mathematics - 7-2 - edison · mathematics 7-2 table of contents ... applying rational numbers 11...

PUBLIC SCHOOLS OF EDISON TOWNSHIP

OFFICE OF CURRICULUM AND INSTRUCTION

Mathematics - 7-2

Length of Course: Term

Elective/Required: Required

Schools: Middle Schools

Eligibility: Grade 7

Credit Value: N/A

Date Approved: August 24, 2014

Mathematics 7-2

Table of Contents

Statement of Purpose 3

Course Objectives 4

Suggested Time Line 5

Chapter 1: Algebraic Reasoning 6

Chapter 2: Integers and Rational Numbers 8

Chapter 3: Applying Rational Numbers 11

Chapter 4: Proportional Relationships 13

Chapter 5: Graphs 15

Chapter 6: Percents 17

Chapter 7: Collecting, Displaying, and Analyzing Data 19

Chapter 8: Geometric Figures 21

Chapter 9: Measurement and Geometry 22

Chapter 10: Probability 24

Chapter 11: Multi-Step Equations and Inequalities 27

Modifications will be made to accommodate IEP mandates for classified students.

Mathematics 7-2 3

Statement of Purpose

This course of study has been designed for Grade 7 level 2 and was created and organized in line with the areas of focus as identified by the Common Core State Standards and the PARCC Model Content Frameworks. Each unit is comprised of standards that are considered major content along with standards that are supporting and/or additional content. The fluency standards are presented throughout and will be assessed for student accuracy. However, the expectation is that students will have many opportunities to develop fluency, defined as speed and accuracy, with rational number arithmetic and solving multi-step problems (including those involving positive and negative rational numbers and word problems leading to one variable equations) throughout the school year. Unit content will build on the students’ understanding of rational numbers concepts presented in grade 6 to develop fluency with addition, subtraction, multiplication and division of rational numbers and to use these skills in a problem solving context. Success with problem solving and developing fluency with rewriting linear expressions and solving linear equations will be dependent upon the completion of the work with rational numbers. Units will combine rational number arithmetic and linear expressions and equations concepts to build on the work from grade 6. These standards require the students to analyze proportional relationships and use them in problem solving. The geometry standards will provide opportunities for the students to use proportional reasoning in context. Students will continue to use ratios and proportional reasoning in multi-step ratio and percent problems. The standards from the Statistics and Probability domain will support the use of proportional reasoning in context.

Mathematics 7-2 4

Course Objectives

The student will be able to:

1. Investigate properties of numbers. 2. Write, simplify, and evaluate variable expressions. 3. Perform all four operations with integers. 4. Compare and order rational numbers. 5. Investigate operations with rational numbers (decimals and fractions) and some

of their applications. 6. Use division to find unit rates and ratios in proportional relationships. 7. Find solutions to application problems involving proportional relationships. 8. Define similarity and apply knowledge to determining if figures are similar and

use ratios and proportions in scale drawings and scale models. 9. Understand coordinate planes and relations that can be graphed on coordinate

planes. 10. Solve real life word problems using percents. 11. Apply properties of rational numbers to simplify and solve equations. 12. Determine the appropriate representation for displaying relationships among

data. 13. Choose among mean, median, mode, or range to describe a set of data. 14. Make inferences and convincing arguments based on analysis of data. 15. Identify angle relationships. 16. Use congruence to solve problems involving polygons. 17. Find the area and circumference of a circle. 18. Calculate the surface area and volume of three-dimensional figures. 19. Understanding of probabilities by calculating simple and compound probabilities. 20. Representing them in different forms, and interpreting the results in terms of

likelihood. 21. Solve two-step and multi-step equations and equations with variables on both

sides. 22. Solve equations for a variable. 23. Write, solve and graph inequalities.

Mathematics 7-2 5

SUGGESTED TIME LINE

CHAPTER # OF PERIODS COMPLETE FOR PBA COMPLETE FOR EOY

1. Algebraic Reasoning 10 1.1 - 1.3, 1.5 1.2-1.3, 1.5, 1.4

2. Integers and Rational Numbers 20 2.1 - 2.7 2.1 - 2.7

3. Applying Rational Numbers 20 (end MP1) 3.1 - 3.8 3.1 - 3.8

4. Proportional Relationships 18 4.1 - 4.4 4.1 - 4.4, 4.5 - 4.6

5. Graphs 9 5.1 - 5.4 5.1 - 5.4

6. Percents 12 (end MP2) 6.1 - 6.2 6.1 - 6.2, 6.3 - 6.6

7. Collecting, Displaying, and Analyzing Data 10 7.1, 7.2 - 7.3

8. Geometric Figures 15 8.1 - 8.5

9. Measurement and Geometry 14 (end MP3) 9.1 - 9.6

10. Probability 25 10.1 - 10.9

11. Multi-Step Equations and Inequalities 15 11.1 - 11.7 11.1 - 11.7

Mathematics 7-2 6

Chapter 1: Algebraic Reasoning

Targeted Standards: 7.NS.1, 7.EE.1, 7.EE.2, 7.EE.3, 7.EE.4 Unit Objectives/Conceptual Understandings: Students will be able to investigate properties of numbers. Students will be able to write, simplify, and evaluate variable expressions. Essential Questions: How do the properties of number and the rules for order of operations apply to algebraic expressions? Unit Assessment: Multiple Choice Tests, Free-Response Tests, Performance Assessment

Core Content Objectives

Instructional Actions

Cumulative Progress Indicators

Concepts What students will know.

Skills What students will be

able to do.

Activities/Strategies Technology Implementation/ Interdisciplinary Connections

Assessment Check Points

7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light

Order of operations is a mathematical process Identify mathematical properties of rational numbers and utilize them to simplify numerical expressions How to evaluate algebraic expressions Translate expressions between verbal and algebraic formats Understand and identify like terms Simplify algebraic expressions by combining like terms

Evaluate expressions using the proper order of operations Understand the use of parentheses and how their placement changes the given problem Identify properties shown Simplify expressions using properties Substitute then evaluate expressions using order of operations when needed Write algebraic expressions from verbal models Write verbal statements given algebraic expressions Look at the variable part of a term and identify if it is “like” other terms given After identifying like terms,

Power Presentation Lesson Tutorial Videos Homework Help Online Ready to Go On Technology Lab: Explore Order of Operations

● Checkpoint exercises type A, B,C for different type learners

● Extra examples in

book and worksheets

● Homework quick

check ● Mid-Chapter

Quizzes ● Tests/Standard

Tests ● Chapter Reviews

● Extension Projects

http://www.corestandards.org/Math/Content/7/NS/A/1/

http://www.corestandards.org/Math/Content/7/NS/A/1/d/

http://www.corestandards.org/Math/Content/7/EE/B/3/

http://www.corestandards.org/Math/Content/7/EE/A/2/

Mathematics 7-2 7

Chapter 1: Algebraic Reasoning






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on the problem and how the quantities in it are related. 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

use the coefficient to combine the terms

Resources: Chapter Resource Book Vol 1: Practice, Review for Mastery, Challenge and Problem Solving Homework Practice Workbook Problem-Solving Workbook Know-It Notebook

Instructional Adjustments: Ready to Go On? Intervention Vocabulary Connections Reading Strategies (Chapter Resource Book)




Mathematics 7-2 8

Chapter 2: Integers and Rational Numbers

Targeted Standards: 7.NS.1, 7.NS.2, 7.NS.3, 7.EE.4 Unit Objectives/Conceptual Understandings: Students will be able to perform all four operations with integers. Students will be able to compare and order rational numbers. Essential Questions: How do we solve integer problems? How are fraction and decimals related? Unit Assessment: Multiple Choice Tests, Free-Response Tests, Performance Assessment






able to do.



7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.1.b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 7.NS.1.c Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 7.NS.2 Apply and extend previous understandings of multiplication

Use a number line or real-life relations to decide which integer(s) are smaller or larger Determine a number’s distance from zero on a number line Use a number line or counters to add integers Use a number line or counters to subtract integers Use the fact that multiplication is repeated addition Use integer rules to determine products and quotients of integers Use algebraic process, inverse operations, to solve integer equations Quantities can be represented with either a fraction or decimal

Compare and order integers Determine absolute value Add integers Subtract integers Multiply integers Multiply and divide integers Solve equations involving integers Convert fractions into decimals by dividing Convert decimals into fractions using place value Numbers need to be converted to the same format in order to be compared or ordered

Power Presentation Lesson Tutorial Videos Homework Help Online Ready to Go On Hands on Lab: Model Integer Addition Extension: Additive Inverse and Absolute Value Hands On Lab: Model Integer Subtraction Hands On Lab: Model Integer Multiplication and Division Hands On Lab: Model Integer Equations Technology Lab: Explore Order of Operations Extension: Additive Inverse and Absolute Value



book and worksheets

● Homework quick






http://www.corestandards.org/Math/Content/7/NS/A/1/b/

http://www.corestandards.org/Math/Content/7/NS/A/1/c/


Mathematics 7-2 9

Chapter 2: Integers and Rational Numbers (cont.)






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and division and of fractions to multiply and divide rational numbers. 7.NS.2.a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. 7.NS.2.b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts. 7.NS.2.c Apply properties of operations as strategies to multiply and divide rational numbers. 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7.NS.3 Solve real-world and

Fractions and decimals can be compared and ordered

http://www.corestandards.org/Math/Content/7/NS/A/2/a/

http://www.corestandards.org/Math/Content/7/NS/A/2/b/

http://www.corestandards.org/Math/Content/7/NS/A/2/c/



Mathematics 7-2 10

Chapter 2: Integers and Rational Numbers (cont.)






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mathematical problems involving the four operations with rational numbers. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.





Mathematics 7-2 11

Chapter 3: Applying Rational Numbers

Targeted Standards: 7.NS.1, 7.NS.2, 7.EE.4 Unit Objectives/Conceptual Understandings: Students will be able to investigate operations with rational numbers (decimals and fractions) and some of their applications. Essential Questions: How do operations affect decimals and fractions? Unit Assessment: Multiple Choice Tests, Free-Response Tests, Performance Assessment






able to do.



7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

How to align the decimal points, use zeroes as place-holders, and where to place the decimal point in answer. How to set the problem up and where to place the decimal in the product and the quotient. Solving equations with decimals using inverse operations. Any two fractions can be combine by using equivalent fractions with common denominators. A common denominator is unnecessary to find the product of two fractions. Mixed numbers must be converted to improper fractions before multiplying.

Combine decimals. Multiply decimals by whole numbers and decimals. Divide decimals by whole numbers and decimals. Solve one-step equations that contain decimals. Combine fractions with like and unlike denominators. Multiply fractions and mixed numbers. Divide fractions and mixed numbers.

Power Presentation Lesson Tutorial Videos Homework Help Online Ready to Go On Technology Lab: Adding and Subtracting Decimals Hands-On Lab: Multiplying Fractions and Mixed Numbers Technology Lab: Multiplying Fractions and Mixed Numbers Hands-On Lab: Dividing Fractions and Mixed Numbers



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Tests

● Chapter Reviews


● Think and Discuss

SE

● Write About It SE

● Journal TE

Mathematics 7-2 12

Chapter 3: Applying Rational Numbers (cont.)






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7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

When dividing, mixed numbers must be converted to improper fractions before doing the reciprocal. A reciprocal of a fraction is a multiplicative inverse which, when multiplied, has a product of 1. Solving equations with fractions using inverse operations.

Solve one-step equations that contain fractions.



Mathematics 7-2 13

Chapter 4: Proportional Relationships

Targeted Standards: 7.RP.1, 7.RP.2, 7.RP.2a, 7.RP.2c, 7.G.1

Unit Objectives/Conceptual Understandings: Students will be able to use division to find unit rates and ratios in proportional relationships; find solutions to application problems involving proportional relationships, define similarity and apply knowledge to determining if figures are similar and use ratios and proportions in scale drawings and scale models.

Essential Questions: How do you determine a proportional relationship? How can proportional relationships be used to solve applications including determining similarity?

Unit Assessment: Multiple Choice Tests, Free-Response Tests, Performance Assessment






able to do.



7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.RP.2 Recognize and represent proportional relationships between quantities. 7.RP.2a Decide whether two quantities are in a proportional relationship 7.RP.2 Recognize and represent proportional relationships between quantities. 7.RP.2c Represent proportional relationships by equations. 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Rate is a ratio that compares two quantities measured in different units. Unit rates have a denominator of one. Proportion is an equation stating that two ratios are equivalent. Determine if ratios are proportional. Cross products created an equation that is equal on both sides. Similar figures have the same shape, but not necessarily the same size. Corresponding angles and sides are in the same relative position. Indirect measurement is a

Calculate and compare unit rates, such as average speed and unit price. Compare ratios. Find equivalent ratios and identify proportions. Solving proportions using cross products. Determine if two figures are similar using ratios. Identify corresponding angles and corresponding sides of two or more similar figures. Find unknown measures of similar figures. Find scale factor. Determine unknown lengths using scale factors.

Power Presentation Lesson Tutorial Videos Homework Help Online Ready to Go On Hands-On Lab: Identifying and Writing Proportions Technology Lab: Solving Proportions Hands-On Lab: Similar Figures and Proportions Hands-On Lab: Using Similar Figures Hands-On Lab: Making Scale Drawings and Models Hands-On Lab: Use Scale Drawings


● Extra examples in book and worksheets

● Homework quick check

● Mid-Chapter

Quizzes

● Tests/Standard

Tests

● Chapter Reviews



SE


● Journal TE

Mathematics 7-2 14

Chapter 4: Proportional Relationships (cont.)






able to do.



method to find unknown length or distance in similar figures. Scale drawings are proportional two-dimensional representations of an object. The ratio of the scale drawings dimensions and the object’s dimensions are represented by the scale factor. Scale models are proportional three- dimensional representations of an object. The ratio between two sets of measurements is the scale.

Determine distances using ratios and proportions with a scale.



Mathematics 7-2 15

Chapter 5: Graphs

Targeted Standards: 7.RP.1, 7.RP.2, 7.RP2a, 7.RP.2d, 7.NS.1 Unit Objectives/Conceptual Understandings: Students will be able to understand coordinate planes and relations that can be graphed on coordinate planes. Essential Questions: How are relations represented on coordinate planes? How does information represented in a graph give you an understanding of the relation?







able to do.



7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.RP.2.d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 7.RP.2 Recognize and represent proportional relationships between quantities. 7.RP.2.a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

The coordinate plane is the intersection of two number lines. Integers can be used to plot points on the coordinate plane. Graphs can be used to show a representation of situations The slope of a line. Graphing lines. Recognize rates of change. Direct variation is a special linear relationship between variables.

Label and identify the parts of a coordinate plane.

Plot and identify ordered pairs on the coordinate plane.

Different characteristics of a graph represent specific relationships.

Determine the slope of a line using two points.

Graph a line given a point and the slope or two points.

Identify constant versus variable rates of change of a graph.

A relationship with direct variation can be represented by an equation in the form y=kx or by a linear graph which passes through the origin.

Determine the equation for a direct variation given an included point

Power Presentation Lesson Tutorial Videos Homework Help Online Ready to Go On Hands On Lab: Graph Proportional Relationships


● Extra examples

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● Extension

Projects

http://www.corestandards.org/Math/Content/7/RP/A/1/

http://www.corestandards.org/Math/Content/7/RP/A/2/d/

http://www.corestandards.org/Math/Content/7/RP/A/2/

http://www.corestandards.org/Math/Content/7/RP/A/2/a/


Mathematics 7-2 16

Chapter 5: Graphs



Mathematics 7-2 17

Chapter 6: Percents

Targeted Standards: 7.EE.3, 7.EE.2, 7.NS.1d, 7.RP.3 Unit Objectives/Conceptual Understandings: Students will be able to solve real life word problems using percents. Apply properties of rational numbers to simplify and solve equations. Essential Questions: What is the percent of a number and how is it used in real world applications? Unit Assessment: Multiple Choice Tests, Free-Response Tests, Performance Assessment






able to do.



7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. 7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

● Decimals, percents, and fractions

● Estimate percents

● Distributive Property and

Multiplication Property of Equality

● Solve equations

● Percent of Change

● Percent applications

● Simple Interest

● Compare and order decimals, fractions and percents

● Solve real life word

problems by estimating

● Use properties of rational

numbers to write, then solve equivalent expressions and equations

● Find the percent of

change of a quantity

● Solve real life word

problems involving markups and discounts

● Calculate commission,

sales tax, and percent of earnings

● Calculate simple interest

earned on account balances

● Power Presentation

● Lesson Tutorial Videos

● Homework Help Online

● Ready to Go On

● Technology Lab: Explore

Compound Interest


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check

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Quizzes

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Reviews

● Extension

Projects

Mathematics 7-2 18

Chapter 6: Percents (cont.)



Mathematics 7-2 19

Chapter 7: Collecting, Displaying, and Analyzing Data

Targeted Standards: 7.SP.1, 7.SP.2, 7.SP.4

Unit Objectives/Conceptual Understandings: Students will be able to determine the appropriate representation for displaying relationships among data; choose among mean, median, mode, or range to describe a set of data; and make inferences and convincing arguments based on analysis of data.

Essential Questions: How do outliers affect the data in any form central tendency? What can you tell about a data set from a box-and-whisker plot? How can we compare and analyze the different sampling methods?







able to do.



7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. 7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Mean, median, and mode are all measures of central tendency. Range is the difference between the greatest and lowest values. Outliers are extreme values that different greatly from the rest of the set of data and effect the measure of central tendency. Box-and-whisker plots show a distribution of a set of data. Population represents the entire group in which the data is about. Part of the population is the sample.

Compute the mean, median, mode and range of a data set. Compute the range by subtracting. Determine how outliers effect a set of data. Construct, interpret and analyze data in a box-and-whisker plot. Analyze the different sampling methods. Identify biased samples. Verify claims based on statistical data.

Power Presentation Lesson Tutorial Videos Homework Help Online Ready to Go On Hands-On Lab: Mean, Median, Mode and Range Technology Lab: Mean, Median, Mode and Range Hands-On Lab: Explore Samples Hands-On Lab: Use Random Samples



book and worksheets

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SE


● Journal TE

Mathematics 7-2 20

Chapter 7: Collecting, Displaying, and Analyzing Data (cont.)



Mathematics 7-2 21

Chapter 8: Geometric Figures

Targeted Standards: 7.G.5, 7.RP.2c, 7.G.2

Unit Objectives/Conceptual Understandings: Students will be able to identify angle relationships. Use congruence to solve problems involving polygons.

Essential Questions: How can we classify angle relationships? How can we find the measures of the angles of a polygon and congruent figures?







able to do.



7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. 7.RP.2c Represent proportional relationships by equations. 7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

● Key terms and phrases: point, line, plane, ray, line segment, congruent, complementary, supplementary, transversal, skew lines, parallel, perpendicular, adjacent angles, vertical angles, side-side-side rule

● Acute, obtuse, right angles

● Angle pairs

● Parallel, perpendicular,

skew lines, and angles

● Polygons have congruent

angles

● Congruent figures

● Identify lines, points, planes and segments in a diagram

● Classify angles as acute,

obtuse or right

● Classify angles as

complementary, supplementary or neither.

● Identify lines and angles

formed by a transversal

● Calculate the number and measure of the angles in polygons

● Calculate unknown angle measures in triangles and quadrilaterals

● Determine unknown measures of congruent polygons




● Ready to Go On

● Hands on Lab: Explore

Parallel Lines and Transversals

● Hands on Lab: Construct

Bisectors and Congruent Angles

● Technology Lab: Explore

Compound Interest



book and worksheets

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Mathematics 7-2 22

Chapter 9: Measurement and Geometry

Targeted Standards: 7.G.4, 7.G.3, 7.G.6, 7.RP.3 Unit Objectives/Conceptual Understandings: Students will be able to find the area and circumference of a circle. Calculate the surface area and volume of three-dimensional figures. Essential Questions: How do we calculate the area and perimeter of two-dimensional figures? How do we calculate the volume and surface area of prisms and cylinders? Unit Assessment: Multiple Choice Tests, Free-Response Tests, Performance Assessment






able to do.



7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

● Key terms and phrases: perimeter, circumference, area, composite figure, cross section, polyhedron, net, lateral face, lateral area

● Perimeter is the distance around a figure

● Circumference is the distance around a circle

● Area of a circle

● Area of irregular figures can be estimated using graph paper or shapes of known formulas

● A cylinder is a solid figure that has 2 congruent, parallel circles as it bases

● A rectangular prism is a solid figure that has three sets of parallel congruent sides shaped like rectangles

● Calculate the perimeter of a geometric figure

● Calculate the circumference of a circle using the formula

● Calculate the area of a circle using the formula

● Calculate the area of irregular figures

● Classify three-dimensional figures

● Describe the two-

dimensional shape formed when slicing a three-dimensional figure

● Calculate the volume of a

rectangular prism by

multiplying the length, the

width, and the height




● Ready to Go On

● Hands on Lab: Explore

Perimeter and Circumference

● Lesson Extension: Cross

Sections. Pg. 378

● Hands on Lab: Explore the

Volume of Prisms and Cylinders

● Hands on Lab: Use Nets to

Build Prisms and Cylinders



book and worksheets

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Mathematics 7-2 23

Chapter 9: Measurement and Geometry (cont.)






able to do.



● Volume is the measure of the space occupied by a solid figure

● Formulas are used to find

the surface area and volume of prisms and cylinders

● Calculate the volume of a cylinder by using the

formula

● Calculate the surface area

of a prism using the

formula

● Calculate the surface area

of a cylinder using the formula



Mathematics 7-2 24

Chapter 10: Probability

Targeted Standards: 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8

Unit Objectives/Conceptual Understandings: Students will demonstrate understanding of probabilities by calculating simple and compound probabilities, representing them in different forms, and interpreting the results in terms of likelihood.

Essential Questions: What do probabilities represent? How can we compare probabilities? How can we use probability to predict future events?







able to do.



7. SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

7. SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

7. SP.7.B Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

7. SP.8.B Represent sample spaces for compound events using methods such as organized lists, tables and

Categorize a probability using the terms impossible, unlikely, as likely as, likely or certain. Given a probability, find the probability of a complementary event by subtracting from 1. Calculate experimental probability given data from a set of trials. Determine a sample space by counting outcomes, constructing tree diagrams and using the fundamental counting principle. Find the theoretical probability of simple events.

Use probability to make predictions

Find the theoretical probability of independent and dependent compound events

Find combinations through the use of tables, tree diagrams and other methods

Power Presentation Lesson Tutorial Videos Homework Help Online Ready to Go On Exploration: Experimental Probability Exploration: Sample Spaces Hands on Lab: Develop a Probability Model Technology Lab: Simulations Hands on Lab: Experimental and Theoretical Probability Focus on Problem Solving


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SE


● Journal TE

http://www.corestandards.org/Math/Content/7/SP/C/7/b/


Mathematics 7-2 25

Chapter 10: Probability (cont.)






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tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.

7. SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

7. SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy

7.SP.8.A Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

7.SP.8.B Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.

7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Determine the likelihood of an event as impossible, unlikely, as likely as, likely or certain. Determine the probability of complementary events Experimental probability of an event uses data from a series of trials A sample space is the set of all possible outcomes. Theoretical probability is used when all outcomes are equally likely and experimental data is not use Theoretical and experimental probabilities can be used to predict future events The dependency of compound events will affect probability. A combination, or grouping in which order does not matter, can be determined through different methods A permutation, or grouping in which order does matter, can be determined through different methods Lists and diagrams can be used to find the probability of compound events.

Find permutations through the use of lists, the fundamental counting principle and factorials. Find the probability of compound events by using organized lists, tree diagrams and tables

http://www.corestandards.org/Math/Content/7/SP/C/8/



http://www.corestandards.org/Math/Content/7/SP/C/8/a/



Mathematics 7-2 26

Chapter 10: Probability (cont.)






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7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

7.SP.8.A Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.


Instructional Adjustments: Ready to Go On? Intervention Vocabulary Connections Reading Strategies (Chapter Resource Book) Reaching All Learners (TE)



http://www.corestandards.org/Math/Content/7/SP/C/8/a/

Mathematics 7-2 27

Chapter 11: Multi-Step Equations and Inequalities

Targeted Standards: 7.EE.1, 7.EE.4

Unit Objectives/Conceptual Understandings: Students will be able to solve two-step and multi-step equations and equations with variables on both sides. Students will be able to solve equations for a variable. Students will be able to write, solve and graph inequalities.

Essential Questions: How do properties and rules of operations apply to equations and inequalities?







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7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

7.EE.4.A Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

7.EE.4 Use variables to represent quantities in a real-world or

The properties of inverse operations are used to solve two-step equations.

The distributive and associative properties can be used in conjunction with inverse operations to solve multi-step equations.

The properties of inverse operations can be applied to variables.

Solutions to inequalities can be represented by graphing on a number line.

The properties of inverse operations are used to solve inequalities.

The properties of inverse operations are used to solve inequalities.

The distributive and associative properties can be used in conjunction with inverse operations to solve multi-step inequalities.

Solve two-step equations. Solve multi-step equations by combining like terms and using the distributive property. Solve equations that have variables on both sides. Read and write inequalities and graph them on a number line. Solve one-step inequalities by adding or subtracting. Solve one-step inequalities by multiplying or dividing. Solve multi-step inequalities by combining like terms and using the distributive property.

Power Presentation Lesson Tutorial Videos Homework Help Online Ready to Go On Hands-On Lab: Model Two-Step Equations Exploration: Solving Multi-Step Equations Exploration: Solving Equations with Variables on Both Sides Extension: Examine Solution Methods Focus on Problem Solving Exploration: Inequalities Exploration: Solving Multi-Step Inequalities



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http://www.corestandards.org/Math/Content/7/EE/B/4/a/




Mathematics 7-2 28

Chapter 11: Multi-Step Equations and Inequalities (cont.)






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mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7.EE.4.A Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7.EE.4.B Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers.









http://www.corestandards.org/Math/Content/7/EE/B/4/b/

http://www.corestandards.org/Math/Content/7/EE/B/4/b/

Mathematics 7-2 29

Chapter 11: Multi-Step Equations and Inequalities (cont.)






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Graph the solution set of the inequality and interpret it in the context of the problem.


Instructional Adjustments: Ready to Go On? Intervention Vocabulary Connections Reading Strategies (Chapter Resource Book) Reaching All Learners (TE)

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