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Curriculum and Instruction – Office of Mathematics2nd Nine Weeks Grade 7

Introduction

In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,

80% of our students will graduate from high school college or career ready 90% of students will graduate on time 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

In order to achieve these ambitious goals, we must collectively work to provide our students with high-quality, College and Career Ready standards-aligned instruction. Acknowledging the need to develop competence in literacy and language as the foundation for all learning, Shelby County Schools developed the Comprehensive Literacy Improvement Plan (CLIP). The CLIP ensures a quality balanced literacy approach to instruction that results in high levels of literacy learning for all students across content areas. Destination 2025 and the CLIP establish common goals and expectations for student learning across schools. CLIP connections are evident throughout the mathematics curriculum maps.

The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and Career Ready Standards are rooted in the knowledge and skills students need to succeed in post-secondary study or careers. While the academic standards establish desired learning outcomes, the curriculum provides instructional planning designed to help students reach these outcomes. Educators will use this guide and the standards as a roadmap for curriculum and instruction. The sequence of learning is strategically positioned so that necessary foundational skills are spiraled in order to facilitate student mastery of the standards.

These standards emphasize thinking, problem-solving and creativity through next generation assessments that go beyond multiple-choice tests to increase college and career readiness among Tennessee students. In addition, assessment blueprints (http://www.tn.gov/education/article/tnready-blueprints ) have been designed to show educators a summary of what will be assessed in each grade, including the approximate number of items that will address each standard. Blueprints also detail which standards will be assessed on Part I of TNReady and which will be assessed on Part II.

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Curriculum and Instruction – Office of Mathematics2nd Nine Weeks Grade 7

Our collective goal is to ensure our students graduate ready for college and career. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation and connections.

The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations) procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics and sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy). Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

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Problem Solving

Reasoning and Proof

CommunicationRepresentation

Connecton

Mathematical Practices

Make sense of problems and persevere in solving them

Reason abstractly and quatitatively

Construct viable arguments and

crituqe the reasoning of

others

Model with mathematics

Use appropriate tools

strategically

Attend to precision

Look for and make use of

structure

Look for and express

regularity in repeated reasoning

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Curriculum and Instruction – Office of Mathematics2nd Nine Weeks Grade 7

How to Use the Mathematic Curriculum Maps

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their instructional practice in alignment with the three College and Career Ready shifts in instruction for Mathematics. We should see these shifts in all classrooms:

1) Focus2) Coherence3) Rigor

Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around each of the three shifts that teachers should consistently access:

The TNCore Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-standards

Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.

Mathematical ShiftsFocushttp://achievethecore.org/shifts-mathematics

The standards are focused on fewer topics so students can learn more

Coherencehttp://achievethecore.org/shifts-mathematics

Topics within a grade are connected to support focus, and learning is built on understandings from previous grades

Rigorhttp://achievethecore.org/shifts-mathematics

The standards set expectations for a balanced approach to pursuing conceptual understanding, procedural fluency, and application and modeling

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Curriculum and Instruction – Office of Mathematics2nd Nine Weeks Grade 7

Curriculum Maps:

Locate the TDOE Standards in the left column. Analyze the language of the standards and match each standard to a learning target in the second column.

Consult your McGraw-Hill or Holt Teachers’ Edition (TE) and other cited references to map out your week(s) of instruction. Plan your weekly and daily objectives, using the standards' explanations provided in the second column. Best practices tell us that

making objectives measureable increases student mastery. Carefully review the web-based resources provided in the 'Content and Tasks' column and use them as you introduce or assess a

particular standard or set of standards. Review the CLIP Connections found in the right column. Make plans to address the content vocabulary, utilizing the suggested

literacy strategies, in your instruction. Examine the other standards and skills you will need to address in order to ensure mastery of the indicated standard. Using your McGraw-Hill or Holt TE and other resources cited in the curriculum map, plan your week using the SCS lesson plan

template. Remember to include differentiated activities for small-group instruction and math stations.

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Curriculum and Instruction – Office of Mathematics2nd Nine Weeks Grade 7

TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS

Topic: Solving Word Problems Using Equations and Inequalities( 3 weeks)

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.

7.EE.B.4a 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.B.4b 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. Graph the solution set of the inequality and interpret it in the context of the problem.

Math Station Activities: p. 88

Students write and solve an equation or inequality that models the situation.

Students should be provided plenty of opportunities to explore inequalities such as 1/2x +3 > 2 in order to solve and graph their solution on a number lineExample(s):Amy had $26 dollars to spend on school supplies. After buying 10 pens, she had $14.30 left. How much did each pen cost including tax?Solution:x = number of pens26 = 14.30 + 10xSolving for x gives $1.17 for each pen.

Steven has $25 dollars to spend. He spent $10.81, including tax, to buy a new DVD. He needs to save $10.00 but he wants to buy a snack. If peanuts cost $0.38 per package including tax, what is the maximum number of packages that Steven can buy?Solution:x = number of packages of peanuts25 ≥ 10.81 + 10.00 + 0.38xx = 11.03 Steven can buy 11 packages of peanuts

Solve -0.5x – 5 < -1.5 and graph the solution on a number line. Solution: x > -7

GlencoeAdditional Lessons 7-9 p.780-790

4-1D Solve One-step Equations(Pg. 208 – 211)4- 2A Multiply Equations with Bar Diagrams (Pg. 214)4-2B Solve One-step Multiplication and Division Equations (Pg. 215-219)4- 2C-D Solve Equations with Rational Coefficients (Pg. 220-226)4- 3A Two-step Equations with Bar Diagrams (Pg. 228-229)4-3B Solve Two-step Equations (Pg. 230-234)4- 3C Variables on Both Sides (Pg. 235)4- 3D Solve Equations with Variables on Each Side (Pg. 236-239)Impact Math Unit J, Inv. 4 pp. 164-166

Holt12-1 Solving Two Equations12-2 Solving Multi-Step Equations12-3 Solving Equations with variables on Both Sides.12-3A Extension Examine Solution MethodsCMP: Variables and Patterns Investigation 1, 2 & 3Variables and Patterns Teacher Guide

CMP: Moving Straight Ahead Investigations 1-4Moving Straight Ahead Teacher Resources

Engage NY Lesson: 7.EE.4a

Engage NY Lesson: 7.EE.4b

Illustrative Math Task: 7.EE.4

Language Objective(s):Students will describe how to determine whether to write an equation or inequality and the properties of the real number system that should be used to find a solution of a word problem.

Vocabulary:Algebraic expression, numeric expression, solution set

Graphic Organizer(s):Solving Inequalities Graphic OrganizerSolving Word Problems

Journal:Have students write about how to define a variable in the context of a problem.

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Curriculum and Instruction – Office of Mathematics2nd Nine Weeks Grade 7

TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONSCMP: Variables and Patterns Investigation 1, 2 & 3Variables and Patterns Teacher Guide

CMP: Moving Straight Ahead Investigations 1-4Moving Straight Ahead Teacher Resources

Engage NY Lesson: 7.EE.4a

Engage NY Lesson: 7.EE.4b

Illustrative Math Task: 7.EE.4

Solving EquationsShort Equation TasksFencing TaskseReader Sales(EE.B.4)Fixing Up the Yard(EE.B.4)Holiday Party(EE.B.4)Scuba Dive(EE.B.4)Shipping Rates(EE.B.3&4)Equation GameUsed Video GamesSolving Two-Step Equations

Solving EquationsShort Equation TasksFencing TaskseReader Sales(EE.B.4)Fixing Up the Yard(EE.B.4)Holiday Party(EE.B.4)Scuba Dive(EE.B.4)Shipping Rates(EE.B.3&4)Equation GameUsed Video GamesSolving Two-Step EquationsSolving Equations

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Curriculum and Instruction – Office of Mathematics2nd Nine Weeks Grade 7

TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS

Solving Equations

Topic: Ratio and Proportion(3 weeks)

7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems7.RP.A.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.A.2 Recognize and represent proportional relationships between quantities.7.RP.A.2b Identify the constant of proportionality (unit rate) in tables, graphs and equations, diagrams and verbal descriptions of proportional relationship.7.RP.A2c Represent proportional relationships by equations.7.RP.2cd 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.

Math Station Activities pp. 1, 21, 28 & 37

Ratio is a unit or batch, for example, there are 3 cups of apple juice for every 2 cups of grape juice in the mixture. This way uses a composed unit: 3 cups apple juice and 2 cups grape juice. Any mixture that is made from some number of the composed unit is in the ratio 3 to 2. In the table, each of the mixtures of apple juice and grape juice are combined in a ratio of 3 to 2:

The table below gives the price for different numbers of books. Do the numbers in the table represent a proportional relationship?

Number of Books Price1 33 9

Glencoe5-1A Unit Rates (pgs. 265)5-1B Rates(pgs. 266-271)Additional Lesson 15-1C Proportional & Non-proportional Relationships(pgs. 272-275)5-1D Solve Proportions(pgs. 276-280)Additional Lesson 25-1E Extend Wildlife Sampling (pgs. 281)5-2A Problem-Solving Investigation(pgs. 282-283)5-2B Scale DrawingsAdditional Lesson 106-3B Percent of Change (pgs. 346-350)

CCSS CMP Investigations: Graphing Proportions

CMP Comparing and Scaling Investigations 1-4Comparing and Scaling Teacher

Holt4-2 Rates4-4 Solving Proportions4-3 Identifying and Writing ProportionsFigures and Proportion 5-8 Direct Variation

CCSS CMP Investigations: Graphing Proportions

CMP Comparing and Scaling Investigations 1-4Comparing and Scaling Teacher Guide

TNCore Plant Species Task(RP.A.1-3)Proportion Word ProblemsRatios and Rates Involving Fractions(RP.A.1,3,EE.4a) (lesson, p. 101)Similar Figures Lesson

Language Objective(s):

Visualize vocabulary: Use a bubble map to help students review vocabulary associated with ratios. In each bubble have an example and students should write one or more review words associated with it.

Understand Vocabulary: Use the following explanations to help students learn the preview words.When a car moves at a constant rate of speed, the relationship between distance and time a proportional relationship because the ratio of distance to time remains constant.In a proportional relationship, the rate of change is constant and is called the constant of proportionality.

Graphic Organizer: Three panel flip chartBefore beginning the chapter have the students create a three panel flip chart to help them organize what they will learn. Label each

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Curriculum and Instruction – Office of Mathematics2nd Nine Weeks Grade 7

TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS4 127 18

Solution:Students can examine the numbers to determine that the price is the number of books multiplied by 3, except for 7 books. The row with seven books for $18 is not proportional to the other amounts in the table; therefore, the table does not represent a proportional relationship.Students graph relationships to determine if two quantities are in a proportional relationship and to interpret the ordered pairs. If the amounts from the table above are graphed (number of books, price), the pairs (1, 3), (3, 9), and (4, 12) will form a straight line through the origin (0 books, 0 dollars), indicating that these pairs are in a proportional relationship. The ordered pair (4, 12) means that 4 books cost $12. However, the ordered pair (7, 18)would not be on the line, indicating that it is not proportional to the other pairs.The ordered pair (1, 3) indicates that 1 book is $3, which is the unit rate. The y-coordinate when x = 1 will be the unit rate. The constant of proportionality is the unit rate. Students identify this amount from tables (see example above), graphs, equations and verbal descriptions of proportional relationships.

Guide

TNCore Plant Species Task(RP.A.1-3)Proportion Word ProblemsRatios and Rates Involving Fractions(RP.A.1,3,EE.4a) (lesson, p. 101)Similar Figures Lesson

TNCore Assessment Tasks: Car Wash, Deshawn's Run, Digging a Ditch, Lemonade Stand, Orange Juice for Sale, Snack Mix, Amusement Park, Babysitting Fees or Basketball Scores(Choose from this list)Math Shell Concept Development Lesson: Classifying Proportion and Non-Proportion Situations

TNCore Assessment Tasks: Car Wash, Deshawn's Run, Digging a Ditch, Lemonade Stand, Orange Juice for Sale, Snack Mix, Amusement Park, Babysitting Fees or Basketball Scores(Choose from this list)Math Shell Concept Development Lesson: Classifying Proportion and Non-Proportion Situations

flap with one of the lesson titles. As they study each lesson, write important ideas like the vocabulary, properties, and formulas under the appropriate flap.Three-panel flip chart examples

Topic: Percents(3 weeks)

7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems.Math Station Activities pp. 1 & 14

Students should become familiar with the following terms: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Glencoe6-1B Percent of a Number (p. 320-324)6-1C Percent & Estimation (p. 325-

Holt4-1 Ratios6-1 Percent6-2 Fractions, Decimals and

Language Objective(s):Students will describe how to solve ratio and percent problems using proportional relationships.

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TN STATE STANDARDS Explanations/Examples/Questions CONTENT & TASKS CLIP CONNECTIONS

Example(s):Students write and solve 1-step equations as a part of their work with percents; for example, the question “ If Kevin paid a total of 13.50, including 8% sales tax, what was the price of the item he purchased?” can be represented by the equation 1.08x =13.50

After eating at a restaurant, Mr. Jackson’s bill before tax is $52.50 The sales tax rate is 8%. Mr. Jackson decides to leave a 20% tip for the waiter based on the pre-tax amount. How much is the tip Mr. Jackson leaves for the waiter? How much will the total bill be, including tax and tip? Express your solution as a multiple of the bill.Solution:The amount paid = 0.20 x $52.50 + 0.08 x $52.50 = 0.28 x $52.50 or $14.70 for the tip and tax. The total bill would be $67.20.

Example using the within ratios format:Three candies cost a total of $2.40. At that same price, how much would 10 candies cost?

The within ratios proportion is: $ 2.40

3candies

= x

10 candies. To determine the factor of

change (unit cost) for one candy, divide $2.40 by 3.

The factor of change is 1

0.8 (or $0.80 for one

candy), meaning that as the number of candies increases by one, the total cost increases by $0.80. So, 10 candies ($0.80 x 10) would cost $8.00.

330)6-2B The Percent Proportion (p. 332-336)6-2C The Percent Equation (p. 337 – 341)6-3C Sales Tax & Tips (p.351 – 354)6-3D Discount (p.355-358)6-3E Simple Interest (p.359-362)

Comparing and Scaling SEInvestigations 1-4Comparing and Scaling CMP 3 Teacher Guide

Ratios and ProportionsEngage NY ModulesGlencoe HandoutsSolving Ratio Word ProblemsAll About RatiosRatio and Proportion in the Workplace

Math Shell Lesson: Comparing Strategies for Proportion Problems

Illustrative Math Tasks: 7.RP.3

Percent6-3Estimating with Percent6-4 Percent of a Number6-5 Solving Percent Problems6-6 Percent of Change6-7 Simple Interest

Comparing and Scaling SEInvestigations 1-4Comparing and Scaling CMP 3 Teacher Guide

Ratios and ProportionsEngage NY ModulesGlencoe HandoutsSolving Ratio Word ProblemsAll About RatiosRatio and Proportion in the Workplace

Math Shell Lesson: Comparing Strategies for Proportion Problems

Illustrative Math Tasks: 7.RP.3

Journal Prompt:Give two examples of real-world situations in which you find the percent of a number.

Critical Thinking:Have students research languages spoken in the United States. Have them find out which languages are spoken by less than 1% of the population and choose five to six of them. Then have students use the population of the United States to estimate how many people in the country speak each language. Have students place all information in a table and discuss their findings.

Vocabulary:Proportion, percent increase, percent decrease

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RESOURCE TOOLBOXTextbook Resourceswww.myhrw.comwww.connected.mcgraw-hill.com

Tennessee State StandardsTennessee’s State Mathematics Standards

Common Core Standards-Mathematics

TN Core

The Mathematics Common Core ToolboxTN Math e matics Curricu lum Center

VideosKhan Academy

Calculator

Texas Instruments Education CASIO Activities

Interactive Manipulatives:National Library of Virtual Manipulatives

Additional Sites:

http://functions.wolfram.com

http://www.opensourcemath.org

http://www.analyzemath.com/Graphing/piecewise_functions.html

http://education.ti.com/calculators/downloads/US/Activities/Detail?id=9530

http://www.purplemath.com/

http://www.onlinemathlearning.com/math-word-problems.html

CLIP ResourcesBest Practices: Integrating Math and ELAMath Graphic OrganizersTeaching Academic Vocabulary in the math classroomMiddle School Mathematics Vocabulary Word Wall Cards

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