🟠 Level 0 — Most Support. This is the most-supported version. Press then tap any text to hear it. Go slowly and use every hint — that is okay here.
Name: ___________________________ Date: ______________ Class: ____________
LEVEL 1 · SUPPORT

The Number System & Expressions

Standards: 6.NS.A.1 (Dividing Fractions) · 6.NS.B.4 (GCF/LCM) · 6.EE.A.1–4 (Exponents & Expressions)

Directions: Read the vocabulary box and the worked examples first. Then complete each problem in the space provided. Use the hint cues if you get stuck. Show your steps.

Vocabulary Helper

🔄 Keep-Change-Flip
To divide fractions: keep the first, change ÷ to ×, flip the second.
⬆️ Exponent
A small number that tells how many times to multiply. 4³ = 4 × 4 × 4.
🤝 Greatest Common Factor (GCF)
The biggest number that divides evenly into two numbers.
🔁 Least Common Multiple (LCM)
The smallest number that two numbers both divide into.
🔤 Algebraic Expression
A math phrase with numbers, letters (variables), and operations, like 2x + 3.
📦 Distributive Property
Multiply the outside number by each term inside: a(b + c) = ab + ac.

Worked Examples

EXAMPLE A — Dividing Fractions (Keep-Change-Flip)

Solve: ¾ ÷ ⅖

  1. Keep the first fraction: ¾
  2. Change ÷ to ×
  3. Flip the second fraction: ⅖ becomes 5/2
  4. Multiply: ¾ × 5/2 = 15/8 = 1 ⅞
EXAMPLE B — Evaluate an Expression

Evaluate 3x² + 2 when x = 4

  1. Replace x with 4: 3(4)² + 2
  2. Exponent first: 4² = 16 → 3(16) + 2
  3. Multiply: 3 × 16 = 48 → 48 + 2
  4. Add: 48 + 2 = 50

Sentence Frames

To divide ¾ ÷ ½, I the first fraction, change ÷ to , and the second fraction.
The GCF of 12 and 18 is because it is the largest factor they share.
The expression 4³ means 4 multiplied by itself times, which equals .

Guided Practice

1. ½ ÷ ¼ = ?

Hint: Keep ½, change to ×, flip ¼ to 4/1.

2. ⅔ ÷ ⅙ = ?

Hint: Flip ⅙ to 6/1, then multiply.

3. What is 5³?

Hint: 5³ means 5 × 5 × 5.

4. What is the GCF of 12 and 18?

Hint: Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Pick the biggest shared one.

5. What is the LCM of 4 and 6?

Hint: Multiples of 4: 4, 8, 12... Multiples of 6: 6, 12... Find the first shared one.

6. Evaluate 2x + 7 when x = 3.

Hint: Replace x with 3: 2(3) + 7.

7. Simplify: 5x + 3 + 2x

Hint: Combine like terms. 5x and 2x are like terms; 3 stays.

8. Use the distributive property: 4(x + 3)

Hint: Multiply 4 by x, then 4 by 3.

9. ⅗ ÷ ⅗ = ?

Hint: Any number divided by itself equals 1.

10. Evaluate 10 − 2³ + 1

Hint: Do the exponent first: 2³ = 8. Then left to right.

Answer Key

  1. 2 — ½ × 4/1 = 4/2 = 2
  2. 4 — ⅔ × 6/1 = 12/3 = 4
  3. 125 — 5 × 5 × 5 = 125
  4. 6 — Both 12 and 18 divide by 6
  5. 12 — Smallest number in both lists
  6. 13 — 2(3) + 7 = 6 + 7 = 13
  7. 7x + 3
  8. 4x + 12
  9. 1 — ⅗ × 5/3 = 15/15 = 1
  10. 3 — 2³ = 8, then 10 − 8 + 1 = 3