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      Like terms

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      Lesson details

      Learning outcome

      I can identify like terms in an expression, generalising an understanding of unitising (equality).

      Key learning points

      1. Bar models can be used to represent an expression.
      2. Each term can be unitised just like numbers when using place value.
      3. Like terms can be identified and described.
      4. Coefficients help us describe terms.

      Keywords

      • Unitising - Unitising means treating groups that contain, or represent, the same numbers of things as ‘ones’ or ‘units’.

      • Like terms - Like terms are terms that have the same set of variables and corresponding exponents.

      Common misconception

      2y and 3y are not like terms because they have different coefficients.

      Think of 'Unitising'. 3cm and 8cm. What are the units? 8mg and 10mg. What are the units? 2y and 3y. What are we 'unitising' here?

      Teacher tip

      Visually representations are really powerful here. If you can use concrete manipulatives, or get students to make some, or draw them. That will support their learning.

      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

      Download starter quiz questions (PDF)

      6 Questions

      Q1.
      In the expression $$x^2+7x+10$$ the $$x^2$$, the $$7x$$ and the $$10$$ are all known as what?

      Variables
      Constants
      Correct answer: Terms
      Equations
      Integers

      Q2.
      How do you write $$7\times a$$ using correct algebraic notation?

      $$a \div 7$$
      $$a^7$$
      $$a+7$$
      Correct answer: $$7a$$

      Q3.
      Which of these show a correctly written identity?

      $$a+a+a=a^3$$
      Correct answer: $$a+a+a\equiv 3a$$
      $$a+a+a=3a$$

      Q4.
      Match the expressions to their simplified form.

      Correct Answer:$$3 \times x$$,$$3x$$
      Correct Answer:$$2 \times x$$,$$2x$$
      Correct Answer:$$x \times x$$,$$x^2$$
      Correct Answer:$$x \times x \times x$$,$$x^3$$

      Q5.
      Which of the below simplifies to $$a^3b$$?

      $$3 \times a \times b$$
      $$a \times 3 \times b$$
      $$a \times a \times b$$
      Correct answer: $$a \times a \times a \times b$$
      $$a \times b \times b \times b$$

      Q6.
      Match the expressions to their simplified form.

      Correct Answer:$$x \times y$$,$$xy$$
      Correct Answer:$$x \times y \times z$$,$$xyz$$
      Correct Answer:$$y \times z$$,$$yz$$
      Correct Answer:$$y \times z \times z$$,$$yz^2$$
      Correct Answer:$$y \times y \times z$$,$$y^2z$$
      Correct Answer:$$y \times z \times 2$$,$$2yz$$

      Assessment exit quiz

      Download exit quiz questions (PDF)

      6 Questions

      Q1.
      Which of these show pairs of like terms?

      Correct answer: $$-5e$$ and $$5e$$
      Correct answer: $$5e$$ and $$5e$$
      $$5c$$ and $$5e$$
      $$5e$$ and $$5f$$
      Correct answer: $$ {{1} \over {2}} e $$ and $$7e$$

      Q2.
      $$3a, 10a, {{1} \over {3}}a, 0.5a,$$ and $$a$$ are all examples of what in algebra?

      Correct answer: Like terms
      Constants
      Integers
      Equations

      Q3.
      Match each term with a like term.

      Correct Answer:$$2xy$$,$$-xy$$
      Correct Answer:$$5xyz$$,$${{1} \over {2}}xyz$$
      Correct Answer:$$-xz$$,$$0.1xz$$
      Correct Answer:$${{1} \over {2}}yz$$,$$2yz$$
      Correct Answer:$$0.1y$$,$$5y$$

      Q4.
      $$5x$$ and $$5x^2$$ are not like terms because the variables do not have corresponding .

      Correct Answer: exponents, indices, powers

      Q5.
      Select all of the like terms.

      Correct answer: $$3x^2$$
      $$2x^3$$
      $$3x$$
      Correct answer: $$2x^2$$
      $$3x^2y$$

      Q6.
      Match each term with a like term.

      Correct Answer:$$-a^2b$$,$$5a^2b$$
      Correct Answer:$$ab^2$$,$$-ab^2$$
      Correct Answer:$$2ab^2c$$,$$ab^2c$$
      Correct Answer:$$3a^2b^2$$,$$2a^2b^2$$
      Correct Answer:$$4a^2bc$$,$$3a^2bc$$
      Correct Answer:$$5a^2bc^2$$,$$4a^2bc^2$$

      To help you plan your 7 maths lesson on: Like terms, download all teaching resources for free and adapt to suit your pupils' needs...