Convert a number of quarters from an improper fraction to a mixed number | Maths

Starter quiz

Look at this number ${7} \over {4}$ We say it as seven ______.
- 'quarters' ✓
Match the equation to its quotient.
- 4 ÷ 4 =
  
  ⇔
  
  1 ✓
- 12 ÷ 4 =
  
  ⇔
  
  3 ✓
- 20 ÷ 4 =
  
  ⇔
  
  5 ✓
- 40 ÷ 4 =
  
  ⇔
  
  10 ✓
- 48 ÷ 4 =
  
  ⇔
  
  12 ✓
Select the mixed numbers.
- $1{{3} \over {4}}$ ✓
- ${7} \over {4}$
- ${3} \over {4}$
- $4{{1} \over {4}}$ ✓
- ${13} \over {4}$
Select the improper fractions.
- ${1} \over {4}$
- ${2} \over {4}$
- ${3} \over {4}$
- ${6} \over {4}$ ✓
- ${10} \over {4}$ ✓
Look at this counting sequence. What comes next? 12 quarters 16 quarters 20 quarters ______ quarters.
- '24' ✓
A whole has been divided into four equal parts. Which unit do we need to think about?
- halves
- thirds
- quarters ✓
- fifths
- tenths

Exit quiz

Four quarters is equivalent to ______ whole.
- 'one' ✓
Match the improper fractions to their equivalent whole number.
- ${12} \over {4}$
  
  ⇔
  
  3 ✓
- ${20} \over {4}$
  
  ⇔
  
  5 ✓
- ${32} \over {4}$
  
  ⇔
  
  8 ✓
- ${40} \over {4}$
  
  ⇔
  
  10 ✓
- ${44} \over {4}$
  
  ⇔
  
  11 ✓
$Use the part-part-whole model to express <Math> {7} \over {4}</Math> as a mixed number.$

Use the part-part-whole model to express ${7} \over {4}$ as a mixed number.
- ${4} \over {4}$
- ${3} \over {4}$
- $1{{3} \over {4}}$ ✓
- $2{{3} \over {4}}$
- $1{{1} \over {4}}$
Which of these represents this improper fraction ${6} \over {4}$ as a mixed number?
- $1{{1} \over {4}}$
- $1{{2} \over {4}}$ ✓
- $1{{3} \over {4}}$
- $1{{3} \over {5}}$
$Use the part-part-whole model to express <Math> {14} \over {4}</Math> as a mixed number.$

Use the part-part-whole model to express ${14} \over {4}$ as a mixed number.
- ${2} \over {4}$
- ${12} \over {4}$
- $2{{3} \over {4}}$
- $3{{1} \over {4}}$
- $3{{2} \over {4}}$ ✓
Match the improper fractions to their equivalent mixed number.
- ${13} \over {4}$
  
  ⇔
  
  $3{{1} \over {4}}$ ✓
- ${21} \over {4}$
  
  ⇔
  
  $5{{1} \over {4}}$ ✓
- ${35} \over {4}$
  
  ⇔
  
  $8{{3} \over {4}}$ ✓
- ${42} \over {4}$
  
  ⇔
  
  $10{{2} \over {4}}$ ✓
- ${47} \over {4}$
  
  ⇔
  
  $11{{3} \over {4}}$ ✓

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Lesson Details

Key learning points

An improper fraction is a fraction where the value of the numerator is greater than the value of the denominator.
An improper fraction is greater than 1
Four quarters are equal to one whole or 1
If there are quarters left, they form the fraction part of the mixed number.

Common misconception

Children may not fully convert and may leave the fractional part of the mixed number as an improper fraction e.g. 13/4 = 2 and 5/4

Support via questioning: How many quarters make one whole? How many full groups of four quarters can you make? Emphasise the fractional part needs to have a numerator smaller than the denominator and take time to discuss why.

Keywords

Mixed number - A mixed number is a whole number and a fraction combined.
Improper fraction - An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number).