Explain how to balance equations with addition or subtraction expressions | Maths

Starter quiz

Which of the following expressions has the same sum as 41.6 + 7? Can you reason without calculating?
- 41 + 7.6 ✓
- 41 + 7
- 40.6 + 6
- 1.6 + 47 ✓
What is the area of this rectangle? ______ $cm^2$
- '80' ✓
What is the area of this rectangle? Check the measurements carefully. ______ $cm^2$
- '25.2 ' ✓
What is the perimeter of this rectangle? ______ cm
- '36' ✓
Use an efficient strategy to calculate 132.7 + 489.92 = ______
- '622.62' ✓
Complete the equation that is represented by the bar model. 1,267 + c = ______
- '2,145 + 3,012 = 1,267 + c' ✓

Exit quiz

True or false. Lawn A and lawn B have the same perimeter.
- True ✓
- False
Which expressions can be used to represent the perimeter of this lawn?
- 8.8 + 12.5 + 8.8 + 12.5 ✓
- 8.8 × 2 + 12.5
- 8.8 × 12.5 × 2
- 8.8 × 12.5 + 2
What is the missing dimension labelled x for this pair of lawns? ______ m
- '38.6' ✓
Lawn A and lawn B have the same area. What is the missing dimension labelled x on lawn B? ______ m
- '4' ✓
A is made up of lawn and pond. What is the area of the lawn? ______ $m^2$
- 54
The area of the whole garden is 99 $m^2$ and the area of the lawn is 78 $m^2$ What is the missing dimension of the pond labelled x? ______ m
- '7' ✓

Worksheet

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Lesson Details

Key learning points

If one addend is increased and the other is decreased by the same amount, the sum stays the same.
If the minuend and subtrahend are changed by the same amount, the difference stays the same.

Common misconception

Pupils are inefficient when calculating the perimeter of a rectangle or do not recognise why more efficient strategies (summing length and width and doubling) works.

Encourage pupils to see the efficient calculation and connection with smaller integers to support the generalisation before progressing to values in the lesson. Consider adapting values for some learners where required.

Keywords

Peimeter - The perimeter is the distance around a 2D shape.
Expression - An expression contains one or more values, where each value is separated by an operator.
Area - Area is the measurement of a flat surface. It measures 2D space.