Identify when there will be a remainder | Maths | Quizalize & Oak National Academy

Starter quiz

1. A remainder in a division equation is always __________ the divisor.
- greater than
- equal to
- less than ✓
Which of these representations shows 23 ÷ 5?
- A
- B
- C ✓
Which equation does this number line represent?
- 24 ÷ 4 = 6
- 25 ÷ 4 = 6 r 1
- 26 ÷ 4 = 6 r 2
- 27 ÷ 4 = 6 r 3 ✓
Which equation represents this image correctly?
- 25 ÷ 6 = 4 r 1 ✓
- 25 ÷ 6 = 3 r 7
Match each division expression to the result of it.
- 56 ÷ 8 =
  
  ⇔
  
  7 ✓
- 58 ÷ 8 =
  
  ⇔
  
  7 r 2 ✓
- 59 ÷ 8 =
  
  ⇔
  
  7 r 3 ✓
- 62 ÷ 8 =
  
  ⇔
  
  7 r 6 ✓
- 64 ÷ 8 =
  
  ⇔
  
  8 ✓
The remainder when 70 is divided by 12 is ______
- '10' ✓

Exit quiz

1. Match the parts of the sentence correctly.
- There will be no remainder
  
  ⇔
  
  if the dividend is a multiple of the divisor. ✓
- There will be a remainder
  
  ⇔
  
  if the dividend is not a multiple of the divisor. ✓
Which of the following will not have a remainder?
- 48 ÷ 9
- 48 ÷ 8 ✓
- 48 ÷ 7
- 48 ÷ 6 ✓
42 balls are sorted into 8 buckets for sports day. Are there any balls left over?
- Yes, because 42 is not a multiple of 8 ✓
- No, there are no balls left over
Which of these numbers will have a remainder when the divisor is 7?
- 35
- 37 ✓
- 47 ✓
- 56
- 60 ✓
We know that multiples of 3 have a digit sum that is divisible by 3 Which of these numbers will have a remainder when divided by 3?
- 54
- 55 ✓
- 56 ✓
- 57
Multiples of 9 have a digit sum that is divisible by 9 Which of these numbers will have a remainder when divided by 9?
- 135
- 153
- 145 ✓
- 171
- 163 ✓

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Lesson Details

Key learning points

If the dividend is a multiple of the divisor, there will be no remainder.
If the dividend is not a multiple of the divisor, there will be a remainder.
Times table knowledge can help to identify if there will be a remainder.
The rules of divisibility can help to identify if there will be a remainder.

Common misconception

Children may work inefficiently, e.g. they may find the digit sum of 27 to find if it is a multiple of 6, instead of first reasoning that it cannot be because it is an odd number.

Encourage children to consider what they know about a number first (e.g. all even numbers have even multiples) before applying other parts of rules so that they work in the most efficient way. Display models of these to enable recall of them.

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.