Lesson 6.4 Comparing Fractions

Steps

1. Warm-up

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

   • Ask: “7 × 5” Listen for: 35
   • Ask: “3 × 6” Listen for: 18
   • Ask: “2 × 6” Listen for: 12
   • Ask: “3 × 10” Listen for: 30
   • Ask: “2 × 10” Listen for: 20
2. Teach the new idea

   Say this: “Same denominator: compare the numerators. 5/8 > 3/8.”

   Say this: “Same numerator: the smaller denominator is bigger. ⅓ > ⅕.”

   Say this: “Compare: decide which is greater.”

3. Show how

   Show: Write < or > : \tfrac{1}{2} ___ \tfrac{1}{4}

   Say this: “Both have 1 part. Fewer cuts make bigger parts, so the smaller denominator wins.”

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

   Answer: \tfrac{1}{2} > \tfrac{1}{4}

   Show: Write < or > : \tfrac{1}{6} ___ \tfrac{1}{3}

   Say this: “Both have 1 part. Fewer cuts make bigger parts, so the smaller denominator wins.”

   Say this: “\tfrac{1}{6} < \tfrac{1}{3}”

   Answer: \tfrac{1}{6} < \tfrac{1}{3}

4. Practice together

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

   Ask: Write < or > : \tfrac{5}{8} ___ \tfrac{7}{8}

   Listen for: \tfrac{5}{8} < \tfrac{7}{8}

   If stuck: The parts are the same size, so compare the numerators: 5 and 7.

   Ask: Write < or > : \tfrac{3}{4} ___ \tfrac{1}{4}

   Listen for: \tfrac{3}{4} > \tfrac{1}{4}

   If stuck: The parts are the same size, so compare the numerators: 3 and 1.

   Ask: Write < or > : \tfrac{1}{6} ___ \tfrac{5}{6}

   Listen for: \tfrac{1}{6} < \tfrac{5}{6}

   If stuck: The parts are the same size, so compare the numerators: 1 and 5.

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

5. Watch for
   • Thinking ⅕ is bigger than ⅓ because 5 is bigger.
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: Compare fractions with the same denominator or the same numerator.

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.