New
New
Year 8
Brackets in equations
I can appreciate the significance of the bracket in an equation.
New
New
Year 8
Brackets in equations
I can appreciate the significance of the bracket in an equation.
Lesson details
Key learning points
- Multiplying both sides of an equation by the same term can be shown using brackets.
- An expression involving brackets can be expanded.
- Equations involving brackets can be expressed in words.
- Equations involving brackets can be represented using bar models.
Common misconception
That "$$x$$ times five, plus three" is the same as "$$x$$ plus three, times five".
Use visual representations to demonstrate why and how they are different. Use algebra tiles if you have them, or get pupils to draw them.
Keywords
Equation - An equation is used to show two expressions that are equal to each other.
In addition to using visual representations to show the difference between $${5x+3}=10$$ and $$5(x+3)=10$$ you can also work backwards. Give them visual representations and ask them to write the equation.
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).
Video
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Starter quiz
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6 Questions
Q1.
Turning the expression $$5(y-2)$$ into $$5y-10$$ is known as the brackets.
Correct answer: multiplying out
multiplying out
erasing
factorising
Correct answer: expanding
expanding
Q2.
$$2(x+4)$$ and $$2x+4$$ are the equivalent expressions. True or false?
True. There is a $$2$$, an $$x$$, and a $$+4$$. That means they are the same.
Correct answer: False. $$2$$ lots of $$(x+4)$$ is $$(x+4)+(x+4)$$ which is $$2x+8$$ not $$2x+4$$
False. $$2$$ lots of $$(x+4)$$ is $$(x+4)+(x+4)$$ which is $$2x+8$$ not $$2x+4$$
You cannot know until you know the value of $$x$$.
Q3.
Which of these are expressions for the perimeter of this square?
$$5y+3$$
$$4\times5y+3$$
Correct answer: $$4(5y+3)$$
$$4(5y+3)$$
$$20y+3$$
Correct answer: $$20y+12$$
$$20y+12$$
Q4.
What equation does this bar model represent?
$$4y=12$$
$$4y=20$$
Correct answer: $$4y+12=20$$
$$4y+12=20$$
$$4y+20=12$$
$$4(y+12)=20$$
Q5.
Expand $$7(y+8)$$.
$$7y+8$$
$$7y+15$$
Correct answer: $$7y+56$$
$$7y+56$$
$$y+56$$
Q6.
Expand $$-7(y+8)$$.
$$7y-56$$
Correct answer: $$-7y-56$$
$$-7y-56$$
$$-7y+56$$
$$7y+56$$
Exit quiz
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6 Questions
Q1.
If you multiply both sides of an equation by $$2$$, you will maintain .
the value
Correct answer: equality
equality
equation
the expressions
Q2.
True or false? Multiplying by $$5$$ and then adding $$10$$ is the same as adding $$10$$ then multiplying by $$5$$.
True. Both have $$\times 5$$ and $$+10$$ so they are the same function.
Correct answer: False. Order matters.
False. Order matters.
Q3.
What equation does this bar model represent?
Correct answer: $$3\times x + 5 = 17$$
$$3\times x + 5 = 17$$
$$x + 5 \times 3 = 17$$
$$(x + 5) \times 3 = 17$$
$$x + 5 = 17$$
Correct answer: $$3x + 5 = 17$$
$$3x + 5 = 17$$
Q4.
What does this bar model represent?
$$3\times x + 5 = 17$$
Correct answer: $$(x + 5) \times 3 = 17$$
$$(x + 5) \times 3 = 17$$
Correct answer: $$3(x + 5) = 17$$
$$3(x + 5) = 17$$
$$x + 5 \times 3 = 17$$
Correct answer: $$3x + 15 = 17$$
$$3x + 15 = 17$$
Q5.
Multiply both sides of this equation $${1\over3}x-5 = 2x+7$$ by $$3$$.
$$x-5=6x+7$$
Correct answer: $$x-15=6x+21$$
$$x-15=6x+21$$
$$3x-15=6x+21$$
Correct answer: $$3({1\over3}x-5) = 3(2x+7)$$
$$3({1\over3}x-5) = 3(2x+7)$$
Q6.
Which of the below is the most efficient first step to solve the equation $${3\over{x}}= 10$$ ?
$$3({3\over{x}})= 3(10)$$
Correct answer: $$x({3\over{x}})= x(10)$$
$$x({3\over{x}})= x(10)$$
$$10({3\over{x}})= 10(10)$$
$$10x({3\over{x}})= 10x(10)$$