SpringBoard Mathematics with Meaning Middle School Levels At A Glance (Grades 6, 7, and 8: Middle School Math 1, 2, 3, and Algebra 1)

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Middle School Mathematics 1 Unit Essential Questions Embedded Assessments Unit Focus on Embedded Assessment Goals Academic Vocabulary Unit 1 How can you use a prime EA#1: Divisibility, GCF, and LCM

1 Middle School Mathematics 1 Unit Essential Questions Embedded Assessments Unit Focus on Embedded Assessment Goals Academic Vocabulary Unit 1 How can you use a prime EA#1: Divisibility, GCF, and LCM Embedded Assessment 1 Winter Sports absolute value Number factorization to find the o Use divisibility rules additive inverse Concepts greatest common factor of two EA#2: Fractions, Decimals, and o Find the GCF and LCM of two numbers exponent or more numbers? Integers Embedded Assessment 2 Snowfall Statistics factors o Compare and order fractions, decimals, and integers integer Why can you use either a o Convert improper fractions to mixed numbers prime number fraction or a decimal to name the same rational number? o Convert mixed numbers to improper fractions Unit 2 How are operations with EA#1: Adding and Subtracting Embedded Assessment 1 My Cat Sam equation Operations fractions similar to and Fractions and Mixed Numbers o Add and subtract fractions and mixed numbers expression with Numbers different from operations with o Solve problems by adding, subtracting, and estimating with factoring whole numbers? EA#2: Using Fractions with mixed umbers integer Measurements Embedded Assessment 2 Juan s Bookcase order of operations What kinds of numbers do you o Multiply and divide fractions and mixed numbers property know about and how do EA#3: Order of Operations o Work with fractions in the context of customary measures reciprocal mathematical properties apply o Write problems about a given situation involving fractions to operations with different Embedded Assessment 3 The Lost of After School Activities kinds of numbers? o Operate with decimals in the context of money o Use mathematical properties and order of operations to write and evaluate expressions Unit 3 Why are tables, graphs, and EA#1: Linear Graphs Embedded Assessment 1 Library Lines inverse operations Linear Patterns equations useful for o Write and graph linear equations linear representing relationships? EA#2: Solving Linear Equations o Use equations to solve real world problems ordered pair Embedded Assessment 2 Functional Formulas rate of change How can you use equations to o Write and solve two step equations variable solve real world o Use formulas to solve problems Unit 4 Why are proportional EA#1: Ratios and Rates Embedded Assessment 1 A Summer Job percent Ratio and relationships an important part o Find and use unit rates rate Rates of mathematics? EA#2: Percents o Write and use ratios unit rate o Write and solve proportions How is percent related to Embedded Assessment 2 A Special Birthday fractions and decimals, and why o Find simple interest is it such a useful tool in o Use percent to find discounts, sales taxes, and tips everyday life? o Use mental math to estimate a percent of a number Page 1

2 Unit 5 Geometry Unit 6 Data Analysis And Probability What characteristics do various quadrilaterals share, and why is it possible to determine perimeter and area of quadrilaterals using related formulas? In what ways is symmetry important in real world situations? How does understanding probability help you make decisions? Why is it important for you to understand how data is organized and presented in real world situations? EA#1: Area and Perimeter EA#2: Polygons, Trans formations, and Geometry EA#1: Probability EA#2: Data Display and Summary Statistics Embedded Assessment 1 Designing a Clubhouse o Find area of various shapes making up a composite figure and calculate total area of the composite figure o o Find perimeter of a composite figure o Compare areas and perimeters of composite shapes Embedded Assessment 2 Graphic Geometry o Classify triangles and quadrilaterals o Plot coordinates on a 4 quadrant grid o Translate and reflect shapes on a 4 quadrant grid o Identify symmetry in a band pattern o Identify and find the volume of a cylinder Embedded Assessment 1 Out of the Hat o Find sample space and probability of given events o Find the complement of an event o Find probabilities for events on spinners o Determine whether a game is fair Embedded Assessment 2 Baseball Hall of Fame o Analyze data o Make a circle graph and a bar graph o Represent data with a stem plot o Write questions for a survey o Create a misleading bar graph altitude bisect congruent equilateral perimeter regular polygon solid transformation volume outcome population probability sample survey variable Page 2

3 Middle School Mathematics 2 Unit Essential Questions Embedded Assessments Unit Focus on Embedded Assessment Goals Academic Vocabulary Unit 1 Why is it important to EA#1: Integers and Exponents Embedded Assessment 1 Raise the Roof exponential form Integers and understand properties and o Integer operations principal Rational operations involving integers EA#2:Computation with Rational o Exponents scientific notation Numbers and negative rational numbers? Numbers o Real numbers set of real numbers Embedded Assessment 2 Muffin Madness set notation How can number lines and o Computation with decimals and fractions diagrams be used to interpret solutions of real world o Percent applications: profit and percent profit, markup and percent o increase, discount and percent decrease o Percents >100 and <1 o Commission o Simple and compound interest o Scientific notation Unit 2 Equations, Inequalities, and Linear Relationships Why is it important to understand how to solve linear equations and inequalities? How can graphs be used to interpret solutions of real world EA#1: Expressions and Equations EA#2: Equations and Graphs EA#3: Inequalities and Direct Variation Embedded Assessment 1 Fundraising Fun o Patterns o Concept of variable o Linear functions o Writing and solving linear equations o Combining like terms Embedded Assessment 2 Negotiating an Allowance o Graphing on the coordinate plane o Slope o Writing and solving linear equations Embedded Assessment 3 Parkside Amusements o Writing one variable inequalities from verbal descriptions o Graphing and solving one variable inequalities o Direct variation direct variation function inequality like terms open sentence Page 3

4 Unit 3 Two Dimensional Geometry and Similarity Why is it important to understand properties of angles and figures to solve How can diagrams be used to interpret solutions to real world EA#1: Polygons EA#2: Transformations EA#3: Scale Drawings and Right Triangles Embedded Assessment 1 Stained Glass Designs o Area of two dimensional figures o Perimeter of two dimensional figures o Angle pairs o Angles of convex polygons Embedded Assessment 2 A Geometric Artwork o Transformations Embedded Assessment 3 The Bermuda Triangle o Ratios and rates o Proportions o Measurement conversions o Scale drawings o Similar figures o Pythagorean theorem angle coordinate plane polygon Pythagorean Theorem ratio Unit 4 Three Dimensional Geometry Why is it important to be able to relate two dimensional drawings with threedimensional figures? How can surface area and volume be used to find answers to real world EA#1: Surface Area and Volume EA#2: Surface Area and Changes in Dimension Embedded Assessment 1 Under the Sea o Representing a three dimensional figure with an isometric drawing and a net o Determining the surface area and volume of a rectangular prism o Determining the volume of a prism, cylinder, and cone o Describing the relationship between the volume of a prism and a pyramid Embedded Assessment 2 Bird s Eye View o Determining the surface area of a prism, pyramid, and cylinder o Determining and applying the ratio of the areas and volumes in similar solids area net similar solid volume Unit 5 Data and Probability Why is it important to be able to represent data using graphs and measures of central tendency? How can data and probabilities be used to predict the outcome of future events? EA#1: Data Display and Interpretation EA#2: One and Two Stage Probability Embedded Assessment 1 Data Dilemma o Creating data displays o Interpreting data displays Embedded Assessment 2 State Quarters o Sample space o Probability of independent and dependent events o Probability of compound events o Mutual exclusivity bivariate data event five number summary measures of center random trend line Page 4

5 Middle School Mathematics 3 Unit Essential Questions Embedded Assessments Unit Focus on Embedded Assessment Goals Academic Vocabulary Unit 1 How are fractions, percents and EA#1: Patterns and Exponents Embedded Assessment 1 Contagious Mathematics hypothesis Patterns and decimals related? o Identifying and describing patterns power Numerical EA#2: Rational Numbers o Operations with exponents reciprocal Relationships Why is it important to Embedded Assessment 2 A Recipe for Success scientific notation understand the procedures for o Operations with fractions working with different kinds of o Equivalent forms of numbers numbers? o Rational and irrational numbers o Scientific notation o Inverse operations Unit 2 Expressions, Equations, And Inequalities How are the properties of real numbers useful when solving equations and simplifying expressions? What are the similarities and differences in the procedures for solving and expressing the solutions of equations and inequalities? EA#1: Patterns, Expressions, Equations, Formulas EA#2: Equations and Inequalities Embedded Assessment 1 A Penny for Your Thoughts o Linear patterns o Multiple representations o Solving equations o Evaluating expressions o Properties of real numbers o Literal equations Embedded Assessment 2 A Gold Medal Appetite o Writing and solving equations o Writing, graphing, and solving inequalities o Using formulas o Solving literal equations equation expression inequality inverse operation literal equation n th property sequence solution Unit 3 Equations and the Coordinate Plane Why is it important to consider slope, domain, and range in problem situations? How can graphs be used to interpret solutions of real world EA#1: Linear Relationships and Functions EA#2: Slopes and Intercepts EA#3: Bivariate Data and Systems Embedded Assessment 1 Education Pays o Linear relationships o Function vs. relation o Discrete vs. continuous Embedded Assessment 2 Linear Kindness o x and y intercepts o Graphing an equation of a line in slope intercept form o Finding the equation of a line given a table o Finding the equation of a line given a graph Embedded Assessment 3 Is It Hot in Here or Is It Me? o Bivariate data association o Systems of equations bivariate data continuous data discrete data domain function linear data range rate of change relation slope solution to a system of linear equations system of linear equations trend line x intercept y intercept Page 5

6 Unit 4 Proportional Relationships How is proportional reasoning used to solve real world What are transformations and how are they useful in solving real world EA#1: Lines, Angles, Transformations EA#2: Proportions, Similarity, and Conversions Embedded Assessment 1 Sweet Hexagons o Parallel lines and special pairs of angles o Sum of angle measures in a triangle o Angles in a polygon (hexagon) o Rigid transformations Embedded Assessment 2 Golden Rectangles o Ratios and proportions o Percents o Similarity and scale factor o Unit conversion angle similar figures transformation (geometric) Unit 5 Probability and Statistics Unit 6 Three Dimensional Geometry How do different displays help you interpret data? Why is it important to know if events are dependent or independent when calculating probabilities? How are two and threedimensional figures related? How do changes in dimensions of a geometric figure affect area, surface area, and volume? EA#1: Probability, Box Plot, Mean EA#2: Data Displays and Random Samples EA#1: Right Triangles EA#2: Area and Volume Embedded Assessment 1 How Much Off? o Counting Principle o Independent/dependent events o Complement of an event o Outlier s effect on measures of center and the range o Representations: tree diagram, box and whisker plot Embedded Assessment 2 Field Day Results o Histogram o Five number summary o Population of the sample o Assign labels to population of center and the range o SRS from random number table o Scatterplot o Line of good fit o Predictions using model o Outlier Embedded Assessment 2 Camp Euclid o Pythagorean theorem Embedded Assessment 2 Air Dancing o Lateral area o Volume categorical variables experimental probability numerical data outlier range simple random sample (SRS) theoretical probability solid Page 6

7 Algebra 1 Unit Essential Questions Embedded Assessments Unit Focus on Embedded Assessment Goals Academic Vocabulary Unit 1 How are patterns, equations, EA#1: Multiple Representations of Embedded Assessment 1 Shooting Stars expression Patterns and and graphs related? Data o Multiple representations of data variable Equations o Pattern recognition distributive property Why are the properties of real o Linear versus nonlinear data equation numbers important when EA#2: Properties and Solving Embedded Assessment 2 Checking Group Work solution solving equations? Equations o Solving multi step equations compound inequality o Properties of numbers absolute value equation EA#3: Inequalities and Absolute o Solution of an equation absolute value inequality Value Embedded Assessment 3 A Healthy Pool o Writing and graphing linear inequalities on a number line o Solving absolute value inequalities o Translating information from a tabular display to a symbolic representation Unit 2 How can you show EA#1: Representations of Embedded Assessment 1 Bryce Canyon Hiking dependent variable Linear mathematical relationships? Functions o Definition of function direct variation Functions o Representations of functions domain Why are linear functions useful EA#2: Linear Functions o Function notation function in real world settings? and Equations o Slope independent variable Embedded Assessment 2 Text Message Plans inverse variation o Discrete linear functions linear equation EA#3: Linear Equations and Slope o Writing linear equations range as Rate of Change o Tabular and graphical representations x intercept o Domain and range y intercept o Evaluating functions o Direct and inverse variation Embedded Assessment 3 A 10K Run o Linear functions o Writing linear equations o Slope as a rate of change o Domain Page 7

8 Unit 3 Extensions of Linear Concepts Unit 4 Exponents, Radicals, and Polynomials Unit 5 Quadratic Functions Unit 6 Data Analysis And Surveys Why would you use multiple representations of linear equations and inequalities? How are systems of linear equations and Inequalities useful in interpreting real world situations? How do multiplicative patterns model the physical world? How are adding and multiplying polynomial expressions different from each other? How are quadratic functions used to model, analyze and interpret mathematical relationships? Why is it advantageous to know a variety of ways to solve and graph quadratic functions? How do sampling methods affect the evaluation of survey results? How can displays and summaries be used to interpret and communicate the results of surveys? EA#1: Graphing Inequalities and Piecewise Functions EA#2: Systems of Equations and Inequalities EA#1: Exponential Functions EA#2: Polynomial Operations and Factoring EA#1: Graphing Quadratics EA#2: Solving Quadratic Equations EA#1: Inferences Based on Data EA#2: Analyzing Group Project Results Embedded Assessment 1 Earnings on a Graph o Write linear inequalities o Graph linear inequalities o Write piecewise defined functions o Graph piecewise defined functions Embedded Assessment 2 All systems Go o Represent problem situations with systems of linear equations o Use multiple methods to solve systems of equations o Solve systems of linear inequalities Embedded Assessment 1 Decisions, Decisions o Laws of exponents o Simplifying radicals o Exponential functions (growth and decay) Embedded Assessment 2 Measuring Up o Multiplying and factoring polynomials o Applying the properties of exponents Embedded Assessment 1 Quadratic Introduction o Graph quadratic functions with transformations of the form y = a x 2 + c o Identify quadratic functions Embedded Assessment 2 Egg Drop o Modeling and solving quadratic equations Embedded Assessment 1 Plots and Sampling o Stem and leaf plot o Box and whisker plot o Five number summary o Mean absolute deviation o Random number table o Sampling and measurement error Embedded Assessment 2 Who Am I? o Develop survey questions o Select random samples o Conduct surveys o Present survey results o Identify bias Substitution Method Elimination Method Linear inequality Piecewise defined function System of linear equations System of linear inequalities coefficient degree of a polynomial difference of two squares factor polynomial radical expression rational expression term parabola parent function quadratic formula quadratic function real roots of an equation transformation vertex of a parabola bias categorical variable census fi ve number summary margin of error mean absolute deviation quantitative variable sample simple random sample Page 8

Syllabus for Grade 7. More details on each of the topics is covered in the following pages.

Syllabus for Grade 7. More details on each of the topics is covered in the following pages. Syllabus for Grade 7 Chapter 1 Algebraic Reasoning Chapter 2 Integers and rational numbers Chapter 3 Number Theory Chapter 4 Rational number Chapter 5 Patterns and functions Chapter 6 Proportional Relationships