Curriculum and Instruction – Office of Mathematics3rd 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. 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. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

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 Shelby County Schools 2015/2016

Revised 12/1/15(CSH)

1 of 13

Focus

The Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. For grades K–8, each grade's time spent in instruction must meet or exceed the following percentages for the major work of the grade. For grade 7, 71% or more time on instruction is spent on the major focus standards.Supporting Content - information that supports the understanding and implementation of the major work of the grade.Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency.

Coherence

Thinking across grades:The Standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding on to foundations built in previous years. Each standard is not a new event, but an extension of previous learning. Linking to major topics:Instead of allowing additional or supporting topics to detract from the focus of the grade, these concepts serve the grade level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.

Rigor

Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures.Application: The Standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.

Problem Solving

Reasoning and Proof

CommunicationRepresentation

Connecton

Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 7

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.

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.

How to Use the Mathematics Curriculum Maps

This curriculum map is designed to help teachers make effective

Shelby County Schools 2015/2016Revised 12/1/15(CSH)

2 of 13

Mathematical Practices

Make sense of problems and persevere in solving them

Reason abstractly and quatitatively

Construct viable arguments and

critique 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

Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 7

decisions about what mathematical content to teach so that 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, as described above, in instruction for Mathematics.

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 the standards and teaching practices that teachers should consistently access:

Shelby County Schools 2015/2016Revised 12/1/15(CSH)

3 of 13

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 Teaching Practiceshttps://mathprojectsjournal.files.wordpress.com/2015/05/nctm-teaching-practices.pdf

NCTM – Mathematics Teaching Practices

Curriculum and Instruction – Office of Mathematics3rd 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 an example 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.

Shelby County Schools 2015/2016Revised 12/1/15(CSH)

4 of 13

Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 7

TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONS

Topic: Ratio and Proportions - Expression and Intro to Equations(5 weeks)

7.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.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.RP.A.2.B Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

7.RP.A.2.C Represent proportional relationships by equations.

7.RP.2D 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.A.3 Use proportional relationships to solve multistep ratio and percent problems.

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

Students should be able to explain or show their work using a representation (numbers, words, pictures, physical objects, or equations) and verify that their answer is reasonable. Models help students to identify the parts of the problem and how the values are related. For percent increase and decrease, students identify the starting value, determine the difference, and compare the difference in the two values to the starting value.

Example(s):• Gas prices are projected to increase 124% by April 2015. A gallon of gas currently costs $4.17. What is the projected cost of a gallon of gas for April 2015?A student might say: “The original cost of a gallon of gas is $4.17. An increase of 100% means that the cost will double. I will also need to add another 24% to figure out the final projected cost of a gallon of gas. Since 25% of $4.17 is about $1.04, the projected cost of a gallon of gas should be around $9.40.”$4.17 + 4.17 + (0.24 • 4.17) = 2.24 x 4.17

Students may use a content web site and/or interactive white board to create tables and graphs of proportional or non-proportional relationships. Graphing proportional relationships represented in a table helps

Engage NY TASKS: 7.RP (Choose desired lesson)

Coupon Book Sales Task: 7.RP.A.2 & 7.EE.B.4

Robot Races: 7.RP.A.2

Leaky Faucet Task: 7.RP.2d(Includes rubric and student work)

Solving Ratio Word Problems

Percent word problems

Percent Problems

Percent of Change Power Point

Distance/Rate/Time Problems Worksheet

Discount and Sales Tax Worksheet

Mathshell Lesson: Percent Increase & Decrease

Glencoe Worksheets: Ratios

Dirt Bike Proportions: Game

Better Lesson: 7.EE.B.4 Lessons/Centers

Class discussion:Chart the responses to the following questions to create a visual aid for all students to read.

How many of you have heard the word proportional?In which situations have you encountered the word proportional?What does it mean to be proportional?

Journal/Writing PromptSolve the equation 3(x + 4) = 21, and identify which properties you used for each step.

Discuss the meanings of the words commutative and associative in the real world. (commute, associate)

Construct an Argument: Explain how complex fractions can be used to solve problems involving rations.

Reasoning:A powdered drink mix calls for a ration of 1:8. If there are 32 cups of powder, how many total cups of water are needed? Explain your reasoning.

Vocabulary:Unit rate, ratio, proportional relationship, equivalent ratios, constant of proportionality, graph, origin, ordered pair, numeric expressions, algebraic expressions

Shelby County Schools 2015/2016Revised 12/1/15(CSH)

5 of 13

100% 100% 24%

$4.17 $4.17 ?

Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 7

TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONS 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

Math Station Activities: Refer to pp. 117, 125 & 132

students recognize that the graph is a line through the origin (0,0) with a constant of proportionality equal to the slope of the line.

Example(s):The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

A student is making trail mix. Create a graph to determine if the quantities of nuts and fruit are proportional for each serving size listed in the table. If the quantities are proportional, what is the constant of proportionality or unit rate that defines the relationship? Explain how you determined the constant of proportionality and how it relates to both the table and graph.

The relationship is proportional. For each of the other serving sizes there are 2 cups of fruit

Khan Academy: 7.EE.B.4

MICA Sample Items for 7.RP.A and 7.EE.B.4:7.RP.A.1: IDs 41932, 41933, and 419357.RP.A.2: IDs 41892, 43993, 41937, & 440147.RP.A.3: IDs 42131 and 421387.EE.B.4a: IDs 41905 and 421397.EE.B.4b: IDs 42140, 41907, and 36800

Shelby County Schools 2015/2016Revised 12/1/15(CSH)

6 of 13

Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 7

TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONS

for every 1 cup of nuts (2:1). The constant of proportionality is shown in the first column of the table and by the slope of the line on the graph.

As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Solve 12

x + 3 > 2 and graph your

solution on a number line.

Topic: Scale Drawings(4 weeks, this includes the TNReady Part 2 testing window, Feb 29-Mar 4, 2016)

7.G.A.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.

Students will determine the dimensions of figures when given a scale and identify the impact of a scale on actual length and area.Example(s):Julie showed you the scale drawing of her room. If each 2 cm on the scale drawing equals 5 ft, what are the actual dimensions of Julie’s room? Reproduce the drawing at 3 times its current size.

Solution: 5.6 cm --- 14 ft1.2 cm --- 3 ft

Glencoe5-2B Scale Drawings (pgs. 284-290)

5-2C Extend Scale Drawings (pg. 291)

IMPACT Math Unit D, Inv. 1, pp. 53-55.

5-3A Similar Figures (pgs.293-298)

Additional Lesson 22

5-3B Perimeter & Area of Similar Figures (pgs.299-302)

Additional Lesson 23

5-3C Extend The Golden Rectangle (pgs. 303)

11-2A Make a Model

Language Objective: Students will discuss how proportions can be used to solve scale problems.

Writing Prompt: After the lessons are taught have students free write for a fixed amount of time on proportional relationships related to similar figures.

Vocabulary:Scale drawing, scale factor, dimensions

Shelby County Schools 2015/2016Revised 12/1/15(CSH)

7 of 13

Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 7

TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONS2.8 cm --- 7 ft4.4 cm --- 11 ft4 cm --- 10 ft

11-2B Changes in Scale (pgs.652)

11-2C Changes in Dimensions (pgs.655)

Holt4-8 Similar Figures

4-9 Using Similar Figures

4-10 Scale Drawing and ModelingSimilar Figures Lesson

Revisit Ch. 12 Lessons

Focus on Problem Solving p. 709

Real-World Connections p. 729

Connected Math: Stretching and ShrinkingInv. 1-5Similar Figures Lesson

Revisit Ch. 4 Lessons (H.O.T)

MICA Sample Items for 7.G.A.1:IDs 41909, 41910, and 41911

7.G.A.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.

7.G.A.3 Describe the two-dimensional figures that result from slicing three-

Students draw geometric shapes with given parameters. Parameters could include parallel lines, angles, perpendicular lines, line segments, etc.

Examples:Is it possible to draw a triangle with a 90˚ angle and one leg that is 4 inches long and one leg that is 3 inches long? If so, draw one. Is there more than one such triangle?

GlencoeCh. 10 All Lessons12-1A – 1E (pp. 674-698)

Holt8-3 Line and Angle Relationships

8-8 Angles in Polygons

9-2 Circumference

Language Objective(s):Students will analyze given conditions based on the three measures of angles or sides of a triangle to determine when there is a unique triangle, more than one triangle, or no triangle.

Students will describe the shape of the cross section when cutting through a three-dimensional figure.

Shelby County Schools 2015/2016Revised 12/1/15(CSH)

8 of 13

Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 7

TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONSdimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

7.G.B.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.G.B.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.G.B.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.Math Station Activities: pp. 95, 102 & 110

Draw a triangle with angles that are 60 degrees. Is this a unique triangle? Why or why not?

Draw an isosceles triangle with only one 80 degree angle. Is this the only possibility or can you draw another triangle that will also meet these conditions?

Through exploration, students recognize that the sum of the angles of any triangle will be 180.

Students need to describe the resulting face shape from cuts made parallel and perpendicular to the bases of right rectangular prisms and pyramids. Cuts made parallel will take the shape of the base; cuts made perpendicular will take the shape of the lateral (side) face. Cuts made at an angle through the right rectangular prism will producea parallelogram;

Students understand the relationship between radius and diameter. Students also understand the ratio of circumference to diameter can be expressed as pi. Building on these understandings, students generate the formulas for circumference and area.

The illustration shows the relationship between

9-5 Area of Circles10-1 Intro to 3D FiguresCross sections p. 592

Labs pp. 606, 612, 618 & 625

Illuminations: Making Triangles 7.G.2

Better Lessons 7.G.2

Cross Sections 7.G.3

Lessons for 7.G.A.2, 3; 7.G.B.4,5Scroll to: Drawing Triangles; Any way you slice it; Circumference and Diameter RelationshipEngage NY Lessons: 7.G.2, 3, 5 & 6

Learnzillion Geometric Shapes

Two-dimensional figures Lesson Plan

Internet4classrooms 7.G.3

Area and Circumference of a Circle

Various Types of Angles

MICA Sample Items for 7.G.A.2, 7.G.A.3, 7.G.B.4, 7.G.B.5, 7.G.B.6:7.G.A.2: IDs 23850, 36802, 41913, and 419147.G.A.3: IDs 43859, 41918, and 437957.G.B.4: IDs 41921, 41923, and 420687.G.B.5: ID 419247.G.B.6: ID 42112

Students will describe the relationship between the area and circumference of a circle.Students will identify angle pairs and find the measure of one angle when the measure of another angle is known.

Students will compare and contrast finding the volume of a rectangular prism and a triangular prism.

Vocabulary:Surface area, prism, pyramid, face, base, plane sections, right rectangular prisms, right rectangular pyramids, supplementary, complementary, vertical, adjacent, compose, decompose, inscribed

Opening Discussion:Have students discuss their own definitions for volume and surface area. Have them share some examples of common objects that have volume and surface area.

Journal/Writing Prompt(s):Explain what conditions make angles complimentary, supplementary, vertical and adjacent.

Suppose the height of a square pyramid is doubled. Explain what happens to the volume of the pyramid. Support your reasoning with an example.

Graphic Organizers:Cross Sections

Shelby County Schools 2015/2016Revised 12/1/15(CSH)

9 of 13

Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 7

TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONSthe circumference and area. If a circle is cut into wedges and laid out as shown, a parallelogram results. Half of an end wedge can be moved to the other end and a rectangle results. The height of the rectangle is the same as the radius of the circle. The base

length is

12 the circumference (2πr). The area

of the rectangle (and therefore the circle) is found by the following calculations:

Anet= Base x Height

Area=

12

(2πr)(r)Area = (πr)(r)Area = πr2

http://mathworld.wolfram.com/Circle.html

Students solve problems (mathematical and read-world) involving circles or semi-circles.Note: Because pi is an irrational number that neither repeats nor terminates, the measurements of area approximate when 3.14 is used in place of π.

Volume Frayer Model – Solid Figures 3-D models Geometry Formula Sheet

Shelby County Schools 2015/2016Revised 12/1/15(CSH)

10 of 13

Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 7

TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONS

ExampleThe center of the circle is at (5, -5). What is the area of the circle?Solution:The radius of the circle is 4. Using the formula, Area = Πr2, the area of the circle is approximately 50.24 units2.

Students use understandings of angles and deductive reasoning to write and solve equationsExampleWrite and solve an equation to find the measure of angle x.

Solution:Find the measure of the missing angle inside the triangle (180 – 90 – 40), or 50°.The measure of angle x is supplementary to 50°, so subtract 50 from 180 to get a measure of 130° for x.

Students do not need to memorize formulas. They must have an understanding of why the formula works and how the formula relates to the measure (area and volume) and the figure. This understanding should be for all students.Example(s):A triangle has an area of 6 square feet. The

Shelby County Schools 2015/2016Revised 12/1/15(CSH)

11 of 13

Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 7

TN STATE STANDARDS ESSENTIAL UNDERSTANDINGS CONTENT & TASKS CLIP CONNECTIONSheight is four feet. What is the length of the base?Solution:One possible solution is to use the formula for the area of a triangle and substitute in the known values, then solve for the missing dimension. The length of the base would be 3 feet.

The surface area of a cube is 96 in2. What is the volume of the cube?Solution:The area of each face of the cube is equal. Dividing 96 by 6 gives an area of 16 in2 for each face. Because each face is a square, the length of the edge would be 4 in. The volume could then be found by multiplying 4 x 4 x 4 or 64 in3.

RESOURCE TOOLBOXTextbook Resources

My.hrw.com www.connected.mcgraw-hill.com

StandardsTennessee’s State Mathematics Standards Common Core Standards-MathematicsTN CoreThe Mathematics Common Core Toolbox

TN Math e matics Curricu lum Center

VideosKhan Academy

Calculator Interactive Manipulatives Additional Sites

Shelby County Schools 2015/2016Revised 12/1/15(CSH)

12 of 13

Curriculum and Instruction – Office of Mathematics3rd Nine Weeks Grade 7

Texas Instruments Education www.casioeducation.com Statistics Virtual Manipulatives

NLVM Statistics Manipulatives

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

CLIP Connections:FoldablesMath Graphic OrganizersVocabulary Math CardsTeaching Academic Vocabulary in the math classroomMiddle School Mathematics Vocabulary Word Wall Cards

Other:

Shelby County Schools 2015/2016Revised 12/1/15(CSH)

13 of 13