Match Equal Quotients

Teaching Notes

Focus: Scaling Dividend and Divisor by the Same Factor. 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. If the divisor has decimal places, multiply both numbers by the same power of ten until the divisor is a whole number.
2. The quotient stays the same.
3. Divide using place value, keeping track of the decimal point in the quotient.
4. These worksheets use the answers supplied by the existing calculation bank; do not round unless a question explicitly asks you to.
5. For a matching problem, solve each item before drawing its connection. Check that the connected representations have equal values.

Worked Examples

Evaluate 1.26/0.3.

1. Multiply both numbers by 10: 12.6 ÷ 3.
2. Divide to get 4.2.
3. Check: 4.2 × 0.3 = 1.26.

Answer: 4.2

Common Mistakes and How to Help

Moving only the divisor’s decimal point changes the problem. Apply the same shift to the dividend, and keep any zero needed to hold a quotient place.

Multiply the quotient by the original divisor. The result should return the original dividend.

Questions to Check Understanding

• Multiply the quotient by the original divisor. The result should return the original 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.