Complete the Vertical Calculation

Teaching Notes

Focus: Two Digits ÷ Two Digits. 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. Decide how many complete groups of the divisor fit into the current amount.
2. Write a quotient digit, multiply it by the divisor, and subtract.
3. Bring down the next digit and repeat.
4. A zero quotient digit may be needed to hold a place.
5. At the end, the remainder must be smaller than the divisor.
6. For a blank, identify the missing quantity. Substitute the completed value back into the original statement to check it.

Worked Examples

Find the quotient and remainder: 87 ÷ 23.

1. Use multiples of 23 to find a quotient of 3.
2. 23 × 3 = 69.
3. 87 − 69 = 18.
4. 18 is less than 23. Check: 23 × 3 + 18 = 87.

Answer: 3 R 18

Common Mistakes and How to Help

Do not stop just because a current digit is smaller than the divisor. Check whether more digits remain to be brought down. A remainder equal to or larger than the divisor means another complete group fits.

Multiply the quotient by the divisor and add the remainder. This must equal the dividend.

Questions to Check Understanding

• Multiply the quotient by the divisor and add the remainder. This must equal the 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.