MATHLINKS: GRADE 7 CORRELATION OF STUDENT PACKETS TO THE RESOURCE GUIDE Referenced here is the vocabulary, explanations, and examples from the Resource Guide that support the learning of the goals in each MathLinks: Grade 7 student packet, as well as the Common Core State Standards for Mathematics for each lesson. Packet Summary MathLinks: Grade 7 Resource Guide (Part 1) Student Packet 7-1 Fractions and Decimals 1.1 Terminating Decimals Students learn strategies to convert between fractions and terminating decimals. Standards 4.NF.A, 6.NS.B 1.2 Repeating Decimals Students change thirds, sixths, and ninths to decimals and explore patterns in repeating decimals. Students continue to convert between fractions and decimals. Students continue to compare, order, and add simple fractions and decimals. Standards 5.NF.A, 7.NS.A 1.3 Graphing Fractions and Decimals Students order fractions and decimals. Students graph fractions and decimals on a number line. Students graph ordered pairs in the first quadrant of the coordinate plane. Standards 4.NF.A, 4.NF.C Student Packet 7-2 Rational Numbers on the Number Line 2.1 Integers and the Number Line Students extend the positive number line to represent all integers. Students extend the axes of the quarter plane (1 st quadrant) to create a four-quadrant coordinate plane. Students use arrows to represent direction and distance. Students solve problems involving integers and temperature. Standards 6.NS.C 2.2 Opposites and Absolute Value Students learn to interpret and evaluate the opposite and absolute value of a number. Standards 6.NS.C 2.3 Rational Numbers and the Number Line Students locate and order rational numbers on the number line. Students graph ordered pairs in the coordinate plane. Standards 6.NS.C benchmark fraction coordinate plane decimal division fraction ordered pair repeating decimal terminating decimal unit fraction absolute value opposite of a number distance origin equation quadrant inequality rational number integer Integer Concepts Rational Number Operations
Packet Summary MathLinks: Grade 7 Resource Guide (Part 1) Student Packet 7-3 Integer Addition and Subtraction 3.1 Integer Models Students think about positive and negative numbers using hot pieces and cold nuggets in the context of a temperature change model. Students represent positive and negative integers with counters. 3.2 Addition: Counters and Temperature Students use counter and temperature change models to generalize rules for integer addition. 3.3 Subtraction: Counters and Temperature Students use counter and temperature change models to generalize rules for integer subtraction. absolute value addend additive identity property additive inverse property difference integers minuend opposite of a number subtrahend sum Integer Concepts Integer Operations Student Packet 7-4 Addition and Subtraction on the Number Line 4.1 Addition on the Number Line Students deepen their understanding of integer addition by exploring this operation on a number line. Standards 6.NS.C, 7.NS.A 4.2 Subtraction on the Number Line Students use their knowledge of addition and subtraction as inverse operations to create adding up statements from subtraction statements. Students deepen their understanding of integer subtraction by exploring this operation on a number line. Standards 6.NS.C, 7.NS.A 4.3 Addition and Subtraction: Rational Numbers Students extend their knowledge of integer addition and subtraction to adding and subtracting rational numbers. absolute value origin addend quadrant difference rational number distance subtrahend minuend sum Integer Operations Rational Number Operations
Packet Summary MathLinks: Grade 7 Resource Guide (Part 1) Student Packet 7-5 Rational Numbers: Multiplication and Division 1 5.1 Multiplication: Models Students develop integer multiplication rules using the counter and temperature change models. Students verify the rules for multiplication using arrows on a number line. Standards 6.NS.C, 7.NS.A 5.2 Multiplication and Division: Patterns Students use patterns and the inverse relationship between multiplication and division to establish sign rules for division. Students solve multiplication and division problems. 5.3 Reasoning about Products and Quotients Students use inductive reasoning to make conjectures and deductive reasoning to draw conclusions based on accepted facts and logic. Students write quotients of integers in different forms. Students explore why division by zero is not defined, and prove that (-1)(-1) = 1. Student Packet 7-6 Rational Numbers: Multiplication and Division 2 6.1 Order of Operations Students learn conventions for the order of operations and apply them to evaluate expressions. Standards 7.EE.B 6.2 Ratios of Fractions Students compute the unit rate for various measurements. Students learn strategies for working with ratios of fractions. Standards 6.RP.A, 7.RP.A, 7.EE.B 6.3 Multiplication and Division: Rational Numbers Students multiply and divide rational numbers., 7.EE.B conjecture deductive reasoning inductive reasoning inverse operation product quotient rational number Integer Operations Rational Number Operations complex fraction exponential notation order of operations ratio rational number unit rate Order of Operations Ratios and Proportional Relationships
Packet Summary MathLinks: Grade 7 Resource Guide (Part 1) Student Packet 7-7 Probability 7.1 Introduction to Probability Students use vocabulary related to probability. Students write the probability of events using fractions, decimals and percents. Students perform a probability experiment., 7.SP.C 7.2 Spinners Students use spinners and puzzles to explore probability concepts. Students compare experimental probability to theoretical probability. Students use logical reasoning to determine the probability of different events., 7.SP.C event probability experiment experimental sample probability fair game sample space outcome theoretical probability probability trial Probability 7.3 Flips, Rolls, and Fair Games Students explore probability concepts as they flip a coin and roll a number cube. Students learn techniques for organizing data. Students analyze experiments by comparing experimental probabilities to the theoretical probability. Students use probability to determine if games are fair., 7.SP.C Student Packet 7-8 Exploring Expressions and Equations 8.1 Equivalent Expressions Students write numerical expressions to represent geometric patterns, describe patterns in words, and generalize using variable expressions. Students apply properties to generate equivalent expressions that include integers. Standards 6.NS.B, 7.EE.A, 7.EE.B 8.2 Hundreds Chart Patterns Students investigate patterns on the hundreds chart. Students write algebraic expressions and use them to prove conjectures based on the patterns. Students find equivalent expressions that involve variables and rational numbers. Standards 6.NS.B, 7.EE.A, 7.EE.B deductive reasoning expression distributive property greatest common factor equation inductive reasoning equivalent solve an equation expressions evaluate variable Variables and Expressions 8.3 Polygon Area Puzzle Students create expressions and equations based upon the areas of polygon puzzle pieces. Students evaluate expressions, solve equations, and solve problems. Standards 6.NS.B, 6.EE.B, 7.NS.A, 7.EE.A, 7.EE.B
Packet Summary MathLinks: Grade 7 Resource Guide (Part 1) Student Packet 7-9 Solving Equations 9.1 Solving Equations: Mental Math Strategies Students will solve equations using mental strategies. Students will solve problems involving the lengths of sides, the perimeter, and the area of triangles, rectangles and regular polygons. Standards 6.EE.A, 6.EE.B, 7.NS.A, 7.EE.B 9.2 Solving Equations: Balance Strategies Students explore the concept of balance and apply it to solving equations. Students solve problems using algebra. Standards 6.EE.A, 6.EE.B, 7.NS.A, 7.EE.B 9.3 Solving Equations with Rational Coefficients Students solve equations with coefficients that are rational numbers. Students solve problems using algebra. Standards 6.EE.A, 6.EE.B, 7.NS.A, 7.EE.A, 7.EE.B Student Packet 7-10 Inequalities 10.1 Linear Inequalities Students write linear inequalities in one variable and graph their solutions. Standards 6.NS.C, 6.EE.B, 7.EE.B 10.2 Solving Linear Inequalities Students solve linear inequalities in one variable and graph their solutions. Standards 6.NS.C, 6.EE.B, 7.EE.B addition property of equality consecutive integers equation equivalent expressions inequality Equations and Inequalities boundary point of a solution set equation Equations and Inequalities multiplication property of equality perimeter rational numbers solve an equation inequality 10.3 Inequality Problems Students solve problems that involve inequalities. Standards 6.NS.C, 6.EE.B, 7.EE.B
Packet Summary MathLinks: Grade 7 Resource Guide (Part 2) Student Packet 7-11 Proportional Reasoning 11.1 Proportional Reasoning Students use different strategies to solve proportional reasoning problems. Standards 6.RP.A, 7.RP.A, 7.NS.A, 7.EE.B 11.2 Rate Problems Students solve a variety of rate problems. Standards 6.RP.A, 7.RP.A, 7.NS.A, 7.EE.B 11.3 Best Buy Problems Students use tables, graphs, and symbolic representations to determine whether a relationship is proportional. Standards 6.RP.A, 7.RP.A, 7.NS.A, 7.EE.B Student Packet 7-12 Percent 12.1 Percent Increase and Decrease Students learn some common vocabulary related to percent. Students learn how to find percent increases and decreases. Standards 6.RP.A*, 7.RP.A, 7.NS.A, 7.EE.A, 7.EE.B 12.2 Simple Interest Students learn what interest means, why it is important, and how it is used. Standards 6.RP.A*, 7.RP.A, 7.NS.A, 7.EE.A, 7.EE.B cross-multiplication property proportion proportional relationship ratio unit price unit rate Ratios and Proportional Relationships discount (markdown) percent interest percent of a number interest rate principal markup simple interest Percents 12.3 Sales and Commissions Students solve problems involving sales, sales tax, markups, discounts, and commissions. Standards 6.RP.A*, 7.RP.A, 7.NS.A, 7.EE.A, 7.EE.B
Packet Summary MathLinks: Grade 7 Resource Guide (Part 2) Student Packet 7-13 Sampling 13.1 Introduction to Sampling Students use measures of center and spread to describe data sets. Students make predictions about a population based on a sample of the population. Students display data sets using dot plots, box plots, and other visual representations. Standards 6.SP.A, 6.SP.B 13.2 Comparing Samples Students compare two data sets using visual displays and statistics. Students compute and interpret the mean absolute deviation for samples. Students explore the effect of potential outliers on a data set. Standards 6.SP.A, 6.SP.B, 7.SP.A, 7.SP.B box plot dot plot five number summary interquartile range mean mean absolute deviation Statistics and Data Displays median mode population range sample simulation 13.3 Fish in a Lake Students do a sampling experiment to estimate the fish population in a lake. Students make inferences about populations using data displays and measures of center and spread. Standards 7.RP.A, 7.SP.A, 7.SP.B Student Packet 7-14 Angles, Triangles, and Quadrilaterals 14.1 Angle Measurements Students explore angle measures by creating their own protractors. Students use a protractor to measure and draw angles. Students review facts about triangles and quadrilaterals. Standards 7.EE.B, 7.G.A, 7.G.B 14.2 Angle Explorations Students use patterns to learn facts about angles. Students use these facts to write equations and solve for unknown angle measures in diagrams. Standards 7.EE.B, 7.G.B 14.3 Drawing Triangles and Quadrilaterals Students classify triangles based on the measure of their sides and angles. They draw figures freehand, using rulers and protractors, and with technology. Students observe conditions that make a triangle unique. Standards 7.G.A adjacent angles angle complementary angles quadrilateral Greek and Latin Word Roots Number Prefixes Plane Figures supplementary angles triangle vertical angles
Packet Summary MathLinks: Grade 7 Resource Guide (Part 2) Student Packet 7-15 Scale Drawings and Circle Measurements 15.1 Scale Drawings Students make scale drawings by applying different scale factors. Students use ratio strips and rulers to construct and read drawings made to scale., 7.G.A 15.2 Circumference of Circles Students explore the relationship between a circle's diameter and its circumference. Students learn about historical approximations for π. Students establish the formula for the circumference of a circle and use it to solve problems., 7.G.B 15.3 Area of Circles Students use their knowledge of the area of rectangles and circumference of circles to give an informal derivation of the area formula for a circle. Students use the formula to solve problems., 7.EE.A, 7.G.B Student Packet 7-16 Plane and Solid Figures 16.1 Problems Involving Plane Figures Students solve real world and mathematical problems involving area and scale drawings., 7.EE.B, 7.G.A, 7.G.B 16.2 Problems Involving Solid Figures Students solve real world and mathematical problems involving surface area and volume., 7.EE.B, 7.G.B 16.3 Cross Sections of Solid Figures Students describe two-dimensional figures that result from slicing three-dimensional figures by planes. Standards 7.G.A center of a circle chord circle circumference diameter Greek and Latin Word Roots Number Prefixes Scale Drawings Plane Figures apex cross section lateral face plane plane figure Solid Figures pi radius scale scale drawing scale factor right prism right rectangular pyramid solid figure vertex