{"id":1142,"date":"2026-11-06T12:55:26","date_gmt":"2026-11-06T07:25:26","guid":{"rendered":"https:\/\/iqreasoningacademy.com\/blog\/?p=1142"},"modified":"2026-11-06T12:55:26","modified_gmt":"2026-11-06T07:25:26","slug":"year-7-maths-topics","status":"publish","type":"post","link":"https:\/\/iqreasoningacademy.com\/blog\/year-7-maths-topics\/","title":{"rendered":"Year 7 Maths: 5 Topics That Catch Children Out After Primary School"},"content":{"rendered":"\n

Many children who felt confident in Year 6 find Year 7 maths<\/strong> surprisingly hard. Usually, it isn’t that they have got worse at maths. Instead, familiar topics suddenly go a step further, and secondary school teachers expect more working and explanation.<\/p>\n\n\n\n

This guide covers the five topics that change most from primary to secondary school, with Year 7-level example questions, the most common mistakes, and simple ways to help at home. There is also a free printable worksheet<\/strong> with 30 practice questions and answers.<\/p>\n\n\n\n

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Download the free Year 7 maths worksheet (PDF)<\/a><\/div>\n<\/div>\n\n\n\n

The 5 Year 7 maths topics that catch children out<\/h2>\n\n\n\n

1. Negative numbers<\/h3>\n\n\n\n

What changes:<\/strong> In Year 6, children mostly use negative numbers in context, such as temperatures, and count across zero. In Year 7, they add, subtract, multiply and divide them.<\/p>\n\n\n\n

Common mistake:<\/strong> Using “two negatives make a positive” for adding. For example, writing \u22127 + (\u22125) = 12 instead of \u221212. The rule only works for multiplying and dividing.<\/p>\n\n\n\n

Try these:<\/strong><\/p>\n\n\n\n

    \n
  1. \u22124 \u00d7 \u22123<\/li>\n\n\n
  2. \u22127 + (\u22125)<\/li>\n\n\n
  3. 3 \u2212 (\u22128)<\/li>\n<\/ol>\n\n\n\n
    Show answers<\/strong><\/summary>\n
      \n
    1. 12<\/li>\n\n\n
    2. \u221212<\/li>\n\n\n
    3. 11<\/li>\n<\/ol>\n<\/details>\n\n\n\n

      Tip for home:<\/strong> Use a number line for adding and subtracting, and practise the sign rules for multiplying separately.<\/p>\n\n\n\n

      2. Fractions<\/h3>\n\n\n\n

      What changes:<\/strong> In Year 6, children multiply simple pairs of fractions and divide a fraction by a whole number. In Year 7, they use all four operations with any fractions, including mixed numbers and dividing one fraction by another.<\/p>\n\n\n\n

      Common mistake:<\/strong> Adding the tops and the bottoms: 3\/4 + 2\/3 = 5\/7. The fractions need a common denominator first.<\/p>\n\n\n\n

      Try these:<\/strong><\/p>\n\n\n\n

        \n
      1. 3\/4 + 2\/3<\/li>\n\n\n
      2. 3\/4 \u00f7 3\/8<\/li>\n\n\n
      3. 1 1\/3 \u00d7 2 1\/4<\/li>\n<\/ol>\n\n\n\n
        Show answers<\/strong><\/summary>\n
          \n
        1. 17\/12, or 1 5\/12<\/li>\n\n\n
        2. 2<\/li>\n\n\n
        3. 3<\/li>\n<\/ol>\n<\/details>\n\n\n\n

          Tip for home:<\/strong> Make sure times tables are completely secure. Almost every fraction mistake in Year 7 is really a times-table or common-denominator slip.<\/p>\n\n\n\n

          3. Algebra<\/h3>\n\n\n\n

          What changes:<\/strong> In Year 6, algebra means simple formulae and “missing number” problems. In Year 7, children simplify expressions, expand brackets and solve equations step by step.<\/p>\n\n\n\n

          Common mistake:<\/strong> Multiplying only the first term in a bracket: 4(2x \u2212 3) = 8x \u2212 3 instead of 8x \u2212 12.<\/p>\n\n\n\n

          Try these:<\/strong><\/p>\n\n\n\n

            \n
          1. Simplify 3a + 5b \u2212 a + 2b<\/li>\n\n\n
          2. Expand 4(2x \u2212 3)<\/li>\n\n\n
          3. Solve 3x + 5 = 20<\/li>\n<\/ol>\n\n\n\n
            Show answers<\/strong><\/summary>\n
              \n
            1. 2a + 7b<\/li>\n\n\n
            2. 8x \u2212 12<\/li>\n\n\n
            3. x = 5<\/li>\n<\/ol>\n<\/details>\n\n\n\n

              Tip for home:<\/strong> Ask your child to check equation answers by substituting them back in: 3 \u00d7 5 + 5 = 20.<\/p>\n\n\n\n

              4. Percentages and ratio<\/h3>\n\n\n\n

              What changes:<\/strong> In Year 6, children find percentages of amounts and solve simple sharing problems. In Year 7, they work out percentage increases and decreases, share amounts in a ratio, and solve proportion problems.<\/p>\n\n\n\n

              Common mistake:<\/strong> Working out a percentage increase using the new amount. For a rise from \u00a340 to \u00a350, the increase is 10 \u00f7 40 = 25%, not 10 \u00f7 50 = 20%.<\/p>\n\n\n\n

              Try these:<\/strong><\/p>\n\n\n\n

                \n
              1. Increase \u00a360 by 15%<\/li>\n\n\n
              2. Share \u00a356 in the ratio 3 : 5<\/li>\n\n\n
              3. A price rises from \u00a340 to \u00a350. What is the percentage increase?<\/li>\n<\/ol>\n\n\n\n
                Show answers<\/strong><\/summary>\n
                  \n
                1. \u00a369<\/li>\n\n\n
                2. \u00a321 and \u00a335<\/li>\n\n\n
                3. 25%<\/li>\n<\/ol>\n<\/details>\n\n\n\n

                  Tip for home:<\/strong> Use real shopping: sale prices, recipes for more people, and splitting bills are perfect everyday practice.<\/p>\n\n\n\n

                  5. Powers, roots and order of operations<\/h3>\n\n\n\n

                  What changes:<\/strong> Children already use the order of operations with the four operations in Year 6. In Year 7, powers and roots join in, with longer calculations that need BIDMAS (Brackets, Indices, Division and Multiplication, Addition and Subtraction).<\/p>\n\n\n\n

                  Common mistake:<\/strong> Working left to right: 3 + 4 \u00d7 2 = 14 instead of 11.<\/p>\n\n\n\n

                  Try these:<\/strong><\/p>\n\n\n\n

                    \n
                  1. 5\u00b2 \u2212 3\u00b3<\/li>\n\n\n
                  2. \u221a81 + \u221a16<\/li>\n\n\n
                  3. 20 \u2212 18 \u00f7 (2 + 1)\u00b2<\/li>\n<\/ol>\n\n\n\n
                    Show answers<\/strong><\/summary>\n
                      \n
                    1. \u22122<\/li>\n\n\n
                    2. 13<\/li>\n\n\n
                    3. 18<\/li>\n<\/ol>\n<\/details>\n\n\n\n

                      Tip for home:<\/strong> Learn the square numbers up to 15\u00b2 and the first five cube numbers by heart. They come up constantly.<\/p>\n\n\n\n

                      Why does Year 7 maths feel harder?<\/h2>\n\n\n\n

                      Apart from the new content, two things change:<\/p>\n\n\n\n