6th Grade SPED Resource Mathematics Curriculum

6th Grade SPED Resource Mathematics Curriculum Course Description: In grade 6, instructional time will focus on four critical areas: (1) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (2) writing, interpreting, and using expressions and equations; (3) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; and (4) developing understanding of statistical thinking. Scope and Sequence:

Time Frame Unit

20 class periods Number Systems

21 class periods 24 class periods

Expressions & Equations

20 class periods 18 ½ class periods

Ratios & Proportional Relationships

10 class periods 14 class periods

Geometry

12 ½ class periods 6 class periods

Statistics

*This document contains the entire 6th Grade Math curriculum that is taught in a regular education setting. Items that are highlighted in yellow have been designated as priority information that should be taught in the 6th Grade Resource class.

Board Approved: July 23, 2015 2 | Page Revised, April, 2016 MLS Alignment: April, 2017

Curriculum Revision Tracking April, 2017 Unit 1:

• Pacing adjusted from 22 to 20 class periods Unit 2:

• Pacing adjusted from 31 class periods to 21 class periods • Topics 13 and 14 were removed from this unit and become unit 4.

Unit 4:

• This is an entirely new unit with topics 13 and 14 that used to be in Unit 2. April, 2016 Unit 1

● Pacing adjusted from 31 class periods to 22 class periods ● Topic 13 was moved to Unit 2 ● Order of topics changed to 8 & 9, 6, and 7

Unit 2:

● Pacing adjusted from 23 class periods to 31 class periods ● Topics 13 and 14 combined and added to this unit

Unit 4:

● Pacing adjusted from 12 to 12 ½ class periods


Unit 1: Number Systems

Subject: Mathematics Grade: 6 Name of Unit: Number Systems Length of Unit: 20 class periods Overview of Unit: Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems. Students extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane. Priority Standards for unit:

● Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

● MA.6.NS.A.1: Compute and interpret quotients of positive fractions. ○ Solve problems involving division of fractions by fractions.

■ For example, 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.) How much chocolate will each person get if 3 people share 1/2 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?

● Compute with non-negative multi-digit numbers, and find common factors and multiples.

● MA.6.NS.B.1: Demonstrate fluency with division of multi-digit whole numbers.

● MA.6.NS.B.2: Demonstrate fluency with addition, subtraction, multiplication and division of decimals.

● Apply and extend previous understandings of numbers to the system of rational numbers.

● MA.6.NS.C.2: Locate a rational number as a point on the number line. a. Locate rational numbers on a horizontal or vertical number line. b. Write, interpret and explain problems of ordering of rational

numbers. c. Understand that a number and its opposite (additive inverse) are

located on opposite sides of zero on the number line. ● MA.6.NS.C.3: Understand that the absolute value of a rational number is its

distance from 0 on the number line.


Supporting Standards for unit: ● MA.6.NS.C.1: Use positive and negative numbers to represent quantities. (e.g.,

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.

● MA.6.NS.C.4: Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

● MA.6.GM.A.3: Solve problems by graphing points in all four quadrants of the Cartesian coordinate plane.

a. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane

b. 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 distances between points with the same first coordinate or the same second coordinate.

d. Construct polygons in the Cartesian coordinate plane. ● MA.6.EEI.B.4: Solve one-step linear equations in one variable involving non-

negative rational numbers.

Priority Standard

Unwrapped Concepts (Students need to know)

Unwrapped Skills (Students need to be

able to do) Bloom’s

Taxonomy Levels Webb's DOK

6.NS.A1 quotients of positive

fractions Interpret Apply 1


fractions Compute Apply 1


fractions Solve Evaluate 4

6.NS.B2

fluency with division of multi-division of multi-

digit whole numbers Demonstrate Apply 1

6.NS.B3 fluency with addition of

decimals Add Apply 1

6.NS.B3 fluency with subtraction

of decimals Subtract Apply 1

6.NS.B3 fluency with

multiplication of decimals Multiply Apply 1

6.NS.B3 fluency with division of

decimals Divide Apply 1


6.NS.C6

Positive and negative numbers to represent

quantities. Use Remember 1

6.NS.C6

rational numbers on a horizontal or vertical

number line Locate Remember 1

6.NS.C6 Problems of ordering of

rational numbers Write Remember 1


rational numbers Interpret Analyze 2


rational numbers Explain Apply 2

6.NS.C6

A number and its opposite are located on opposite sides of zero

on the number line Understand Understand 1

6.NS.7b

The absolute value of a rational number is its distance from 0 on the

number line. Understand Understand 1

6.NS.7c

Absolute value as magnitude for a negative quantity in a real-world

situation Interpret Analyze 3

6.NS.7d

Comparisons of absolute value from statements

about order Distinguish Understand 2 Essential Questions:

1. How is dividing by a fraction like dividing by a whole number and how is it different? 2. How can the meaning of division be extended from whole numbers to fractions? 3. How can you extend the use of place value with whole number operations to decimal

operations? 4. How do you know when to use positive numbers and when to use negative numbers? 5. Why do we need positive and negative numbers?


Enduring Understanding/Big Ideas: 1. You can use a number line model to show division of whole numbers or division of

fractions: when you divide whole number, the quotient is always less than (or equal to) the dividend: when you divide fractions, the quotient can be greater than the dividend

2. When you divide whole numbers, the quotient is always less than or equal to the dividend. When you divide fractions, the quotient can be greater than the dividend.

3. Adding decimals is like adding whole numbers; in both situations you line up place values before you start. Multiplying decimals is like multiplying whole numbers, but you have to count up the number of decimal places in the factors and use that sum to place the decimal point in the product. Dividing decimals is like dividing whole numbers but if there is a decimal point in the divisor you have to multiply the divisor and the dividend by a power of ten before you start.

4. Positive numbers are used to describe quantities having a value greater than zero, Negative numbers are used to describe quantities having a value less than zero. Rational numbers include positive and negative fractions, integers, and decimals: You can compare rational numbers using the same ideas that you use to compare integers: before you use negative rational numbers to describe a situation, you should make sure you understand what zero means in the problem situation

5. Integers include positive and negative numbers: opposites and absolute value are important ideas when you solve problems with integers; before you use negative numbers to describe a situation, you should make sure you understand what zero means in the problem situation

Unit Vocabulary:

Topic Academic Cross-Curricular Words

Content/Domain Specific

8: Integers Compare Credit Debit

Deposit Describe

Directions Distance

Horizontal Justify Order

Mirror (image) Number Line

Signs Vertical

Withdrawal

Absolute Value Coordinate Plane

Integers Image

Line of Reflection Negative Numbers

Opposites Ordered Pair

Origin Positive Numbers

Quadrant Reflection

Transformation x-axis

x-coordinate


y-axis y-coordinate

9: Rational Numbers Compare Describe

Directions Distance

Horizontal Justify

Number Line Order Signs

Vertical

Polygon Rational Numbers

Segment Vertex

7: Decimals Area Compare

Equivalent Factors Interpret Justify Order

Perimeter Product

Algorithm Compatible numbers

Decimal Difference Dividend Divisor

Equation Quotient Rounding

Sum Whole number

6: Division of Fractions Compare Interpret Justify Order

Rounding

Denominator Divisor

Expression Improper Fractions

Mixed Numbers Numerator

Proper Fractions Reciprocal

Unit Fraction

Resources for Vocabulary Development: Use CI Quality tools


digits Topic 8: Integers and Topic 9: Rational Numbers

Note: Since Integers are a subset of Rational Numbers, it was decided to teach much of the Integers unit through the Rational Numbers unit so students will understand the relationship between the two types of numbers & to save time. It is imperative to ask guiding questions that lead students to the understanding of an Integer, Rational Number & that Integers are a type of Rational Number (i.e. 4 is both an integer & a rational number) Standard Topic &

Section Suggested # of Days

Notes TenMarks

Readiness Lesson

1 class period

Optional Readiness Lesson Topic 8:

● Comparing & Ordering Whole Numbers

● Comparing & Ordering Decimals

● Graphing in the First Quadrant of the Coordinate Plane

Topic 9: ● Writing Fractions as Decimals ● Comparing & Ordering

Decimals and Fractions ● Graphing on a Coordinate Plane

6.NS.C5, 6.NS.C6 6.NS.C6

8.1: Integers and the Number Line

½ class period

Combine with 8.3. Notice we are doing 8.2 when we do 9.3. 6.NS.6a The negative sign can also be read as, “the opposite of”. The standard states that students are expected to “recognize that the opposite of the opposite of a number is the number itself”. For example, -(-4)=4. Understanding that the negative sign also means “the opposite of” will greatly help in Algebra where they have -x = 15. They can read it as, “The opposite of x is 15.” Rather than, “Negative x is 15.” 6.NS.6c requires both horizontal and vertical number lines. 8-1 does not explicitly show/use vertical number lines. There is an opportunity in Part 3 when talking about elevation. May want to add more opportunities for students to use vertical number lines.

Using integers to represent quantities Identifying Opposite Numbers Rational Numbers on Number Lines and Coordinate Planes

6.NS.C.6 Lesson 6: Rational Numbers on

½ class period

Supplemental Material Emphasize the importance of accuracy when creating number lines. Students


the Number Line

may want to use rulers to ensure there are equal segments.

6.NS.C.6 Lesson 7: Ordering Integers and Other Rational Numbers

½ class period

6.NS.C.6 Lesson 8: Ordering Integers and Other Rational Numbers

½ class period

6.NS.C.6 Lesson 9: Comparing Integers and Other Rational Numbers

½ class period

6.NS.C.7

Lesson 10: Writing and Interpreting Inequality Statements Involving Rational Numbers

½ class period

6.NS.C.7

8.3: Absolute Value

½ class period

Discuss “distance vs direction”. Distance is always positive, because it is how far. Direction describes what way you are going that distance (positive, negative, north, south, etc.).

Understanding Absolute Value and Rational Numbers Absolute Value and Statements About Order

6.NS.C.5 6.NS.C.6

9.1: Rational Numbers and the Number Line

6.NS.C.7 9.2: Comparing Rational Numbers


6.NS.C.6 6.NS.C.7

8.2: Comparing and Ordering Integers 9.3: Ordering Rational Numbers

6.NS.C.6

8.4: Integers and the Coordinate Plane 9.4: Rational Numbers and the Coordinate Plane

1 class period

This is the first time students see plotting points in Quadrants II-IV. 8-4: Teaches the basics of graphing in all 4 Quadrants using Integers 9-4 Applies graphing with Rational Numbers in all 4 Quadrants. No review of coordinate plane essentials.

Opposite Numbers on the Coordinate Plane Rational Numbers on Number Lines and Coordinate Planes

6.NS.C.7 8.5: Distance ½ class period

Review “distance vs direction”. Distance is always positive, because it is how far. Direction describes what way you are going that distance (positive, negative, north, south, etc.). Review expressions for finding perimeter of rectangles and squares, and area of rectangles, squares and triangles

Solving Problems with Points on the Coordinate Plane

6.NS.C6 6.GM.A.1

9.5: Polygons in the Coordinate Plane

½ class period

When naming polygons, make sure students know they can start at any vertex, but must name the rest of the vertices in clockwise or counterclockwise order. SPED MODIFICATION: Give students graph paper to do examples and if needed, assign paper/pencil homework instead of online.

Polygons on a Coordinate Plane

6.NS.C.6 6.NS.C.7 6.GM.A.1

8.6: Problem Solving 9.6: Problem Solving Review for Test

½ class period

Post-Test 1 class period


digits Topic 6: Division of Fractions

Standard Topic & Section

Suggested # of Days

Notes TenMarks

Readiness Lesson

1 class period

Highly Recommended Readiness Lesson: Making Pizzas Reviews:

● Multiply Fractions ● Simplify Fractions ● Dividing Whole Numbers ● Write a mixed number as

an Improper Fraction ● Write an Improper

Fraction as a mixed number

● Cross Simplify

To review these skills, it is a 5th grade standard in Ten Marks.

6.NS.A.1 6.1: Dividing Fractions and Whole Numbers

½ class period

The number line models are difficult for students to understand. Review the divisibility rules in Math Ed. Digits emphasizes the inverse operation to show the relationship between multiplication & division of fractions. A review of Fact Families with whole numbers, prior to this lesson, may help with understanding.

Dividing Fractions and Whole Numbers

6.NS.A.1 6.2: Dividing Unit Fractions by Unit Fractions

½ class period

Dividing Two Fractions

6.NS.A.1 6.3: Dividing Fractions by Fractions

1 class period

Review cross simplifying and area. Review reading fractions on a number line

Dividing Two Fractions

6.NS.A.1 6.4: Dividing Mixed Numbers

1 class period

Review converting from mixed to improper

Dividing Fractions and Mixed Numbers


6.NS.A.1 6.EEI.B.4

6.5: Problem Solving and Review for Test

½ class period

Solving Problems Involving the Division of Fractions

6.NS.C.1 Post-Test 1 class period


digits Topic 7: Decimals


Suggested # of Days

Notes TenMarks

Readiness Lesson

1 class period

Optional Readiness Lesson: Fast Food Nutrition Reviews:

● Adding & Subtracting Whole Numbers

● Multiplying Whole Numbers (algorithm & expanded form)

● Dividing by Single-Digit Whole Numbers

6.NS.B3 7.1: Adding and Subtracting Decimals

½ class period

Emphasize place value when adding & subtracting decimals. For example: 23.45 - 1.23 “five-hundredths minus three-hundredths is how many hundredths?” replaces “five minus three is 2”

Estimate all operations answers: Multi-digit decimals Add/Subtract/Multiply/Divide: Multi-digit decimals

6.NS.B3 7.2: Multiplying Decimals

1 class period

Examples in Digits include finding area and rounding money Place value when multiplying whole numbers is emphasized in elementary. For example: 48.23 x 3.9, “three times forty” replaces “three times four”

Estimate all operations answers: Multi-digit decimals Add/Subtract/Multiply/Divide: Multi-digit decimals

6.NS.B.2 7.3: Dividing Multi-Digit Numbers

1 class period

Use compatible numbers to estimate the quotient, problems involving area are included again. Review vocabulary: divisor, dividend & quotient; Review translating from 243 ÷23 to long-division form.

Dividing multi-digit numbers


Uses “R” for remainder in this section. No adding a decimal and/or 0’s when there is a remainder.

6.NS.B.3 7.4: Dividing Decimals

1 class period

Dividing decimals by whole numbers and dividing decimals by a decimal This is the first time students have been asked to add a decimal and/or 0, instead of using R for remainder. Emphasize they are multiplying both the divisor & dividend by 10 each time they move the decimal to the right

Estimate all operation answers: Multi-digit decimals Add/subtract/multiply/divide: Multi-digit decimals

6.NS.C.8 7.5: Decimals and Fractions

Do not teach this section. This is not an explicit 6 standard, but it is a skill needed. Addressed in Math Ed during September.

6.NS.C.7 7.6: Comparing and Ordering Decimals and Fractions

Do not teach this section. This skill will be addressed during Topic 8 & 9.

6.NS.C.7 6.EEI.B.4


1 class period

This section has students writing & solving one-step equations involving decimals & fractions. May want to come back to this after students learn to solve one-step equations.



Unit 2: Expressions & Equations

Subject: Mathematics Grade: 6 Name of Unit: Expressions & Equations Length of Unit: 31 class periods Overview of Unit: Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expression, and use expression and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students construct and analyze tables, such as tables of quantities that are in equivalent rations, and they use equations (such as 3x=y) to describe relationships between quantities. Priority Standards for unit:

● Apply and extend previous understandings of arithmetic to algebraic expressions.

● MA.6.EEI.A.1: Describe the difference between an expression and an equation.

● MA.6.EEI.A.2: Create and evaluate expressions involving variables and whole number exponents. ○ Identify parts of an expression using mathematical terminology. ○ Evaluate expressions at specific values of the variables. ○ Evaluate non-negative rational number expressions. ○ Write and evaluate algebraic expressions. ○ Understand the meaning of the variable in the context of the

situation. ● MA.6.EEI.A.3: Identify and generate equivalent algebraic expressions

using mathematical properties. ○ For example, apply the distributive property to the expression 3 (2

+ x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

● Reason about and solve one-variable equations and inequalities. ● MA.6.EEI.B.1: Use substitution to determine whether a given number in

a specified set makes a one-variable equation or inequality true. ● MA.6.EEI.B2: Understand that if any solutions exist, the solution set for

an equation or inequality consists of values that make the equation or inequality true.


● MA.6.EEI.B.3: Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation.

● MA.6.EEI.B.4: Solve one-step linear equations in one variable involving non-negative rational numbers.

● MA.6.EEI.B.5: Recognize that inequalities may have infinitely many solutions.

a. Write an inequality of the form x > c, x < c, x ≥ c, or x ≤ c to represent a constraint or condition.

b. Graph the solution set of an inequality. Supporting Standards for unit:

● MA.6.EEI.B.5: Recognize that inequalities may have infinitely many solutions.

a. Write an inequality of the form x > c, x < c, x ≥ c, or x ≤ c to represent a constraint or condition.

b. Graph the solution set of an inequality. ● MA.6.EEI.B.3: Write and solve equations using variables to represent

quantities, and understand the meaning of the variable in the context of the situation.

● MA.6.EEI.B.4: Solve one-step linear equations in one variable involving non-negative rational numbers.

● MA.6.EEI.C.1: Identify and describe relationships between two variables that change in relationship to one another.

a. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable.

b. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other.

● MA.6.NS.B.3: Find common factors and multiples. a. Find the greatest common factor (GCF) and the least common

multiple (LCM). b. Use the distributive property to express a sum of two whole

numbers with a common factor as a multiple of a sum of two whole numbers.

● MA.6.GM.A.1: Find the area of polygons by composing or decomposing the shapes into rectangles or triangles.

● MA.6.GM.A.2: Find the volume of right rectangular prisms. a. Understand that the volume of a right rectangular prism can be

found by filling the prism with multiple layers of the base. b. Apply V = l * w * h and V = Bh to find the volume of right

rectangular prisms. ● MA.6.GM.A.4: Solve problems using nets.


a. Represent three-dimensional figures using nets made up of rectangles and triangles.

b. Use nets to find the surface area of three-dimensional figures whose sides are made up of rectangles and triangles.

Priority Standard


Unwrapped Skills (Students need to

be able to do)

Bloom’s Taxonomy

Levels Webb's DOK

6.EEI.A.1 difference between an expression and

an equation Describe Remember 1

6.EEI.A.2a parts of an expression using mathematical terminology Identify

6.EEI.A.2b expressions at specific values of the

variables Evaluate

6.EEI.A.2c non-negative rational number

expressions Evaluate 6.EEI.A.2d algebraic expressions Write 6.EEI.A.2d algebraic expressions Evaluate

6.EEI.A.2e the meaning of the variable in the

context of the situation Understand

6.EEI.A.3 equivalent algebraic expressions using mathematical properties Identify

6.EEI.A.3 equivalent algebraic expressions using mathematical properties Generate

6.EEI.B.1

substitution to determine whether a given number in a specified set

makes a one-variable equation or inequality true Use Apply 2

6.EEI.B.2

that if any solutions exist, the solution set for an equation or

inequality consists of values that make the equation or inequality true Understand Understand 2

6.EEI.B.3 equations using variables to represent

quantities Write Evaluate 3

6.EEI.B.3 equations using variables to represent

quantities Solve Evaluate 4

6.EEI.B.3 the meaning of the variable in the

context of the situation Understand Understand 1

6.EEI.B.4

one-step linear equations in one variable involving non-negative

rational numbers Solve Evaluate 4

6.EEI.B.5a

an inequality of the form x>c, x<c, x≥c, or x≤c to represent a constraint

or condition Write Evaluate 3 6.EEI.B.5b the solution set of an inequality Graph Apply 1


6.EEI.C.1a

an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent

variable Write Evaluate 3

6.EEI.C.1b

the relationship between the dependent and independent variables

using graphs, tables and equations Analyze Analyze 3 6.EEI.C.1b these representations to each other Relate Analyze 3 Essential Questions:

1. How are mathematical equations used to represent real-world situations? 2. What is an advantage of using mathematical expressions? 3. What are properties? How are properties useful? 4. How can you represent relationships that are equal? How can you represent relationship

that are not equal? Why would you want to? 5. How are two-variable relationships different from one-variable relationships? When do

you need two variables? Enduring Understanding/Big Ideas:

1. A lot of real world situation can be represented with numbers. 2. When you don’t know all of the information, a numerical expression isn’t enough and

you need to write an algebraic expression 3. They allow you to rewrite expression in different ways. Rewriting an expression allows

you to see the problem in a new way, which can sometimes help you see a solution path, or a new way of looking at the problem

4. You can represent a relationship with a verbal description, math symbols, or you can draw a diagram. You can write an equation to represent an equal relationship. You can write an inequality to represent an unequal relationship.

5. Sometimes there are two unknown quantities in a problem situation, so you need two variables. In a two variable situation, a change in one quantity affects the other quantity. You can solve an equation with one variable by undoing operation, and the answer is usually a single number. Equations with two variables have many solutions, and you can find one of the solutions by substituting a value for one of the variables and solving for the other variable.


Unit Vocabulary:

Topic Academic Cross-Curricular Words Content/Domain Specific

1: Variable and Expressions

Base Equivalent Evaluate

Inequality Power

Quantities Variable

Algebraic Expressions Coefficient Constant Equation

Equivalent Equations Equivalent Expressions

Expression Exponent

Numerical Expression Order of Operations

Quantity Term

Variable Variable Quantity

2: Equivalent Expressions

Apply Equivalent Illustrate Substitute

Not teaching, but may need

addressing: *Associative Property

*Commutative Property *Identity Property

*Zero Property

Common Multiple Composite Numbers Distributive Property

Greatest Common Factor Least Common Multiple

Multiple Prime Factorization

Prime Numbers Properties

Whole Numbers

3: Equations and Inequalities

Balancing Equivalent Evaluate Infinite

Number Line

Equation Equivalent Expressions

False Equation Inequality

Inverse Operations Open Sentence

Solution True Equation

4: Two-Variable Relationships

Analyze Classify Express Patterns Relate

Substitute

Constant Coordinate Plane

Dependent Variable Independent Variable

Resources for Vocabulary Development: Use CI Classroom quality tools


digits Topic 1: Variables and Expressions


Suggested # of Days

Notes TenMarks

Readiness Lesson

Life Ed Optional Readiness Lesson: Rating Music Artists Reviews:

● Adding whole numbers

● Subtracting whole numbers

● Multiplying whole numbers

6.EEI.A.2a 6.EEI.A.2c

1.1: Numerical Expressions

½ class period

Identifying Equivalent Expressions by Evaluation

6.EEI.A.2b 6.EEI.B.2 6.EEI.B.3

1.2: Algebraic Expressions

½ class period

Parts of an Expression Writing Equations Using Variables

6.EEI.A.2a 6.EEI.B.2 6.EEI.B.3

1.3: Writing Algebraic Expressions

½ class period

Students need to define the variable used for each expression written.

Translate Addition Sentences to Algebraic Expressions Translate Subtraction Sentences to Algebraic Expressions Translate Multiplication Sentences to Algebraic


Expressions Translate Division Sentences to Algebraic Expressions Identifying Expressions that Represent Situations

6.EEI.A.2c

1.4: Evaluating Algebraic Expressions

½ class period

Using Order of Operations to Evaluate Expressions

6.EEI.A.1 6.EEI.A.2c

1.5: Expressions with Exponents

½ class period

May use calculator for exponents SPED MODIFICATIONS: Use time in Life Ed to review exponents.

Exponents Using Order of Operations to Evaluate Expressions

6.EEI.A.2a 1.6: Problem Solving & Review for Test

1 class period

This is the first time the bar diagrams are introduced in digits. Students use them quite a bit in elementary. Bar diagrams are very helpful for students to visually see what is happening when writing expressions, and later equations. If you are not familiar with using bar diagrams to write expressions, this video explains them fairly well. https://www.youtube.com/watch?v=iSTP8WWLveg


https://www.youtube.com/watch?v=iSTP8WWLveg

https://www.youtube.com/watch?v=iSTP8WWLveg


digits Topic 2: Equivalent Expressions

Standard Topic & Section Suggested # of Days

Notes TenMarks

Readiness Lesson

1 class period

Optional Readiness Lesson: Renting Movies Reviews:

● Writing & Simplifying Numerical Expressions

● Writing Algebraic Expressions

● Evaluating Algebraic Expressions

2.1: The Identity and Zero Properties

Do Not Teach - Addressed in Math Ed SPED MODIFICATION: Discuss with team math teachers on including our LifeEd/Strategies students

Identity and Zero Property Applying Properties of Operations

2.2: The Commutative Properties


Commutative Property

2.3: The Associative Properties


Associative Property


6.NS.B.4 2.4: Greatest Common Factor

½ class period

GCF will also be covered in Math Ed. Lesson 2.4 uses Prime Factorization to teach GCF Optional calculator to find factors SPED MODIFICATIONS: Allow students to use a calculator and/or a multiplication chart to find factors

Identifying the Greatest Common Factor

6.NS.B.4 6.EEI.A.3

2.5: The Distributive Property

½ class period

Identifying Equivalent Expressions: The Distributive Property

6.NS.B.4 2.6: Least Common Multiple

½ class period

Optional calculator SPED MODIFICATIONS: Allow students to use a calculator and/or a multiplication chart to find factors

Identifying the Least Common Multiple

6.NS.B.4 6.EEI.A.3

2.7: Problem Solving & Review for Test

1 class period

2.7 Reviews all of the properties in this topic.



digits Topic 3: Equations and Inequalities


Notes TenMarks

Readiness Lesson

1 class period

Optional Readiness Lesson: Video Game Economics Reviews:



● Comparing numbers using <, =, and >

6.EE.A.2 6.EE.B.1

3.1: Expressions to Equations

½ class period

Emphasize to students that an equation is two expressions that have the same value or are equal to each other. Correct any misconception that one side of the equal sign is the “answer”. The whole number “answer” is an expression, also.

Using Substitution to Determine Solutions

3.2: Balancing Equations

1 class period

Balancing Equations is not explicitly required by the standards. However, it builds a solid foundation for students to understand how & why the process to solve equations works. Optional Activity - Matching Balancing Equations Cards

6.EEI.B.4 3.3: Solving Addition & Subtraction Equations

½ class period

SPED MODIFICATION: Review/reteach in Life Ed

Solving Word Problems Involving Equations


6.EEI.B.4 3.4: Solving Multiplication & Division Equations

½ class period

SPED MODIFICATION: Review/reteach in Life Ed

Solving Word Problems Involving Equations

6.EEI.B.5 3.5: Equations to Inequalities

½ class period

6.EEI.B.1 6.EEI.B.5

3.6: Solving Inequalities

½ class period

Students are not expected to solve inequalities using inverse operations. Students are only expected to solve inequalities by substituting values in for the variable.

Using Substitution to Determine Solutions Solving Word Problems Involving Inequalities

6.EEI.B.4 6.EEI.B.1


1 class period

Bar Diagrams are used to help students write equations from word problems. This tool is very a very helpful scaffold for students who may struggle converting words into an equation. If you are not familiar with using bar models to write and solve equations, there are 4 videos at the link below to help you. https://learnzillion.com/lessonsets/577-solve-problems-by-writing-and-solving-equations-of-the-form-x-p-q-and-px-q


https://learnzillion.com/lessonsets/577-solve-problems-by-writing-and-solving-equations-of-the-form-x-p-q-and-px-q





digits Topic 4: Two-Variable Relationships


Notes TenMarks

Readiness Lesson

1 class period

Optional Readiness Lesson: Working at an Amusement Park Reviews:



● Graphing on a Coordinate Plane

6.EEI.C.1 4.1: Using Two Variables to Represent a Relationship

½ class period

Independent and Dependent Variables and Equations

6.EEI.C.1

4.2: Analyzing Patterns Using Tables and Graphs

½ class period

Emphasize accuracy & precision when creating graphs. Students should label axes, have equal intervals and a title. (MP 6)


6.EEI.C.1

4.3: Relating Tables and Graphs to Equations

½ class period


6.EEI.A.2c 6.EEI.C.1


1 class period


U


Unit 3: Ratios & Proportions

Subject: Mathematics Grade: 6 Name of Unit: Ratios & Proportions Length of Unit: 20 class periods/24 class periods Overview of Unit: Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates. Priority Standards for unit:

● 6.RP.A.1 Understand a ratio as a comparison of two quantities and represent these comparisons.

○ For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

● 6.RP.A.2 Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate.

○ For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (non-complex fractions)

● 6.RP.A.3 Solve problems involving ratios and rates. ○ For example, by reasoning about tables of equivalent ratios, tape diagrams,

double line diagrams, or equations. A. Create tables of equivalent ratios, find missing values in the tables

and plot the pairs of values on the Cartesian coordinate plane. B. Solve unit rate problems

● For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

C. Solve percent problems. ● (e.g., 30% of a quantity means 30/100 times the quantity);

solve problems involving finding the whole, given a part and the percent.

D. Convert measurement units within and between two systems of measurement


Priority Standard



able to do)

Bloom’s Taxonomy

Levels Webb's DOK

6.RP.A.1 a ratio as a comparison of two

quantities Understand Understand 1 6.RP.A.1 these comparisons Represent create 2

6.RP.A.2 the concept of a unit rate associated

with a ratio Understand understand 2 6.RP.A.2 the meaning of unit rate Describe understand 1 6.RP.A.3a tables of equivalent ratios create create 2 6.RP.A.3a missing values in the tables find Apply 1

6.RP.A.3a the pairs of values on the Cartesian

coordinate plane plot apply 2 6.RP.A.3b unit rate problems solve evaluate 3 6.RP.A.3c percent problems solve evaluate 3

6.RP.A.3d

measurement units within and between two systems of

measurement convert apply 2 Essential Questions:

1. Which models are helpful in which situations? 2. How are models helpful in making comparisons? 3. Why might one representation be more useful than another?

Enduring Understanding/Big Ideas:

1. Usefulness of equivalent ratios/fractions for making predictions and scaling up and down. Usefulness of ratios as fractions for comparing terms of ratios. Usefulness of ratios as decimals for comparing ratios. A rate is a number that compares two quantities with different units. Comparing unit prices is helpful when you have to decide what to purchase. You can use rates to convert measurements from one unit to another.

2. Two ratios that are equivalent form a proportion. You can use tables, graphs, and equations to represent a proportional relationship and make comparisons. You can use a percent to represent a part to a whole ratio.

3. Being able to analyze a situation and communicate it effectively.


Unit Vocabulary:



10: Ratios Analyze Compare Describe Equality Model Reduce

Equation Equivalent Ratio

Decimal Formula

Greatest Common Factor Isolate the Variable

Ratio Simplest Form Terms of a ratio

11: Rates Analyze Conversion

Metric vs Customary Relationship

Constant speed Equation Fraction

Rate Ratios

Reciprocal Unit Rate

12: Ratio Reasoning Analyze Graphing Plotting

Proportionality

Coordinate plane Equivalent ratios

Expression Ordered pairs

Percent Ratio

Resources for Vocabulary Development: Use CI Classroom Quality Tools


digits Topic 10: Ratios


Notes TenMarks

Readiness Lesson

1 class period

Optional Readiness Lesson: Working with Playlists Reviews:

● Dividing Whole Numbers

● Represent Fractions ● Simplify Fractions

6.RP.A.1 10.1: Ratios ½ class period

Also asks for students to explain in words the ratio. For example: For every 4 chairs, there was 1 table. digits does not ask for this language. Provide opportunities for students to use this ratio language, both verbal and written forms. The Key Concept addresses the different types of ratios (Part:Part, Part:Whole & Whole:Part), however there is not much reference throughout the rest of the topic. Provide opportunities for students to explain what type of ratio is in the different examples and/or homework problems.

Representing Ratios

6.RP.A.1 6.RP.A.3a

10.2: Exploring Equivalent Ratios

½ class period

Explicitly states that students use a multiplication chart to find equivalent ratios. A multiplication chart might already be in your interactive notebook from earlier in the year.

6.RP.A.1 6.RP.A.3a

10.3: Equivalent Ratios

½ class period

Double number lines are used as a model. If you are not familiar with double number lines, this video will explain. https://learnzillion.com/lessons/588-solve-ratio-problems-using-double-number-lines

Ratio Tables and Graphs

https://learnzillion.com/lessons/588-solve-ratio-problems-using-double-number-lines





6.RP.A.1 6.RP.A.3a

10.4: Ratios as Fractions

½ class period

Review simplifying fractions. Representing Ratios

6.RP.A.1 10.5: Ratios as Decimals

1 class period

Allow calculators when converting non-benchmark ratios into decimals. Students should use prior knowledge to convert ratios written as decimal-fractions to fractions. Students are not required to convert using long-division until 7th grade

Representing Ratios

6.RP.A.1 6.RP.A.3a


1 class period

Representing Ratios Ratio Tables and Graphs



digits Topic 11: Rates


Notes TenMarks

Readiness Lesson 1 class period

Optional Readiness Lesson: School Fundraisers Reviews:

● Multiplying Decimals and Whole Numbers

● Writing and Comparing Fractions

● Solving Multiplications

6.RP.A.2 11.1: Unit Rates ½ class period

Ask students to state the rate and the unit rate. digits focuses on the unit rate. Provide opportunities for students to state the rate prior to finding the unit rate. SPED MODIFICATIONS: Review/Reteach in Life Ed Use visuals to model situations Do homework as whole group guided practice.

Expressing Unit Rate

6.RP.A.2 6.RP.A.3b

11.2: Unit Prices ½ class period

Students should attend to precision by correctly labeling each price.

Expressing Unit Rate Solving Problems Involving Unit Rate

6.RP.A.2 6.RP.A.3b

11.3: Constant Speed

1 class period

Review solving one-step equations.

Expressing Unit Rate Solving Problems Involving Unit Rate

6.RP.A.2 6.RP.A.3d

11.4: Measurements and Ratios

1 class period

Students are expected to use dimensional analysis when converting units.

Expressing Unit Rate Converting


When teaching dimensional analysis, focus on units first, before including numbers into the equation. Review types of measurements, customary vs metric SPED MODIFICATIONS: Allow students to use a measurement conversion chart.

Measurement Units Using Ratio Reasoning

6.RP.A.2 6.RP.A.3d

11.5: Choosing the Appropriate Rate

1 class period

Students are expected to use dimensional analysis when converting units. SPED MODIFICATIONS: Have students convert by multiplying and dividing instead of dimensional analysis.

Expressing Unit Rate Converting Measurement Units Using Ratio Reasoning

6.RP.A.2 10.6: Problem Solving and Review for Test

1 class period

Expressing Unit Rate



digits Topic 12: Ratio Reasoning


Notes TenMarks


Optional Readiness Lesson: Recycling Reviews:


● Finding Equivalent Ratios

● Graphing in the Coordinate Plane

6.RP.A.3a 12.1: Plotting Ratios and Rates

½ class period

Review graphing in the coordinate plane. digits does not explain the relationship between the equivalent ratios & the linear equation until 12.2. Spend time helping the students understand the relationship in Part 2 Example before moving on. Emphasize accuracy & precision when creating graphs. Students should label axes, have equal intervals and a title. (MP 6


6.RP.A.3a 6.RP.A.2

12.2: Recognizing Proportionality

½ class period

Review simplest form and equivalent fractions. We do not teach part 3. Students are not expected to recognize a proportional relationship algebraically in 6. May want to supplement more examples using tables and graphs.


6.RP.A.3c

12.3: Introducing Percents

½ class period

Use 10x10 grids for shading percents.

Expressing Percents

6.RP.A.3c 12.4: Using ½ class During the Examples & Got Its, Expressing


Percents period review the different scenarios of part:part, part:whole, and whole:part ratios. Also, discuss how a part:part ratio can lead to a part:whole ratio. Students are not expected to set up and solve proportions in 6. This is a 7th grade standard. 6’s focus is for students to have an understanding of what determines a proportional relationship. Emphasize the part: whole relationship in Part 4. Review circle graphs.

Percents Percent Relationships Solving Percent Word Problems

6.RP.A.3c


1 class period

Percent Relationships Solving Percent Word Problems



Unit 4: Geometry

Subject: Mathematics Grade: 6 Name of Unit: Geometry Length of Unit: 10 class periods/14 class periods Overview of unit: The Geometry unit in Grade 6 consists of two topics, one on area and one on surface area and volume. The underlying theme for the unit is helping students understand where formulas come from, so that they can recreate a formula if they forget it. Decomposing two- and three-dimensional figures is an important lesson in looking at the information they are given and seeing where else it can lead. This skill is important for students’ continued success in geometry and is the goal of the seventh Standard for Mathematical Practice of the Common Core State Standards, look for and make use of structure. Once students understand where formulas are derived from, you can encourage them to use formulas to make calculations easier. The study of surface area is new, and decomposition in the form of nets can help students connect a new concept to previous learning. Only prisms and pyramids are included. The study of volume is limited to rectangular prisms, which can easily be decomposed into unit squares. Students will encounter surface area and volume again in Grades 7 and 8; this Grade 6 topic is where they gain a general understanding of both concepts. Priority Standards for unit:

● G.GM.A.1 Find the area of polygons by composing or decomposing the shapes into rectangles or triangles.

● 6.GM.A.2 Find the volume of right rectangular prisms. A. Understand that the volume of a right rectangular prism can be found fy filling

the prism with multiple layers of the base. B. Apply V = L * w * h and V=BH to find the volume of right rectangular prisms.

● 6.GM.A.3 Solve problems by graphing points in all four quadrants of the Cartesian coordinate plane.

A. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane.

B. 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 distances between points with the same first coordinate or the same second coordinate.

D. Construct polygons in the Cartesian coordinate plane. ● 6.GM.A.4 Solve problems using nets.

A. Represent three-dimensional figures using nets made up of rectangles and triangles.

B. Use nets to find the surface area of three-dimensional figures whose sides are made up of rectangles and triangles.


Supporting Standards for unit: ● 6.DSP.A.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.

● 6.NS.C.2 Locate a rational number as a point on the number line. A. Locate rational numbers on a horizontal or vertical number line. B. Write, interpret and explain problems of ordering of rational numbers. C. Understand that a number and its opposite (additive inverse) are located on

opposite sides of ze D. Understand a rational number as a point on the number line.

Priority Standard



able to do)

Bloom’s Taxonomy

Levels Webb's DOK

6.GM.A.1

Find the area of polygons by composing or decomposing shapes

into rectangles or triangles Find Analyze 2

6.GM.A.2a

Understand that the volume of a right rectangular prism can be found by

filling the prism with multiple layers of the base. Understand Understand 2

6.GM.A.2b

Apply V=l*w*h and V=b*h to find the volume of right rectangular

prisms Apply Apply 1

6.GM.A.4a

Represent three-dimensional figures using nets made up of rectangles and

triangles Represent Analyze 2

6.GM.A.4b

Use nets to find the surface area of three-dimensional figures whose

sides are made up of rectangles and triangles. Use Apply 3

6.EE.A.2c Evaluate non-negative rational

number expressions Evaluate Apply 3 Essential Questions:

1. How can you rearrange shapes to makes other shapes? Why would you want to? 2. If you want to compare boxes, what do you compare?


Enduring Understanding/Big Ideas: 1. Making connections between shapes and their area formulas. The ability to decompose

shapes into basic polygons. 2. Utilizing nets of three-dimensional figures to finding surface areas and then to finding

volumes. Breaking three-dimensional figures into surface pieces for finding surface areas. Unit Vocabulary:



13. Area Area Base

Height Evaluate

Expression Rectangle

Square Diagonal

Right Triangle Parallelogram Acute Triangle Obtuse Triangle

Hexagon Octagon

Trapezoid Polygon

Regular Polygon Decompose Compose

14. NETS and Three-Dimensional Shapes

Area Base

Evaluate

Volume Center Cube Net

Prism Pyramid

Cubic Unit Rectangular Prism

Face Edge

Lateral Face Vertex

Surface Area



digits Topic 13: Area and Topic 14: Surface Area & Volume


Suggested

# of Days

Notes TenMarks

Readiness Lesson

1 class period

Optional Readiness Lesson: Designing a Playground Reviews:

● Identifying Two-Dimensional Figures


● Finding Areas of Squares and Rectangles

SPED MODIFICATION: Review Geometry vocabulary prior to beginning topic.

6.GM.A.1 13.1: Rectangles and Squares 13.3: Parallelograms

1 class period

13.1 explains the formulas for area of a rectangle & square. There are examples that give the area and students are expected to find the other dimension. Since equations are not until next unit, discuss the concept of area and use their understanding of inverse operations to determine how to find the unknown dimension, without solving an equation. Use Math Ed time to construct construction paper models of decomposing and composing one shaped into another to find the find the formula of Area of a parallelogram SPED MODIFICATION:


Incorporate concrete models when introducing area of parallelograms.

6.GM.A.1 13.2: Right Triangles 13.4: Other Triangles

1 class period

Question: Do I always have to use two right triangles of the same shape & size to make a rectangle? Why or Why not? Question: Why can I use any two triangles of the same shape & size to make a parallelogram? Question: Would two right triangles also form a parallelogram? Why or why not? Use Math Ed. time to create models of composing triangles to form parallelograms to find the formula of Area of a triangle. SPED MODIFICATION: Incorporate concrete models when introducing area of triangles.

6.GM.A.1 13.5: Polygons 1 class period

6.G.1 Students are expected to find the area of a trapezoid by decomposing into triangles & quadrilaterals or by finding the area of a parallelogram and dividing by 2. Students are not expected to use or know the formula for the area of a trapezoid. digits has students derive the formula in Part 1. You may choose to do this or not, however students should not be assessed over their use or knowledge of the formula.


6.GM.A.1 13.6: Problem Solving

1 class period

6.GM.A.4 14.1: Analyzing Three-Dimensional Figures 14.2: Nets

1 class period

Each teacher has a classroom set of three-dimensional figures to use as hands-on practice in Math Ed 14.2 Part 2 uses a hexagonal prism as an example. 6.G.4 states that nets should be made of rectangles and triangles. You may choose to teach Part 2, but students should only be assessed over any nets that are constructed with rectangles and triangles. SPED MODIFICATION: Skip Part 2

6.GM.A.4 Lesson 16: Constructing Nets

½ class period

Supplemental Material

6.GM.A.4 Lesson 17: From Nets to Surface Area

½ class period

Supplemental Material 6.G.4 Students are not required to know the formula for Surface Area. They are expected to find the surface area by adding the area of each of the faces, only. The standard specifies that the faces of the 3D shapes should only be rectangles and triangles. Each teacher has a classroom set of three-dimensional figures to use as hand-on practice in Math Ed.

Finding the Surface Area of 3-D Figures Using Nets

6.GM.A.4 14.3: Surface Areas of Prisms

Do not teach. Addressed in Supplemental Material.


14.4: Surface Areas of Pyramids

6.GM.A.2 14-5: Volumes of Rectangular Prisms

1 class period

Find the Volume of a Rectangular Prism



Unit 5: Statistics

Subject: Mathematics Grade: 6 Name of Unit: Statistics Length of Unit: 12 ½ class periods/6 class periods Overview of Unit: Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected. Priority Standards for unit:

● 6.DSP.A2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

● 6.DSP.A.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.

● 6.DSP.A.4 Display and interpret data. A. Use dot plots, histograms and box plots to display and interpret numerical data. B. Create and interpret circle graphs.

● 6.DSP.A.5 Summarize numerical data sets in relation to their context. 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 from the overall pattern with reference to the context in which the data were gathered. d. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data.


Supporting Standards for unit: ● 6.DSP.A.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.

● 6.NS.C.2 Locate a rational number as a point on the number line. A. Locate rational numbers on a horizontal or vertical number line. B. Write, interpret and explain problems of ordering of rational numbers. C. Understand that a number and its opposite (additive inverse) are located on

opposite sides of zero D. Understand a rational number as a point on the number line.

Priority Standard



able to do)

Bloom’s Taxonomy

Levels Webb's DOK

6.DSP.A.1

A statistical question as one that anticipates variability in the data

related to the question and accounts for it in the answer Recognize Understand 1

6.DSP.A.2

a set of data collected to answer a statistical question has a distribution which can be

described by its center spread and overall shape. Understand Understand 2

6.DSP.A.3

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 from

a single number. Recognize Understand 2

6.SDP.B.4

Dot plots, histograms and box plots to display and interpret

numerical data. Display Analyze 2

6.SDP.B.4

Dot plots, histograms and box plots to display and interpret

numerical data. Describe Apply 1 6.DSP.B.5 The number of observations Report Apply 1

6.DSP.B.5

the nature of the attribute under investigation, including how it was measured and its units of

measurements. Describe Apply 1 6.DSP.B.5 quantitative measures of center Report Understand 1

6.SP.5b The nature of the attribute under Describe Understand 2


investigation in a numerical data set including how it was measured

6.SP.5b

The nature of the attribute under investigation in a numerical data

set including its units of measurement Describe Understand 2

6.SP.5c

Quantitative measures of center (median and/or mean) in a

numerical data set Give Understand 1

6.SP.5c

Quantitative measures of variability (interquartile range

and/or mean absolute deviation) in a numerical data set Give Understand 1

6.SP.5c Any overall pattern Describe Understand 2

6.SP.5c

Any striking deviations from the overall pattern with reference to

the context in which the data were gathered Describe Understand 2

6.SP.5d

The choice of measures of center to the shape of the data

distribution in which the data were gathered Relate Analyze 2

6.SP.5d

The choice of measures of center to the context of the data

distribution in which the data were gathered Relate Analyze 2

6.SP.5d

The choice of variability to the shape of the data distribution in which the data were gathered Relate Analyze 2

6.SP.5d

The choice of variability to the context of the data distribution in

which the data were gathered Relate Analyze 2 Essential Questions:

1. What kinds of data displays show and hide how things vary? 2. When do you use each kind? 3. What can you do with data to make it more useful? 4. How does what you are looking for determine how data is best used and represented?

Enduring Understanding/Big Ideas:

1. A dot plot can show you cluster, gaps, and data that stray. It shows you individual dots to represent each value in a data set. A histogram can show you the general distribution of data that are grouped in intervals. A box plot can show you the general distribution of data in relation to five boundary points.


2. Analyzing the situations and determining the effectiveness of your data display will help guide you on the most effective way to present your data.

3. Mean and median are measures of center. Range, interquartile range, and mean absolute deviation are measures of variation.

4. Knowing which model best describes the different measures of center will determine the display that will be most effective to use.

Unit Vocabulary:



15. Data Displays Cluster Data

Frequency Gap

Maximum Minimum

Box plot Dot plot

Histogram Statistical question

Stray data value (Outlier)

16. Measures of Center and Variation

Cluster Dot plot

Gap Maximum

Mean Minimum

Range Variability

Absolute deviation from the mean Box plot

Deviation from the mean First quartile

High variability Interquartile range

Low variability Mean absolute deviation

Measure of Center Measure of variability

Median No variability Third quartile



digits Topic 15: Data Displays

Note: 6.SP.5a: Report the number of observations Only included in 15.6 Problem Solving. If you do not plan to teach this section, you will need to provide opportunities for students to do this throughout the entire unit. You can do so by asking students how many data points there are prior to creating data displays or finding a measure of center or a measure of variability.


Notes TenMarks


Optional Readiness Lesson: Organizing a Book Fair Reviews:

● Making and Interpreting Bar Graphs

● Making and Interpreting Line Plots

6.DSP.A.1 6.DSP.B.5b

15.1: Statistical Questions

½ class period

Recognizing Statistical Questions

6.DSP.B.4 6.DSP.B.5c 6.NS.C.6c

15.2: Dot Plots ½ class period

There are two types of dot plots. One type looks like a line plot. The second type has both an x- and y-axis. The latter is not addressed in digits. Please see the video below for a brief explanation of the two types. https://youtu.be/HK8fEqwLZCQ SPED MODIFICATION: Only require students to read and interpret data. Do not require students to create the dot plots. Only teach the dot plot that

Displaying Numerical Data

https://youtu.be/HK8fEqwLZCQ

https://youtu.be/HK8fEqwLZCQ


looks like a line plot. Review/Reteach in Life Ed


15.3: Histograms ½ class period

Discuss the similarities and differences between a bar graph and a histogram. Emphasize accuracy & precision when creating scales, labeling axes, and drawing the bars between the two intervals.(MP 6) SPED MODIFICATIONS: Only require students to read & interpret data. Do not require students to create the histograms.

Review/Reteach in Life Ed



15.4: Box Plots ½ class period

In 15.4, digits only uses data sets with an odd number of data points. Even number of data sets are addressed in 16.1. They also do not use the term “median” until Topic 16. They use the term “middle value”, “middle value of upper/lower half of the data set” Emphasize accuracy & precision when creating scales, labeling axes, and drawing the bars between the two intervals.(MP 6) On Schoology, there is a Box and whisker plot power point under review for test. SPED MODIFICATIONS:



Only require students to read and interpret data. Do not require students to create the box plots. Review/Reateach in Life Ed

6.DSP.B.4 6.NS.C.6c

15.5: Choosing an Appropriate Display

½ class period


6.DSP.B.4 6.DSP.B.5a

15.6: Problem Solving

½ class period


Post Test 1 class period


digits Topic 16: Measure of Center and Variation


Suggested # of Days

Notes TenMarks

Readiness Lesson

1 class period Optional Readiness Lesson: Planning a Camping Trip Reviews:

● Ordering Rational Numbers

● Dividing by a Whole Number

● Finding Absolute Values

6.DSP.A.3 6.DSP.B.4 6.DSP.B.5c 6.DSP.B.5d

16.1: Median ½ class period Allow students to use calculators, if needed. SPED MODIFICATION: Only require students to read and interpret data. Do not require students to create the histograms. Review/Reteach in Life Ed

Recognize Measures of Center & Measures of Variation Find: Measures of Center and Variability of Data Sets Measures of Center and Variability: Shape Data Display

6.DSP.A.3 6.DSP.B.5c 6.DSP.B.5d

16.2: Mean ½ class period Allow students to use calculators, if needed.

Recognize Measures of Center & Measures of Variation Find: Measures of Center and Variability of Data Sets Measures of Center


and Variability: Shape Data Display

6.DSP.A.2 6.DSP.A.3 6.DSP.B.5c 6.DSP.B.5d

16.3: Variability ½ class period Describe Data Distribution: Use Center/Spread/Shape Recognize Measures of Center & Measures of Variation Find: Measures of Center and Variability of Data Sets Measures of Center and Variability: Shape Data Display


16.4: Interquartile Range

½ class period Recognize Measures of Center & Measures of Variation Find: Measures of Center and Variability of Data Sets Measures of Center and Variability: Shape Data Display


16.5: Mean Absolute Deviation

½ class period Recognize Measures of Center & Measures of Variation Find: Measures of Center and Variability of Data Sets Measures of Center and Variability:


Shape Data Display

6.DSP.A.3 6.DSP.B.5d

16.6: Problem Solving and Test Review

1 class period Recognize Measures of Center & Measures of Variation Measures of Center and Variability: Shape Data Display

Post Test 1 class period


Unit of Study Terminology Appendices: All Appendices and supporting material can be found in this course’s shell course in the District’s Learning Management System. Assessment Leveling Guide: A tool to use when writing assessments in order to maintain the appropriate level of rigor that matches the standard. Big Ideas/Enduring Understandings: Foundational understandings teachers want students to be able to discover and state in their own words by the end of the unit of study. These are answers to the essential questions. Engaging Experience: Each topic is broken into a list of engaging experiences for students. These experiences are aligned to priority and supporting standards, thus stating what students should be able to do. An example of an engaging experience is provided in the description, but a teacher has the autonomy to substitute one of their own that aligns to the level of rigor stated in the standards. Engaging Scenario: This is a culminating activity in which students are given a role, situation, challenge, audience, and a product or performance is specified. Each unit contains an example of an engaging scenario, but a teacher has the ability to substitute with the same intent in mind. Essential Questions: Engaging, open-ended questions that teachers can use to engage students in the learning. Priority Standards: What every student should know and be able to do. These were chosen because of their necessity for success in the next course, the state assessment, and life. Supporting Standards: Additional standards that support the learning within the unit. Topic: These are the main teaching points for the unit. Units can have anywhere from one topic to many, depending on the depth of the unit. Unit of Study: Series of learning experiences/related assessments based on designated priority standards and related supporting standards. Unit Vocabulary: Words students will encounter within the unit that are essential to understanding. Academic Cross-Curricular words (also called Tier 2 words) are those that can be found in multiple content areas, not just this one. Content/Domain Specific vocabulary words are those found specifically within the content. Symbols: This symbol depicts an experience that can be used to assess a student’s 21st Century Skills using the rubric provided by the district. This symbol depicts an experience that integrates professional skills, the development of professional communication, and/or the use of professional mentorships in authentic classroom learning activities.

6th Grade SPED Resource Mathematics Curriculum

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Transcript of 6th Grade SPED Resource Mathematics Curriculum