to develop a solution to my problem?

    Through this unit, first grade students become plant and animal scientists who use their powers of observation and curiosity to develop their understanding of how plants and animals grow and survive.  Students learn about structures and functions of animals and plants as well as their survival needs.  Students also use observations to develop initial theories on why organisms look and behave the way they do and work to create a solution for a problem.

    Unit 4: Seasonal Changes

    Essential Questions

    Unit 4 Overview

    • How do living things prepare and behave in order to survive in their different seasons?
    • How can seasonal patterns be described?
    • How do living things prepare and behave in order to survive in the different seasons?
    • How are offspring similar and different from their parents?

    In this last unit, students will learn what it is like to be a field biologist.  They will explore how living things respond to seasonal changes on Earth and the influence of sunlight on living things' actions and survival.  Using a variety of media, students will investigate how living things change and record their findings as a field biologist.

  • Parent Guide to the Science Curriculum - Grade 2

    Unit 1: 4th Little Pig

    Essential Questions

    Unit 1 Overview

    • What materials are best suited to design a home for the 4th Little Pig?
    • How do you sort and classify objects based on their properties?
    • What happens when materials are heated or cooled?
    • Why are different materials better suited for certain purposes than others?
    • How can objects be made and remade into new objects using existing pieces?

    Students in second grade begin with an engineering unit that centers around matter and its properties.  They are faced with a design problem where they plan for and construct the 4th Little Pig’s shelter.  Using what they learn about the types and properties of matter, they design and test a structure for the 4th Little Pig.

    Unit 2: Koa Tree

    Essential Questions

    Unit 2 Overview

    • How does the Koa tree grow in two places 10,000 miles apart?
    • Do all plants need the same amount of water and sunlight?
    • Can the Koa tree survive and grow in Connecticut?
    • How do plants depend on animals?
    • How does water and temperature determine if a Koa seed survives?

    In this unit, second grade students explore plants and animals and their interdependent relationship with each other and their environment.  This is focused around the scenario of the Koa tree, located both in Hawaii and off the western coast of Africa.  Like scientists before them, students hypothesize how the Koa seed traveled from island to island and are focused on a real-life science mystery that gives purpose to their study on plants, animals, and habitats.

    Unit 3: Beavers

    Essential Questions

    Unit 3 Overview

    • How do beavers change the landscape?
    • How do we prevent wind or water from changing the land?
    • Why do beavers need dams?
    • What is an engineer? How are beavers nature’s engineers?
    • How do rivers and dams change the land? How quickly does this happen?
    • What are the other ways that landforms can be created, besides erosion along river beds?

    This unit engages students on natural engineers, beavers, and the impact they have on the ecosystems around them.  Students will use investigation and observation to describe the impact beavers have on the environment as well as the impact of erosion on landforms.

  • Parent Guide to the Science Curriculum - Grade 3

    Unit 1: Playground Engineers

    Essential Questions

    Unit 1 Overview

    • How can the motion on the playground be changed and/or improved?
    • How can force be used to make an object move?
    • How does the direction of force impact the direction of motion?
    • How can motion be predicted?
    • What are magnetic forces and how could they impact motion on the playground?
    • What are electrostatic forces and how do they impact motion on the playground?

    In this unit, students become playground engineers to investigate a variety of forces and interactions that affect motion.  Students learn a variety of ways that motion is affected (balanced and unbalanced forces, gravity, friction, etc) and use their learning to design a dream playground model that incorporates their understanding.

    Unit 2: Harper’s Fossil Find

    Essential Questions

    Unit 2 Overview

    • What can we learn from Harper’s fossil find?
    • What can we learn from fossils?
    • How are organisms today similar and different from their ancestors?
    • What patterns can you see in an organism within its life span? What patterns can you see between different organisms’ life spans?
    • Why do offspring look similar to their parents?  How can we use traits to identify parents and offspring in fossils?
    • Why are flamingos pink? How do environmental conditions impact an organism’s traits?

    Students pose as secret agents from the paleontology unit using fossils to uncover the diet and environment needed for Harper’s fossil to survive.  Students develop their understanding of life cycles and apply their understanding of traits and inheritance to make determinations about eggs and fossils.

    Unit 3: Case of the Missing Monarchs

    Essential Questions

    Unit 3 Overview

    • Why are the monarch butterflies disappearing?
    • What are the monarch butterfly’s survival secrets?
    • How has the monarch population changed?  What factors influence this change?
    • What features do monarchs have to promote survival?
    • Why does the monarch butterfly migrate? Is migration necessary for survival?
    • What are the seasonal climate patterns in the different regions of North America? If the climate patterns change, how will the monarch butterflies be affected?
    • How do characteristic variations help an organism survive, find a mate and/or reproduce? Does this connect to the monarch butterfly population decline?
    • Why do some animals live in groups?

    Students explore the causes and effects behind the declining monarch butterfly population.  Students use analysis to look at weather and climate data, use observation to predict differences between male and female butterflies, and identify needs for monarch survival.

    Unit 4: Grand Canyon Seashells

    Essential Questions

    Unit 4 Overview

    • How did marine fossils end up in the Grand Canyon?
    • What types of evidence do we look for to determine a fossil’s story?
    • How might a change in the environment affect the organisms living in it?
    • How does a region’s location impact its climate?
    • How do severe weather events impact the environment and the organisms living there?
    • How could the Grand Canyon environment change so drastically over time?

    This unit anchors student investigation to a mystery of marine fossils that have been found in the Grand Canyon.  Students will learn how different environments affect living things and research and compare different environments.  Students ultimately use their knowledge to create theories on how the marine fossils came to be in the desert environment of the Grand Canyon.

  • Parent Guide to the Science Curriculum - Biology

    Unit 1: Forest Regrowth

    Essential Questions

    Unit 1 Overview

    • How does a forest regrow after a forest fire?
    • What does a forest need to regrow after a forest fire?
    • How do plants convert solar energy into chemical energy/food? 
    • How is chemical energy released for use in living systems? 
    • How does carbon and energy move through organisms and ecosystems?

    In this unit, students will explore the chemical and physical properties of carbon and the cycling of carbon in an ecosystem. Students will follow the movement of carbon, in the form of biomass, through trophic levels of an ecosystem and hypothesize why matter and energy is “lost” moving up through the trophic levels.  They will apply their knowledge and understanding to answer the unit’s driving question: What does a forest need in order to regrow after a forest fire?

    Unit 2: Wolves

    Essential Questions

    Unit 2 Overview

    • How can biotic (wolves) components of an ecosystem alter the abiotic (river course, flow) components of the ecosystem? 
    • Why are systems necessary for something to function? 
    • What determines population size of different organisms? 
    • How do ecosystems respond to change?

    In this unit,  students will be exploring the dynamics of ecosystems including energy flow, homeostasis, and populations. Students will investigate the factors affecting  systems from the micro to the macro level. The anchoring phenomenon of this Unit is “How Do Wolves Change Rivers” which is based upon the reintroduction of wolves into Yellowstone National Park.

    Unit 3: Little People

    Essential Questions

    Unit 3 Overview

    • How can siblings from the same family be so different? 
    • How does the structure of DNA relate to its function and the difference in traits seen in the Little People Big World family (anchoring phenomena)? 
    • How does DNA direct the production of proteins?  
    • How do multicellular organisms grow, heal and create differentiated cells? 
    • How does the process of meiosis create new genetic combinations and thus more genetic variation?  
    • How are traits inherited? 
    • What role does the environment play in inheritance?

    In this unit, students will be exploring how genetics and environment affect traits and offspring.  Students will anchor to the Roloff family from Little People Big World and the inheritance of Achondroplasia.  Students will use computer-based model situation to propose a genetic strategy to treat patients with progeria.  They describe the step in gene expression they will target and explain their reasoning on why and how that intervention would treat the disease.

    Unit 4: Raising the Mammoth

    Essential Questions

    Unit 4 Overview

    • What caused the woolly mammoth to go extinct and should the species be de-extinct? 
    • How has Earth changed over geologic time? How has life altered the planet and atmosphere? 
    • How do ecosystems respond to disturbances? 
    • What are the roles of selection and variation in the changing of a population? 
    • Can  behavior contribute to an organism’s survival?
    • What evidence tells us the elephant and woolly mammoth are related?

    Students begin the unit with viewing a short video clip of the raising of the woolly mammoth from ice and the possibility of de-extincting* the species. They generate and share questions about their observations from the video and generate a list of causes of why organisms become extinct. The following lessons will provide students the ability to explore multiple factors that contribute or hinder the survival rates of different organisms and their relationship to one another through evolutionary principles. Students will make connections within each lesson to the overarching idea of the extinction of the woolly mammoth and the implications if the woolly mammoth species is de-extinct.

    Unit 5: Coral Reefs *

    Essential Questions

    Unit 5 Overview

    • Why are coral reef ecosystems dying? 
    • What are the abiotic and/or biotic factors that have had a negative impact on the coral reef ecosystem?  
    • What are the (natural or human-related) environmental stresses that are causing changes in biodiversity, speciation and extinction? 
    • What are humans doing to affect ecosystem sustainability and biodiversity? 
    • How are humans solving the problems of loss of biodiversity and sustainability?

    In this unit, students will evaluate the evidence supporting claims that changes in environmental conditions may result in (1) increases in the number of individuals of some species, (2) the emergence of new species over time, and (3) the extinction of other species. They will apply their knowledge and understanding to answer the unit’s driving question: Why are the coral reefs dying?

  • Parent Guide to the Science Curriculum - IEPS

    Unit 1: Big Bang

    Essential Questions

    Unit 1 Overview

    • What are the origins of our universe and how do we know that? 
    • What is sound and what affects sounds? 
    • What can light tell us about the universe? How do different types of radiation affect matter? 
    • What can a beam of light tell us about where it came from? 
    • How can astronomers know what stars are made of? What else can astronomers deduce from starlight? 
    • How do observations today allow astronomers to determine the origins of the universe?

    Today’s “Universe Creation Story” describes an event from over 14 billion years ago, namely a great explosion in which the universe came into being as we now know it – the “Big Bang.” In this bundle students will explore and relate how oscillations or vibrations in various massive or energy mediums are related and provide the understandings that have led us to these conclusions, or the “Big Bang Theory.” In six sequential explorations, students will build on their knowledge of waves and what waves can tell scientists about the nature of stars and galaxies well beyond our possible physical exploration.

    Unit 2: Apophis Asteroid

    Essential Questions

    Unit 2 Overview

    • What is the Apophis Asteroid and why should I care? 
    • How will the motion of Apophis change as it approaches Earth? 
    • What factors will affect the severity of the collision between Earth and Apophis? What would affect the collision between an exploratory lander and the asteroid? 
    • What is needed to change the motion of an object, and what factors affect those changes? 
    • How does Apophis stay in orbit around the sun? How do we stay on Earth?
    • How can we predict the motion of the asteroid? 
    • What are some engineering solutions to the possible collision of Earth and Apophis?

    Students are introduced to the phenomenon of the Apophis Asteroid and begin wondering about the possible consequences for life on Earth. Students will take on the role of astrophysics advisors to the UN as they design and present their solution to the impending Apophis crisis. Individual students will be tasked with evaluating all presented solutions and defending their choice for what is ‘best.’

    Unit 3: Pangea

    Essential Questions

    Unit 3 Overview

    Coming soon

    Coming soon

    Unit 4: Extreme Weather

    Essential Questions

    Unit 4 Overview

    Coming soon

    Coming soon

    Unit 5: Water Bottles

    Essential Questions

    Unit 5 Overview

    Coming soon

    Coming soon

  • Parent Guide to the Science Curriculum - Physics

    Unit 1: Asteroid Collisions

    Essential Questions

    Unit 1 Overview

    • How can we protect the Earth from asteroid collisions? 
    • What happens in a collision? What would happen if an asteroid hit Earth? 
    • How do we protect ourselves from collisions? 
    • How do objects move in space? 
    • Where did all of the objects that could be threats come from? 
    • How can we protect the Earth from asteroid collisions?

    In this unit, students will answer the question, “How do we protect ourselves from collisions?” through the framing phenomenon of an asteroid crashing into the Earth. Using an online asteroid simulator called Impact EARTH!, students will gain initial experience with using computational data to understand cause and effect and begin to formulate ideas about the phenomenon. At a smaller scale, students will use car crashes to understand the basic mechanics of collisions, such as momentum and Newton’s Second Law, through laboratory explorations and activities.  Students will work through this unit to understand where spaceobject come from, learning the Big Bang Theory and applying Kepler’s Law.

    Unit 2: Natural Disasters

    Essential Questions

    Unit 2 Overview

    • Where does the energy for natural disasters come from and where does it go?
    • What happens to the energy of a system as a process takes place?  
    • How is energy distributed on Earth and used to do work? 
    • How are materials and energy transferred between Earth’s systems? 
    • What role does water play in storing energy and moving it from one place to another? 
    • What factors influence weather and climate? 
    • Where does the energy for natural disasters come from and where does it go?

    Students will investigate, model, and develop understandings for how energy is transformed in Earth’s systems to create natural disasters.Students will then use this understanding of the energy cycles and systems in the Earth to create an emergency action plan for a vacation to a disaster-prone area.

    Unit 3: Battery Fires

    Essential Questions

    Unit 3 Overview

    Coming soon

    Coming soon

    Unit 4: Global Communication Failure

    Essential Questions

    Unit 4 Overview

    Coming soon

    Coming soon

  •  

    Parent Guide to the Science Curriculum - Chemistry

    Unit 1: Radium Girls

    Essential Questions

    Unit 1 Overview

    • How does a poor understanding of chemistry impact society? 
    • What is radioactivity, and how does this relate to the structure and origins of matter? 
    • How does the body mistake radium for calcium?
    • What makes an atom stable?
    • How can one atom turn into another?
    • How long will radium be around?
    • Why does radium glow? 
    • How do radium girls compare to other nuclear events?

    Students anchor their learning of chemical properties to the phenomena of the “Radium Girls” in Waterbury,CT to explore the impact a poor understanding of chemistry can have on society.  Students explore properties of atoms, create an understanding of isotopes and their stability, and create models relating the periodic table to elements from cell phones.  Students will also explore the fluctuations of energy.

    Unit 2: Toxic Waste

    Essential Questions

    Unit 2 Overview

    • Is there a way to predict which substances will be the most reactive? 
    • How do things exert forces without ever touching? How does this occur, and what factors affect the amount of push? 
    • How are millions of substances created from a small number of elements? 
    • How can similar molecules have different properties? 
    • Why do substances have the properties that they do?  
    • How do we create “designer” materials like Kevlar, plastics, and sticky notes?

    Students are presented with a hypothetical situation where three unlabeled drums of liquid are dumped near a reservoir and the students, acting as an environmental forensics team, must identify the contents. However, before they can attempt to identify what substances were in the barrels, students must first generate and prioritize a series of questions that will help them solve this mystery. Students then read about environmental forensics in preparation for their culminating performance task - identifying the contents of three unlabeled drums dumped into a nearby reservoir. Students design and conduct an investigation to determine the identity of the liquids and write a formal laboratory report of their findings to conclude this unit on bonding.

    Unit 3: Cooking Chemistry

    Essential Questions

    Unit 3 Overview

    Coming soon

    Coming soon

     

  • Parent Guide to the Science Curriculum - Grade 4

    Unit 1: National Parks

    Essential Questions

    Unit 1 Overview

    • Why does the topography change across the United States? 
    • How did the landforms that make up Grand Staircase - Escalante National Park come to take their current shape?
    • How does water help shape the land?
    • What forces cause weathering and erosion? 
    • What can humans do to prevent or decrease the damage caused by erosion or the rate of erosion in an area?  
    • How can patterns of rock formations and fossils help us learn about Earth’s history?

    Throughout the unit, students will investigate various national parks and monuments in order to build their conceptual understanding of energy, collisions, weathering and erosion. At the start of the unit, students are introduced to the regions of the United States through a topographic and satellite map of the United States. They observe the images and ask questions about the different appearances of the landscape across the US. Students not only generate questions, but they also improve and prioritize questions about the image; these questions will drive student learning throughout the unit. Students will be introduced to a summary table/interactive notebook to track their learning.

    Unit 2: Mimicking the Natural World

    Essential Questions

    Unit 2 Overview

    • What is biomimicry and how have human innovations been inspired by observing the natural world? 
    • How do sense receptors receive and perceive energy? 
    • What human innovations were inspired by mimicking the way the natural world receives and perceives sound? 
    • What human innovations were inspired by mimicking the way the natural world receives and perceives light? 
    • What human innovations were inspired by mimicking the way plants respond to different energy stimuli? 
    • How do animals use electricity?

    Biomimicry is how humans mimic the natural world in their innovations and designs.  This bundle will compare and contrast energy transfer in the natural and designed worlds focusing on how electric currents, light and sound are received and perceived by both.  As a result of observing those interactions in nature, much of human innovation and design can be directly attributed to how organisms survive all manner of energy inputs.

    Unit 3: Forces that Move Earth

    Essential Questions

    Unit 3 Overview

    • What forces are responsible for the movement of the Earth’s surface (and everything on it)?
    • What energy and forces are acting on the Earth’s crust during an earthquake?
    • What are waves and how do they affect the Earth’s crust and humans?
    • How do hurricanes contribute to weathering and erosion and how do each of these processes sculpt the Earth’s surface?
    • How are renewable and nonrenewable resources impacting our environment? How do we utilize renewable energy?

    This unit focuses on the forces responsible for the movement of the Earth’s surface (and everything on it)..  Students view slides showcasing the destructive forces of earthquakes, tsunamis and hurricanes as a jumping off point. They connect plate tectonics to the ever-changing Earth’s crust and how fossil fuel use is related to climate change.  They learn how humans react to those changes, and what resources are available to meet our ever growing energy consumption demands.

  • Parent Guide to the Science Curriculum - Grade 5

    Unit 1: Spectacular Sights in the Sky: Scale, Proportion, & Quantity

    Essential Questions

    Unit 1 Overview

    • What causes these spectacular sights? 
    • Why do stars vary in brightness and color? 
    • What is matter? 
    • Why is it warmer in the summer than in the winter? 
    • Is matter lost or destroyed when a meteorite enters Earth's atmosphere?
    • What causes the moon to appear to have different phases? 
    • Why does the super blue blood moon occur?

    Students study stars, matter, and celestial bodies, as well as the relationship between the Earth, the sun, and the moon. Projects include the creation of explanatory models and writing tasks.

    Unit 2: Golden Jellies

    Essential Questions

    Unit 2 Overview

    • What conditions are necessary for the golden jellyfish to survive and thrive? 
    • What do species need to survive and thrive? 
    • Why is an ecosystem a system and how does matter move through it? 
    • How do the predictable patterns of the Sun affect living things, including zooxanthellae and golden jellyfish, on Earth? 
    • How does human activity negatively impact areas around the world and what can humans do to reduce those negative impacts?

    This unit is designed to build student’s understanding of life on Earth and the factors which allow species to survive and thrive and humanity’s role in this. Students study the golden jellyfish of Lake Palau as an anchoring phenomenon. Students come to understand the role of sunlight and other abiotic factors to the success of an organism within an ecosystem. Students build their understanding of the word ecosystem and research various ways that humans negatively impact the world.

    Unit 3: Antarctica

    Essential Questions

    Unit 3 Overview

    • What will you need to learn about Antarctica to survive?
    • What patterns can be observed due to the movement of the Earth?
    • How does the distribution of water on Earth impact the Antarctica Research Expedition?
    • How are glaciers formed and how do they interact with the Earth’s spheres?
    • Why do icebergs flip?

    In this unit, students become members of an Antarctic Expedition Research Team.   Throughout the journey, students encounter a unique series of situations requiring them to discover and apply scientific knowledge to get them to their destination.  Through this unit, students learn about Antarctic conditions, design and test sled prototypes, compare day and night patterns in Connecticut and Antarctica, explore ice cores and the distribution of water on Earth, learn how glaciers form and change over time, and explore gravity and its impact on objects.

  • Parent Guide to the Science Curriculum - Grade 6

    Unit 1: Lyme Disease

    Essential Questions

    Unit 1 Overview

    • What is the timeline for the transmission of Lyme disease (LD)? 
    • What characteristics do all living things have in common? 
    • How are cells organized? Does the structure of a cell provide evidence for its function?
    • How do tissues organize themselves to create a complex organism? How do the body’s subsystems interact?  
    • How does the nervous system respond to stimuli? 
    • How can we reduce the transmission of Lyme Disease in Connecticut?

    Students are asked to depict how a host gets Lyme disease. Students explore the 7 common characteristics of living things, both unicellular and multicellular. Students investigate cellular structure and function to understand how scientists use this information about the bacterium to treat and prevent its transmission.

    Unit 2: Bees

    Essential Questions

    Unit 2 Overview

    • Why does the declining bee population matter?
    • How do animals sense and react to their world?  
    • How do plants and animals improve their ability to survive and reproduce? 
    • Why do organisms reproduce in different ways? 
    • How do traits get passed on to organisms?
    • How can we predict the probability of traits occurring?

    This unit is about reproduction and growth and focuses on how systems interact between plants and animals, how plants have specialized structures, and how animals have specific behaviors to help aid reproduction. It includes how environmental and genetic factors can affect survival. It also provides evidence for the genetic variation that occurs with sexual reproduction and the lack of variation that occurs with asexual reproduction.

    Unit 3: Penguin Habitat

    Essential Questions

    Unit 3 Overview

    • How can a temperature controlled habitat for penguins be designed?
    • How does heat affect matter?
    • How is temperature related to energy?
    • How can temperature be controlled so that cold is maintained?
    • How does heat move?

    During this unit students will develop an understanding of heat transfer through convection, conduction and radiation, and then apply that knowledge as they work as engineers to design, build, and test temperature-controlled habitats for penguins.

    Unit 4: Destructive Weather

    Essential Questions

    Unit 4 Overview

    • What factors impact weather?
    • What are the processes involved in the cycling of water through Earth’s systems?
    • What are the major factors that determine regional climates?
    • What is the relationship between air masses and changes in weather conditions?
    • How does oceanic circulation affect regional weather?

    This unit examines several aspects of weather and climate including Earth’s large-scale system interactions and the roles of water, temperature, and human activity  Students explore the factors that impact weather, the water cycle, the major factors affecting regional climate,  the relationship between air masses and changes in weather conditions, how ocean water circulation affects regional weather, and how humans affect Earth’s systems.

  • Parent Guide to the Science Curriculum - Grade 7

    Unit 1 Energy Drinks

    Essential Questions

    Unit 1 Overview

    • Should energy drinks be regulated for people under 16
    • What is in energy drinks?
    • How does temperature affect the fizziness of an energy drink
    • What is in energy drinks and how is this determined?
    • Why are they bad for you?  What happens to your body after drinking it?
    • Are energy drinks worse for you than coffee or soda?

    In this unit, students will explore the chemistry of energy drinks and how the body processes chemical compounds. Students  engage in model building to investigate the basic structures and properties of matter, as well as how synthetic materials are created from natural resources.

    Unit 2 Closed Beach

    Essential Questions

    Unit 2 Overview

    • Why is the recreation area (park with body of water, pool, beach) closed? How can we make it usable again?
    • How is energy transferred throughout an ecosystem
    • Where does energy come from
    • Describe the process of photosynthesis.
    • How do organisms get what they need to survive?
    • Why/How is biodiversity important to an ecosystem's success?
    • How does a change  in one part of  the ecosystem impact the ecosystem as a whole?
    • How are humans interdependent on ecosystem resources and biodiversity?

    The students will learn about the basics of food webs and ecosystems to understand that all life within an area is connected and impacts each other.  After we have discussed the ins and outs of ecosystems, we then discuss how humans are affected by the ecosystems and our reliance on resources from the environment.  Once students have an understanding of all these concepts we tie it all together with a project to explain why an imaginary or hypothetical local Recreational Area is closed and provide possible solutions to this issue based on research, reasoning, and evidence.

    Unit 3 Disaster Movie Trailers

    Essential Questions

    Unit 3 Overview

    • Is what happens in disaster movies credible?
    • How has Earth’s surface changed over time?
    • How is the new crust formed
    • How do Earth’s surface movements occur?
    • How has the Earth’s surface changed by natural events both suddenly as well as over time
    • How is the surface of the Earth changed by weathering, erosion, and deposition?
    • How are natural resources classified and distributed on Earth?
    • How do disaster movies compare to real life events?

    In this unit students explore the line between reality and entertainment as they learn about destructive natural events that occur on Earth.  Students explore the structure of Earth looking for patterns as they analyze data, researching theories, investigating what drives Earth’s movement, and examining the processes that change Earth’s surface (both rapidly and slowly).

  • Parent Guide to the Science Curriculum - Grade 8

    Unit 1: Car Collisions

    Essential Questions

    Unit 1 Overview

    • What happens when two objects collide?
    • When two objects collide, what happens to their motion?
    • How do safety barriers work? 
    • What factors affect the size and strength of non-contact forces? 
    • What types of collisions occur in our Solar System?

    Students will be exploring how forces cause objects to change their motion. Through student-designed experimentation, they will explore the relationships among mass, speed, and distance relative to colliding objects. As a result, students will be developing a deeper understanding of the cause-and-effect relationships between action and reaction pairs related to colliding objects. Students will explore and explain various factors that affect the outcomes of collisions.

    Unit 2: Waves

    Essential Questions

    Unit 2 Overview

    • How can sound be heard and audio spectrums seen?
    • What are the parts of a wave, and how can a basic understanding of waves be used to design a 1-second pendulum? 
    • What are the properties of waves, and what are the differences in sound and light waves?
    • What happens to light waves as they travel and how are they visible?  
    • Why might you prefer watching TV produced with a digital signal vs. an analog signal?

    Students are introduced to the anchor phenomenon (mystery sound - music generated by a music box) and ask questions about sound.  They explore visual representation of the sound, ask questions, make predictions, and model their initial explanation of this mystery sound, identify devices that might make this sound, and explain how it is transmitted to them. Students will create a model in which they use the information they have obtained to synthesize the use of sound and light waves in a culminating performance, in which they design a concert venue and event that allows attendees to experience the concert in a variety of ways (sound, lights, motion, et al.).

    Unit 3: Jurassic Park

    Essential Questions

    Unit 3 Overview

    • Is it possible to clone a dinosaur?
    • What can the fossil record tell us about the history of life on Earth?
    • How do an organism’s physical modifications made over time (natural selection) affect the likelihood of survival by individuals, populations, and species, and are the results different when humans alter the process (genetic engineering) to induce faster changes?
    • How are modern organisms related to ancient organisms?
    • How do genetic mutations occur and how might they impact an organism?
    • How do the stages of embryological development of organisms compare?

    Students engage in a critical look at an excerpt from Jurassic Park. They decide which parts of the movie they consider fact or fiction and which topics they need to find out more about in order to determine how organisms have changed over time.

     

    Students look at the fossil record,  explore how radiometric dating helps determine the age of a fossil, investigate how organisms have changed over time and that some organisms have gone extinct, and explore natural selection and genetic engineering.

    Unit 4: Adventure to Mars

    Essential Questions

    Unit 4 Overview

    • How was Earth formed, and how has it changed over time?
    • How does gravity affect the motion of planetary objects?
    • What is the scale relationship of planet sizes as well as their distances from the Sun?
    • How do patterns in the Earth-Sun-Moon system allow scientists to predict events such as eclipses, and seasons?
    • What can the rock layers tell us about Earth’s history?
    • How do artifacts including fossils provide information about the era in which they were formed?
    • How does a human population that is changing in size and consumption affect natural resource availability?

    In this unit, students explore the formation of the solar system and Earth and how they have changed over time, including the progression of life through the anchoring phenomenon of living on Mars. Students engage in activities involving the scale properties of objects within our solar system, observing patterns in size, distance, and movement, and the role of gravity in the universe. Students explore, model, and explain the causes of these moon phases, eclipses, and seasons, and the predictability of their patterns. Additionally, students explore how humans obtain and use Earth’s natural resources, and how a change in population size can affect the use and availability of the natural resources. Students propose engineering changes to the production and/or use of consumer products to mitigate the related impact on the environment.

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For additional information, please contact:

Misty Hofer

Assistant Education Administrator for

Mathematics/STEM

hoferm@norwalkps.org

203-854-4026