Grade 8 Curriculum Map 2007-2008 Moving Straight Ahead 25 Days Curriculum Map 2007-2008 CMP2 Investigations Notes Standards 1.2 Finding and Using Rates Walking Rates and Linear Relationships 1.3 Raising Money 1.4 Using the Walkathon Money Good introduction This can be demonstrated in class by having students actually walk at various rates (whole class) This investigation will be referenced later in the year. It is time consuming, but worth the time. 0 2.1 Walking to Win 0 2.2 Crossing the Line 2.3 Comparing Costs 0 0 1 Introduce concept of pattern of change between independent, dependent variables for linear relationships Describe the patterns of change between the independent, dependent variables for linear relationships that are represented in tables. Construct tables, graphs, and equations to represent linear patterns of change. Construct graphs and tables to model problem situations Translate information about linear relations given in a table, a graph, or an equation to one of the other forms Informally explore the y-intercept Understanding negative rates of change and how they are represented in equations, tables, and graphs Continue to explore y-intercept Describe the information the variables and numbers in an equation represent Find solutions to a problem using a table or graph Understand the connections between linear equations and patterns in tables and graphs of those relations, including rate of change and x-and y-intercepts Translate information on linear relations given in table, graph or equation to those given in other forms Find solutions to problem using table or graph Connect solutions in graphs and tables to solutions of equations Understand the connections between linear equations and patterns in tables and graphs of those relations, including rate of change and x-and y-intercepts Translate information on linear relations given in table, graph or equation to those given in other forms Find solutions to problem using table or graph Connect solutions in graphs and tables to solutions of equations Understand how the y-intercept appears in tables and equations 2.4 Connecting Tables, Graphs and Understand the connections between linear equations and patterns in tables and graphs of those relations, including rate of change and x-and
Equations 0 3.1 Solving Equations 8.P.2 3.2 Exploring Equality 1 y-intercepts Translate information on linear relations given in table, graph or equation to those given in other forms Write equations for linear relationships and describe what information the variables and numbers represent Find solutions to problem using table or graph Connect solutions in graphs and tables to solutions of equations Understand how the y-intercept appears in tables and equations 1 Describe the information the variables and numbers in an equation represent Solve linear equations in one variable using tables, graphs and symbols Connect solutions to equations to a table or graph of the equation Develop understanding of equality Begin to use properties of equality to solve equations that are represented pictorially 3.3 From Pouches to Use the properties of equality to solve equations Variables Check solutions to equations 3.4 Solving Linear Develop strategies for solving linear equations Equations Recognize subtle shifts in equations and how they affect the solutions 3.5 Finding the Point of Intersection Interpret equations in an applied setting Find the point of intersection of two lines 4.1 Climbing Stairs Introduce slope as the ratio of vertical change to horizontal change between two points of a line or ratio of rise over run 4.2 Finding the Slope of a Line 1 4.3 Exploring Patterns With Lines 4.4 Writing Equations With Two Variables 0 1 Connect slope to patterns or change Find the slope of a line from data in a table, graph, or equation Find the y-intercept of a line from data in a table, graph, or equation Use the slope m and y-intercept b to write an equation in the form y = mx + b Explore patterns among lines with the same slope-parallel lines Explore patterns among lines whose slopes are negative reciprocals of each other-perpendicular lines Write an equation for an applied situation when the only information given is two data points Looking for Pythagoras 25 Days Curriculum Map 2007-2008 CMP2 Investigation Notes Standards Driving Around Euclid Review the coordinate system. Explore the distances on a coordinate grid.
1.2 Planning Parks 1.3 Finding Areas 2.1 Looking For Squares 2.2 Square Roots good lesson 2.3 Finding Lengths ACE questions are good 3.1 3.2 The Pythagorean Theorem A Proof of the Pythagorean Theorem 8.N.9 8.N.9 3.3 Finding Distances 3.4 4.1 4.2 4.3 4.4 Measuring the Egyptian Way Analyzing the Wheel of Theodorus Stopping Sneaky Sally Analyzing Triangles Finding the Perimeter Ace questions are good optional 8.N.9 8.N.9 4 4 4 4 4 Review the properties of quadrilaterals. Connect properties of figures to coordinate representations Draw shapes on a coordinate grid Develop strategies for finding areas of irregular figures on a grid Draw squares on 5 dot by 5 dot grids and find their areas Introduce the concept of square root Understand square roots geometrically, as the side length of a square with known area Use geometric understanding of square roots to find lengths of line segments on a dot grid Deduce the Pythagorean Theorem through exploration Use the Pythagorean Theorem to find unknown side lengths of right triangles Reason through a geometric proof of the Pythagorean Theorem Use the Pythagorean Theorem to find the distance between two points on a grid Relate areas of squares to the lengths of sides Determine whether a triangle is a right triangle based on its side lengths Relate areas of squares to the lengths of the sides Learn the meaning of rational number and irrational number Estimate the values of square roots that are irrational numbers Estimate lengths of hypotenuses of right triangles Estimate the lengths of hypotenuses of right triangles Apply the Pythagorean Theorem to a problem situation optional Investigate the special properties of a 30-60-90 triangle omit
Thinking With Mathematical Models 20 days Curriculum Map 2007-2008 CMP 2 Investigation Notes Standards 1.2 1.3 Testing Bridge Thickness Testing Bridge Lengths Custom Construction Parts 2.1 Linear Models.2 2.3 2.4 3.1 Equations for Linear Relationships Solving Linear Equations Intersecting Linear Models Rectangles With Fixed Area ACE # 7-30 are good review Students may need help writing the equations in A. 0. 0 0 8.N.1 0 0 0 0 8 Make tables and graphs to represent data Describe relationships between variables Use data patterns to make predictions Make tables and graphs to represent data Describe relationships between variables Use data patterns to make predictions Make tables and graphs to represent data Describe relationships between variables Use data patterns to make predictions Compare and contrast linear and nonlinear relationships Fit a line to data that show a linear trend Write an equation for a line based on a graph of the line Use mathematical models to answer questions about linear relationships Practice effective strategies for writing linear equations from verbal, numerical or graphical information Develop skill in solving linear equations with approximation and exact reasoning methods. Write inequalities to represent at most situations Use equations to represent questions about problem situations and interpret the solutions in the context of the problem Explore situations that can be modeled by inverse variation relationships
3.2 Bridging the Distance 3.3 Average Cost Optional Inverse variation not in frameworks Optional Inverse variation not in frameworks 0 8.N.12 8.N.12 4 4 4 Explore situations that can be modeled by inverse variations relationships Investigate the nature of inverse variation in familiar contexts Compare inverse variations with linear relationships Explore situations that can be modeled by inverse variations relationships Investigate the nature of inverse variation in familiar contexts Compare inverse variations with linear relationships Say it With Symbols 25 Days Curriculum Map 2007-2008 CMP 2 Investigation Notes Standards Tiling Pools 1.2 Thinking in Different Ways 1.3 The Pool Problem 1.4 Diving In 2.1 Walking Together Great problem to do with manipulatives (colored tiles). Omit Look at ACE problems that merge two shapes. Omit Uses quadratics. Could be used with advanced students. ACE p. 14 # 5 and # 6 Recall Leanne, Gilberto, and Alana with the Walk-A-Thon Model situations with symbolic statements Interpret the information equivalent expressions represent in a given context. Determine if two or more expressions are equivalent Interpret the information equivalent expressions represent in a given context. Determine if two or more expressions are equivalent Review the Distributive Property Write equivalent expressions using the Distributive Property Determine if two or more expressions are equivalent by using the Distributive Property and other properties of the real numbers Use several pieces of information to write one symbolic statement Continue to use parentheses and the Distributive Property to write equivalent expressions Interpret information represented by equivalent expressions
2.2 Predicting Profits 2.3 Using Equations Relate parts of a symbolic statement or expression to the underlying relationship and to the context of the problem Rewrite an equation that contains two variables by replacing one of the variables by an equivalent expression representing that variable Model situations with symbolic statements Write a new algebraic expression by combining expressions ACE pp.28-31 # 1-14, 19-24 INV 3,4 0mit all 5.1 Using Algebra to Solve a Puzzle 5.2 Odd and Even Revisited 5.3 Squaring Odd Numbers Translate verbal statements into algebraic statements Write a series of equivalent expressions to show why a particular number trick works Write conjectures about numbers as symbolic statements Use the properties of numbers to confirm conjectures Translate verbal statements into algebraic statements Write a series of equivalent expressions to show why a particular number trick works Samples and Populations 18 Days Curriculum Map 2007-2008 CMP 2 Investigation Notes Standards From Line Plots to Histograms 1.2 Using Histograms 1.3 1.4 Box and Whisker Plot Making a Quality Choice Review outliers ACE questions. 7 Compare sample distributions using measures of center (mean, median), measures of variability (minimum, maximum, and range) and data displays that group data (histograms) Compare sample distributions using measures of center (mean, median), measures of variability (minimum, maximum, and range) and data displays that group data (histograms) Compare sample distributions using measures of center (mean, median), measures of variability (minimum, maximum, and range) and data displays that group data (box and whisker plots) Compare sample distributions using measures of center (mean, median), measures of variability (minimum, maximum, and range) and data displays that group data (histograms, box and whisker plots) 2.1 Asking About Honesty 8.D.1 Distinguish between a sample and a population Use data from samples to make predictions about a population
2.2 Selecting a Sample 8.D.1 8 2.3 2.4 Choosing Random Samples Choosing a Sample Size INV 3 OMIT Are Quality 4.1 Ratings and Prices Related? Writing An Equation to 4.2 Describe a Relationship Human Development Index 4.3 and Life Expectancies good ACE questions 8.D.1 8.D.1 7 7 8 Consider various ways of developing a sample plan Select a random sample from a population Use sampling distributions, measures of center, and measures of variability to describe and compare samples Apply elementary probability with spinners or calculators to choosing from random samples Use data from a sample to estimate a characteristic of a population Use sampling distributions, measures of center, and measures of variability to describe and compare samples Explore relationships between paired values of numerical attributes Explore relationships between paired values of numerical attributes Explore relationships between paired values of numerical attributes Shapes of Algebra 20 days Curriculum Map 2007-2008 CMP2 Investigation Notes Standards 1.2 Equations for Circles Parallels and Perpendiculars 1.3 Finding Midpoints 2.1 Graphs of Linear Systems 8.N.2 8.G.3 8.G.2 8.G.7 8.P.2 7-12 3 8-7 Find equations describing points on circles centered at the origin Find inequalities describing coordinates of points in the interior of a circle Construct special quadrilaterals on a coordinate grid Use slopes of parallel and perpendicular lines to reason about parallelograms and rectangles on coordinate grids. Find the midpoint of any given line segment Explore the special properties of figures determined by connecting midpoints of sides of quadrilaterals Identify situations calling for systems of linear equations and related inequalities
2.2 Linear Inequalities 2.3 3.1 3.2 3.3 4.1 Solving Linear Inequalities Solving Equations With Two Variables Connecting y = mx + b and ax + by = c Intersection of Lines The y = mx + b Case 8.P.2 8.P.2 8-7 8-7 8-7 8.9 Write systems of equations and related inequalities Use graphs to estimate solutions to systems of linear equations and related inequalities Identify questions involving linear inequalities in one variable Develop techniques for working with inequalities and in finding their solutions Use systematic methods for solving linear inequalities in one variable Make number line graphs of solutions to linear inequalities Introduce linear equations in two variables in standard form Connecting the two forms of linear equations y = mx + b and ax + by = c Practice working with algebraic equations Use graphical methods to solve systems of linear equations in standard form Review student skills in solving equations of the form m 1 x + b = m 2 x + b 4.2 4.3 4.4 The ax + by= c Case Solving Systems by Substitution Solving Systems by Combination 8.9 8.9 8.9 Develop and use the strategy for solving systems of linear equations by solving each individual equation for the same variable Develop and use the strategy for solving systems of linear equations by substitution Use linear combinations to solve systems of linear equations Choose among the three algebraic methods which to use for a particular system of linear equations