Lesson 6.2 Fractions on a Number Line

Steps

1. Warm-up

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

   • Ask: “4 × 9” Listen for: 36
   • Ask: “2 × 4” Listen for: 8
   • Ask: “5 × 3” Listen for: 15
   • Ask: “5 × 5” Listen for: 25
   • Ask: “4 × 5” Listen for: 20
2. Teach the new idea

   Say this: “Split the space from 0 to 1 into equal parts. Each jump is one unit fraction.”

   Say this: “Fractions can be greater than 1: 5/4 is past 1.”

   Say this: “Number line: a line with numbers in order at equal spaces.”

3. Show how

   Show: What fraction does the arrow point to?

   

   Say this: “Each whole is cut into 6 equal parts, so each step is \tfrac{1}{6} .”

   Say this: “The arrow is 5 steps from 0, so it points to \tfrac{5}{6} .”

   Answer: \tfrac{5}{6}

   Show: What fraction does the arrow point to?

   

   Say this: “Each whole is cut into 4 equal parts, so each step is \tfrac{1}{4} .”

   Say this: “The arrow is 2 steps from 0, so it points to \tfrac{2}{4} .”

   Answer: \tfrac{2}{4}

4. Practice together

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

   Ask: What fraction does the arrow point to?

   

   Listen for: \tfrac{1}{2}

   If stuck: Each whole is cut into 2 equal parts, so each step is \tfrac{1}{2} .

   Ask: What fraction does the arrow point to?

   

   Listen for: \tfrac{2}{3}

   If stuck: Each whole is cut into 3 equal parts, so each step is \tfrac{1}{3} .

   Ask: What fraction does the arrow point to?

   

   Listen for: \tfrac{2}{4}

   If stuck: Each whole is cut into 4 equal parts, so each step is \tfrac{1}{4} .

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

5. Watch for
   • Counting the tick marks instead of the spaces.
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: Place fractions on a number line.

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.