Carnegie Learning Math Series Course 2, A Florida Standards Program

Transcription

1 to the students previous understanding of equivalent ratios Introduction to. Ratios and Rates Ratios, Rates,. and Mixture Problems Rates and Tables to Solve Problems to Solve Problems Unit Rates in Real World Applications Carnegie Learning Math Series Course, Chapter : Ratios and Rates This chapter begins with a review of ratio and unit rate concepts, and scaling up and scaling down strategies to determine equivalent ratios. The means and extremes strategy for solving proportions is introduced and connected Identify ratios, rates, and unit rates. Use ratios, rates, and unit rates to analyze problems. Use ratios to make comparisons. Use rates and proportions to solve mixture problems. Write ratios and rates. Write proportions. Scale up and scale down proportions Use tables to represent equivalent ratios. Solve proportions using unit rates. Solve proportions using the scaling method. Solve proportions using the unit rate method. Solve proportions using the means and extremes method. Estimate and calculate values using rates. Use unit rates to determine the best buy. Chapter : Direct Variation and Constant of Proportionality 7.RP.. 7.RP.. 7.RP.. 7.RP.. 7.RP.. 7.RP.. 7.RP.. 7.RP..3 7.RP.. 7.RP.. 7.RP..3 This chapter develops the representations of proportional relationships between quantities using words, tables, equations, and graphs. The constant of proportionality is introduced and used to solve various real-world problems.. Introduction to Direct Variation Determine how quantities in different situations vary. Use multiple representations to explore the types of variation. 7.RP.. 7.RP... Determining Equivalent Ratios Determine if the points on a graph are equivalent ratios. 7.RP...3 Determining and Applying the Constant of Proportionality to Determine the constant of proportionality. Solve problems using the proportional relationship between two variables. 7.RP...4 the Constant of Proportionality to Solve Determine if there is a constant of proportionality between two variables. 7.RP.. 7.RP..3 Carnegie Learning Math Series Course, of 9

2 Graph relationships that are directly proportional..5 Graphing Direct Interpret the graphs of relationships that are directly proportional. 7.RP...6 Direct Determine if two variables are directly proportional or vary directly. Interpret relationships that are direct proportions. Solve direct variation problems using the equation y = kx. 7.RP...7 Interpreting Multiple Representations of Direct Determine if relationships represented in words, tables, equations, or graphs are directly proportional. Interpret the meaning of direct proportions represented in words, tables, equations, and graphs. Determine and interpret the constant of proportionality for variables that are directly proportional and represented in words, tables, equations, and graphs. 7.RP.. Chapter 3: Rates and Percents This chapter extends the use of proportional reasoning to solve percent problems Estimating and Calculating with Percents and Rates Solving Percent Problems and Percent 3.4 Percents Estimate and calculate values using rates. Estimate and calculate the values of percents. Solve problems involving percents. Solve proportions. Solve percent equations. Calculate simple interest. Calculate the percent of increase. Calculate the percent of decrease. Calculate discount of base price. Calculate tax on a purchase. Calculate depreciate. 7.RP.. 7.RP..3 7.RP.. 7.RP.. 7.RP..3 7.RP.. 7.RP..3 7.RP.. 7.RP Solving Percent Problems Involving Models to understand Integers Solve percent problems using direct variation. Write equations to show the constant of proportionality. Represent numbers as positive and negative integers. Use a model to represent the sum of a positive and a negative integer. 7.RP.. 7.RP..3 Chapter 4: Addition and Subtraction with Rational Numbers This chapter uses models to develop a conceptual understanding of addition and subtraction with respect to the set of integers. These strategies are formalized through questioning, and then extended to operations with respect to the set of rational numbers. 7.NS.. Carnegie Learning Math Series Course, of 9

3 Model the addition of integers on a number line. Adding Integers, 4. Develop a rule for adding integers 7.NS.. Part Adding Integers, Part Subtracting Integers Adding and Subtracting Rational Numbers Multiplying and Dividing Integers Multiplying and Dividing Rational Numbers Simplifying Arithmetic with Rational Numbers Evaluating with Rational Numbers Model the addition of integers using two-color counters. Develop a rule for adding integers. Model subtraction of integers using two-color counters. Model subtraction of integers on a number line. Develop a rule for subtracting integers. 7.NS.. 7.NS.. Add and subtract rational numbers. 7.NS.. Chapter 5: Multiplication and Division with Rational Numbers This chapter use models to develop a conceptual understanding of multiplication and division with respect to the set of integers. These strategies are formalized, and then extended to operations with respect to the set of rational numbers Exact Decimal Representations of Fractions Multiply integers. Divide integers. Multiply rational numbers. Divide rational numbers. Simply arithmetic expressions using the number properties and the order of operations Model a situation with an expression using rational numbers. Evaluate rational expressions. Use decimals and fractions to evaluate arithmetic expressions. Convert fractions to decimals. Represent fractions as repeating decimals. Chapter 6: Numerical and Algebraic and 6. Evaluating Algebraic 7.NS.. 7.NS.. 7.NS.. 7.NS.. 7.NS.. 7.NS.. 7.NS..3 7.NS.. 7.NS.. This chapter focuses on the use of properties to interpret, simplify, add, subtract, and factor linear expressions. Evaluate algebraic expressions 7.NS..3 Carnegie Learning Math Series Course, 3 of 9

4 Simplifying 6. Write and use the distributive properties. 7.EE.. Use distributive properties to simplify expressions. 7.EE.. Distributive 7.NS..3 Properties Factoring Algebraic Verifying That Are Equivalent Use the distributive properties to factor expressions. Combine like terms to simplify expressions. Simplify algebraic expressions. Verify that algebraic expressions are equivalent by graphing, simplifying, and evaluating expressions. 7.EE.. 7.EE.. 7.EE.. 7.EE Simplifying Algebraic Operations and Their Properties Simplify algebraic expressions using operations and their properties. 7.EE.. 7.EE.. Chapter 7: Solving and Inequalities This chapter uses models, properties of rational numbers, and operations to develop strategies for solving equations and inequalities. Algebraic reasoning is used to solve real-world problems. 7. Picture Algebra 7. Solving Use drawings to represent daily life situations. Develop different methods to represent daily life situations mathematically. 7.EE.. Develop an understanding of equality. Use properties of equality to solve equations represented with algebra tiles. Solve one-step equations 7.3 Solving Two- Step Write two-step equations. Solve two-step equations. Check solutions algebraically. Verify solutions within a problem context Two-Step Solving and Graphing Inequalities in One Variable Write two-step equations. Solve two-step equations. Verify solutions within a problem context. Write simple inequalities. Graph one-variable inequalities. Solve one-variable inequalities. Chapter 8: Solving Problems with and Inequalities 7.EE.. 7.EE.. Carnegie Learning Math Series Course, 4 of 9

5 This chapter focuses on the use of algebraic reasoning to solve real-world problems posed with positive and negative rational numbers. Tables, graphs, and equations are used throughout Multiple Representations of Problem Situations Two-Step Solving More Complicated Use different methods to represent a problem situation. Identify advantages and disadvantages of using a particular representation. Solve two-step equations. Write and use two-step equations. Compare two problem situations Solve equations containing fractions. Solve equations with variables on both sides. Verify solutions within a problem context. 8.4 Making Sense of Negative Solutions Use multiple representations to analyze problem situations. Interpret negative solutions to problem situations. Identify independent and dependent variables. Evaluate algebraic expressions. Solve algebraic equations. 8.5 Rate of Change 8.6 Multiple Representations to Solve Problems Chapter 9: Geometry Introduction to Geometry and Geometric Constructions Measuring and Constructing Angles Calculate the unit rate of change. Interpret the unit rate of change in a problem situation. Use multiple representations to analyze problem situations. to Sketch and draw figures. Use a compass to construct circles. Use geometric tools to duplicate line segments. Measure and construct angles. Duplicate angles. Bisect angles. Review congruent figures This chapter introduces points, lines, and planes as the essential building blocks of geometry. Key terms and basic constructions are introduced that will allow students to construct and compare triangles in the Chapter 0. 7.G.. 7.G Complements, Supplements, Midpoints, Perpendiculars, and Perpendicular Bisectors Chapter 0: Triangles Calculate the supplement of an angle. Calculate the complement of an angle. Construct a perpendicular line. Construct a perpendicular bisector. Construct the midpoint of a segment. Classify adjacent angles, linear pairs, and vertical angles. 7.G.. 7.G..5 Carnegie Learning Math Series Course, 5 of 9

6 This chapter investigates the conditions that determine unique triangles Triangle Sum, Exterior Angle, and Exterior Angle Inequality Theorems Constructing Triangles Congruent Figures and Constructing Congruent Triangles Triangle Inequality Theorem Prove the Triangle Sum Theorem. Explore the relationship between the interior angle measures and the side lengths of a triangle. Identify the remote interior angles of a triangle. Identify the exterior angle of a triangle. Explore the relationship between the exterior angle measures and two remote interior angles of a triangle. Prove the Exterior Angle Theorem. Prove the Exterior Angle Inequality Theorem. 7.G.. Construct triangles to determine uniqueness. 7.G.. Define congruent figures. Determine whether figures are congruent. Determine whether triangles are congruent. Construct congruent triangles. Explore the relationships between the side lengths of a triangle and the measures of its interior angles. Prove the Triangle Inequality Theorem Chapter : Scale Drawings and Scale Factor This chapter explores scale drawings, scale models, and scale factors through real-world problems. 7.G.. 7.G... Scale Drawings, Scale Models, and Scale Factors Use scale models to calculate measurements. Use scale factors to enlarge and shrink models. 7.G Applications of Ratio Exploring Scale Drawings Creating Blueprints Chapter : Circles Work with applications of similarity and scale factor. 7.G.. Work with applications of similarity and scale factor. Use scale drawings and maps. Use scale drawings to create three-dimensional models. Use three-dimensional models to create blueprints. 7.G.. 7.G.. This chapter develops the formula for the area of a circle. Problems are solved involving circles and circle formulas.. Circles, Radius, and Diameter Define circle. Identify the center, radius, and diameter of a circle. 7.G..4. Circumference of a Circle Measure the circumference of a circle. Explore the relationship between the diameter and the circumference of a circle. Write a formula for the circumference of a circle. Use a formula to determine the circumference of a circle. 7.G..4 Carnegie Learning Math Series Course, 6 of 9

7 Explore the circumference and area of circles inscribed in regular polygons. Write a formula for the area of a polygon in terms of the.3 Area of a Circle perimeter. 7.G..4 Explore the relationship between the circumference of a circle and the area of a circle.4 Unknown Measurements Use the area and circumference formulas to solve for unknown measurements. Use composite figures to solve for unknown measurements. 7.G..4 Chapter 3: Slicing Three-Dimensional Figures This chapter explores planes intersected with three-dimensional geometric figures. Real-world problems are solved involving area, volume, and surface area of three-dimensional figures Slicing Through a Cube Slicing Through Right Rectangular Prisms Slicing Through Right Rectangular Pyramids Introduction to Volume and Surface Area Applying Volume and Surface Area Formulas Chapter 4: Data Collection Sketch, model, and describe cross-sections formed by a plane passing through a cube Sketch, model, and describe cross-sections formed by a plane passing through a right rectangular prism Sketch, model, and describe cross-sections formed by a plane passing through a right rectangular pyramid. Explore the volume of a solid. Explore the surface area of a solid. Create a net for a concave polyhedron. Explore the volume of a pyramid. Explore the surface area of a pyramid. This chapter emphasizes data collection, sampling, random samples, and frequencies Formulating Questions and Collecting Data Collecting Data through Random Sampling Collect data from a survey and analyze the results. Differentiate between a census and a sample. Differentiate between a parameter and a statistic. Differentiate between a random sample and a sample that is not chosen randomly. Use several methods to select a random sample. 7.G..3 7.G..3 7.G..3 7.G..6 7.G..6 7.SP.. 7.SP.. 7.SP.. 7.SP.. Carnegie Learning Math Series Course, 7 of 9

8 Investigate how results from a random sample are more reliable in representing the population than results from a 4.3 Random sample that is not random. 7.SP.. Sampling Use sampling and proportional reasoning to predict the value 7.SP.. of a population parameter. 4.4 Samples, Centers, and Spreads to Describe Data to Analyze measures of center for samples from a population. Analyze measures of variation for samples from a population. 7.SP.. 7.SP.. 7.SP Sample Size Investigate the sample size of a survey. Investigate the concept that as the sample size increases, the 7.SP.. statistic obtained gets closer to the actual population 7.SP.. parameter. Chapter 5: Comparing Populations This chapter uses measures of variability to compare inferences across two populations Comparing Measures of Center of Two Populations Comparing Measures of Center of Two Populations Drawing Conclusions About Two Populations Chapter 6: Introduction to Calculate the measures of center and measures of variability for two populations. Compare the difference of the measures of center for two populations to their measures of variability. Compare the measures of center for random samples from two populations. Use measures of center to draw conclusions about two populations Compare the measures of variability for random samples from two populations. Use measures of variability to draw conclusions about two populations. 7.SP..3 7.SP..4 7.SP.. 7.SP..3 7.SP..4 7.SP.. 7.SP..3 7.SP..4 This chapter investigates experimental and theoretical probabilities. models are developed and used to calculate probabilities of events. 6. Defining and Representing Differentiate between an outcome and an event for an experiment. List the sample space for an experiment. Determine the probability for an event. Understand that the probability for an event is between 0 and that can be expressed as a fraction, decimal, or percent. Determine that the sum of the probabilities of the outcomes of an experiment is always. 7.SP.3.5 Carnegie Learning Math Series Course, 8 of 9

9 Conduct trials of an experiment. 6. Predict the experimental probability of an event using the Determining 7.SP.3.5 results from the trials of an experiment. Experimental to 7.SP.3.6 Use proportional reasoning to predict the probability of random events. 6.3 Determining Theoretical Calculate the experimental and theoretical probability of an experiment. Determine the difference between experimental and theoretical probability. Use proportional reasoning to predict probability of random events. 7.SP SP Simulating Experiments Conduct trials using a simulation to determine probability. Conduct a large number of trials to demonstrate that experimental probability approaches theoretical probability. 7.SP SP Technology for Simulations Models for Use technology to simulate a large number of trials of an experiment. Determine the probability model for an experiment. Construct and interpret a uniform probability model. Construct and interpret a non-uniform probability model 7.SP.3.6 Chapter 7: of Compound Events This chapter focuses on probabilities of compound events. Simulations are used to generate frequencies for compound events Creating and Models Determining Compound Simulating of Compound Events Determine the probability model for an experiment. Construct and interpret a non-uniform probability model Use probability models to calculate compound probabilities. 7.SP SP.3.8 Use simulations to estimate compound probabilities. 7.SP.3.8 Carnegie Learning Math Series Course, 9 of 9