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.
Please see below for a parent guide to each math curriculum from kindergarten to high school.
Unit 1: Adding, Subtracting and Working with Data 

Essential Questions 
Unit 1 Overview 

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 yearlong 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 

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. 
Unit 3: Adding and Subtracting Within 20 

Essential Questions  Unit 3 Overview 

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 

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 twodigit 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 twodigit numbers. 
Unit 5: Adding Within 100 

Essential Questions  Unit 5 Overview 

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 

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 

In this unit, students focus on geometry and time, expanding their knowledge of two and threedimensional 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. 

Unit 1: Introducing Multiplication 

Essential Questions 
Unit 1 Overview 

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 

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 

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. 
Unit 4: Relating Multiplication to Division 

Essential Questions 
Unit 4 Overview 

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 equalsized groups to form the basis for their sense of multiplication; this unit has them also use equalsized 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 

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

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Unit 6 Overview 

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: Twodimensional Shapes and Perimeter 

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Unit 7 Overview 

In this unit, students reason about attributes of twodimensional shapes and learn about perimeter, building on their previously built geometric knowledge from earlier grades. Students learn to classify geometric shapes into subcategories 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 

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. 
Unit 1: Finding Volume 

Essential Questions 
Unit 1 Overview 

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 realworld problems. 
Unit 2: Fractions as Quotients and Fraction Multiplication 

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Unit 2 Overview 

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 

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Unit 3 Overview 

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 MultiDigit Numbers 

Essential Questions 
Unit 4 Overview 

In this unit, students multiply multidigit whole numbers using the standard algorithm and begin working toward endofgrade expectation for fluency. They also find wholenumber quotients with up to fourdigit dividends and twodigit divisors. 
Unit 5: Place Value Patterns and Decimal Operations 

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Unit 5 Overview 

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 

In this unit, students deepen their understanding of placevalue 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 

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Unit 7 Overview 

In this unit, students learn about the coordinate grid, deepen their knowledge of twodimensional 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 

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 realworld problems about volume and have opportunities to model with mathematics, and revisit work with operations with decimals and fractions. 

Unit 1: Scale Drawings 

Essential Questions 
Unit 1 Overview 

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 nonunits (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 

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Unit 2 Overview 

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 

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Unit 3 Overview 

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 

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Unit 4 Overview 

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 multistep problems that are set in a wide variety of contexts that involve fractions and percentages. 
Unit 5: Rational Number Arithmetic 

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Unit 5 Overview 

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 

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Unit 6 Overview 

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 

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Unit 7 Overview 

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 useâŻthe 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 crosssections 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 

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Unit 8 Overview 

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 longrun relative frequency. 
Unit 1: Factors and Multiples 

Essential Questions 
Unit 1 Overview 

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 

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Unit 2 Overview 

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 

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. 
Unit 4: From Hundredths to HundredThousands 

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Unit 4 Overview 

In this unit, students learn to express both small and large numbers in base ten, extending their understanding to include numbers from hundredths to hundredthousands. 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 

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. 
Unit 6: Multiplying and Dividing MultiDigit Numbers 

Essential Questions 
Unit 6 Overview 

In this unit, Students multiply and divide multidigit whole numbers using partial products and partial quotients strategies, and apply this understanding to solve multistep problems using the four operations. Students multiply up to four digits by singledigit numbers, and to multiply a pair of twodigit 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 multistep problems about measurement in various contexts. Parent video: Area model for multiplication 
Unit 7: Angles and Angle Measurement 

Essential Questions 
Unit 7 Overview 

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 twodimensional figures. 
Unit 8: Properties of TwoDimensional Shapes 

Essential Questions 
Unit 8 Overview 

In this unit, students deepen their understanding of the attributes and measurement of twodimensional shapes. Students classify triangles and quadrilaterals based on the properties of their side lengths and angles, and learn about lines of symmetry in twodimensional 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 

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. 
Unit 1: Rigid Transformations and Congruence 

Essential Questions 
Unit 1 Overview 

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 

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Unit 2 Overview 

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 

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 

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 

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 

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Unit 6 Overview 

In this unit, students analyze bivariate data—using scatter plots and fitted lines to analyze numerical data, and using twoway tables, bar graphs, and segmented bar graphs to analyze categorical data. 
Unit 7: Exponents and Scientific Notation 

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Unit 7 Overview 

In grade 6, students studied wholenumber 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 baseten 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 

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 

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. 
Unit 1: One Variable Statistics 

Essential Questions 
Unit 1 Overview 

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 

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Unit 2 Overview 

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 

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Unit 3 Overview 

In grade 8, students informally constructed scatter plots and lines of fit, noticed linear patterns, and observed associations in categorical data using twoway 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 bestfit lines (found using technology). The unit also revisits twoway tables to find associations in categorical data using relative frequencies. 
Unit 4: Functions 

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Unit 4 Overview 

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 realworld situations. 
Unit 5: Introduction to Exponential Functions 

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Unit 5 Overview 

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 

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Unit 6 Overview 

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 patternsâŻgrow more quickly than linear patterns but more slowly than exponential patterns. 
Unit 7: Quadratic Equations 

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Unit 7 Overview 

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. 
Unit 1: Sequences and Functions 

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Unit 1 Overview 

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 

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Unit 2 Overview 

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 

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Unit 3 Overview 

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 

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Unit 4 Overview 

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)=aà£Şbx, 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 

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Unit 5 Overview 

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 

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Unit 6 Overview 

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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Unit 1: Area and Surface Area 

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Unit 1 Overview 

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 

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Unit 2 Overview 

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 

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Unit 3 Overview 

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 

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Unit 4 Overview 

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 

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Unit 5 Overview 

In this unit, students compute sums, differences, products, and quotients of multidigit whole numbers and decimals, using efficient algorithms. They use calculations with whole numbers and decimals to solve problems set in realworld contexts. 
Unit 6: Expressions and Equations 

Essential Questions 
Unit 6 Overview 
How can variables be used to represent and solve equations in realworld 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 wholenumber exponents and wholenumber, fraction, or variable bases and solve for linear equations that include exponents. 
Unit 7: Rational Numbers 

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Unit 7 Overview 

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 

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Unit 8 Overview 

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 

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Unit 9 Overview 

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. 
The curriculum and instruction in elementary, middle and high school is handson 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.
Please see below for a parent guide to each science curriculum from kindergarten to high school.
Unit 1: Mystery Class Pet 

Essential Questions 
Unit 1 Overview 

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 

Through this yearlong 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 

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. 
Unit 1: Playground Shadows 

Essential Questions 
Unit 1 Overview 

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 

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 

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 

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. 
Unit 1: 4th Little Pig 

Essential Questions 
Unit 1 Overview 

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 

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 reallife science mystery that gives purpose to their study on plants, animals, and habitats. 
Unit 3: Beavers 

Essential Questions 
Unit 3 Overview 

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. 
Unit 1: Playground Engineers 

Essential Questions 
Unit 1 Overview 

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 

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 

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 

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. 
Unit 1: Forest Regrowth 

Essential Questions 
Unit 1 Overview 

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 

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 

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 computerbased 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 

Students begin the unit with viewing a short video clip of the raising of the woolly mammoth from ice and the possibility of deextincting* 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 deextinct. 
Unit 5: Coral Reefs * 

Essential Questions 
Unit 5 Overview 

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? 
Unit 1: Big Bang 

Essential Questions 
Unit 1 Overview 

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 

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 
Unit 1: Asteroid Collisions 

Essential Questions 
Unit 1 Overview 

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 

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 disasterprone 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 
Unit 1: Radium Girls 

Essential Questions 
Unit 1 Overview 

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 

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 
Unit 1: National Parks 

Essential Questions 
Unit 1 Overview 

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 

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 

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

Essential Questions 
Unit 1 Overview 

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 

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 

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. 
Unit 1: Lyme Disease 

Essential Questions 
Unit 1 Overview 

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 

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 

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 temperaturecontrolled habitats for penguins. 
Unit 4: Destructive Weather 

Essential Questions 
Unit 4 Overview 

This unit examines several aspects of weather and climate including Earth’s largescale 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. 
Unit 1 Energy Drinks 

Essential Questions 
Unit 1 Overview 

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 

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 

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). 
Unit 1: Car Collisions 

Essential Questions 
Unit 1 Overview 

Students will be exploring how forces cause objects to change their motion. Through studentdesigned 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 causeandeffect 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 

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 

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 

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
2038544026