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Year 7

Multiplying an expression by a term

I can use the distributive law to multiply an expression by a term.

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New
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Year 7

Multiplying an expression by a term

I can use the distributive law to multiply an expression by a term.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. The distributive law can make multiplication easier.
  2. The distributive law can be understood using an area model.
  3. A bar model can be used to represent the distributive law.
  4. An expression can be multiplied by any term.

Keywords

  • Constant - A constant is a term that does not change; it contains no variables.

  • Variable - A variable is a quantity that can take on a range of values.

Common misconception

How to deal with exponents. y^2 times by y makes 3y. Or at least has a coefficient that is not 1.

Unsimplifying first. Not sure? Break it down. What is it? a^2 is a x a. So a^2 x a must be a x a x a.

Area models become really powerful here. x^2 times y^2 is a tough one to do with algebra tiles! If students get confused around exponents unsimplifying helps. 2a x 3a^2 is 2 x a x 3 x a x a. Commuted to 2 x 3 x a x a x a makes the question far easier
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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).

Lesson video

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Starter quiz

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6 Questions

Q1.
In the expression $$x-7$$ the $$-7$$ is a constant. What do we call the $$x$$?
An exponent.
Correct answer: A variable term.
An equation.
Q2.
Match the expressions to their simplified form.
Correct Answer:$$x+x$$,$$2x$$

$$2x$$

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

$$x^2$$

Correct Answer:$$x \times y$$,$$xy$$

$$xy$$

Correct Answer:$$y \times y$$,$$y^2$$

$$y^2$$

Correct Answer:$$y+y$$,$$2y$$

$$2y$$

Q3.
This area model helps us with which multiplication?
An image in a quiz
$$9x \times 7$$
$$7 \times 9x$$
Correct answer: $$9(x+7)$$
$$7(x+9)$$
$$9 \times 7x$$
Q4.
This area model is used to expand $$9(x+7)$$. What is hidden by the ink blots?
An image in a quiz
$$9x$$ and $$7$$
$$63x$$
Correct answer: $$9x$$ and $$63$$
$$9x$$ and $$16$$
$$7x$$ and $$63$$
Q5.
Using distributive law $$6(2x+3 +y)$$ can also be written as which of the below?
Correct answer: $$12x+18 +6y$$
$$62x+3+y$$
$$36xy$$
$$30xy$$
$$6+2x+3+y$$
Q6.
Match together the expressions which are always equal to each other.
Correct Answer:$$2(x+5)$$,$$2x+10$$

$$2x+10$$

Correct Answer:$$2(x-5)$$,$$2x-10$$

$$2x-10$$

Correct Answer:$$-2(x-5)$$,$$10-2x$$

$$10-2x$$

Correct Answer:$$-2(x+5)$$,$$-2x-10$$

$$-2x-10$$

Exit quiz

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6 Questions

Q1.
In the expression $$5b^4 + 7$$, the 4 is __________.
an equation
a term
Correct answer: an exponent
a multiplier
a constant
Q2.
Expand $$x(x+1)$$
$$2x+1$$
$$2x+2$$
$$2x+x$$
Correct answer: $$x^2+x$$
$$x^2+1$$
Q3.
Algebra tiles shown are being used to model which of these?
An image in a quiz
$$x(x+1)$$
Correct answer: $$x(x+4)$$
$$2(x+4)$$
$$x(x^2+4x)$$
Q4.
What is hidden by the ink blots in this area model?
An image in a quiz
$$2a$$ and $$9a^2$$
$$2a^2$$ and $$9a$$
$$a^3$$ and $$9a$$
$$9a^3$$ and $$9a^2$$
Correct answer: $$a^3$$ and $$9a^2$$
Q5.
Expand $$2e^2(3e +7f -5)$$
Correct answer: $$6e^3 +14e^2f -10e^2$$
$$2e^3 +14e^2f -10e^2$$
$$6e^3 +14ef -10e^2$$
$$6e^3 +14e^2f -10e$$
Q6.
Expand $$-5y^2(3x-4y^3)$$
Correct answer: $$20y^5-15xy^2$$
$$15xy^2-20y^5$$
$$20y^5-15x^2y$$
$$-15xy^2-20y^5$$