Match Equivalent Results

Teaching Notes

Focus: Mixed Number − Mixed Number: Regrouping. 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. Use a common denominator so both fractions name the same-sized parts.
2. Subtract the numerators in the stated order and keep that common denominator.
3. With mixed numbers, you can first convert to improper fractions.
4. Simplify the difference; if it is greater than one, read the equivalent improper and mixed forms together.
5. For a matching problem, solve each item before drawing its connection. Check that the connected representations have equal values.

Worked Examples

Evaluate (3 1/5)-(1 3/5).

1. Rewrite each mixed number as an improper fraction: 3 1/5 = 16/5; 1 3/5 = 8/5.
2. Use denominator 5: 16/5 = 16/5 and 8/5 = 8/5.
3. Keep denominator 5: (16 − 8)/5 = 8/5.
4. Simplify to 8/5.
5. 8/5 = 1 3/5.

Answer: 8/5 = 1 3/5

Common Mistakes and How to Help

Keep the subtraction order. Subtracting denominators or changing only a numerator does not preserve the original quantities.

Add the difference to the fraction subtracted. Simplify or find a common denominator to compare it with the starting amount.

Questions to Check Understanding

• Add the difference to the fraction subtracted. Simplify or find a common denominator to compare it with the starting amount.
• 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.