6th Grade Math Guide

Instructional Guide 2026-2027

6 th Grade

Math

Instructional Guide 2026-2027

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

10

New scopes and sequences for new Reveal Curriculum.

10

Link to sample calendaring for adding in differentiation days on year at a glance.

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AI use in Math

59

Digital Tools in Math

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

Middle School Assessment Calendar

DWSBA dates

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 2026-2027

Scope and Sequence

Grade 6

YEAR AT A GLANCE

Unit 1 Math Is…

Unit 2 Understanding

Unit 3 Ratios and Rates

Unit 4 Understand and Use Percentages

Unit 5 Solve Area, Surface Area, and Volume Problems

Unit 6 Numerical and Algebraic Expressions

Unit 7 Integers, Rational Numbers, and the Coordinate Plane

Unit 8 Equations and Inequalities

Unit 9 Relationships Between Two Variables

Unit 10 Math Is…

the World Around Us Through Statistics

Aug 17 - Aug 28 (10 days)

Suggested Pacing

Aug 31 - Oct 6 (26 days)

Oct 7 - Nov 6 (20 days)

Nov 9 - Dec 2 (15 days)

Dec 3 - Jan 14 (21 days)

Jan 19 - Feb 19 (22 days)

Feb 22 - Mar 19 (19 days)

Mar 23 - Apr 20 (16 days)

Apr 21 - May 7 (13 days)

May 10 - May 27 (15 days)

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

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

6.NS.5 6.NS.6 6.NS.7 6.NS.8 6.G.3

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

6.RP.3

6.NS.1 6.NS.4 6.EE.1 6.EE.2 6.EE.3 6.EE.4 6.EE.6

6.EE.5 6.EE.6 6.EE.7 6.EE.8

6.EE.9

Standards

DWSBA & Testing Window

DWSBA #1

DWSBA #2

DWSBA #3

MAP Window

August 18 - September 24

December 2 - January 14

March 30 - May 7

Additional calendaring details with differentiation days

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.

Unit 1

MATH IS…

CALCULATOR

PACING

KEY LANGUAGE USES

No

August 17 - August 28 (10 days)

EXPLAIN

STANDARDS Math Practice Standard 3 Construct viable arguments and critique the reasoning of others. END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can see myself as a doer of mathematics. Language Supports: ●​ Vocabulary (strategy)

I can build mathematical habits of mind Language Supports: ●​ Vocabulary (analyze)

I can build an understanding of the norms of interaction that allow for a productive math learning environment. Language Supports: ●​ Vocabulary (strategy, norms)

LEARNING INTENTIONS

●​ I can describe the ways in which we are all doers of math. ●​ I can compare and contrast my math biography with those of my classmates.

●​ I can explain different ways to think about numbers. ●​ I can represent a real-world situation using mathematics.

●​ I can describe tools I can use to solve a problem. ●​ I can construct an argument to explain my thinking. ●​ I can explain my thinking with clear and appropriate terms. ●​ I can use patterns to develop efficient strategies to solve problems. ●​ I can explain why patterns are useful to solve problems. ●​ I can recognize the behaviors and attitudes that support a productive classroom learning environment. ●​ I can identify the mindsets that help me problem solve.

KEY VOCABULARY

●​ Inventory ●​ Quantities ●​ Strategy ●​ Analyze

●​ Model ●​ Rotation ●​ Visualize

●​ Cubic Units ●​ Volume ●​ Critique ●​ Justify

●​ Efficient ●​ Generalizations ●​ Reasonable

UNDERSTANDING THE WORLD AROUND US THROUGH STATISTICS

Unit 2

CALCULATOR

PACING

KEY LANGUAGE USES

Yes (Sections 2.8 - 2.10)

August 31 - October 6 (24 days)

EXPLAIN

STANDARDS Standard 6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students’ ages.

Standard 6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread/range and overall shape.

Standard 6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Standard 6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms and box plots. Choose the most appropriate graph/plot for the data collected.

Standard 6.SP.5 Summarize numerical data sets in relation to their context, such as by:

a. ​ Reporting the number of observations. b. ​ Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. ​ Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations (for example, outliers) from the overall pattern with reference to the context in which the data were gathered. d. ​ Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. 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. Standard 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can collect, analyze, and display data. Language Supports: ●​ Vocabulary (analyze, data) DIFFERENTIATION IN ACTION Skill Building

Have students find examples of formulas. Point out that formulas are like examples without words.

Extension

Mathematical Modeling: Water Conservation choice of projects.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

6.SP.1

2.1

6.SP.2

2.1, 2.2, 2.3, 2.4, 2.5, 2.8, 2.9

6.SP.3

2.3, 2.5, 2.8, 2.9

6.SP.4

2.1, 2.2, 2.4

6.SP.5

2.2, 2.3, 2.4, 2.5, 2.8, 2.9, 2.10

6.NS.2

2.6, 2.7, Additional Resources

6.NS.3

2.7

LEARNING INTENTIONS

●​ I can explain what a statistical question is. ●​ I can explain how a dot plot is used to represent the number of observations in a data set. ●​ I can use repeated reasoning to describe a data set based on the visual attributes of its data display. ●​ I can display numerical data in a histogram and explain how this type of display is different from a dot plot. ●​ I can use repetition to describe the data by its shape. ●​ I can use the median to describe a data set. ●​ I can use repeated reasoning to describe a data set using the median. ●​ I can describe a data set displayed in a box and whistler plot in terms of median, quartiles, and spread. ●​ I can attend to precision to compare two data sets displayed in box plots in terms of data distribution.

●​ I can use the interquartile range to describe the variability in a data set. ●​ I can use repeated reasoning to compare two data sets displayed in box plots. ●​ I can divide multi-digit whole numbers using an algorithm as a tool. ●​ I can extend the dividend two decimal places to address a remainder. ●​ I can divide a multi-digit decimal by a whole number using an algorithm. ●​ I can divide a multi-digit decimal by a decimal using an algorithm. ●​ I can use place-value patterns to divide with decimals. ●​ I can determine the mean of a data set. ●​ I can use a target mean to find a missing value in a data set. ●​ I can connect strategies for determining the mean.

●​ I can determine the mean absolute deviation (MAD) of a data set. ●​ I can compare data sets using the MAD. ●​ I can explain the concept of mean absolute deviation and how to determine it for a data set. ●​ I can determine the most appropriate measure of center and measure of variation to describe the data in relation to its context. ●​ I can describe visual displays of data with reference to symmetry and measures of center and variation.

KEY VOCABULARY

●​ Distribution ●​ Dot Plot ●​ Statistical Question ●​ Statistics ●​ Symmetric ●​ Interval ●​ Uniform ●​ Frequency Table ●​ Histogram ●​ Measure of Center

●​ Median ●​ Manipulate ●​ Utilize ●​ Box Plot ●​ Lower Extreme ●​ Quartile ●​ Upper Extreme ●​ Maximum ●​ Minimum ●​ Interquartile Range (IQR)

●​ Measures of Variation ●​ Range ●​ Denote ●​ Display ●​ Dividend ●​ Divisor ●​ Quotient ●​ Accurate ●​ Compute ●​ Compare ●​ Determine

●​ Mean ●​ Empirical ●​ Reveal ●​ Mean Absolute Deviation (MAD) ●​ Deviate ●​ Infer ●​ Cluster ●​ Gap ●​ Outlier ●​ Skewed ●​ Differentiate ●​ Exhibit

Unit 3

RATES AND RATIOS

CALCULATOR

PACING

KEY LANGUAGE USES

Yes

October 7 - November 6 (20 days)

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, find 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 finding 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 find a unit rate. Language Supports:

●​ Vocabulary (rate, unit rate, speed)

I can use my knowledge of ratios and unit rates to find a percent of a number and explain why it works. Language Supports: ●​ Vocabulary (percent, percentage) DIFFERENTIATION IN ACTION Skill Building Unit 3 Fluency Practice with multiplying fractions and mixed numbers.

Extension

Lesson 3.2 STEM Adventure: Students learn about fish farms, overfishing, and efforts to sustain fish populations. Then they use rates and ratios to make fish feed, analyze population data, and model how fishing rates affect fish populations.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

6.RP.1

3.1

6.RP.2

3.2

6.RP.3

3.3, 3.4, 3.5,3.6, 3.7

LEARNING INTENTIONS

●​ I can describe the relationship between quantities using ratios. ●​ I can make sense of quantities to represent ratios using tape diagrams and double number lines. ●​ I can make use of structure to describe a unit rate as a rate with 1 as the second term. ●​ I can use multiplication and division to generate equivalent ratios. ●​ I can use appropriate tools to explain whether a set of ratios is equivalent. ●​ I can represent ratios on a coordinate plane. ●​ I can look for structure on the graph of a ratio relationship to determine equivalent ratios. ●​ I can compare ratio relationships using tables. ●​ I can make sense of ratio problems and formulate a strategy to solve them. ●​ I can use ratio reasoning to convert between units of the same measurement system. ●​ I can reason abstractly and quantitatively to manipulate and transform units of measure.

●​ I can use ratio reasoning to convert units of different measurement systems. ●​ I can attend to precision to convert units of different measurement systems.

KEY VOCABULARY

●​ Unique ●​ Rate

●​ Identical ●​ Coordinate Plane ●​ Ordered Pairs ●​ Accurate ●​ Input ​ ●​ Equivalent Ratios

●​ Compare ●​ Inspect ●​ Double Number Line

●​ Double Number Line ●​ Part-to-part Ratio ●​ Part-to-whole Ratio ●​ Ratio ●​ Tape Diagram

●​ Unit Price ●​ Unit Rate ●​ Adapt ●​ Transform ●​ Equivalent Ratios ●​ Display

●​ Convert ●​ Decade ●​ Exhibit ●​ Reverse

●​ Term ●​ Topic

UNDERSTAND AND USE PERCENTAGES

Unit 4

CALCULATOR

PACING

KEY LANGUAGE USES

November 9 - December 2

EXPLAIN

Yes

STANDARDS 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, find 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 finding 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 understand what percentages indicate about real-world values and changes. Language Supports: ●​ Vocabulary (Percentage) I can use percentages to analyze and compare real–world problems involving percent. Language Supports: ●​ Vocabulary (Percent) DIFFERENTIATION IN ACTION Skill Building Unit 4 Fluency Practice with division and multi-digit decimals.

Extension

Lesson 4.3 STEM Adventure: Students learn about honey bees and the environmental factors that affect the health of a colony. Then they use percentages to monitor a honey bee hive’s population health.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

6.RP.3

4.1, 4.2, 4.3, 4.4, 4.5

LEARNING INTENTIONS

●​ I can understand the meaning of a percent as a rate per 100. ●​ I can explain that percentages greater than 100% represent numbers greater than 1. ●​ I can analyze decimal grids and tape diagrams that represent percentages to solve real-world problems. ●​ I can determine equivalent fractions, decimals, and percentages. ●​ I can connect the values of fractions and decimals to percentages. ●​ I can demonstrate how to estimate a percent and a percent of a number using benchmark percentages. ●​ I can attend to precision to estimate percentages and the percent of a number. ●​ I can determine the percent of a number by using double number lines or equations. ●​ I can find the percent, given the part and the whole, using equivalent fractions. ●​ I can use the correct vocabulary to describe the elements of a percent problem. ●​ I can determine the whole by visually representing the part and the percent. ●​ I can determine the whole by dividing the percent by 100, then dividing the part by the quotient. ●​ I can make sense of real-world percent problems and apply strategies to solve the problem.

KEY VOCABULARY

●​ Percent ●​ Ratio ●​ Foundation ●​ Visible

●​ Confirm ●​ Rational ●​ Percent ●​ Evaluate

●​ Exceed ●​ Discriminate ●​ Highlight

●​ Benchmark Percentages

●​ Estimate ●​ Flexible

SOLVE AREA, SURFACE AREA, AND VOLUME PROBLEMS

Unit 5

CALCULATOR

PACING

KEY LANGUAGE USES

December 3 - January 14 (21 days)

EXPLAIN

Yes

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 find 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 figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Standard 6.EE.2 Write, read, and evaluate expressions in which letters represent numbers. a. ​ Write expressions that record operations with numbers and with letters representing numbers. For example, express the calculation "Subtract y from 5" as 5 – y and express “Jane had $105.00 in her bank account. One year later, she had x dollars more. Write an expression that shows her new balance” as $105.00 + x. b. ​ Identify parts of an expression using mathematical terms (for example, sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity and a sum of two terms. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. c. ​ Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, applying the Order of Operations when there are no parentheses to specify a particular order. For example, use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2 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 Unit 5 fluency practice on applying operations with multi-digit decimals.

Extension

Lesson 5.1 STEM Adventure: Students put their geometry skills to work as an urban forester. They help calculate tree loss due to construction, plan areas for reforestation, and design furniture using salvaged wood from deforested urban land.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

6.G.1

5.1, 5.2, 5.3, 5.4

6.G.2

5.5

6.G.4

5.6, 5.7, 5.8

6.EE.2

5.1, 5.2, 5.3, 5.4, 5.5, 5.7, 5.8

LEARNING INTENTIONS

●​ I can find the area of parallelograms and rhombuses by composing them into rectangles. ●​ I can find the area of parallelograms and rhombuses by using a formula. ●​ I can attend to precision to find a missing dimension by using the area formula.

●​ I can find the area of a triangle by composing it into a parallelogram and by using a formula. ●​ I can attend to precision to find the missing dimension of a triangle by using the area formula. ●​ I can find the area of a trapezoid by decomposing it into triangles or composing it into a rectangle. ●​ I can make use of structure to find the area of a trapezoid by composing it into a rectangle or by using a formula. ●​ I can find the volume of rectangular prisms by filling them with unit cubes. ●​ I can find the volume of a rectangular prism by using a formula. ●​ I can attend to precision to find an unknown dimension of a rectangular prism by using the volume formula. ●​ I can use a three-dimensional figure to create a two-dimensional net. ●​ I can look for and make use of structure when using a two-dimensional net to find a three-dimensional figure.

●​ I can use nets and a formula to determine the surface area of rectangular prisms. ●​ I can use nets and a formula to determine the surface area of triangular prisms. ●​ I can look for and make use of structure to find the surface area of prisms. ●​ I can use nets and formulas to find the surface area of square pyramids ●​ I can use nets and formulas to find the surface area of triangular pyramids. ●​ I can look for and make use of structure to find the surface area of pyramids.

KEY VOCABULARY

●​ Diagonal ●​ Perpendicular ●​ Compute ●​ Determine ●​ Dimensions ●​ Composing ●​ Compare ●​ Explicit

●​ Isosceles Trapezoid ●​ Accurate ●​ Highlight ●​ Volume ●​ Reinforce ●​ Topic ●​ Net ●​ Pyramid

●​ Three-

●​ Infer ●​ Lateral ●​ Pyramid ●​ Denote ●​ Evaluate

Dimensional

●​ Two-

Dimensional

●​ Reveal ●​ Visual ●​ Congruent ●​ Surface Area ●​ Differentiate

NUMERICAL & ALGEBRAIC EXPRESSIONS

Unit 6

CALCULATOR

PACING

KEY LANGUAGE USES

No

January 19 - February 19 (22 days)

EXPLAIN

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

Standard 6.EE.2 Write, read, and evaluate expressions in which letters represent numbers. a. ​ Write expressions that record operations with numbers and with letters representing numbers. b. ​ Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity and a sum of two terms. c. ​ Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, applying the Order of Operations when there are no parentheses to specify a particular order.

Standard 6.EE.3 Apply the properties of operations to generate equivalent expressions.

Standard 6.EE.4 Identify when two expressions are equivalent.

Standard 6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, and number in a specified set.

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.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.Use the distributive property to express a sum of two whole numbers 1 - 100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2). END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can find quotients of fractions, whole numbers, and mixed numbers by using equations and models. Language Supports: ●​ Vocabulary (quotient, equation)

I can use the order of operations to evaluate numerical and algebraic expressions and create equivalent expressions. Language Supports: ●​ Vocabulary (expressions, equivalent)

I can find the greatest common factor or least common multiple of two numbers. Language Supports: ●​ Vocabulary (factor, multiple) DIFFERENTIATION IN ACTION Skill Building

Lesson 6.6 Take another look lessons to reinforce skills such as: ●​ Determine Equivalent Simple Expressions ●​ Determine Equivalent Complex Expressions Lesson 6.6 STEM Adventure: Students learn what practices help make agriculture sustainable. Then they use their knowledge of numerical and algebraic expressions to help solve problems as they farm and produce food in a sustainable way. Finally, they help a food truck calculate their profits.

Extension

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

6.EE.1

6.3, 6.4

6.EE.2

6.5

6.EE.3

6.8

6.EE.4

6.6

6.EE.6

6.5, 6.6, 6.8

6.NS.1

6.1, 6.2

6.NS.4

6.7, 6.8

LEARNING INTENTIONS

●​ I can use appropriate tools to divide whole numbers by fractions using fraction models. ●​ I can divide fractions by whole numbers using fraction models and equations. ●​ I can divide fractions by using fraction models or equations. ●​ I can divide mixed numbers and fractions by using fractions models or equations. ●​ I can attend to precision to divide fractions and mixed numbers.

●​ I can make sure of structure to write a product of factors to find its value. ●​ I can evaluate numerical expressions using the correct order of operations. ●​ I can make sense of problems to write numerical expressions. ●​ I can reason abstractly and quantitatively to write an algebraic expressions, using variables for any unknown quantities. ●​ I can use the order of operations to evaluate a multi-step algebraic expression for the given values. ●​ I can attend to precision to identify whether two expressions are equivalent. ●​ I can find the greatest common factor of two whole numbers.

●​ I can find the least common multiple of two whole numbers. ●​ I can make sense of problems to find the greatest common factor or least common multiple of two whole numbers. ●​ I can use repeated reasoning and the properties of operations to generate equivalent expressions.

KEY VOCABULARY

●​ Reciprocal ●​ Determine ●​ Differentiate ●​ Confirm ●​ Visual ●​ Exponent ●​ Factors ●​ Power ●​ Reinforce ●​ Terms

●​ Reverse ●​ Expression ●​ Order of Operations ●​ Evaluate ●​ Visible ●​ Algebraic Expression ●​ Coefficient ●​ Constant ●​ Like Term

●​ Substitution Property of Equality ●​ Variable ●​ Clarify ●​ Revise ●​ Associative Property ●​ Commutative Property ●​ Distributive Property

●​ Like Terms ●​ Factor ●​ Greatest Common Factor ●​ Least Common Multiple ●​ Multiple ●​ Analyze ●​ Presume ●​ Denote ●​ Unique

INTEGERS, RATIONAL NUMBERS, AND THE COORDINATE PLANE

Unit 7

CALCULATOR

PACING

KEY LANGUAGE USES

February 22 - March 19 (19 days)

EXPLAIN

No

STANDARDS Standard 6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (for example, temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

Standard 6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

a. ​ Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, for example: -(-3) = 3, and that 0 is its own opposite. b. ​ Understand that the signs of numbers in ordered pairs indicate their location in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. ​ Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

Standard 6.NS.7 Understand ordering and absolute value of rational numbers.

a. ​ Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example: Interpret –3 > –7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right. b. ​ Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 o C > –7 o C to express the fact that –3 o C is warmer than –7 o C. c. ​ Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world context. For example: for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. d. ​ Distinguish comparisons of absolute value from statements about order. For example: Recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

Standard 6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same x-coordinate or the same y-coordinate.

Standard 6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same x coordinate or the same y coordinate. Apply these techniques in the context of solving real-world and mathematical problems. END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS

I can reason about a situation involving negative numbers Language Supports: ●​ Vocabulary (negative, positive)

I can plot points on the coordinate plane, and describe the location of points. Language Supports: ●​ Vocabulary (coordinate)

DIFFERENTIATION IN ACTION Skill Building

Lesson 7.2 Take Another Look Lessons to reinforce skills such as ●​ Opposites on a Number Line ●​ Graph Different Forms (Rational Numbers) ​

Extension

Lesson 7.2 STEM Adventure: Students apply their understanding of integers and rational numbers to investigate if extreme weather is random or are there patterns to be observed?

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

6.NS.5

7.1, 7.2

6.NS.6

7.1, 7.2, 7.5, 7.6, 7.7

6.NS.7

7.3, 7.4

6.NS.8

7.6, 7.7

6.G.3

7.7

LEARNING INTENTIONS

●​ I can use integers to represent quantities in everyday life, and explain the meaning of zero within each real world context. ●​ I can reason abstractly and quantitatively to represent integers and their opposites on a number line. ●​ I can graph rational numbers and their opposites on vertical and horizontal numbers lines. ●​ I can look for and make use of structure to locate the opposite of a number on a numbers line. ●​ I can explain that the absolute value of a number is the distance between the number and zero on a number line. ●​ I can use repeated reasoning to find the absolute value of a number. ●​ I can use number lines to interpret statements of inequality of two rational numbers. ●​ I can attend to precision to write, interpret, and explain statements of order for rational numbers and distinguish between comparisons of absolute value from statements about order. ●​ I can determine in which quadrant a point (x, y) is located. ●​ I can identify and plot ordered pairs in the four quadrants of the coordinate plane. ●​ I can make use of structure to demonstrate a reflection of a point across one or both axes. ●​ I can count the units between two points to find the horizontal or vertical distance between points on the coordinate plane. ●​ I can make use of structure and the absolute values of the unlike x- or y-coordinates to find distances between points on the coordinate plane. ●​ I can use the absolute values of the unlike x- and y-coordinates to find side lengths of polygons drawn on the coordinate plane. ●​ I can make sense of problems involving polygons on the coordinate plane and formulate a strategy to solve them.

KEY VOCABULARY

●​ Integers ●​ Opposites ●​ Acknowledge ●​ Convert ●​ Opposites ●​ Rational Number ●​ Rational

●​ Reinforce ●​ Absolute Value ●​ Interval

●​ Quadrants ●​ Reflection

●​ X-coordinate ●​ Y-coordinate

●​ X-axis ●​ Y-axis ●​ Clarify ●​ Confirm

●​ Compare ●​ Identical ●​ Display ●​ Utilize

●​ Minimum ●​ Accurate ●​ Determine ​

EQUATIONS AND INEQUALITIES

Unit 8

CALCULATOR

PACING

KEY LANGUAGE USES

March 23 - April 20 (16 Days)

EXPLAIN

Yes

STANDARDS Standard 6.EE.5 Understand solving an equation or inequality as a process of answering the question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Standard 6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, and number in a specified set.

Standard 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + a = b and ax= b for cases in which a, b and x are all non-negative rational numbers.

Standard 6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can write and solve equations and inequalities involving one variable. Language Supports: ●​ Vocabulary (equation, inequality, solve)

DIFFERENTIATION IN ACTION Skill Building

Lesson 8.4 Take Another Look Lesson to reinforce representing real-world inequalities.

Extension

Lesson 8.4 STEM Adventure: Students apply their understanding of equations and inequalities to find out if the air we breathe every day is healthy or harmful.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

6.EE.5

8.1, 8.5

6.EE.6

8.1, 8.2, 8.3, 8.4, 8.5

6.EE.7

8.2, 8.3

6.EE.8

8.5

LEARNING INTENTIONS

●​ I can make sense of one-step equations in order to solve them using substitution. ●​ I can solve one-step equations using guess, check, and revise strategy. ●​ I can write and solve one-step addition equations using the Subtraction Property of Equality. ●​ I can write and solve one-step subtraction equations using the Addition Property of Equality. ●​ I can make sense of quantities to write and solve one-step equations. ●​ I can write and solve one-step multiplication equations using the Division Property of Equality. ●​ I can write and solve one-step division equations using the Multiplication Property of Equality. ●​ I can make sense of quantities to write and solve one-step equations. ●​ I can write inequalities to represent a real-world or mathematical problem. ●​ I can use repeated reasoning to understand ways that problems can be represented by inequalities. ●​ I can represent an inequality with an inequality statement or on a number line. ●​ I can find solutions of inequalities using substitution. ●​ I can make use of structure to graph solutions of inequalities on a number line.

KEY VOCABULARY

●​ Equation ●​ Confirm ●​ Estimate ●​ Addition

●​ Inverse

●​ Division

●​ Input ●​ Inequality ●​ Determine ●​ Revise ●​ Compare ●​ Display

Operations ●​ Subtraction Property of Equality

Property of Equality ●​ Multiplication Property of Equality ●​ Clarify

Property of Equality ​

●​ Exceed ●​ Isolate ​

RELATIONSHIPS BETWEEN TWO VARIABLES

Unit 9

CALCULATOR

PACING

KEY LANGUAGE USES

April 21 - May 7 (13 days)

EXPLAIN

Yes

STANDARD Standard 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can use tables and graphs to find and analyze the relationship between two quantities. Language Supports: ●​ Vocabulary (analyze, quantity)

I can write an equation to show the relationship between dependent and independent variables. ●​ Vocabulary (dependent, independent)

DIFFERENTIATION IN ACTION Skill Building

Lesson 9.3 Take Another Look Lesson to reinforce understanding of equations of two-variable relationships.

Extension

Lesson 9.3 STEM Adventure: Students apply algebraic thinking to investigate if glaciers are melting and if sea ice is shrinking.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

6.EE.9

9.1, 9.2, 9.3, 9.4

LEARNING INTENTIONS

●​ I can recognize when two quantities relate to each other, i.e., as one quantity changes independently, the other quantity changes in a related way. ●​ I can make sense of quantities to identify the independent variable and dependent variable and determine the value of the dependent variable given the relationship between two quantities. ●​ I can use a table and a graph to determine the relationship between two variable quantities. ●​ I can use a graph as a tool to analyze the relationship between two variable quantities.

●​ I can write an equation from a table to model the relationship between the dependent and independent variables. ●​ I can write an equation from a graph to model the relationship between the dependent and independent variables. ●​ I can write an equation to represent the relationship between two variable quantities and use it to solve a problem. ●​ I can make sense of problems to write and solve equations that represent relationships given a scenario in which there are multiple related variable quantities.

KEY VOCABULARY

●​ Dependent Variable ●​ Independent Variable

●​ Analyze ●​ Infer ●​ Determine ●​ Display

●​ Denote ●​ Reveal

●​ Compare ●​ Evaluate ●​ Identical

Unit 10

MATH IS…

CALCULATOR

PACING

KEY LANGUAGE USES

Yes

May 10 - May 27 (15 days)

EXPLAIN

STANDARDS Math Practice Standard 3 Construct viable arguments and critique the reasoning of others.

Math Practice Standard 4 Model with mathematics.

Math Practice Standard 7 Look for and make use of structure.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can explore different ways to use mathematics to represent and find creative solutions to real-world problems. Language Supports: ●​ Vocabulary (strategy)

I can use generalizations derived from repeated reasoning to solve problems. Language Supports: ●​ Vocabulary (pattern)

LEARNING INTENTIONS

●​ I can see applications of math outside of school. ●​ I can see the beauty in math. ●​ I can use bilateral symmetry to describe structure in nature and in human creations. ●​ I can use patterns or relationships to help me make sense of a puzzle or game and to think logically about solutions. ●​ I can use the playfulness of math to imagine different ways to visualize the problem.

●​ I can use models to come up with creative solutions to everyday problems. ●​ I can apply mathematics that I know to solace problems in everyday life. ●​ I can use models to come up with creative solutions to everyday problems. ●​ I can apply mathematics that I know to solve problems in everyday life. ●​ I can create and describe designs that are boundless. ●​ I can use patterns, repetition, and rhythm to create designs with math structure. ●​ I can see how my math biography has changed. ●​ I can recognize ways in which we are all doers of math.