Power Standards

6th grade Power Standards

Add and Subtract

• Fractions

• Mixed Numbers

Multiply and Divide

• Fractions

• Whole Numbers

Simplify Expressions

• Combining Like Terms

• Using the Distributive Property

Solving One-Step Equations

7th grade Power Standards

Everything listed above plus:

Fraction Arithmetic

• with positive and negative numbers

Simplify Expressions

• with positive and negative numbers

Evaluate Expressions

• with positive and negative numbers

Solving Multi-Step Equations

8th grade Power Standards

Everything listed above plus:

Identify the slope and y-intercept

• given a graph

• given a table

• given an equation in slope-intercept form

Study for Power Standards Test using Khan Academy:

https://docs.google.com/spreadsheets/d/1scjjYPlOUnWKXZOUnAkRqZeYbtT5kBf4YUl2pY-pjpA/edit?usp=sharing

I can add and subtract using whole numbers and fractions.

A visual approach to learning fractions. Each topic in this series has a pretest, an instruction section, online practice sessions, worksheet practice, and a test.

http://www.visualfractions.com/progress/progress.html

Fraction Games from visual fractions:

http://www.visualfractions.com/Games.htm

Unlimited worksheets - Fraction addition and subtraction

• Add & subtract unlike fractions - proper fractions, denominators 2-12

• Add & subtract unlike fractions - denominators 2-12

• Add & subtract unlike fractions - larger denominators

• Add & subtract 3 unlike fractions - proper fractions, denominators 2-8

• Add & subtract 4 unlike fractions - proper fractions, denominators 2-8

• Add & subtract 3 unlike fractions, denominators 2-12

• Add & subtract two mixed numbers - denominators 2-12

• Add & subtract two mixed numbers - larger denominators

• Add & subtract three mixed numbers - denominators 2-12

• Add & subtract whole numbers, fractions, or mixed numbers - mixed practice; denominators 2-12

I can multiply and divide using whole numbers and fractions.

A visual approach to learning fractions. Each topic in this series has a pretest, an instruction section, online practice sessions, worksheet practice, and a test.

http://www.visualfractions.com/progress/progress.html

Unlimited worksheets - Fraction multiplication

In all fraction multiplication and division problems, it helps to simplify before you multiply.

• Fraction times a whole number

  • Fraction multiplication 1 - 3 fractions, denominators 2-12

  • Fraction multiplication 2 - 3 fractions, denominators 2-20

  • Fraction multiplication 3 - 4 fractions, denominators 2-12

• Mixed number times a fraction

• Mixed number times a mixed number

  • Mixed multiplication practice 1 (two numbers; fractions, mixed numbers, or whole numbers)

  • Mixed multiplication practice 2 (three numbers; fractions, mixed numbers, or whole numbers)

• A whole number times a fraction - missing factor

• A fraction times a fraction - missing factor

Unlimited worksheets - Fraction division

• • Divide a whole number, fraction, or mixed number by a fraction - mental math, as the answers are whole numbers

• Fraction divided by a fraction

• Mixed number divided by a mixed number

• Mixed division practice (by fractions, mixed numbers, or whole numbers)

I can add and subtract using integers.

Unlimited worksheets - Addition and Subtraction

• Add two integers (-10 to 10)

• Add two integers (-30 to 30)

• Add three integers

• Add four integers

• Add integers: missing number (easy)

• Add integers: missing number (medium)

• Subtract two integers (-10 to 10)

• Subtract three integers (-30 to 30)

• Subtract integers: missing number

• Subtract three integers

• Subtract four integers

• Mixed addition and subtraction problems (within -20 and 20)

• Challenge: mixed addition and subtraction problems: missing numbers

I can multiply and divide using integers.

Unlimited worksheets - Multiplication and Division

• Multiply two integers: easy

• Multiply two integers: medium

• Simple missing factor problems

• Multiply whole tens

• Multiply three integers

• Multiply four integers

• Simple division of integers

• Simple division of integers, missing dividend or divisor

• Mixed multiplication and division problems

I can use order of operations to simplify numeric expressions.

Unlimited worksheets - Order of Operations, positive numbers

• Review: expressions with exponents

• Solve in the correct order: two or three operations

• Solve in the correct order: three or four operations

  • Solve in the correct order: three or four operations with decimal numbers (round to two decimal digits)

I can substitute a number for a variable and simplify the expression using the order of operations.

Unlimited worksheets - Expressions

• Evaluate simple expressions

• Write a number expression from a verbal expression

  • Simplify expressions (by combining like terms; no negative numbers)

• Multiply using the distributive property

• Factor the expressions

I can simplify algebraic expressions.

Unlimited worksheets - Simplify expressions

• • Simplify expressions (for example −6z + z − 5 or −7v³ · v²)

  • Simplify expressions - no negative numbers (for example 4w + 2w or c · 3 · c · c · 7)

I can add and subtract linear expressions.

I can solve linear equations with one variable.

Unlimited worksheets - Solving equations

• One-step equations with whole numbers (no negative numbers involved)

• Solve the simplest equations involving integers

• Solve one-step equations involving integers

• Equations with decimals (answers may be rounded)

  • Two-step equations - constants and coefficients are non-negative whole numbers

  • Two-step equations - constants and coefficients may be negative integers

• Variable on both sides

• Equations with parentheses

• Equations: mixed practice

  • Challenge: the constants and coefficients are "larger" numbers (have a larger absolute value)

• Challenge: equations with decimals

Interactive Solving Equations Lesson/Practice:

http://www.mathplayground.com/AlgebraEquations.html

I can identify the slope and y-intercept of a linear relationship when given a table, a graph, an equation, or a situation.

Unlimited worksheets - Graphing & Slope

• • Graph linear equations - easy (slope is a whole number)

  • Graph linear equations - medium (slope can be a fraction)

  • Find the slope of the line, either from the graph or from the two given points (slope is a whole number)

  • Find the slope of the line, either from the graph or from the two given points (slope can be a fraction)

  • Graph a line with a given slope and point on it (slope is a whole number)

  • Graph a line with a given slope and point on it (slope may be a fraction)

Power Standards

5.NF.1

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12.

(In general, a/b + c/d = (ad + bc)/bd.)

6.NS.1

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. 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?.

5.NF.7a

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

5.NF.7b

Interpret division of a whole number by a unit fraction, and compute such quotients.For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

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.

5.OA.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

8.EE.7b

Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

7.NS.1d

Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.2c

Apply properties of operations as strategies to multiply and divide rational numbers.

6.EE.2c

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 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

7.EE.1a

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

8.F.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.