Lesson 6.3 Equivalent Fractions

Steps

1. Warm-up

   Do this: Ask these out loud. Your child answers out loud; no paper needed.

   • Ask: “8 × 5” Listen for: 40
   • Ask: “6 × 7” Listen for: 42
   • Ask: “7 × 5” Listen for: 35
   • Ask: “10 × 3” Listen for: 30
   • Ask: “3 × 6” Listen for: 18
2. Teach the new idea

   Say this: “½ = 2/4 = 4/8: the same amount cut into more pieces.”

   Say this: “Multiply the top and bottom by the same number to get an equivalent fraction.”

   Say this: “Equivalent: equal in value.”

3. Show how

   Show: Fill in the missing number: \tfrac{1}{2} = \tfrac{?}{4}

   Say this: “The denominator went from 2 to 4: 2 × 2 = 4.”

   Say this: “Multiply the numerator by 2 too: 1 × 2 = 2”

   Say this: “\tfrac{1}{2} = \tfrac{2}{4}”

   Answer: 2

   Show: Fill in the missing number: \tfrac{1}{6} = \tfrac{?}{24}

   Say this: “The denominator went from 6 to 24: 6 × 4 = 24.”

   Say this: “Multiply the numerator by 4 too: 1 × 4 = 4”

   Say this: “\tfrac{1}{6} = \tfrac{4}{24}”

   Answer: 4

4. Practice together

   Do this: Your child does these with you. Let them try first; help only after a real try.

   Ask: Fill in the missing number: \tfrac{3}{4} = \tfrac{?}{8}

   Listen for: 6

   If stuck: The denominator went from 4 to 8: 4 × 2 = 8.

   Ask: Fill in the missing number: \tfrac{1}{4} = \tfrac{?}{8}

   Listen for: 2

   If stuck: The denominator went from 4 to 8: 4 × 2 = 8.

   Ask: Fill in the missing number: \tfrac{1}{2} = \tfrac{?}{4}

   Listen for: 2

   If stuck: The denominator went from 2 to 4: 2 × 2 = 4.

   7 more practice items on the lesson page, and on Worksheet A and Worksheet B.

5. Watch for
   • Adding the same number to top and bottom.
6. Game: Fraction Strip Race

   Each player rolls a die (1–6) and takes that many sixths, or halves of that number in thirds. First to build one whole exactly wins.

7. Narration

   Say this: “Tell me what you learned today. Show me with your hands or the counters if you like.”

   Listen for: Find equivalent fractions with models.

8. Daily habit

   Fact drill (× and ÷) twice a week. Count by halves and fourths on the number line.

Spread over the week

5 sessions of 25–30 minutes. Stop while it is still going well.

1. Session 1. Warm-up, then teach the new idea (steps 1 and 2).
2. Session 2. Warm-up again, then show how with the examples.
3. Session 3. Practice together, then play the game.
4. Session 4. More practice on the worksheet, and the daily habit.
5. Session 5. Quick check: narration and a few practice items. Move on when it is mostly right.