Match Equivalent Results

Teaching Notes

Focus: Whole Number × Proper Fraction. 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. Write whole numbers over one and convert mixed numbers to improper fractions.
2. Multiply the numerators and multiply the denominators.
3. You may cancel common factors between a numerator and a denominator before multiplying, or simplify the product afterward.
4. A common denominator is not required for multiplication.
5. For a matching problem, solve each item before drawing its connection. Check that the connected representations have equal values.

Worked Examples

Evaluate (4) × (2/3).

1. Write the factors as fractions: (4) × (2/3).
2. Multiply numerators and denominators: (4 × 2)/(1 × 3).
3. Simplify to 8/3.

Answer: 8/3

Common Mistakes and How to Help

Do not multiply a mixed number’s whole part and fractional part separately and join them. Convert the entire mixed number first. Cancellation removes common factors, not digits that merely look alike.

Estimate the size of each factor. A positive factor below one reduces the other positive factor. Check by dividing by a nonzero original factor.

Questions to Check Understanding

• Estimate the size of each factor. A positive factor below one reduces the other positive factor. Check by dividing by a nonzero original factor.
• 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.