Solve division problems involving grouping, including those with remainders | Maths

Starter quiz

Division means splitting into __________ parts or groups.
- different
- equal ✓
- unequal
Look at the image. 14 has been divided into groups of 3 There are 4 groups of 3 and a remainder of ______
- '2' ✓
Which equation represents this image?
- 16 = 2 × 6 + 4 ✓
- 16 = 2 × 4 + 6
- 16 = 2 × 5 + 6
Which bar model represents this equation? 37 = 4 × 8 + 5
- a
- b
- c ✓
Sofia divides some counters into equal groups of 7 with a remainder of 3 How many counters did she start with? ______
- '38' ✓
Look at the image. What is the remainder? ______
- '6' ✓

Exit quiz

Match the keyword to the correct definition.
- equal grouping
  
  ⇔
  
  making groups with the same number of objects in each group ✓
- division
  
  ⇔
  
  splitting into equal parts or groups ✓
- divisor
  
  ⇔
  
  what we are dividing by ✓
- remainder
  
  ⇔
  
  the amount left over after a division ✓
Match the multiplication and division equations that can represent the same number of groups.
- 2 × 9 = 18
  
  ⇔
  
  18 ÷ 9 = 2 ✓
- 6 × 7 = 42
  
  ⇔
  
  42 ÷ 7 = 6 ✓
- 5 × 8 = 40
  
  ⇔
  
  40 ÷ 8 = 5 ✓
- 7 × 4 = 28
  
  ⇔
  
  28 ÷ 4 = 7 ✓
There are 21 cookies and each bag can hold 3 cookies. Which equations could be used to solve this problem?
- 21 ÷ 3 = 7 ✓
- 3 + 21 = 24
- 21 = 7 × 3 ✓
- 24 - 3 = 21
Alex has 35 pages left to read in his book. He reads 7 pages each day. How many days did it take him to finish reading his book? ______ days
- '5' ✓
Match the multiplication and division equations with remainders that represent the same number of groups.
- 20 ÷ 3 = 6 r 2
  
  ⇔
  
  6 × 3 + 2 ✓
- 23 ÷ 5 = 4 r 3
  
  ⇔
  
  4 × 5 + 3 ✓
- 19 ÷ 6 = 3 r 1
  
  ⇔
  
  3 × 6 + 1 ✓
- 25 ÷ 4 = 6 r 1
  
  ⇔
  
  6 × 4 + 1 ✓
Sofia has 28 cookies and each bag can hold 6 cookies. Which of these statements is correct?
- She can fill 5 bags and will have no cookies left over.
- She can fill 4 bags and will have a remainder of 4 cookies. ✓
- She can fill 4 bags and will have a remainder of 2 cookies.

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Lesson Details

Key learning points

A multiplication equation can be written to solve division problems.
A division equation can be written to solve division problems.
The number of equal groups in a number can be found by counting forwards.
The number of equal groups in a number can be found by counting backwards.
Counting forwards is usually easier because multiplication facts can be used to help.

Common misconception

Children may not understand division as repeated subtraction because they can count forwards to find the number of equal groups in a number.

On a number line, show how counting forwards and backwards in multiples results in the same answer. Discuss the difficulty of using tables facts to count backwards when there is a remainder, so they understand why counting forwards is more efficient.

Keywords

Grouping - Grouping is when we divide a number of objects into equal groups. We know the total number of objects and the number of objects in each group, but we do not know how many equal groups there are.
Division - Division means splitting into equal parts or groups
Divisor - The divisor 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.