Check Using the Remainder's Place Value

Teaching Notes

Focus: Understanding Remainders in Decimal Division. Use the worked example and teaching sequence below to explain the reasoning before independent practice.

Before You Begin

• Understand division and decimal place value.

Teaching Steps for Parents and Teachers

1. Scale both numbers by the same power of ten to make the divisor a whole number.
2. When stopping at a whole-number quotient, subtract divisor × quotient from the original dividend.
3. State the remainder in the original units.

Worked Examples

Divide 2.5 by 0.6 using a whole-number quotient and a remainder.

1. 25 ÷ 6 gives quotient 4 and remainder 1.
2. Return to the original scale: 1 ÷ 10 = 0.1.
3. 0.6 × 4 + 0.1 = 2.5.

Answer: 4 R 0.1

Common Mistakes and How to Help

The remainder in the scaled division must be converted back to the original scale.

Is 0 ≤ 0.1 < 0.6, and does the multiplication check recover 2.5?

Questions to Check Understanding

• Is 0 ≤ 0.1 < 0.6, and does the multiplication check recover 2.5?
• 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.