Match Mixed and Improper Forms

Teaching Notes

Focus: Mixed Numbers to Improper Fractions. Use the worked example and teaching sequence below to explain the reasoning before independent practice.

Before You Begin

• Know numerator and denominator.

Teaching Steps for Parents and Teachers

1. To change an improper fraction to a mixed number, divide the numerator by the denominator.
2. The quotient gives wholes and the remainder gives the fractional numerator.
3. To reverse, multiply the whole number by the denominator and add the numerator.
4. For a matching problem, solve each item before drawing its connection. Check that the connected representations have equal values.

Worked Examples

Write 11/4 as a mixed number.

1. 11 ÷ 4 = 2 R 3.
2. 11 fourths contain 2 wholes and 3 fourths.

Answer: 2 3/4

Common Mistakes and How to Help

Keep the original denominator when writing the remaining fractional part.

Check: 2 × 4 + 3 = 11.

Questions to Check Understanding

• Check: 2 × 4 + 3 = 11.
• 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.