New
New
Year 9

I can appreciate that an additive relationship between variables can be written in a number of different ways.

New
New
Year 9

I can appreciate that an additive relationship between variables can be written in a number of different ways.

## Lesson details

### Key learning points

1. When adding or subtracting, terms may only be combined if the order of each variable in each term is the same.
2. The sum of the terms can be thought of as a term, despite being comprised of multiple terms.
3. a + b = c also means that a = c − b
4. a = c − b can also be written as a = c + (−b)

### Common misconception

Rearranging equations means you can just swap where terms are.

Remind pupils that subtraction and division are not commutative so swapping the order will matter.

### Keywords

• Equation - An equation is used to show two expressions that are equal to each other.

Being able to draw bar models to represent an additive relationship can really support pupils.
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).

## Starter quiz

### 6 Questions

Q1.
63 + 37 = 100 being rearranged to 37 + 63 = 100 is an example of __________.
categorisation
congruency
coordination
cumulation
Q2.
When rearranging equations, you must perform the same operation to both sides in order to maintain __________.
equation
equalness
equilateral
Q3.
In the equation 172 + 398 = 570, the term 570 can be described as the __________ of 172 and 398.
factor
multiple
product
Q4.
Given that 1734 + 2117 = 3851, which of these calculations are correct?
Correct answer: 2117 + 1734 = 3851
1734 + 3851 = 2117
3851 + 2117 = 1734
Correct answer: 3851 − 2117 = 1734
2117 = 1734 − 3851
Q5.
Match each operation to its inverse operation.

Subtraction

Division

Square rooting

Q6.
Which of these equations can be represented by this bar model?
\$\$x=3+15\$\$
\$\$3x=15\$\$
\$\$x-15=3\$\$

## Exit quiz

### 6 Questions

Q1.
\$\$3x^2+4x=13\$\$ being rearranged to \$\$4x+3x^2=13\$\$ is an example of __________.
constants
communication
cumulativity
Q2.
Which of these equations are valid rearrangements of the generalisation \$\$a+b=c\$\$ ?
\$\$b+c=a\$\$
\$\$b-c=a\$\$
Q3.
Which of these equations are valid rearrangements of the equation \$\$100-2x=5y\$\$ ?
\$\$100+5y=2x\$\$
\$\$2x+100=5y\$\$
\$\$2x-100=5y\$\$
Q4.
Which of these equations are represented in this bar model?
\$\$2c-9d=23\$\$
\$\$23-9d=2c\$\$
Q5.
Which of the below are correct rearrangements of the equation 71 + 13 + 15 = 99 ?
Correct answer: 71 = 99 − 15 − 13
71 = 99 − (15 − 13)
Correct answer: 71 = 99 − (15 + 13)
71 = 99 − 15 + 13
71 = 99 + 15 − 13
Q6.
Which of the below are correct rearrangements of the equation \$\$9x^3+2y-7=3z\$\$ ?
\$\$9x^3=3z+2y-7\$\$
\$\$9x^3=3z+(2y-7)\$\$