Lesson 2: Quarters and Eighths by Repeated Halving

Full paper-strip activity

Use two more identical strips.

Strip A: make fourths

1. Fold the strip in half.
2. Fold it in half again.
3. Unfold. You now have 4 equal parts.

Strip B: make eighths

1. Fold the strip in half.
2. Fold it in half again.
3. Fold it in half one more time.
4. Unfold. You now have 8 equal parts.

Repeated halving helps because each fold creates equal parts from the same whole.

Now compare one quarter on Strip A with one eighth on Strip B. Since both strips started as the same whole, one quarter is larger than one eighth.

You can also line up the fold marks. Two eighths cover the same length as one quarter. So one quarter is two eighths of the same whole.

Safe rule: for positive unit fractions of the same whole, a bigger denominator means a smaller piece.

Use that rule carefully. It works for 1/4 and 1/8 of the same whole. Do not stretch it to all fractions, and do not use it when the wholes are different sizes.

Adult prompts

• "Do these strips start as the same whole?"
• "Are the parts equal on each strip?"
• "What does the 4 in 1/4 tell us?"
• "What does the 1 in 1/8 tell us?"
• "How many eighths match one quarter?"

Common mistakes and how to respond

• Mistake: "Eighths are bigger because 8 is bigger than 4." Response: The 8 means the whole was cut into more equal parts, so each part is smaller.
• Mistake: "Any four pieces can be fourths." Response: They must be four equal parts.
• Check the amount: One quarter equals two eighths of the same whole. Explanation: The numerator counts pieces, but fourths and eighths are different-sized pieces. Line up the identical strips to see that two eighths cover exactly one quarter.