New
New
Ordering fractions in different ways
I can compare and order fractions using a range of techniques.
Lesson 15 of 18
New
New
- Year 7
Ordering fractions in different ways
I can compare and order fractions using a range of techniques.
Lesson details
Key learning points
- Two fractions can be compared when they have the same numerator.
- Two fractions can be compared by comparing their respective differences from 1.
Keywords
Denominator - A denominator is the expression in a fraction that is written below the fraction line. It is the divisor.
Numerator - A numerator is the expression in a fraction that is written above the fraction line. It is the dividend.
Proper fraction - A proper fraction is a fraction where the numerator is less than the denominator.
Common misconception
That fractions can only be compared using a common denominator.
Lots of visual representations are useful here looking at what happens to the size of the 'parts' as the denominator increases.
As pupils come into the room have 4 digits on the board, it would be useful if one of the digits was repeated. Ask them to write down 2 fractions and identify the greater. This will allow you to assess if any think of the same same numerator.
Teacher tip
Licence
This content is © Oak National Academy Limited (2025), 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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Prior knowledge starter quiz
6 Questions
Q1.Order the steps to show that $$\frac{12}{20}$$ is not equivalent to $$\frac{48}{100}$$
Order the steps to show that $$\frac{12}{20}$$ is not equivalent to $$\frac{48}{100}$$
1 - $$\frac{12}{20} \times 1$$
1
- $$\frac{12}{20} \times 1$$
2 - $$\frac{12}{20} \times \frac{5}{5}$$
2
- $$\frac{12}{20} \times \frac{5}{5}$$
3 - $$\frac{12 \times 5}{20 \times 5}$$
3
- $$\frac{12 \times 5}{20 \times 5}$$
4 - $$\frac{60}{100}$$
4
- $$\frac{60}{100}$$
Q2.True or false? $$\frac{2}{3} = \frac{34}{48}$$
True or false? $$\frac{2}{3} = \frac{34}{48}$$
True
Correct answer: False
False
Q3.Which of the following are true?
Which of the following are true?
$$\frac{2}{3} = \frac{34}{48}$$
$$\frac{4}{9} = \frac{20}{36}$$
Correct answer: $$\frac{7}{9} = \frac{56}{72}$$
$$\frac{7}{9} = \frac{56}{72}$$
Correct answer: $$\frac{48}{144} = \frac{1}{3}$$
$$\frac{48}{144} = \frac{1}{3}$$
Correct answer: $$\frac{112}{80} = \frac{7}{5}$$
$$\frac{112}{80} = \frac{7}{5}$$
Q4.Select the correct symbol to make the statement true. $$\frac{5}{8}\ \square \ \frac{11}{16} $$
Select the correct symbol to make the statement true. $$\frac{5}{8}\ \square \ \frac{11}{16} $$
Correct answer: <
<
>
=
Q5.Select the correct symbol to make the statement true. $$\frac{6}{5}\ \square \ \frac{108}{90} $$
Select the correct symbol to make the statement true. $$\frac{6}{5}\ \square \ \frac{108}{90} $$
<
>
Correct answer: =
=
Q6.Select the correct symbol to make the statement true. $$\frac{9}{12}\ \square \ \frac{10}{16} $$
Select the correct symbol to make the statement true. $$\frac{9}{12}\ \square \ \frac{10}{16} $$
<
Correct answer: >
>
=
Assessment exit quiz
6 Questions
Q1.True or false? A proper fraction has a numerator which is greater than its denominator.
True or false? A proper fraction has a numerator which is greater than its denominator.
True
Correct answer: False
False
Q2.In which of the following would it be easier to compare the numerators?
In which of the following would it be easier to compare the numerators?
Correct answer: $$\frac{4}{7}$$ and $$\frac{12}{39}$$
$$\frac{4}{7}$$ and $$\frac{12}{39}$$
$$\frac{101}{120}$$ and $$\frac{103}{240}$$
Correct answer: $$\frac{8}{3}$$ and $$\frac{64}{25}$$
$$\frac{8}{3}$$ and $$\frac{64}{25}$$
$$\frac{15}{27}$$ and $$\frac{7}{9}$$
Q3.The the denominator, the smaller the parts.
The the denominator, the smaller the parts.
Correct Answer: larger
larger
Q4.Which statements need the symbol > inserted to make them true?
Which statements need the symbol > inserted to make them true?
$$\frac{11}{22}\ \square \ \frac{11}{20} $$
Correct answer: $$\frac{17}{6}\ \square \ \frac{17}{9} $$
$$\frac{17}{6}\ \square \ \frac{17}{9} $$
$$\frac{5}{1917}\ \square \ \frac{5}{1916} $$
Correct answer: $$\frac{987}{988}\ \square \ \frac{987}{998} $$
$$\frac{987}{988}\ \square \ \frac{987}{998} $$
Q5.Write the following in order from smallest to largest.
Write the following in order from smallest to largest.
1 - $$\frac{17}{300}$$
1
- $$\frac{17}{300}$$
2 - $$\frac{17}{287}$$
2
- $$\frac{17}{287}$$
3 - $$\frac{17}{54}$$
3
- $$\frac{17}{54}$$
4 - $$\frac{17}{53}$$
4
- $$\frac{17}{53}$$
5 - $$\frac{17}{17}$$
5
- $$\frac{17}{17}$$
6 - $$\frac{17}{3}$$
6
- $$\frac{17}{3}$$
Q6.Jun completes a 20 question maths quiz and gets 19 correct. Laura completes a 19 question maths quiz and gets 18 correct. Who did better and why?
Jun completes a 20 question maths quiz and gets 19 correct. Laura completes a 19 question maths quiz and gets 18 correct. Who did better and why?
Correct answer: Jun as he only got one question wrong from a greater number of questions
Jun as he only got one question wrong from a greater number of questions
Laura as she only got one question wrong from a smaller number of questions
Neither as they are both one question away from getting it all correct.
