MATHLINKS: GRADE 8 CORRELATION OF STUDENT PACKETS TO THE RESOURCE GUIDE

Transcription

1 MATHLINKS: GRADE 8 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 8 student packet, as well as the Common Core State Standards for Mathematics for each lesson. Packet Summary MathLinks: Grade 8 Resource Guide (Part 1) Student Packet 8-1 Integers Review 1.1 Integer Operations: Patterns Students use patterns to revisit the rules for adding, subtracting, multiplying, and dividing integers. Standards 6.NS.C, 7.NS.A 1.2 Integer Operations: A Counter Model Students use a model to revisit the rules for adding, subtracting, multiplying, and dividing integers. Standards 6.NS.C, 7.NS.A 1.3 Order of Operations Students review the conventions for the order of operations and apply them to evaluate expressions. Standards 6.EE.A, 7.NS.A Student Packet 8-2 Expressions and Equations Exploring Expressions Students write expressions with numbers and variables. Students simplify numerical expressions using the conventions for order of operations. Standards 6.EE.A 2.2 Exploring Equations Students learn to interpret Students review the difference between expressions and equations. Students find values of variables to make equations true. Standards 6.EE.B 2.3 Mental Equation and Inequality Strategies Students solve equations using mental math strategies. Students solve inequalities and graph their solutions. Standards 7.EE.B absolute value opposite addend product difference quotient factors subtrahend integers sum minuend zero pair Integer Concepts and Models Integer Operations Order of Operations equality inequality equation simplify evaluate solve (an expression equation) variable (unknown) Order of Operations Variables and Expressions

2 Packet Summary MathLinks: Grade 8 Resource Guide (Part 1) Student Packet 8-3 Patterns and Linear Functions Geometric Patterns Students extend geometric toothpick patterns. Students use numbers, pictures, symbols, and words ( the fourfold way ) to describe these patterns. Standards 8.F.A, 8.F.B 3.2 Number Patterns Students observe and extend number sequences. They find recursive and explicit rules for number patterns. Standards 8.F.A 3.3 Saving for a Purchase Students use input-output equations, tables, and graphs to find how much time is needed to save for purchases. Standards 8.EE.C, 8.F.A, 8.F.B function linear function explicit rule ordered pair (input-output rule) recursive rule inductive y-intercept Functions Student Packet 8-4 Patterns and Linear Functions Growing Shapes Students extend square and rectangle patterns. Students represent geometric measures in the patterns using input-output tables, graphs, symbols, and words (the fourfold way ). Standards 8.F.A, 8.F.B 4.2 Going to the Park Students analyze information about friends going to a park after school to understand time, distance, and rate of speed relationships using numbers, graphs, symbols, and words. Standards 8.EE.B, 8.EE.C, 8.F.A, 8.F.B 4.3 Stacking Cups Students measure and record heights of stacked cups, and represent the data using numbers, graphs, and algebraic symbols. Students estimate a line that fits the data. Standards 8.F.A, 8.F.B, 8.SP.A explicit rule (or input-output rule) fourfold way inductive linear function point of intersection rate slope (of a line) y-intercept

3 Student Packet 8-5 Expressions and Equations 2 Packet Summary MathLinks: Grade 8 Resource Guide (Part 1) 5.1 Cups and Counters Expressions Students write and simplify expressions in the context of a model. Standards 6.EE.A, 6.EE.B, 7.EE.B 5.2 Number Tricks Students perform mathematical number tricks and use algebraic expressions to show how the number tricks work. Standards 6.EE.A, 6.EE.B 5.3 Cups and Counters Equations 1 Students solve linear equations with one variable using a visual model, and they record the steps with pictures and algebraic symbols. Standards 7.EE.B, 8.EE.C additive inverse property distributive property expression simplify equation solve (an equation) evaluate substitution additive inverse property Variables and Expressions terms (like terms) Linear Equations in One Variable Mathematical Properties Student Packet 8-6 Solving Equations 6.1 Cups and Counters Equations 2 Students solve linear equations using a model and record the steps with pictures and algebraic symbols. Standards 7.EE.A, 7.EE.B, 8.EE.C 6.2 Solving Equations with Integer Coefficients Students begin to transition from solving equations with a model to using only algebraic notation. Standards 7.EE.A, 7.EE.B, 8.EE.C 6.3 Solving Equations With Rational Coefficients Students solve more algebraic equations using algebraic notation. Students justify the steps used to solve equations. Some equations will involve noninteger values. Standards 7.EE.A, 7.EE.B, 8.EE.C equation rational numbers integers solution to an numerical equation coefficient variable equation rational numbers integers solution to an numerical equation coefficient variable Linear Equations in One Variable Mathematical Properties

4 Student Packet 8-7 Exploring Functions Packet Summary MathLinks: Grade 8 Resource Guide (Part 1) 7.1 Introduction to Functions Students explore the concept of a function. Students define the terms function and graph of a function. Students describe examples of functions and examples of non-functions. Standards 8.F.A 7.2 Rate Graphs Students use words, pictures, tables of numbers, and graphs to represent rates. Students compare representations of functions. Standards 8.F.A, 8.F.B 7.3 Best Buy Problems Students use numbers and graphs to help determine which choices are better buys, based on price. Students learn about a special linear function called a direct proportion. Standards 6.RP.A, 7.RP.A, 8.EE.B, 8.F.A, 8.F.B direct proportion function graph of a function input-output rule Functions linear function rate unit rate variable Student Packet 8-8 Slope and Slope-Intercept Form of a Line 8.1 Introduction to Slope Students count distances and use slope definitions to find slopes of line segments on a grid and on a set of coordinate axes. Students explore the meaning of positive and negative slopes. Standards 8.EE.B 8.2 Input-Output Investigation Student will use input-output tables to help graph and find equations of lines. Standards 8.F.A, 8.F.B, 8.EE.B 8.3 Slope-Intercept Form Students find equations of lines in slope-intercept form. Students extend the meaning of slope to horizontal and vertical lines. Students use properties of parallel lines and similar tri to deepen our understanding of the meaning of slope of a line. Standards 8.EE.B congruent slope (slope of a line) input-output rule x-intercept linear function y-intercept slope-intercept form of a linear equation

5 Packet Summary MathLinks: Grade 8 Resource Guide (Part 2) Student Packet 8-9 Systems of Linear Equations 9.1 Solving Linear Systems by Graphing Students solve systems of linear equations by graphing. Students write linear equations in equivalent forms. Students create a mathematical model (equation) to solve the rope problem. Standards 8.EE.C, 8.F.A, 8.F.B linear function ordered pair slope of a line slope-intercept form of a linear equation solution to a system of equations system of equations y-intercept 9.2 Solving Linear Systems by Substitution Students solve systems of linear equations by the substitution method. Standards 8.EE.C, 8.F.A, 8.F.B 9.3 Solving Linear Systems by Elimination Students solve systems of linear equations by the elimination method. Standards 8.EE.C Systems of Linear Equations Student Packet 8-10 Bivariate Data 10.1 Categorical Data Students use two-way tables to display the frequencies and relative frequencies of categorical data. Students examine patterns of association in bivariate categorical data. Students draw conclusions about possible associations. Standards 8.SP.A 10.2 Numerical Data Students construct scatter plots for bivariate numerical data. Students investigate various patterns of association in bivariate data. Students interpret scatter plots. Standards 8.SP.A 10.3 Lines of Best Fit Students construct linear models for measurement and other numerical data clustered around a straight line. Students draw lines of best fit. Students estimate an equation for the line of best fit. Students use the equation as a model to make predictions. Standards 8.F.B, 8.SP.A association measurement data bivariate data numerical data categorical data outlier data displays population data set relative frequency frequency table table line of best fit scatter plot two-way table Statistics

6 Student Packet 8-11 Exponents and Roots Packet Summary MathLinks: Grade 8 Resource Guide (Part 2) 11.1 Squares and Square Roots Students find squares and square roots of numbers. Students approximate square roots, and they locate square roots on a number line. Standards 8.NS.A 11.2 Conjectures About Exponents Students use patterns to make conjectures about rules for multiplying expressions involving exponents. Students explore rules for exponents, and they apply them to simplifying expressions. Standards 8.EE.A 11.3 Large and Small Numbers Students write large and small numbers using a variety of notations, including scientific notation. Students problems involving large numbers. Standards 8.EE.A conjecture exponential notation factor product quotient Exponent and Roots radical sign radicand Rational and Irrational Numbers scientific notation square of a number square root of a number Student Packet 8-12 Lines, Angles and Tri 12.1 Angles and Tri Students establish relationships among. Students establish facts about angle sums in tri. Students solve problems involving angle measures Parallel Lines Students establish vocabulary and facts related to formed when parallel lines are crossed by a third line. Students use properties of parallel lines to solve problems The Pythagorean Theorem Students explore the relationship among the side lengths of right tri and then understand a proof of the Pythagorean Theorem. Students use the Pythagorean Theorem to solve problems. Standards 8.EE.A, 8.G.B adjacent alternate exterior alternate interior complementary converse of the Pythagorean Theorem corresponding deductive exterior angle of a triangle hypotenuse inductive legs parallel lines perpendicular lines proof Pythagorean Theorem supplementary transversal vertical Points, Lines, and Angles The Pythagorean Theorem Greek and Latin Root Words Prefixes

7 Packet Summary MathLinks: Grade 8 Resource Guide (Part 2) Student Packet 8-13 Translations, Rotations, and reflections 13.1 Translations Students perform a transformation experiment using patty paper. They define transformations of the plane and observe some properties of transformations. Students learn about a transformation called a translation. Standards 8.F.A, 8.G.A 13.2 Rotations Students experiment with rotations and explore their properties. They make conjectures about rotations of coordinate pairs Reflections Students experiment with reflections and explore their properties. They will make conjectures about reflections of coordinate pairs. Students compare properties of translations, rotations, and reflections. angle of rotation reflection center point of rotation rotation transformation function translation image vector line of reflection Transformations of the Plane Student Packet 8-14 Congruence and Similarity 14.1 Congruence Students define congruence and explore its properties Dilations Students experiment with dilations and explore properties of dilations., 8.G.B 14.3 Similarity Students define similarity and explore its properties. Students compare properties of similarity to properties of congruence. congruent figures deductive dilation inductive image ratio of proportionality proof Transformations of the Plane scale factor similar figures transformation

8 Student Packet 8-15 Geometry Discoveries Packet Summary MathLinks: Grade 8 Resource Guide (Part 2) 15.1 Similar Tri Students establish and apply the angle-angle criterion for similarity of tri. Students find missing side lengths of similar tri. Students link properties of similarity to the slope of a line and to a famous theorem. Standards 8.EE.B, 8.G.B 15.2 Volume of Cylinders Students develop the formula for the volume of cylinders and apply it to solve problems. Standards 8.NS.A, 8.G.C 15.3 Volume of Cones and Spheres Students develop formulas for the volumes of cones and spheres and apply them to solve problems. Standards 8.NS.A, 8.G.C area base circumference cone cylinder diameter height hypotenuse legs of a right triangle parallel Transformations of the Plane Volume pi polyhedron prism Pythagorean Theorem right rectangular prism similar tri slope of a line sphere volume Student Packet 8-16 The Real Number System 16.1 Exponents and Roots Revisited Students work with squares, square roots, cubes, and cube roots of rational numbers. Students review rules for exponents and roots. Students solve problems with large and small numbers written in multiple ways, including scientific notation. Standards 8.EE.A 16.2 Rational Numbers Students deepen their understanding of rational numbers. Students learn why the decimal expansion of a rational number eventually repeats. Students learn how to express repeating decimals as quotients of integers. Students familiarize themselves with the decimal expansions of some common fractions by playing a game based on probability. Standards 7.SP.C, 8.NS.A cube of a number cube root of a number square of a number square root of a number integers Exponents and Roots Rational and Irrational Numbers irrational numbers natural numbers rational numbers real numbers repeating decimal terminating decimal whole numbers 16.3 Irrational Numbers Students practice locating decimal numbers on the real number line. Students learn that each real number has a decimal name (address) locating it on the real number line, that repeating decimals represent rational numbers, and that nonrepeating decimals represent irrational numbers. Students learn about two famous irrational numbers, pi and 2. Standards 8.NS.A