Common Core Standard: 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. A. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5”

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Sixth Grade Math

Domain: Expressions and Equations Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Essential Vocabulary Task Analysis Learning Activities/Assessments Resources

Prior

 Order of operations

 Parentheses

 Brackets

 Simplify

 Evaluate

 Numerical expression

Explicit

 Variable

 Exponent

 Power

 Base

 Algebraic expression

 Like terms

 Evaluate

 Coefficient

 Equivalent expression

Introductory  Factor

 Distributive property

 Rational coefficients

 Linear expressions

 Define an exponent and its parts (base, exponents)

 Recognize that the base can be a whole number, positive fraction, or a positive decimal.

 Recognize that a base with an exponent is repeated

multiplication (including variable expressions).

 Write an algebraic expression from a verbal expression

 Use order of operations (now including exponents) to simplify an expression.

 Write and evaluate numerical expressions involving whole-number exponents.

 Exponent Song

o Introduction to exponents & how to evaluate them.  Practice Game (CGW)

 Memory Expressions (CGW, CT, Q) o Students match a verbal

expression with its algebraic form and value. (numerical expressions only)

 Millionaire

PEMDAS/Exponent Review

 Fling the Teacher  WebQuest

This WebQuest contains a video that does not work but the basic idea/format of it is a good way to introduce students to order of operations.

 Order of Operations Hopscotch

A good idea to get PEMDAS engrained in students’ memory.

 Brain Pop Order of Operations

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Sixth Grade Math

Common Core Standard: 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

A.

Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.

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. 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, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3_{and A = 6 s}2_{to find the volume and surface area of a cube with sides of} length s = 1/2.

A.

Prior  Sum

 Difference

 Subtract

 Divide

 Multiply

 Product

 Increased by

 Decreased by

Explicit

 Expression

 Coefficient

 Variable

 Operations

 Order of operations

Introductory



Factor B. Prior

A.



Recognize operational vocabulary (sum, difference, product,

quotient)

 Write expressions from verbal descriptions using letters and numbers.

 Understand that order is important in writing subtraction and division problems.

 Understand that if a value is not given, you can’t evaluate an expression.

 Understand that expressions do not include equal signs (e.g. 5 + x is an expression not 5 + x = 20)



Write expressions that record operations with numbers and with

 Verbal/Algebraic Matching (CGW, Q, CT)

 Expressions Test

o Test made for 6.EE.1 & 6.EE.2. Contains substitution, evaluating & vocabulary recognition.

 Know Your Terms! (WTL)

o Describe a given expression using vocabulary words (quotient, product, constant, coefficient, term, etc.).

 Properties Dice Game (CGW, Q, CT) o Students work in pairs or on their

own. They roll 3 dice and must use the four operations to make a number with all 3 dice. The number must have the property of one on the grid. The aim is to get 4 properties in a row, a

 Math Worksheets Land  Whole Brain Teaching-

PEMDAS

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 Operations vocabulary

 Expressions

Explicit

 Expressions

 Variables

 Coefficients

 Constants

 Term

 Constant

C. Prior

 Operational vocabulary

 Expressions

Explicit

 Expressions

 Variables

 Coefficients

 Constants

 Term

 Constant

 Formula

 Simplify

 Evaluate

letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5-y

B.

 Understand that variables are letters that represent numbers.

 Understand that there are various possibilities for the number they can represent.

 Identify the parts of an algebraic expression including variables, coefficients,

constants, and the names of operations (sum, difference, product, and quotient).

 Identify parts of an expression using mathematical terms (sum, difference, product, factor, quotient, coefficient); view one or more parts of an expression as single entity.

C.

 Identify the value of the placement in the expression.

 Simplify the expression using order of operations.

 Apply to using formulas in real world contexts.

 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, inthe

conventional order when

column or diagonally. Can be played with individual grids or just one in the style of connect four.

 Solve it PEMDAS STYLE!

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there are no parentheses to specify a particular order (Order of Operations).

Sixth Grade Math

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

Prior

 Associative property

 Identity property

 Commutative property

 Factor

Explicit

 Area model

 Recognize and name each property.

 Understand the properties (identity-multiplication and addition,

associative, distributive, and commutative).

 Recognize that repeated addition of variables can be expressed through multiplication (y + y + y =3y).

 Understand area models to illustrate the distributive property with

 Matching Cards (CGW, CT, Q) o Could be played like Memory  You’re On My Property! (CGQ, CT,

Q)

o Given one game board with property examples (associative, commutative, etc.), students draw game pieces and claim a piece of ‘property' on the board.

 Brain Pop Associative Property of Addition & Multiplication

 Brain Pop Distributive Property

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 Factorization variables.

 Use factoring to rewrite an expression so that the distributive property is represented (e.g. 24x + 18y = 6(4x + 3y).

 Apply the properties of operations to generate equivalent expressions.

Sixth Grade Math

Common Core Standard: 6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the

same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are

equivalent because they name the same number regardless of which number y stands for.

Prior

 Substitution

 Equivalent

 Variable

 Equation

Explicit

 Substitution

 Equivalent

 Variable

 Equation

 Substitute values into an

expression to solve an equation.

 Substitute values into expressions to prove equivalency.

 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

 Equivalent Expression Practice (WTL, Q)

o Suggested writing assignment: Students explain why at least 2 of the false pairs of expressions are not equivalent (i.e. using

knowledge & vocabulary of properties, exponents, etc.).  Coloring Like Terms

o Students are given 3x5 cards and color the like terms in different colors.

 Dots (CGW)

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like terms (either terms with an a or b). When done, they must combine their like terms; the student with the highest amount wins.

Sixth Grade Math

Domain: Expressions and Equations Cluster: Reason about and solve one-variable equations and inequalities.

Common Core Standard: 6.EE.5

Understand solving an equation or inequality as a process of answering a 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.

Prior

 Equation

 Number line

 Variable

Explicit

 Inequality

 Greater than

 Less than

 Equal to

 Greater than or equal to

 Less than or equal to

 Solution set

 Inequality symbols

 Substitution

 Inverse operation

 Addition property of equality

 Multiplication property of equality

 Understand the difference between equations and inequalities.

 Know that inequalities represent a range of possible values rather than a single solution.

 Explain the strategies used to determine the answer to an expression or inequality.

 Use substitution to

determine whether a given number in a specified se makes an equation or inequality true

 Model solving equations or inequalities using

manipulatives.

 Understand solving an

 Main Idea Wheels combined with Venn Diagram to compare and contrast equation and inequalities (S, Q, WTL, CT)

o Four categories of main idea wheel: examples, definition, non-examples, types of solutions

o Example:

 Equation Main Idea Wheel  Inequality Main Idea Wheel  Venn Diagram

 Freeology - tons of free graphic organizers  Equations &

Inequalities Unit o Activities & lessons

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 Subtraction property of equality



Division property of equality

equation or inequality as a process of answering a 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.

Sixth Grade Math

Common Core 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, any number in a specified set.

Prior

 Variable

 Expression

 Inequality

 Substitute

 Operations

Explicit

 Unknown number

 Substitute for a variable.

 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, any number in a specified set.

 Dance or Text Activities (Q)

o Might be best used in correlation with 6.EE.8

o Provides scenario and requires students to write

expressions/inequalities. Also requires students to explain portions of solution sets for inequalities.

 Learn Zillion: Write Expressions with Variables

 Big Ideas Math : Example situations to write expressions

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Common Core Standard: 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the

form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Prior

 Expression

 Equation

 Solution

 Operations

 Variable

Explicit  Inverse

 operation

 One step equations

 Justify

 Unknown

 Introductory

 Two-step and three-step equations

 Solve equations involving fractions and decimals.

 Understand the meaning of the equation and the solution in the context of a given problem.

 Write equations from real-world problems.

 Use inverse operations to solve one-step equations based on real world situations.

 Check answer for reasonableness and accuracy.

 Justify their solution.

 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative

 Color By Numbers Picture and Color By Numbers Equations

o Solve equations and use color key to color in picture.  Koosh Ball Smart Board Review

(CGW)

o Students throw a Koosh Ball at Smart Board which selects an equation they need to solve.

o To download, select “Koosh Ball Review” under Math 6 Notebook Files on linked website.

 Solving Equations (+/-) Interactive Lesson (S, CT, Q)

o To download, select “Solve one-step equations by add or subtract” under Math 6 Notebook Files on linked website.

 Solving Equations ( ÷ / × ) Interactive Lesson (S, CT, Q)

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Sixth Grade Math

Common Core 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 orx < c have infinitely many solutions;

represent solutions of such inequalities on number line diagrams.

Prior

 Equation

 Expression

 Variable

 Statement

 Inequality

 Inequality symbols

 Number line

Explicit

 Infinite

 Line diagram

 Constraint

 Condition

Introductory  Slope

 Define infinite.

 Define constraint.

 Recognize a constraint.

 Represent the constraint on a number line using an open circle or a closed circle.

 Plot a given inequality on a number line and represent the constraint (shading in the designated direction).

 Construct an inequality that represents a real-world condition.

 Given a solution on a number line, write the corresponding inequality.

 Plot an inequality that represents a real-world condition.

 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.

 Hershey Park (CGW, LG)

o Students compare height requirements of different rides.

o Can be used as laptop activity

 Learn Zillion

o Inequality Solution Set on a Number Line o Real World

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Sixth Grade Math

Domain: Expressions and Equations Cluster: Represent and analyze quantitative relationships between dependent and independent variables.

Common Core 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.

Prior

 Variable

 Coefficient

 Table

 X-axis

 Y-axis

Explicit

 Dependent variable

 Independent variable

Introductory  Function

 Function table

 Linear functions

 Non-linear functions

 Define and distinguish between dependent and independent variables.

 Understand how the coefficient of the dependent variable is related to the graph and/or table of values.

 Use many forms to represent relationships between two quantities.



Recognize that the independent variable is graphed on the x-axis; the dependent variable is graphed on the y-axis.

 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

 Independent/Dependent Variables Examples (Q)

o Provides examples & questions that could be used as an assessment

o This site contains different forms of this resource: word, PPT, notebook, etc.

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