New
New
Year 7

Simplifying by collecting like terms

I can simplify expressions by collecting like terms.

New
New
Year 7

Simplifying by collecting like terms

I can simplify expressions by collecting like terms.

Lesson details

Key learning points

  1. Like terms and their coefficients can be identified.
  2. Like terms can be represented using a bar model.
  3. Like terms can be collected together, paying careful attention to coefficients.
  4. Expressions are easier to use once you have collected all the like terms.

Common misconception

Simplifying means just grouping the algebraic terms.

Remind pupils that fully simplifying means the expression cannot be simplified further.

Keywords

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

  • Simplify - Simplifying is to write an expression in the most efficient and compact form without affecting the value of the original expression.

Simplifying can make calculations easier (third learning cycle). Ask pupils to write their own algebraic expressions and simplify them to see how much more efficient they can be.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
__________ have the same set of variables and corresponding exponents.
Expressions
Constants
Variables
Equations
Correct answer: Like terms
Q2.
Which of these show pairs of like terms?
$$ 7y $$ and $$ 7x $$
Correct answer: $$n $$ and $$8n $$
Correct answer: $$-x $$ and $$4x $$
$$-6e $$ and $$ -3f$$
Correct answer: $$12y $$ and $$ \frac{1}{2} y$$
Q3.
Which of these will simplify to $$3x$$?
$$x \times x \times x$$
Correct answer: $$x + x + x$$
$$3 + x$$
Correct answer: $$3 \times x$$
Q4.
Match the calculations with the correct answer when evaluated.
Correct Answer:5-2,3

3

Correct Answer:2-5,-3

-3

Correct Answer:5-(-2),7

7

Correct Answer:7-2-5,0

0

Correct Answer:7-2+5,10

10

Correct Answer:-7+2-5,-10

-10

Q5.
Match the like terms.
Correct Answer:$$5a$$,$$-2a$$

$$-2a$$

Correct Answer:$$3b$$,$$b$$

$$b$$

Correct Answer:$$-2c$$,$$12c$$

$$12c$$

Correct Answer:$$8ab$$,$$-ab$$

$$-ab$$

Correct Answer:$$bc$$,$${{1}\over{4}}bc$$

$${{1}\over{4}}bc$$

Q6.
Which of the below is not a like term?
$$3e^2f$$
$$-2e^2f$$
Correct answer: $$3ef^2$$
$$2e^2f$$
$$3000e^2f$$

6 Questions

Q1.
When an expression cannot be simplified further, we say it has been simplified.
Correct Answer: fully, Fully
Q2.
Fully simplify the expression $$2x+3y+7x-y$$
$$5xy-7xy$$
$$2x+7x+3y-y$$
$$9x + 3$$
Correct answer: $$9x + 2y$$
$$9x-2y$$
Q3.
Which of the below statements is true of the expression $$9x+2y$$?
It simplifies to $$11xy$$.
Correct answer: It can not be simplified further.
It simplifies to $$11xy^2$$
Q4.
Which of these best describes what is expressed by this set of algebra tiles?
An image in a quiz
$$4y+6y \equiv 10y$$
$$4y-6y \equiv 2y$$
Correct answer: $$4y-6y \equiv -2y$$
$$6y-4y \equiv 2y$$
Q5.
Simplify $$3x^2+x+2+5x^2+x+5$$
$$8x^2+x^2+7$$
$$8x^4+2x^2+7$$
Correct answer: $$8x^2+2x+7$$
$$8x^4+7$$
$$8x^3+7$$
Q6.
Which is a fully simplified expression for the perimeter of this rectangle?
An image in a quiz
$$6x+14+2x+10y$$
$$3x+7+x+5y+3x+7+x+5y$$
Correct answer: $$8x+10y+14$$
$$4x+5y+7+4x+5y+7$$