New
New
Securing understanding of equality
I can appreciate how to maintain equality between two statements.
Lesson 2 of 17
New
New
- Year 8
Securing understanding of equality
I can appreciate how to maintain equality between two statements.
Lesson details
Key learning points
- Bar models can be used to compare expressions.
- If the expressions are equal the bars will be the same length.
- Operations can be performed on the bars that maintain equality.
- This can be extended to operations on statements expressed algebraically.
Keywords
Equation - An equation is used to show two expressions that are equal to each other.
Variable - A variable is a quantity that can take on a range of values, often denoted by a letter.
Constant - A constant is a term that does not change; it contains no variables.
Like terms - Like terms are terms that have the same set of variables and corresponding exponents.
Common misconception
Trying to double an expression and only doubling one term.
Use the numerical examples to show why this does not work. Use of brackets in working out is also helpful.
Use the numerical examples to show how the processes that work with constants also work exactly the same with algebra. Showing that the process with numbers/ pictures and letters is the same can be really powerful to link the new with the familiar.
Teacher tip
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
6 Questions
Q1.Aisha is $$a$$ years old. Which of these is an expression for her age 2 years ago?
Aisha is $$a$$ years old. Which of these is an expression for her age 2 years ago?
$$a + 2$$
Correct answer: $$a - 2$$
$$a - 2$$
$$2a$$
$$a\over 2$$
$$2 - a$$
Q2.Andeep is thinking of a number, when he adds 2 then multiplies by 5 he gets 27. Which of these equations represents his number?
Andeep is thinking of a number, when he adds 2 then multiplies by 5 he gets 27. Which of these equations represents his number?
$$5a + 2 = 27$$
$$a = 27 + 2 \times 5$$
Correct answer: $$5(a + 2) = 27$$
$$5(a + 2) = 27$$
$${a-2\over 5}=27$$
$$a + 2\times 5 = 27$$
Q3.Which equations are represented by this bar model?
Which equations are represented by this bar model?
Correct answer: $$3x = y + 6$$
$$3x = y + 6$$
$$3x + 6 = y$$
$$3x + y = 6$$
Correct answer: $$6 + y = 3x$$
$$6 + y = 3x$$
$$x = 6 + y$$
Q4.Select the calculation that is equivalent to $$8+4\over 4$$.
Select the calculation that is equivalent to $$8+4\over 4$$.
$$8 + {4\over 4}$$
$${8\over 4} + 4$$
Correct answer: $${8\over 4}+{4\over 4}$$
$${8\over 4}+{4\over 4}$$
$$8\times 4 + 4\times 4$$
$$8\div (4+4)$$
Q5.Which expression is represented by this bar model?
Which expression is represented by this bar model?
$$a + a + 2 $$
Correct answer: $$6a + 6$$
$$6a + 6$$
$$6a + 2$$
$$3(a + 2)$$
Correct answer: $$3(2a + 2)$$
$$3(2a + 2)$$
Q6.Match each expressions containing brackets with its expanded form.
Match each expressions containing brackets with its expanded form.
Correct Answer:$$2(3x - 4)$$,$$6x - 8$$
$$2(3x - 4)$$ -Â $$6x - 8$$
Correct Answer:$$2(4 - 3x)$$,$$-6x + 8$$
$$2(4 - 3x)$$ -Â $$-6x + 8$$
Correct Answer:$$2(3x - 2)$$,$$6x - 4$$
$$2(3x - 2)$$ -Â $$6x - 4$$
Correct Answer:$$2(2 - 3x)$$,$$-6x + 4$$
$$2(2 - 3x)$$ -Â $$-6x + 4$$
Correct Answer:$$-2(-3x - 4)$$,$$6x + 8$$
$$-2(-3x - 4)$$ -Â $$6x + 8$$
Correct Answer:$$-2(4 + 3x)$$,$$-6x - 8$$
$$-2(4 + 3x)$$ -Â $$-6x - 8$$
Assessment exit quiz
6 Questions
Q1.Which of these is the best definition for like terms?
Which of these is the best definition for like terms?
Terms which when added, sum to zero.
Terms with the same coefficient for each variable.
Correct answer: Terms with the same set of variables and corresponding exponents.
Terms with the same set of variables and corresponding exponents.
Identical terms which have the same coefficient and same variables.
Terms with the same variable and different exponents.
Q2.These 5 bar models represent operations performed on the equation $$x + 9 = 22$$. Match the bar models labelled A, B, C, D and E with the equivalent equation they represent.
These 5 bar models represent operations performed on the equation $$x + 9 = 22$$. Match the bar models labelled A, B, C, D and E with the equivalent equation they represent.
Correct Answer:A,$$2(x + 9)= 2(22)$$
A -Â $$2(x + 9)= 2(22)$$
Correct Answer:B,$$x + 9 + x + 9 = 22 + x + 9$$
B -Â $$x + 9 + x + 9 = 22 + x + 9$$
Correct Answer:C,$$x + 9 + 2x + 18= 22 + 2x + 18$$
C -Â $$x + 9 + 2x + 18= 22 + 2x + 18$$
Correct Answer:D,$$3(x + 9) = 3(22) $$
D -Â $$3(x + 9) = 3(22) $$
Correct Answer:E,$$x + 9 + 22 = 22 + 22$$
E -Â $$x + 9 + 22 = 22 + 22$$
Q3.This bar model represents the initial equation $$2a + 6 = 14.$$ What needs to be done to the bottom bar to maintain equality?
This bar model represents the initial equation $$2a + 6 = 14.$$ What needs to be done to the bottom bar to maintain equality?
$$\times 2$$
$$+14$$
Correct answer: $$+2a$$
$$+2a$$
$$+6$$
$$\times a$$
Q4.If $$x + 5 =2$$, which of these equations have maintained equality?
If $$x + 5 =2$$, which of these equations have maintained equality?
$$2x + 5 = 4$$
Correct answer: $$ 2x + 5 = x + 2$$
$$ 2x + 5 = x + 2$$
Correct answer: $$x + 3 = 0$$
$$x + 3 = 0$$
$$ x + 12 = 10$$
Correct answer: $${x+5\over 2}=1$$
$${x+5\over 2}=1$$
Q5.If $$a = b$$, which of the following are true?
If $$a = b$$, which of the following are true?
Correct answer: $$a - c = b - c$$
$$a - c = b - c$$
$$ac = {b\over c}$$
$$a + c = b - c$$
Correct answer: $$ac=bc$$
$$ac=bc$$
$$a + c = b + d$$
Q6.Which expression could fill the blank on the right hand side of this equation to maintain equality?
Which expression could fill the blank on the right hand side of this equation to maintain equality?
$$10$$
Correct answer: $$15$$
$$15$$
$$5 + a + b$$
Correct answer: $$5 + a + b + a + b$$
$$5 + a + b + a + b$$
Correct answer: $$2a + 2b + 5$$
$$2a + 2b + 5$$
