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      Between numbers

      I can appreciate that, for any two numbers, there is always another number in between them.

      Lesson 17 of 18
      New
      New
      • Year 7

      Between numbers

      I can appreciate that, for any two numbers, there is always another number in between them.

      Lesson details

      Key learning points

      1. Using a number line you can find numbers between two integers.
      2. Using a number line you can find numbers between two proper fractions.
      3. Using a number line you can find numbers between two decimals..
      4. Using a number it is always possible to find a number between two other numbers.

      Keywords

      • Equivalent fraction - Two fractions are equivalent if they have the same value.

      • Proper fraction - A proper fraction is a fraction where the numerator is less than the denominator.

      • Lowest common multiple - The lowest common multiple is the lowest number that is a multiple of two or more numbers.

      Common misconception

      When decimals go beyond thousandths you cannot find a number between 2 numbers.

      Use a 'zoomable' number line to show what happens as we zoom in.

      Choose a 'secret' decimal, the number of decimal places can be adapted to the ability of the class. Pupils ask questions 'is it between ... & ...?' You answer yes or no and choose another pupil. They keep 'zooming' in until they get it correct.
      Teacher tip

      Equipment

      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.
      The absolute value of a number is its from zero.

      Correct Answer: distance

      Q2.
      Order the values from smallest to largest.

      1 - $$(-0.241)$$
      2 - $$(-0.24)$$
      3 - $$(-0.239)$$
      4 - $$(-0.237)$$
      5 - $$(-0.024)$$

      Q3.
      Order the values from smallest to largest.

      1 - $$(-72.1)$$
      2 - $$(-72.01)$$
      3 - $$(-70.2)$$
      4 - $$70.2$$
      5 - $$72.01$$
      6 - $$72.1$$

      Q4.
      Order these fractions from smallest to largest.

      1 - $$\left(-17\frac{1}{4}\right)$$
      2 - $$\left(-16\frac{3}{4}\right)$$
      3 - $$\left(-16\frac{1}{2}\right)$$
      4 - $$16\frac{1}{5}$$
      5 - $$16\frac{1}{4}$$
      6 - $$16\frac{1}{2}$$

      Q5.
      Order these fractions from smallest to largest.

      1 - $$\left(-\frac{3}{8}\right)$$
      2 - $$\left(-\frac{7}{24}\right)$$
      3 - $$\left(-\frac{12}{48}\right)$$
      4 - $$\left(-\frac{3}{16}\right)$$

      Q6.
      Order these values from smallest to largest.

      1 - $$\left(-\frac{13}{16}\right)$$
      2 - $$\left(-\frac{5}{8}\right)$$
      3 - $$0.25$$
      4 - $$0.375$$
      5 - $$\frac{17}{32}$$

      Assessment exit quiz

      6 Questions

      Q1.
      The is the lowest number that is a multiple of two or more numbers.

      Correct Answer: LCM, lowest common multiple, lcm

      Q2.
      Sofia writes down the number 0.9999 Select all the numbers below that are greater than Sofia's number.

      0.9999
      0.9990
      Correct answer: 0.99991
      0.9991

      Q3.
      I am rolling a six sided dice and filling in two grids. What number must replace $$a$$ so that the number in the first grid will be greater than the number in the second grid?

      An image in a quiz
      Correct Answer: 6, six

      Q4.
      I am rolling a six sided dice and filling in two grids. If $$a$$ = 5, which of the following numbers can replace $$b$$ so that the second number is greater?

      An image in a quiz
      2
      3
      4
      Correct answer: 5
      Correct answer: 6

      Q5.
      What fraction is halfway between $$\frac{3}{7}$$ and $$\frac{5}{7}$$?

      Correct answer: $$\frac{4}{7}$$
      $$\frac{8}{15}$$
      Correct answer: $$\frac{52}{91}$$
      $$\frac{62}{112}$$

      Q6.
      What fraction is halfway between $$\frac{2}{9}$$ and $$\frac{5}{9}$$?

      $$\frac{3}{18}$$
      $$\frac{4}{18}$$
      $$\frac{5}{18}$$
      $$\frac{6}{18}$$
      Correct answer: $$\frac{7}{18}$$

      Lesson appears in

      UnitMaths / Comparing and ordering fractions and decimals (positive and negative)