Problem solving with expressions and formulae | Maths

Starter quiz

All the lengths in the diagram are given in centimetres. Which calculation will find the area of the rectangle?
- $7 + 3$
- $7\over 3$
- $7 \times 3$ ✓
- $2(7 + 3)$
- $2\times 7 + 2\times 3$
Select the expression that is equivalent to ${1\over2}(6x -2)$ .
- $3x - 1$ ✓
- $3x - 2$
- $6x - 1$
- $12x - 2$
- $12x - 4$
All the lengths in the diagram are given in centimetres. The area of the triangle is ______cm².
- '63' ✓
All the lengths in the diagram are given in metres. The area of the trapezium is ______m².
- '42' ✓
Match each product of two binomials to its expanded form.
- $(x + 5)(x + 1)$
  
  ⇔
  
  $x^2 + 6x + 5$ ✓
- $(x + 5)(x - 1)$
  
  ⇔
  
  $x^2 + 4x - 5$ ✓
- $(x - 5)(x + 1)$
  
  ⇔
  
  $x^2 - 4x - 5$ ✓
- $(x - 5)(x -1)$
  
  ⇔
  
  $x^2 - 6x + 5$ ✓
- $(x + 2)^2$
  
  ⇔
  
  $x^2 + 4x + 4$ ✓
- $(x - 2)^2$
  
  ⇔
  
  $x^2 -4x + 4$ ✓
Which of these is the correct expansion of $(4x + 3)^2$ ?
- $8x^2 + 12x + 9$
- $8x^2 + 14x + 9$
- $16x^2 + 9$
- $16x^2 + 6x + 9$
- $16x^2 + 24x + 9$ ✓

Exit quiz

What do you call a shape which is created using two or more basic shapes?
- a compound shape ✓
- an irregular shape
- a parallelogram
- a polygon
- a trapezium
Which of these is an expression for the area of this rectangle?
- $2x + 10$
- $4x + 20$
- $x^2 + 24$
- $x^2 + 10x + 10$
- $x^2 + 10x + 24$ ✓
Which of these is an expression for the area of this triangle?
- $x^2 + 6x + 8$
- $2x^2 + 6x + 16$
- $2x^2 + 10x + 16$
- $2x^2 + 12x + 16$ ✓
- $4x^2 +24x + 32$
Find an expression for the horizontal length marked with a '?' on this compound shape.
- $x + 7$
- $x + 9$
- $2x + 1$ ✓
- $2x + 11$
- $4x + 11$
Which of these is an expression for the area of this compound shape?
- $5x^2 +19x + 41$
- $7x^2 +13x + 12$
- $7x^2 + 23x + 39$ ✓
- $7x^2 +33x + 53$
- $7x^2 +61x + 57$
All the length marked on this diagram are in centimetres. The area of the shaded part of this shape is 102 cm². The value of $x$ is ______.
- '5' ✓

Worksheet

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Lesson Details

Key learning points

Expressions can be used whenever you wish to generalise.
This can be very useful when there is something you do not know and wish to calculate.
Situations involving expressions can occur in a variety of contexts.

Common misconception

When subtracting expression pupils forget to subtract both terms from the second espression.

Watch out for mistakes with negatives here. Pupils should find it much easier to re-write subtractions as additions of additive inverses and that way they only need to add.

Keywords

Binomial - A binomial is an algebraic expression representing the sum of exactly two unlike terms.