New
New
Year 4

Explain how the remainder relates to the divisor in a division equation

I can explain how the remainder relates to the divisor in a division equation.

New
New
Year 4

Explain how the remainder relates to the divisor in a division equation

I can explain how the remainder relates to the divisor in a division equation.

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Lesson details

Key learning points

  1. In a division equation or problem, the remainder is always less than the divisor.
  2. We can decide if a division equation is incorrect by comparing the size of the remainder to the size of the divisor.

Keywords

  • Dividend - The dividend is the whole amount to be divided into groups or divided into equal parts. It is what we are dividing.

  • Divisor - The divisor is the number in each group or the number of equal parts that the whole is divided into or between. It is what we are dividing by.

  • Remainder - A remainder is the amount left over after division when the dividend does not divide exactly by the divisor.

Common misconception

Rather than using the largest multiple less than or equal to the dividend, children may identify the closest multiple (one that is too high) or one that is less than the dividend but is too low.

Add further examples using counters to explore patterns where one more is added to draw attention to the size of the remainder compared to the divisor. Draw number lines alongside these so children begin to also visualise in a more abstract way.

It is important that children can visualise the parts of the problem or equation, so for those that may experience difficulty initially, continue to use practical equipment and encourage them to predict, then prove, the patterns that occur in the remainder when the dividend increases by one.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
Match the parts of the sentence correctly.
Correct Answer:54 is,the largest multiple of 6 that is less than or equal to 56

the largest multiple of 6 that is less than or equal to 56

Correct Answer:56 is,the largest multiple of 8 that is less than or equal to 60

the largest multiple of 8 that is less than or equal to 60

Correct Answer:63 is,the largest multiple of 9 that is less than or equal to 71

the largest multiple of 9 that is less than or equal to 71

Q2.
What is the largest multiple of 7 that is less than or equal to 44?
4 × 7 = 28
5 × 7 = 35
Correct answer: 6 × 7 = 42
Q3.
Look at this equation. 62 ÷ 5 = The largest multiple of 5 that is less than or equal to 62 is
Correct Answer: 60
Q4.
71 sweets are divided between 9 bags. Which multiplication fact will help you to solve this problem?
6 × 9 = 54
Correct answer: 7 × 9 = 63
8 × 9 = 72
Q5.
Use the given multiples to find the answer to the equation.
An image in a quiz
6 r 1
5 r 5
Correct answer: 5 r 6
Q6.
Find the largest missing multiple to answer this equation. 90 ÷ 8 = ___
11 r 1
Correct answer: 11 r 2
11 r 3
11 r 4

6 Questions

Q1.
True or false. A remainder in a division equation is always less than the divisor.
Correct answer: True
False
Q2.
Which of these representations shows 26 ÷ 4?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q3.
Which equation does this number line represent?
An image in a quiz
30 ÷ 6 = 5
31 ÷ 6 = 5 r 1
Correct answer: 32 ÷ 6 = 5 r 2
33 ÷ 6 = 5 r 3
Q4.
Which equation represents this image correctly?
An image in a quiz
26 ÷ 5 = 4 r 6
Correct answer: 26 ÷ 5 = 5 r 1
Q5.
Match each division expression to the result of it.
Correct Answer:42 ÷ 7 = ,6

6

Correct Answer:43 ÷ 7 = ,6 r 1

6 r 1

Correct Answer:45 ÷ 7 = ,6 r 3

6 r 3

Correct Answer:47 ÷ 7 = ,6 r 5

6 r 5

Correct Answer:48 ÷ 7 = ,6 r 6

6 r 6

Q6.
The remainder when 50 is divided by 9 is
Correct Answer: 5, five