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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
New
Year 7

Multiplying an expression by a term

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

Download all resources
Share activities with pupils

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.

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.

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.

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
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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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: $$20y^5-15xy^2$$
$$15xy^2-20y^5$$
$$20y^5-15x^2y$$
$$-15xy^2-20y^5$$