Find and Fix the Error

Teaching Notes

Focus: Proper Fraction ÷ Mixed Number. Use the worked example and teaching sequence below to explain the reasoning before independent practice.

Before You Begin

• Read the numbers and identify the operation.

Teaching Steps for Parents and Teachers

1. For an error-correction problem, find the first incorrect step. Explain why it is wrong, then recompute all later steps.
2. Convert any mixed numbers to improper fractions and write whole numbers over one.
3. Keep the first fraction, replace division with multiplication, and use the reciprocal of the second fraction.
4. Multiply and simplify.
5. The reciprocal is applied to the divisor only.

Worked Examples

Evaluate (2/3)/(1 1/2).

1. Rewrite each mixed number as an improper fraction: 1 1/2 = 3/2.
2. The reciprocal of 3/2 is 2/3.
3. Multiply (2/3) × (2/3).
4. The result is 4/9.

Answer: 4/9

Common Mistakes and How to Help

Do not flip the first fraction or both fractions. Division by a fraction below one can produce an answer larger than the dividend; this is consistent with asking how many smaller groups fit.

Multiply the quotient by the original divisor, not its reciprocal. The result should equal the dividend.

Questions to Check Understanding

• Multiply the quotient by the original divisor, not its reciprocal. The result should equal the dividend.
• Which step explains your answer?
• Can you apply the same reasoning when the numbers change?

Practice Advice

Work through the example together. Ask the learner to explain the first two problems, then try three independently. Review the first incorrect step before assigning more practice.

Next Practice

• Use New Numbers to practice the same skill with different values.
• If the learner needs help, return to the example and model each step before trying again.