MS Math SPED Resource Map

Instructional Guide 2024-2025

Middle School Special Ed Math

Instructional Guide 2024-2025

Math

Grade

Instructional Guide 2024-2025

Introduction

What’s New and Updated in

6th grade math

What’s New

This section contains a listing of pages in the map that are new this year.

Page Number

Description

Added two different scope and sequence options for 6th grade. The units stay the same, but there are two scope and sequences. School PLC’s have the choice of option.

What’s Updated

This section contains a listing of pages in the page that have received substantial content updates for this year.

Description

Updated dates for all units

Grade 6

Math Overview

ORGANIZATION OF STANDARDS

The Utah Core Standards are organized into strands, which represent significant areas of learning within content areas. Depending on the core area, these strands may be designated by time periods, thematic principles, modes of practice, or other organizing principles. Within each strand are standards. A standard is an articulation of the demonstrated proficiency to be obtained. A standard represents an essential element of learning that is expected. While some standards within a strand may be more comprehensive than others, all standards are essential for mastery.

UNDERSTANDING MATHEMATICS

These standards define what students should understand and be able to do in their study of mathematics. Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness. The standards set grade-specific standards but do not dictate curriculum or teaching methods, nor do they define the intervention methods or materials necessary to support students who are well below or well above grade-level expectations. It is also beyond the scope of the Standards to define the full range of supports appropriate for English language learners and for students with special needs. At the same time, all students must have the opportunity to learn and meet the same high standards if they are to access the knowledge and skills necessary in their post-school lives. The standards should be read as allowing for the widest possible range of students to participate fully from the outset, along with appropriate accommodations to ensure maximum participation of students with special education needs. No set of grade-specific standards can fully reflect the great variety in abilities, needs, learning rates, and achievement levels of students in any given classroom. However, the standards do provide clear signposts along the way to the goal of college and career readiness for all students. What students can learn at any particular grade level depends upon what they have learned before. Ideally then, each standard in this document might have been phrased in the form, "Students who already know… should next come to learn ..." Grade placements for specific topics have been made on the basis of state and international comparisons and the collective experience and collective professional judgment of educators, researchers and mathematicians. Learning opportunities will

continue to vary across schools and school systems, and educators should make every effort to meet the needs of individual students based on their current understanding.

USBE Course Overview Grade 6 The purpose of this document is to provide a brief overview of the most essential content in the grade level along with a progression of how the content was addressed in the prior grade level and will prepare students for content in the future grade level. This is not a comprehensive list of content in the grade level, but rather highlights the major work of the grade level.

Major Work of Grade Band: Grades 6 - 8 ● Apply and use operations with rational numbers ● Understand ratio concepts and apply proportional reasoning ● Simplify expressions and solve equations ● Represent and analyze relationships

Major Work and Vertical Alignment

Major work: Operations with Rational Numbers Grade 6: Apply and extend understanding of operations with rational numbers : Apply previous understanding of all four operations with rational numbers (6.NS.1-3), with the extension of dividing fractions by fractions. Students are introduced to integers via opposite signs, value, and direction; number line models; and absolute value (6.NS.5-7). ● Prior grades : Students understand patterns in place value including decimals and powers of ten (5.NBT.1-3). Add, subtract, multiply and divide decimals to hundredths (5.NBT.7). Multiply a fraction or whole number by a fraction including real-world problems (5.NF.4,6). Divide unit fractions by whole numbers and whole numbers by unit fractions using reasoning about the relationship between multiplication and division (5.NF.7). Fluently multiply multi-digit whole numbers using the standard algorithm (5.NBT.5) and divide whole numbers with up to four-digit dividends and two-digit divisors (5.NBT.6). ● Future Grades : Students will apply previous understanding of operations with rational numbers to include integers in grade 7 (7.NS.1-3) and irrational numbers in grade 8 (8.NS.1-3). In Secondary Math II, students will expand the number system to include imaginary numbers (II.N.CN.1, 2, 7-9).

Major work: Ratio and Rate Reasoning Grade 6: Understand ratio concepts and apply proportional reasoning: Understand ratio concepts (6.RP.1) and understand the concept of unit rate (6.RP.2). Use multiple representations to solve

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ratio/rate problems (tables of equivalent ratios, equations, and plot values on a coordinate plane in all four quadrants) (6.RP.3). ● Prior Grades: In grades 4 and 5, students have created equivalent fractions (4.NF, 5.NF) and use equivalent fractions as a strategy to add and subtract fractions with unlike denominators including mixed numbers (5.NF.1–2). Fractions are interpreted as division of the numerator by the denominator (5.NF.3). Interpret multiplication as scaling (5.NF.5). ● Future Grades: In grade 7, students will recognize and represent proportional relationships between quantities using multiple representations (7.RP.1-2), and use proportional relationships to solve multi-step and percent problems (7.RP.3). In grade 8, students will extend their understanding of proportional relationships to linear equations, recognizing slope as the proportional relationship between quantities (8.EE.5) and that linear functions have a vertical shift of b units (8.EE.5-6, 8.F). In high school, students will identify functions based on rates of change (High School Functions standards). Major work: Simplify Expressions and Solve One Step Equations with one variable one step simple equations Grade 6: Simplify expressions and solve equations: Apply and extend previous understandings of arithmetic to using variables and generating equivalent algebraic expressions (6.EE.1-4). Reason about and, for the first time in their math education, formally solve simple one-variable equations and inequalities, for example: (x+q < r) (6.EE.5-8). ● Prior Grades: Students solve for unknown values starting in the early grades (K.OA.4, 1.OA.1, 2.OA.1, etc.), are introduced to equality and inequality symbols (1.NBT.3) and analyze patterns and relationships (5.OA.3). (1.NBT.3) students introduced to inequality symbols <, >, = ● Future Grades: In grade 7, students will apply properties of operations to factor, expand, and convert between forms and assess reasonableness of an answer (7.EE.1-3). Students will use variables to represent quantities to construct and solve simple equations and inequalities (for example: px+q < r ) (7.EE.4). In grade 8, students will solve complex linear equations and inequalities (8.EE.7). Students solve equations throughout high school and justify why solutions work (High School Algebra standards). Major work: Represent and Analyze Relationships Grade 6: Represent and analyze relationships: Solve simple problems using numerical and algebraic expressions (6.EE.5-8); represent and analyze quantitative relationships between dependent and independent variables and graph the relationship on a coordinate plane (6.NS.8, 6.EE.9).

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● Prior Grades: In grade 5, students will generate two numerical patterns using two given rules (5.OA.3). Students also understand concepts of geometric measurement and relate volume to multiplication and to addition (5.MD.3-5). ● Future Grades: In grade 7, students will solve problems using numerical and algebraic expressions (7.EE-4), draw references between two populations (7. SP.3-4), and investigate probability models (7. SP.5-8). Students will represent two variable relationships, compare quantities, and analyze relationships throughout their mathematics career. In grade 8 and high school, students will continue to study and compare how multiple quantities interact and relate in all strands.

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Instructional Guide 2024-2025

Scope and Sequence

Grade 6 Resource + Math 180

YEAR AT A GLANCE

Unit 8

Mindset

Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

Unit 6

Unit 7

Math180 Series 5 Proportional &Linear Relationships

Math 180 Series 3 Decimals& Integers

Math 180 Series 2 Multiplication &Division Block 3

Math 180 Series 3 Decimals& Integers Block 2

Math 180 Series 4 Rates& Ratios Block 1

Math180 Series 4 Rates& Ratios Block 2

Math180 Series 4 Rates& Ratios Block 3

Growth Mindset Unit

Illustrative Unit 6

Unit

Block 3 Topic 1

Block 1 Topic 1

Aug19 - Aug30

Sept 3 - Oct 4

Oct 7 - Nov 6

Nov 7 - Nov 19

Nov 20 - Dec 20

Jan6 - Feb7

Feb10 - Mar 14

Mar 17 - Apr 25

Apr 29 - May 31

Suggested Pacing

6.EE.1 6.EE.2 6.EE.3 6.EE.4 6.EE.5 6.EE.6 6.EE.7 6.EE.9

Standards/ Performance Expectations

6.RP.1 6.RP.2 6.RP.3

6.RP.1 6.RP.2 6.RP.3

6.RP.1 6.RP.2 6.RP.3

6.NS.2 6.NS.3

6.NS.5 6.NS.6

6.NS.1

6.RP.3

Grade 6

YEAR AT A GLANCE Option 1

Illustrative Unit

Unit 1 Area and

Unit 2 Introducing Ratios (17 sections)

Unit 3 Unit Rates and Percentages (17 sections)

Unit 4 Dividing Fractions (17 sections)

Unit 5 Arithmetic in Base Ten (15 sections)

Unit 6 Expressions and Equations (19 sections)

Unit 7 Rational Numbers (19 sections)

Unit 8 Data Sets and Distributions (18 sections)

Unit 9 Putting it All Together

Surface Area (19 sections)

Suggested Pacing

Aug 19 - Sept 26 (28 days)

Sept 30 - Oct 30 (20 days)

Oct 31 - Nov 26 (19 days)

Dec 2 - Jan 10 (20 days)

Jan 13 - Feb 7 (18 days)

Feb 10 - Mar 12 (21 days)

Mar 13 - Apr 18 (21 days)

Apr 21 - May 16 (20 days)

May 17 - May 30

6.G.1 6.G.2 6.G.4 6.EE.1 6.EE.2

6.RP.1 6.RP.2 6.RP.3

6.RP.2 6.RP.3

6.NS.1 6.G.3

6.NS.2 6.NS.3

6.EE.1 6.EE.2 6.EE.3 6.EE.4 6.EE.5 6.EE.6 6.EE.7 6.EE.9

6.EE.8 6.NS.4 6.NS.5 6.NS.6 6.NS.7 6.NS.8

6.SP.1 6.SP.2 6.SP.3 6.SP.4 6.SP.5

6.G 6.RP 6.NS

Practice Standards

Practice Standards

Practice Standards

Practice Standards

Practice Standards

Standards

Practice Standards

Practice Standards

Practice Standards

Practice Standards

These standards will be assessed along with all other standards on the RISE

DWSBA & Testing Window

DWSBA #1

DWSBA #2

DWSBA #3

Aug 19 - Sept 25

Dec 4 - Jan 16

MAP Window

Apr 1 - May 9

SALTA Extensions

“Are You Ready for More?”

Accessing the District-Wide Standards-Based Assessment (DWSBA)

The DWSBA’s will be done through Canvas on Derivita Instructions to access the DWSBA can be found here.

Grade 6

YEAR AT A GLANCE Option 2

Illustrative Unit

Unit 2 Introducing Ratios (17 sections)

Unit 3 Unit Rates and

Unit 1 Area and

Unit 4 Dividing Fractions (17 sections)

Unit 5 Arithmetic in Base Ten (15 sections)

Unit 6 Expressions and Equations (19 sections)

Unit 7 Rational Numbers (19 sections)

Unit 8 Data Sets and Distributions (18 sections)

Unit 9 Putting it All Together

Surface Area (19 sections)

Percentages (17 sections)

Suggested Pacing

Aug 19 - Sept 24 (26 days)

Sept 25 - Oct 25 (19 days)

Oct 28 - Nov 26 (22 days)

Dec 2 - Jan 10 (20 days)

Jan 13 - Feb 7 (18 days)

Feb 10 - Mar 12 (21 days)

Mar 13 - Apr 18 (21 days)

Apr 21 - May 16 (20 days)

May 17 - May 30

6.RP.1 6.RP.2 6.RP.3

6.RP.2 6.RP.3

6.G.1 6.G.2 6.G.4 6.EE.1 6.EE.2

6.NS.1 6.G.3

6.NS.2 6.NS.3

6.EE.1 6.EE.2 6.EE.3 6.EE.4 6.EE.5 6.EE.6 6.EE.7 6.EE.9

6.EE.8 6.NS.4 6.NS.5 6.NS.6 6.NS.7 6.NS.8

6.SP.1 6.SP.2 6.SP.3 6.SP.4 6.SP.5

6.G 6.RP 6.NS

Practice Standards

Practice Standards

Practice Standards

Practice Standards

Practice Standards

Standards

Practice Standards

Practice Standards

Practice Standards

Practice Standards

These standards will be assessed along with all other standards on the RISE

DWSBA & Testing Window

DWSBA #1

DWSBA #2

DWSBA #3

Aug 19 - Sept 25

Dec 4 - Jan 16

MAP Window

Apr 1 - May 9

SALTA Extensions

“Are You Ready for More?”

Accessing the District-Wide Standards-Based Assessment (DWSBA)

The DWSBA’s will be done through Canvas on Derivita Instructions to access the DWSBA can be found here.

AREA AND SURFACE AREA (SPED Resource)

Unit 1

CALCULATOR

PACING

KEY LANGUAGE USES

Yes

Option 1: August 19 - September 26 (28days) Option 2: October 18 - November 26 (22days)

EXPLAIN

STANDARDS Standard 6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing and decomposing into rectangles, triangles and/or other shapes; apply these techniques in the context of solving real-world and mathematical problems. Standard 6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to fnd volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Standard 6.G.4 Represent three-dimensional fgures using nets made up of rectangles and triangles, and use the nets to fnd the surface area of these fgures. Apply these techniques in the context of solving real-world and mathematical problems.

Standard 6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS

I can explain how to fnd the surface area of a fgure. Language Supports: ● Vocabulary (Surface area, centimeters squared, inches squared, etc.) I can explain how to fnd the area of a fgure by decomposing and rearranging. Language Supports: ● Vocabulary (Area, decompose, rearrange, move, etc.) DIFFERENTIATION IN ACTION

Skill Building

In Lesson 5, practice verbal use of the mathematical language “base” and “height.” As students are comparing parallelograms and examples/non-examples of correct heights, encourage them to re-voice their partners’ reasoning. Reinforce the meaning of “perpendicular” by using visuals (e.g., manipulatives, drawings, gestures) of right angles.

Extension

From Lesson 12 Are You Ready for More? How many sticky notes are

needed to cover the outside of 2 cabinets pushed together (including the bottom)? What about 3 cabinets? 20 cabinets?

RESOURCES

Unit 1 Vocabulary Information about Practice Problems For every unit, use the cool-downs as needed the next day as either a starter or whole class activity as a review.

SPECIAL ED RESOURCES

Lesson

Additional Notes

1.1 Tiling the Plane

Practice Problems 1 - 4

1.1 Which One Doesn’t Belong: Tilings 1.3 More Red, Green, or Blue?

1.2 Finding Area by Decomposing & Rearranging 2.1 What is Area?

For 2.3, have students manipulate the physical shapes to understand the relationship between the triangles and squares.

2.2 Composing Shapes 2.3 Composing Shapes

1.3 Reasoning to Find Area

Practice Problems 1-2 with extra scaffolding on #2

3.1 Comparing Regions 3.2 On the Grid (only A & B) 3.3 Off the Grid (Only A & C)

1.4 Parallelograms

Practice Problems 1, 2, 4 (Sentence frame for #4)

4.1 Features of a Parallelogram 4.2 Area of a Parallelogram

1.5 Bases & Heights of Parallelograms 5.2 The Right Height?

5.2: Do #2 with student after they do #1. 5.3: Do only A & B and the last row: “Any Parallelogram”) Practice Problems #1-6 (not 5c) 6.2: Don’t do #3, and B may need extra support. Practice Problems #1, 2 (calculator), 4 7.2: #3 may need more teacher support. 7.3: Only give one or two pairs of triangles to

5.3 Finding the Formula for Area of Parallelograms

1.6 Area of Parallelograms

6.2 More Areas of Parallelograms

1.7 From Parallelograms to Triangles

7.2 A Tale of Two Triangles (Part 1) 7.3 A Tale of Two Triangles (Part 2)

the groups, not all pairs. Practice Problems #1 - 3

1.8 Area of Triangles

Practice Problems #1b, 2a, 3(do together), 4

8.1 Composing Parallelograms 8.2 More Triangles (Only A & B)

1.9 Formula for the Area of a Triangle

9.1: with scaffolding. 9.3: Only A, B, & E.

9.1 Bases and Heights of a Triangle

9.2 Finding the Formula for Area of a Triangle 9.3 Applying the Formula for Area of Triangles

Mid-unit assessment is given after this lesson, build in a review day. Practice Problems #1, 2

1.10 Bases and Heights of Triangles 10.2 Hunting for Heights

10.2: Only #2 using a 3x5 card. Practice Problems #1 - 3, 6

10.3 Some Bases Are Better Than Others

1.11 Polygons

11.3: Use D as an example to do all together, then have students do C & F. Practice Problems #1 - 3, 5

11.1 Which One Doesn’t Belong: Bases and Heights 11.2 What Are Polygons? 11.3 Quadrilateral Strategies

1.12 What is Surface Area?

12.1: Emphasize the post-it notes are the square units. Instead of showing the video, have a rectangle drawn, fll in the top two rows, and one column, and ask students how to get the rest of the area. NO partial units. 12.3: Do not do #3 but have actual physical snap cubes for students to use. Practice Problems #1, 2(teacher support), 3(with cubes), 4 (with cubes) 13.1: Have the physical shapes available for students to use. 13.2: No#3 Practice Problems #1, 2a, 3, 4, 6(optional) 14.2: Don’t cut them out. Name each polyhedron, then fnd the surface area of just C. Practice Problems 2, 5 Lesson 1.15 #1, 3, 5 Practice Problems #1, 2, 3(Build each shape with blocks), 5b

12.1 Covering the Cabinet (Part 1) 12.3 Building with Snap Cubes

1.13 Polyhedra

13.1 What are Polyhedra? 13.2 Prisms and Pyramids

1.14 Nets and Surface Area 14.1 Matching Nets

14.2 Using Nets to Find Surface Area

1.16 Distinguishing Between Surface Area and Volume 16.1 Attributes and Their Measures 16.2 Building with 8 Cubes

1.17 Squares and Cubes

Take two days 17.1: With Scaffolding

17.1 Perfect Squares 17.3 Perfect Cubes 17.4 Introducing Exponents

17.3: Have students build the cube Practice Problems #1, 2 on day 1 Practice Problems #3, 4, 6 on day 2

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

6.G.1

1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.19

6.G.2

1.15, 1.16, 1.17

6.G.4

1.12, 1.13, 1.14, 1.15, 1.16, 1.18, 1.19

6.EE.1

1.17, 1.18

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfnished Learning Standard

1

1.17

1.2

3.MD.5b

2

1.3

1.3

3.MD.7d

3

1.7

1.4, 1.11

4.G.2

4

1.4

1.7

5.NF.4b

5

1.7, 1.11

1.11

4.G.1

6

1.17, 1.18

1.14

5.MD.5

7

1.11

1.15, 1.16

3.MD.5, 4.MD.1

1.16

5.MD.3b, 5.MD.4

1.16, 1.17

5.MD.5a

LEARNING INTENTIONS

● Find the area of right triangles by composing or decomposing rectangles. ● Find area of polygons by composing and decomposing into basic shapes (rectangles, triangles, and other shapes). ● Solve real-world area problems by decomposing and composing polygons. ● Extend background knowledge of volume with whole units (5.MD.3-5) and tiling area with fractional units (5.NF.4) to fnd volume of right rectangular prisms with fractional edge lengths. ● Recognize the relationship between the volume formula and flling a right rectangular prism with cubes. ● Describe how fnding the volume is the same process whether edge lengths are whole units or fractional units. ● Solve real-world volume problems. ● Visualize how nets relate to three-dimensional fgures. ● Understand how area of two-dimensional fgures relates to surface area of three-dimensional fgures.

KEY VOCABULARY

● Area ● Region

● Base ● Height ● Opposite Vertex ● Quadrilateral ● Vertex (Vertices) ● Edge

● Side ● Polygon ● Surface Area ● Face ● Net ● Polyhedron (polyhedra)

● Prism ● Pyramid ● Squareof a number ● Cubeof a number ● Exponent

● Rearrange ● Compose ● Decompose ● Parallelogram

INTRODUCING RATIOS (SPED Resource)

Unit 2

CALCULATOR

PACING

KEY LANGUAGE USES

Yes

Option 1: September 30 - October 30 (20days) Option 2: August 19 - September 24 (26days)

EXPLAIN

STANDARDS

Standard 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Standard 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 and use rate language in the context of a ratio relationship.

Standard 6.RP.3 Use ratio and rate reasoning to solve real-world (with a context) and mathematical (void of context) problems, using strategies such as reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations involving unit rate problems. a. Make tables of equivalent ratios relating quantities with whole-number measurements, fnd missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed. c. Find a percent of a quantity as a rate per 100. Solve problems involving fnding the whole, given a part and the percent. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can explain the relationship between two numbers using ratio language, including equivalent ratios. Language Supports: ● Vocabulary (ratio, equivalent)

I can represent equivalent traits on a number line, bar diagram, or table. Language Supports: ● Vocabulary (number line, bar diagram, table) DIFFERENTIATION IN ACTION

Skill Building

In Activity 7.3, Briefy review the meaning of the following terms: " parallel," "equal increments," and "line up." Use visuals to show what these terms are in the context of the problem.

Extension

From Lesson 14 “Are you ready for more?” The ratio of cats to dogs in a

room is 2:3. Five more cats enter the room, and then the ratio of cats to dogs is 9:11. How many cats and dogs were in the room to begin with?

RESOURCES

The focus of this unit is on tables. Once you’re done with diagrams, show ratios with diagrams and table side by side (Lessons 2.8 - 2.10) Unit 2 Vocabulary Information about Practice Problems (Go to the tab marked Unit 2)

SPECIAL ED RESOURCES

Lesson

Additional Notes

2.1 Introducing Ratios and Ratio Language 1.1 What Kind and How Many?

Practice Problems #1 - 3, 6 (Modify: Categorize as prisms and pyramids”) Do #4 or 5 as a starter

1.2 The Teacher’s Collection 1.3 The Student’s Collection

2.2 Representing Ratios with Diagrams 2.2 A Collection of Snap Cubes 2.3 Blue Paint and Art Paste

Practice Problems #1 - 4

2.3 Recipes

MUST HAVE pattern blocks May need 2 days: Explore with pattern blocks from 3.1 into 3.2. 3.3: Students will need extra scaffolding to draw diagrams. Practice Problems #1-2 on Day 1. Practice Problems #3, 5 Day 2 with scaffolded diagrams on both. Physically do the activity with the food colors and take whole day just doing the mixtures in class. Practice Problems #1-4, 6(can be done as a starter, or review with time permitting)

3.1 Flower Pattern 3.2 Powdered Drink Mix 3.3 Batches of Cookies

2.4 Color Mixtures

4.2 Turning Green

2.5 Defning Equivalent Ratios

Practice Problems #1 - 5 Lesson 2.6 Practice Problems #4, 5b Lesson 2.7 Practice Problems #4, 6

5.3 What Are Equivalent Ratios?

2.8 How Much for One?

8.3: Bring in physical circulars from grocery stores. Practice Problems #3, 4, 5 Have calculators available

8.2 Grocery Shopping 8.3 More Shopping

2.9 Constant Speed

9.2: Just do #1 (leading into tables) Practice Problems #1, 4, 5, 7

9.2 Moving 10 Meters 9.3 Moving for 10 Seconds

2.10 Comparing Situations by Examining Ratios 10.1 Treadmills 10.2 Concert Tickets 10.3 Sparkling Orange Juice

10.1: Have pre-determined questions to help students. 10.2: Do on a table, do not use the applets. 10.3: No applets Practice Problems #1 - 5 Use the same questions and scaffolding from 11.2. Practice Problems #1, 3, 5, 6

2.11 Representing Ratios with Tables 11.3 Batches of Trail Mix

2.12 Navigating a Table of Equivalent Ratios 12.2 Comparing Taco Prices 12.3 Hourly Wages 2.13 Tables and Double Number Line Diagrams 13.2 Moving 3,000 Meters 13.3 The International Space Station 2.14 Solving Equivalent Ratio Problems 14.1 What Do You Want to Know? 14.2 Info Gap: Hot Chocolate and Potatoes 14.3 Comparing Reading Rates

Practice Problems #1, 2, 3, 7

13.3: Do with just a table. Practice Problems #2, 4, 6

14.2: Every student gets the problem card, and the teacher gets the data card. Students have to fgure out what information they need from the teacher. 14.2: Do with a table Practice Problems #1a-d, 2 - 4, 6

2.15 Part-Part-Whole Ratios

15.3: With a table 15.4: Time Permitting Practice Problems #3, 4, 6 Lesson 2.16 Practice Problems #3 - 5

15.3 Sneakers, Chicken, and Fruit Juice 15.4 Invent Your Own Ratio Problem

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

6.RP.1

2.1, 2.2, 2.3, 2.4, 2.5

6.RP.2

2.10

6.RP.3

2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12, 2.13, 2.14, 2.15, 2.16, 2.17

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfnished Learning Standard

1

2.8

2.1

3.MD.6

2

2.5

2.2

5.NF.3

3

2.10, 2.14

2.3

4.OA.1, 4.NF.4c

4

2.7

2.4

4.NBT.5

5

2.2

2.6, 2.7

4.NF.4b

6

2.3

2.8

4.NBT.1

7

2.9

2.9

5.NBT.1

2.11

5.OA.3

2.15

3.OA.5, 5.NF.7

LEARNING INTENTIONS

● Understand the concept of a ratio as a way of expressing relationships between quantities. ● Distinguish when a ratio is describing part-to-part or part-to-whole comparison. ● Communicate ratio relationships fexibly moving between ratio notation (2:3, 2 to 3, 2/3) and ratio language (two for every three). ● Understand that a rate is a special ratio that compares two quantities with different units of measure. ● Understand that unit rates are the ratio of two measurements in which the second term is one (e.g., x miles per one hour). ● Understand that when using /b to represent a rate, “b” cannot be 0 (because division by 0 is undefned). ● Understand rate language (per, each, or the @ symbol) and correctly use ratio notation and models to represent relationships between quantities. ● Use various representations such as tables of equivalent ratios, tape diagrams and/or double number line diagrams to support the development of ratio and rate reasoning and to solve problems. ● Use a table to compare ratios and fnd missing values using ratios. ● Understand that establishing connections between tables and plotted points on the coordinate plane allows for extended reasoning and synthesis of the concept of ratios and rates. ● Solve problems with and without context that include unit rate, percent, and measurement conversions using ratio reasoning. ● Understand percent as a rate per 100. ● Use rate reasoning to fnd the percent of a number. ● Use rate reasoning to solve problems involving fnding the whole, given a part and the percent. *Teacher Note: This standard is not about setting up proportional relationships algebraically, but focuses on ratio reasoning

KEY VOCABULARY

● Ratio ● Equivalent Ratios

● Unit price ● Meters per second

● Tape Diagram ● Same rate ● Table

● Double

number line diagram

● Per

UNIT RATES & PERCENTAGES (SPED Resource)

Unit 3

CALCULATOR

PACING

KEY LANGUAGE USES

Yes

Option 1: October 30 - November 26 Option 2: September 25 - October 25 (19days)

EXPLAIN

STANDARDS

Standard 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 and use rate language in the context of a ratio relationship.

Standard 6.RP.3 Use ratio and rate reasoning to solve real-world (with a context) and mathematical (void of context) problems, using strategies such as reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations involving unit rate problems. a. Make tables of equivalent ratios relating quantities with whole-number measurements, fnd missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed. c. Find a percent of a quantity as a rate per 100. Solve problems involving fnding the whole, given a part and the percent. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS

I can fnd a unit rate. Language Supports: ● Vocabulary (rate, unit rate, speed)

I can use my knowledge of ratios and unit rates to fnd a percent of a number and explain why it works. Language Supports: ● Vocabulary (percent, percentage) DIFFERENTIATION IN ACTION

Skill Building

From activity 4.2 Ask students to display their approaches to determine whether or not Elena’s mom was speeding. As students share their work, encourage them to explain the meaning of each quantity they use. For example, if they convert 80 miles per hour into kilometers per hour, where 80 is multiplied by 5/8, ask what 5/8 means in this context and why they decide to multiply it by 80. If students used a table or a double number line, ask how these representations connect with other strategies. This will help students make sense of the various approaches to reason about equivalent ratios which can be used for reasoning about converting one

unit of measure to another.

Extension

Lesson 7 Are You Ready for more?Jada eats 2 scoops of ice cream in 5 minutes. Noah eats 3 scoops of ice cream in 5 minutes. How long does it take them to eat 1 scoop of ice cream working together (if they continue eating ice cream at the same rate they do individually)?

RESOURCES

Unit 3 Vocabulary Information about Practice Problems (Go to the tab marked Unit 3)

SPECIAL ED RESOURCES

Lesson

Additional Notes

3.1 The Burj Khalifa

Practice Problems #1 - 4, 6 (with pattern blocks), 7

1.1 Estimating Height 1.2 Window Washing 1.3 Climbing the Burj Khalifa

3.2 Anchoring Units of Measurement 2.3 Card Sort: Measurements

Have the physical objects available. Practice Problems #1 (do the actual measurement of each), 2 - 6 Instead of students in different groups and stations, can be teacher-driven (reach out to Science teachers for materials) Practice Problems #1 - 7, on #5, teach that 0.5 is 1/2 Have rates conversions available.

3.3 Measuring with Different-Sized Units 3.2 Measurement Stations

3.4 Converting Units 4.2 Road Trip

Practice Problems #1-7

4.3 Veterinary Weights

3.5 Comparing Speeds and Prices 5.1 Closest Quotient 5.2 More Treadmills 5.3 The Best Deal on Beans

5.1: with a calculator 5.2: Make sure students understand that 1/2 hour = 30 minutes, and only compare Tyler and Kiran. Practice Problems #1 - 3, 6

3.6 Interpreting Rates

6.2: Scaffolded Practice Problems #1, 2, 5 - 7

6.1 Something per Something 6.2 Cooking Oatmeal 6.3 Cheesecake, Milk, and Raffe

Tickets

3.7 Equivalent Ratios Have the Same Unit Rates 7.1 Which One Doesn’t Belong: Comparing Speeds

Practice Problems #1 - 5, 7

7.2 Price of Burritos 7.3 Making Bracelets

3.8 More about Constant Speed

Practice Problems #1 - 4

8.1 Back on the Treadmill Again 8.2 Picnics on the Rail Trail

3.9 Solving Rate Problems

Do the card sort whole class. Practice Problems #1, 2, 3(together in class), 4(together in class for help with fractions)

9.2 Cart Sort: Is it a Deal?

3.10 What Are Percentages? 10.1 Dollars and Cents 10.2Coins

Practice Problems #1-3, 5 - 7

3.12 Percentages and Tape Diagrams 12.1 Notice and Wonder: Tape Diagrams 12.2 Revisiting Jada’s Puppy 12.3 5 Dollars 12.4 Staying Hydrated

Take two days: Day 1: 12.1 (teach what a tape diagram is here) and 12.2 Practice Problems #1 - 2 Day 2: 12.3, 12.4 Practice Problems #3 - 6 Take two days: Day 1: 13.1, 13.2 Day 2: 13.3 together as a whole class to solidify tape diagrams. 13.4 May have to teach how to fnd percentages at this point. Practice Problems # 1 - 4

3.13 Benchmark Percentages

13.1 What Percentage Is Shaded? 13.2 Liters, Meters, and Hours 13.3 Nine is… 13.4 Matching the Percentage

3.14 Solving Percentage Problems 14.2 Coupons 3.15 Finding This Percent of That 15.2 Audience Size 15.3 Everything is On Sale

Can do as a part of 3.13, and use for review. Practice Problems #1 - 5, 7

15.3: #4 needs teacher scaffold Practice Problems #1 - 7

3.16 Finding the Percentage 16.2 Jumping Rope

Practice Problems #1 - 6

16.3 Restaurant Capacity

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

6.RP.2

3.4, 3.5, 3.6, 3.7

6.RP.3

3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.10, 3.11, 3.12, 3.13, 3.14, 3.15, 3.16

6.G, 6.RP

3.17

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfnished Learning Standard

1

3.2

3.1

4.MD.1, 5.MD.1

2

3.3

3.2

4.MD.1

3

3.4

3.3

2.MD.2

4

3.9

3.4

5.NF.4a

5

3.10

3.5

5.NF.3

3.10

2.MD.8, 5.NBT.3

3.14

5.NBT.7

3.15

5.NBT.6

LEARNING INTENTIONS

● Understand that a rate is a special ratio that compares two quantities with different units of measure. ● Understand that unit rates are the ratio of two measurements in which the second term is one (e.g., x miles per one hour). ● Understand that when using /b to represent a rate, “b” cannot be 0 (because division by 0 is undefned). ● Understand rate language (per, each, or the @ symbol) and correctly use ratio notation and models to represent relationships between quantities. ● Use various representations such as tables of equivalent ratios, tape diagrams and/or double number line diagrams to support the development of ratio and rate reasoning and to solve problems. ● Use a table to compare ratios and fnd missing values using ratios. ● Understand that establishing connections between tables and plotted points on the coordinate plane allows for extended reasoning and synthesis of the concept of ratios and rates. ● Solve problems with and without context that include unit rate, percent, and measurement conversions using ratio reasoning. ● Understand percent as a rate per 100. ● Use rate reasoning to fnd the percent of a number. ● Use rate reasoning to solve problems involving fnding the whole, given a part and the percent. *Teacher Note: This standard is not about setting up proportional relationships algebraically, but focuses on ratio reasoning

KEY VOCABULARY

● Unit Rate ● Pace ● Speed

● Percent ● Percentage

DIVIDING FRACTIONS (SPED Resource)

Unit 4

CALCULATOR

PACING

KEY LANGUAGE USES

December 2 - January 10 (20 days)

No

EXPLAIN

STANDARDS

Standard 6.NS.1 Compute quotients of fractions by fractions.

a. Solve real-world problems involving division of fractions by fractions, and explain the meaning of quotients in fraction division problems. b. Apply strategies such as using visual fraction models, applying the relationship between multiplication and division, and using equations to represent such problems as: How much chocolate will each person get if 3 people share ½ lb. of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? c. Create a story context for (2/3) / (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) / (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) + (c/d) = ad/bc.) when multiplying or dividing quantities. Standard 6.G.2 Find the volume of a right rectangular prism with appropriate unit fraction edge lengths by packing it with cubes of the appropriate unit fraction edge lengths ( for example, 3 1/2 x 2 x 6), and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V= lwh and V=bh to fnd volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. (Note: Model the packing using drawings and diagrams)

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS

I can divide fractions and explain why the algorithm works. Language Supports: ● Vocabulary (divide, reciprocal)

DIFFERENTIATION IN ACTION

Skill Building

From activity 6.2: As groups of 3-4 discuss the frst question, circulate and record language students use to explain how Andre’s tape diagram can be used to solve the equation. Listen for phrases such as “equal parts,” “same size,” and “group of ⅔ .” If groups are stuck, consider asking “How are the number of groups represented in the tape diagram?”, “Where are the values in the equation represented in the diagram?”, or “What do the blue

and white parts represent?” Post the collected language in the front of the room so that students can refer to it throughout the rest of the activity and lesson. This will help students develop mathematical language to explain how a tape diagram can be used to solve a division problem. Lesson 11 “Are You Ready for More?” You have a pint of grape juice and a pint of milk. Transfer 1 tablespoon from the grape juice into the milk and mix it up. Then transfer 1 tablespoon of the mixture back to the grape juice. Which mixture is more contaminated?

Extension

RESOURCES

Start this unit by teaching how to change improper fractions to mixed numbers and vice-versa Unit 4 Vocabulary Information about Practice Problems (Go to the tab marked Unit 4)

SPECIAL ED RESOURCES

Lesson

Additional Notes

4.1 Size of Divisor and Size of Quotient

*Can possible skip the whole lesson for time. For 1.3: Make sure it is done whole class: Look frst to estimate, then check on a calculator. Practice Problems #1, 4, 5 (calculator), 6, 7 *Must explicitly teach the summary Practice Problems #1, 2, 3, 4b, 6, 7 (Multi-column table support, do if there’s time)

1.1 Number Talk: Size of Dividend and

Divisor

1.2 All Stacked Up 1.3 All in Order

4.2 Meanings of Division

2.1 A Division Expression 2.2 Bags of Almonds

4.3 Interpreting Division Situations 3.2 Homemade Jams 3.3 Making Granola 4.4 How Many Groups? (Part 1) 4.1 Equal-Sized Groups

Practice Problems #1 - 5 (Possible scaffold with a picture), 6, 7

Do all Practice Problems

4.2 Reasoning with Pattern Blocks 4.3 Halves, Thirds, and Sixths

4.5 How Many Groups? (Part 2)

Practice Problems #1, 2, 4, 5, 6

5.1 Reasoning with Fraction Strips 5.2 More Reasoning with Pattern Blocks 5.3 Drawing Diagrams to Show

Equal-sized Groups

4.6 Using Diagrams to Find the Number of Groups 6.1 How Many of These in That? 6.2 Representing Groups of Fractions with Tape Diagrams 6.3 Finding Number of Groups

Practice Problems #1-4

4.7 What Fraction of a Group?

Practice Problems #1, 2 (Day 1)

7.2 Fractions of Ropes (Day 1) 7.3 Fractional Batches of Ice Cream

Practice Problems #3 - 6 (Day 2)

(Day 2)

4.8 How Much in Each Group? (Part 1) 8.1 Inventing a Scenario 8.2 How Much in One Batch?

Practice Problems #1 - 5

8.3 One Container and One Section of

Highway

4.9 How Much in Each Group? (Part 2)

Do 9.2 with much scaffolding from the teacher to explain what they are looking at in the video. Practice Problems: all

9.1 Number Talk: Greater Than 1 or

Less Than 1?

9.2 Two Water Containers 9.3 Amount in One Group 9.4 Inventing a Situation

4.10 Dividing by Unit and Non-Unit Fractions 10.2 Dividing by Unit Fractions 10.3 Dividing by Non-unit Fractions 10.4 Dividing by 1/3 and 3/5 4.11 Using an Algorithm to Divide Fractions 11.2 Dividing a Fraction by a Fraction 11.3 Using an Algorithm to Divide Fractions

10.2: Only 1a and 2a whole class 10.3: All of 1 and 2, only 3a and 4a 10.4: All of 1 and 2, skip 3, just 4b Practice Problems #1, 3, 4, 5, 7

11.2: only 1, 3, 5 11.3: 1 & 2 only whole class Practice Problems # 1-6

4.12 Fractional Lengths

12.2: 1a&b 12.3: 1, 2 Practice Problems #2, 3, 5, 6 13.2: #1 only Practice Problems #1, 2, 3, 5, 6, 7

12.2 How Many Would It Take? (Part 1) 12.3 How Many Times as Tall or as Far?

4.13 Rectangles with Fractional Side Lengths 13.1 Areas of Squares 13.2 Areas of Squares and Rectangles 4.14 Fractional Lengths in Triangles and Prisms 14.1 Area of Triangle

14.3: Just #1 & 2 (Only do part of the table) Practice Problems #1, 2, 3a, 4, 5, 6

14.2 Base and Heights of Triangles 14.3 Volumes of Cubes and Prisms

4.15 Volume of Prisms

15.3: only 1a Practice Problems #1, 2a, 2b, 5a, 6

15.1 A Box of Cubes 15.2 Cubes with Fractional Edge

Lengths

15.3 Fish Tank and Baking Pan

4.16 Solving Problems Involving Fractions 16.1 Operations with Fractions 16.2 Situations with 3/4 and 1/2 16.3 Pairs of Problems

16.3:OnlyA1&2,andD1&2 Practice Problems #1, 2, 5, 6

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

6.NS.1

4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.16*

6.G.2

4.13, 4.14, 4.15, 4.17*

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfnished Learning Standard

1

4.1

4.1

5.NBT.6

2

4.2

4.2

3.OA.2

3

4.7

4.3

5.NF.6

4

4.6

4.4, 4.7, 4.10, 4.11 5.NF.4

5

4.6

4.5, 4.10

5.NF.7

6

4.10

4.6

5.NF.3

7

4.15

4.10

5.NF.1

4.12

3.OA.5

4.13

5.NF.4b

4.15

5.MD.5

LEARNING INTENTIONS

● Model division of fractions with manipulatives, visual diagrams, and word problems. ● Interpret what the quotient represents in problems. ● Discover how to fnd the lengths of sides of polygons using the coordinates of the vertices having the same frst coordinate (or second coordinate) and generalize a technique to apply in solving problems.

ARITHMETIC IN BASE 10 (SPED Resource)

Unit 5

CALCULATOR

PACING

KEY LANGUAGE USES

January 13 - February 7 (18 days)

No

ARGUE

STANDARDS

Standard 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

Standard 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. a. Fluently divide multi-digit decimals using the standard algorithm, limited to a whole number dividend with a decimal divisor or a decimal dividend with a whole number divisor. b. Solve division problems in which both the dividend and the divisor are multi-digit decimals; develop the standard algorithm by using models, the meaning of division, and place value understanding.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS

I can explain how to multiply and divide decimals. Language Supports: ● Vocabulary (product, dividend)

DIFFERENTIATION IN ACTION

Skill Building

In Activity 5.2: MLR 2 Collect and Display Use this routine while students are working through the frst two questions. As partners work, circulate and listen to student talk about the connections they see between the problems. Record student language and written representations on a visual display. Listen for language like “the same,” “reciprocal,” and “inverse operation.” Continue to add to the display as students work through other problems during the next three lessons. This will help students read and use mathematical language during their paired and whole-group discussions. Lesson 12 “Are You Ready for More?” A distant, magical land uses jewels for their bartering system. The jewels are valued and ranked in order of their rarity. Each jewel is worth 3 times the jewel immediately below it in the ranking. The ranking is red, orange, yellow, green, blue, indigo, and violet. So a red jewel is worth 3 orange jewels, a green jewel is worth 3 blue jewels, and so on. A group of 4 craftsmen are paid 1 of each jewel. If they split the jewels

Extension

evenly amongst themselves, which jewels does each craftsman get?

RESOURCES

In 5.2 defnitely emphasize the represent 5.15 serves as a review for all students, and you can pull small groups for other intentional review Unit 5 Vocabulary Other resources for unit 5 lessons Information about Practice Problems (Go to the tab marked Unit 5)

SPECIAL ED RESOURCES

Lesson

Additional Notes

5.1 Using Decimals in a Shopping Context 1.1 Snacks from the Concession Stand

Combine Lessons 1 & 2, and just do warmup from Lesson 1 and Practice Problems from Lesson 1 & 2 5.1 Practice Problems #1 - 4, 7 5.2 Practice Problems #3, 4

5.3 Adding and Subtracting Decimals with Many Non-Zero Digits

Practice Problems #2, 3, 5 (calculator), 7, 8

3.1 Do the Zeros Matter? (Calculator on

#1, 2)

3.2 Calculating Sums (Only 2 & 3) 3.3 Subtracting Decimals of Different

Lengths (only 3)

5.4 Adding and Subtracting Decimals with Many Non-Zero Digits 4.2 Decimals All Around (#1, 3, 4)

Practice Problems #1, 3 (with scaffolding), 5, 6b, 6c

5.5 Decimal Points in Products

Practice Problems # 1a, 3(skip fraction part), 5, 6, 7

5.2 Fractionally Speaking: Powers of

Ten

5.6 Methods for Multiplying Decimals

Practice Problems #1, 2, 4, 5, 6

6.3 Using Area Diagrams to Reason

about Multiplication

5.8 Calculating Products of Decimals 8.3 Practicing Multiplication of Decimals Skip lessons 10 - 12 but do some Practice Problems and explicitly teach converting fractions to decimals

Use Practice Problems #4 & 6 from lesson 5.7 as a review 5.8 Practice Problems #4, 6, 7

5.10 Practice Problems #4, 5, 6 5.11 Practice Problems #1 (whole class), 2, 3(calculator), 4 (whole class) 5.12 Practice Problems #4, 5

5.13 Dividing Decimals by Decimals 13.1 Same Values

13.4: Just use a calculator on 1, 2, and 3 Practice Problems #1, 4 - 7

13.4 Practicing Division with Decimals

5.14 Using Operations on Decimals to Solve

Do the Rope and Turtle Problems only