Solving simple linear equations with an additive step | Maths

Starter quiz

Which equations are represented by this bar model?

$12 + x = 21$ ✓

$21 + x = 12$

$21 − 12 = x$ ✓

$21 + 12 = x$

$12 = 21 − x$ ✓
Which equations are represented by this bar model?

$a + 8 = 33$

$33 − 8 = a$

$a = 8 + 33$ ✓

$33 = a − 8$ ✓

$8 = 33 − a$
Match each value with its additive inverse.

$3$

⇔

$−3$ ✓

$-3$

⇔

$3$ ✓

$1\over 3$

⇔

$−{1\over 3}$ ✓

$−{1\over 3}$

⇔

$1\over 3$ ✓

$0.3$

⇔

$−0.3$ ✓

$10\over 3$

⇔

$−{10\over 3}$ ✓
Which of these are zero pairs?

5 and (−5) ✓

(−3) and (−3)

1 and (−0.1)

$1\over 2$ and $2$

$2\over 5$ and $(−0.4)$ ✓
What is the value of the expression $2(3x + 5)$ when $x = −3$ ?

'−8' ✓
The diagram shows a balanced scale on the left. When an operation is performed to the RHS, it is not balanced. What operation must be performed to the LHS to maintain equality?

$\times 2$

$\times 3$

$+9$ ✓

$+ 12$

$+ 18$

What is the value of the unknown in this bar model? $x=$ ______

'10' ✓
Which best describes the mistake that has been made when solving the equation below?

15 add (−8) does not equal 7

The same operation has not been applied to both sides of the equation.

The correct additive inverse has not been added. ✓

The (−8) has not been added to the $x$ term and the constant term on the LHS.
The solution to the equation $x − 5 = 15$ is when $x$ = ______

'20' ✓
Which of these shows the correct working to solve the equation $x + 3.8 = 2.3$ in one additive step?
The solution to the equation $x + 7.2 = 14.6$ is when $x$ = ______

'7.4' ✓
Which of these is the solution to the equation $x − {2\over 3} = {5\over 6}$ ?

$x = {1\over 6}$

$x = {3\over 4}$

$x = {7\over 9}$

$x = 1$

$x = {3\over 2}$ ✓

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An equation involving an additive step can be represented with a bar model.
Using the bar model you can write all the arrangements of the equation with an additive step.
One of the arrangements will give the solution to the equation.
This can be written algebraically to find the solution.

When solving x - 5 = 10 pupils may see the -5 and calculate 10 - 5 = 5

Focus on understanding zero pairs and why adding the additive inverse gives the solution. Bar models are a helpful representation here.

Additive inverse - The additive inverse of a number is a number that, when added to the original number, gives the sum of 0