🟠 Level 0 — Most Support. Same skills as Level 1, with extra help: press then tap any text to hear it. Open every 💡 Hint — that is okay here.

Reveal Math · Unit 6 · Supplemental Resources

Number System & Expressions

Standards: 6.NS.A.1 (Fraction Division) · 6.NS.B.4 (GCF/LCM) · 6.EE.A.1-4 (Expressions)

🖨️ Differentiated Practice Worksheets

Ready-to-print practice at three levels — pick the right fit for each student.

Level 0 · Extra Support Scaffolded steps, worked examples, extra space. Level 1 · Support Guided practice on the core skills. Level 2 · Enrichment Stretch problems and deeper reasoning.

Visual Vocabulary

¾ ÷ ½
Dividing Fractions
Dividir fracciones
Keep the first fraction. Change ÷ to ×. Flip the second fraction.
2⁴ = 2×2×2×2 = 16
Exponent
Exponente
A small number that tells how many times to multiply the base. 2⁴ = 2×2×2×2 = 16
GCF 12: 1,2,3,4,6,12 18: 1,2,3,6,9,18 GCF = 6
Greatest Common Factor
Máximo común divisor (MCD)
The biggest number that divides into two numbers evenly.
LCM 4: 4,8,12,16... 6: 6,12,18,24... LCM = 12
Least Common Multiple
Mínimo común múltiplo (MCM)
The smallest number that both numbers divide into evenly.
3x + 5 x is a variable 3 is the coefficient 5 is a constant
Algebraic Expression
Expresión algebraica
A math phrase with numbers, variables, and operations. No equals sign.
Distributive 3(x + 4) = 3x + 12
Distributive Property
Propiedad distributiva
Multiply the number outside by each term inside the parentheses.

Sentence Frames

To divide ¾ ÷ ½, I   the first fraction,   the operation to multiplication, and   the second fraction.
The GCF of   and   is   because it is the largest factor they share.
The LCM of   and   is   because it is the smallest multiple they share.
The expression 4³ means 4 multiplied by itself   times, which equals  .
To evaluate 2x + 3 when x = 5, I replace x with   and get 2( ) + 3 =  .
I can simplify 6x + 2x to   because they are   terms.

Step-by-Step: Dividing Fractions (Keep-Change-Flip)

Example: ¾ ÷ ⅖

KEEP CHANGE FLIP
¾ ÷ → × ⅖ → 5⁄2
1

Keep the first fraction: ¾

2

Change division (÷) to multiplication (×)

3

Flip the second fraction: ⅖ becomes 5⁄2

4

Multiply: ¾ × 5⁄2 = 15⁄8 = 17⁄8

Step-by-Step: Evaluate an Expression

Example: Evaluate 3x² + 2 when x = 4

1

Write the expression: 3x² + 2

2

Replace x with 4: 3(4)² + 2

3

Exponent first: 4² = 16, so 3(16) + 2

4

Multiply: 3 × 16 = 48, so 48 + 2

5

Add: 48 + 2 = 50

Practice Problems

Problem 1

½ ÷ ¼ = ?

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Keep ½, Change to ×, Flip ¼ to 4⁄1.
2 — ½ × 4⁄1 = 4⁄2 = 2
Problem 2

⅔ ÷ ⅙ = ?

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Keep ⅔, Change to ×, Flip ⅙ to 6⁄1.
4 — ⅔ × 6⁄1 = 12⁄3 = 4
Problem 3

What is 5³?

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5³ means 5 × 5 × 5.
125 — 5 × 5 = 25, then 25 × 5 = 125
Problem 4

What is the GCF of 12 and 18?

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Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Pick the biggest one they share.
6 — Both 12 and 18 can be divided by 6.
Problem 5

What is the LCM of 4 and 6?

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Multiples of 4: 4, 8, 12, 16... Multiples of 6: 6, 12, 18... Find the first one they share.
12 — 12 is the smallest number in both lists.
Problem 6

Evaluate 2x + 7 when x = 3.

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Replace x with 3: 2(3) + 7.
13 — 2(3) + 7 = 6 + 7 = 13
Problem 7

Simplify: 5x + 3 + 2x

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Combine like terms: 5x and 2x are like terms. 3 stays.
7x + 3
Problem 8

Use the distributive property: 4(x + 3)

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Multiply 4 by x, then multiply 4 by 3.
4x + 12
Problem 9

⅗ ÷ ⅗ = ?

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Any number divided by itself equals 1. Or use KCF.
1 — ⅗ × 5⁄3 = 15⁄15 = 1
Problem 10

Evaluate 10 − 2³ + 1

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Exponent first: 2³ = 8. Then left to right: 10 − 8 + 1.
3 — 2³ = 8. 10 − 8 + 1 = 3

Real-World Connections

Sharing Pizza

You have ¾ of a pizza. You want to share it equally among 3 friends. Each person gets ¾ ÷ 3 = ¾ × ⅓ = ¼ of the whole pizza.

Hot Dog Buns Problem

Hot dogs come in packs of 8. Buns come in packs of 6. The LCM of 8 and 6 is 24. So you need 3 packs of hot dogs and 4 packs of buns to have the same amount (24).

Cell Phone Battery

If your phone loses ⅕ of its battery each hour, and you start with ⅘ battery, how many hours until it is empty? ⅘ ÷ ⅕ = 4 hours.

Saving Money

You save $x each week and already have $20. After w weeks you have 20 + xw dollars. If x = 5 and w = 8, you have 20 + 5(8) = $60.

Challenge Problems

Challenge 1

Evaluate: 2³ + 3² − 4 × 2 + 1

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Order of operations: exponents first, then multiplication, then add/subtract left to right.
10 — 8 + 9 − 8 + 1 = 10
Challenge 2

Find the GCF and LCM of 24 and 36.

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Use prime factorization. 24 = 2³ × 3, 36 = 2² × 3².
GCF = 12, LCM = 72 — GCF: take lowest powers of shared primes = 2² × 3 = 12. LCM: take highest powers = 2³ × 3² = 72.
Challenge 3

Simplify using the distributive property: 6(2x + 3) − 4(x − 1)

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Distribute each term, then combine like terms. Watch the negative sign.
8x + 22 — 12x + 18 − 4x + 4 = 8x + 22
Challenge 4

A recipe uses ⅔ cup of flour per batch. How many full batches can you make with 5 cups of flour?

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Divide: 5 ÷ ⅔ = 5 × &frac32;.
7 full batches — 5 × &frac32; = 15⁄2 = 7.5, so 7 full batches.
Challenge 5

Write an expression for: "five less than three times a number n, squared" and evaluate when n = 4.

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Three times n is 3n. Squared means ². Five less means subtract 5. Careful about what is squared.
(3n)² − 5 = 139 — (3×4)² − 5 = 12² − 5 = 144 − 5 = 139. (Or 3n² − 5 = 43 if only n is squared.)
Challenge 6

Two numbers have a GCF of 8 and an LCM of 96. One number is 32. What is the other?

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GCF × LCM = product of the two numbers. So 8 × 96 = 32 × ?
24 — 8 × 96 = 768. 768 ÷ 32 = 24. Check: GCF(32,24) = 8, LCM(32,24) = 96.
Challenge 7

Simplify: 2(3x + 4) + 3(2x − 1) − (x + 5)

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Distribute each, then combine like terms carefully.
11x — 6x + 8 + 6x − 3 − x − 5 = 11x + 0 = 11x
Challenge 8

Without a calculator, find: 2⁵ − 3³ + 4²

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2⁵ = 32, 3³ = 27, 4² = 16.
21 — 32 − 27 + 16 = 21
Challenge 9

A store sells pencils in packs of 8 and erasers in packs of 6. What is the smallest number of each you can buy to have the same number of pencils and erasers?

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Find the LCM of 8 and 6.
24 each — LCM(8,6) = 24. Buy 3 packs of pencils (3×8=24) and 4 packs of erasers (4×6=24).
Challenge 10

If 3(2x − 1) = 4x + 9, what is the value of x? (Bonus: this is a preview of 7th grade equations!)

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Distribute the 3, then get all x terms on one side and numbers on the other.
x = 6 — 6x − 3 = 4x + 9 → 2x = 12 → x = 6

Real-World Investigations

Investigation 1: Party Planner

You are planning a party for 48 guests. Plates come in packs of 8, cups in packs of 12, and napkins in packs of 10. (a) How many packs of each do you need? (b) Which item will have the most leftovers? (c) What is the LCM of 8, 12, and 10? If you were ordering items that come in those pack sizes, how many of each would you need to have the same number of all three?

Investigation 2: Recipe Scaling

A cookie recipe makes 24 cookies and calls for ¾ cup butter, ⅔ cup sugar, and 1½ cups flour. (a) How much of each ingredient do you need for 60 cookies? (b) If you only have 2 cups of butter, what is the maximum number of cookies you can make? Show all fraction calculations.

Investigation 3: Expression Writer

Create a real-world scenario (like a phone plan, shopping trip, or sports scoring) that can be modeled by the expression 2x + 3(x − 5) + 10. Define what x represents. Evaluate your expression for three different values of x and explain what each answer means in your scenario.

Brain Teasers

Teaser 1: The Power Tower

Which is larger: 2⁸ or 8²? Can you explain why without calculating both? What about 2⁹ vs 8³?

Show Answer
2⁸ = 256, 8² = 64. 2⁸ is larger. Since 8 = 2³, we get 8² = (2³)² = 2⁶ = 64. So 2⁸ > 2⁶. For 2⁹ vs 8³: 2⁹ = 512, 8³ = (2³)³ = 2⁹ = 512. They are equal!

Teaser 2: GCF Mystery

Two consecutive even numbers always have a GCF of 2. Can you explain why? What is the GCF of three consecutive even numbers?

Show Answer
Consecutive even numbers are 2 apart (like 10 and 12). Both are divisible by 2, but the difference is only 2, so they can't share a factor larger than 2. Three consecutive even numbers (like 6, 8, 10) also have GCF = 2.

Teaser 3: The Fraction Paradox

When you divide a positive number by a fraction less than 1, the answer is bigger than the original number. Why? Give an example and explain using a real-world story.

Show Answer
Division asks "how many groups?" If you divide 6 by ½, you are asking how many half-portions fit in 6. Since each group is less than 1, you get more groups. 6 ÷ ½ = 12. It's like cutting 6 sandwiches in half — you get 12 pieces.

Teaser 4: Expression Challenge

Find a value of x that makes 3x + 2 equal to 2(x + 5). Is there only one value? What does this tell you about the two expressions?

Show Answer
3x + 2 = 2x + 10 → x = 8. There is exactly one solution. This means the expressions are equal only when x = 8. For any other value of x, one is larger than the other.

Where This Math Leads Next

7th Grade: Solving Equations

You will move from evaluating expressions to solving equations. Instead of "evaluate 3x + 5 when x = 2," you will solve "3x + 5 = 17, find x."

7th Grade: Proportional Relationships

Fraction operations lead directly to ratios, proportions, and unit rates. You will use fraction division to compare prices and speeds.

8th Grade: Exponent Rules

Simple exponents grow into exponent rules: xᵃ × xᵇ = xᵃ⁺ᵇ, negative exponents, and eventually scientific notation for very large or very small numbers.

High School: Polynomials & Factoring

The distributive property and combining like terms lead to multiplying polynomials like (x + 3)(x − 2) and factoring quadratics.

Self-Assessment Checklist