New
New
Year 9

# Problem solving with expressions and formulae

I can use my knowledge of expressions and formulae to solve problems.

New
New
Year 9

# Problem solving with expressions and formulae

I can use my knowledge of expressions and formulae to solve problems.

## Lesson details

### Key learning points

1. Expressions can be used whenever you wish to generalise.
2. This can be very useful when there is something you do not know and wish to calculate.
3. 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.

Pupils could benefit from creating some similar area problems themselves starting with a value for the unknown so that they can make a solvable problem for another pupil.
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.
All the lengths in the diagram are given in centimetres. Which calculation will find the area of the rectangle?
$$7 + 3$$
$$7\over 3$$
Correct answer: $$7 \times 3$$
$$2(7 + 3)$$
$$2\times 7 + 2\times 3$$
Q2.
Select the expression that is equivalent to $${1\over2}(6x -2)$$.
Correct answer: $$3x - 1$$
$$3x - 2$$
$$6x - 1$$
$$12x - 2$$
$$12x - 4$$
Q3.
All the lengths in the diagram are given in centimetres. The area of the triangle is cm².
Q4.
All the lengths in the diagram are given in metres. The area of the trapezium is m².
Q5.
Match each product of two binomials to its expanded form.
Correct Answer:$$(x + 5)(x + 1)$$,$$x^2 + 6x + 5$$

$$x^2 + 6x + 5$$

Correct Answer:$$(x + 5)(x - 1)$$,$$x^2 + 4x - 5$$

$$x^2 + 4x - 5$$

Correct Answer:$$(x - 5)(x + 1)$$,$$x^2 - 4x - 5$$

$$x^2 - 4x - 5$$

Correct Answer:$$(x - 5)(x -1)$$,$$x^2 - 6x + 5$$

$$x^2 - 6x + 5$$

Correct Answer:$$(x + 2)^2$$,$$x^2 + 4x + 4$$

$$x^2 + 4x + 4$$

Correct Answer:$$(x - 2)^2$$,$$x^2 -4x + 4$$

$$x^2 -4x + 4$$

Q6.
Which of these is the correct expansion of $$(4x + 3)^2$$ ?
$$8x^2 + 12x + 9$$
$$8x^2 + 14x + 9$$
$$16x^2 + 9$$
$$16x^2 + 6x + 9$$
Correct answer: $$16x^2 + 24x + 9$$

## Exit quiz

### 6 Questions

Q1.
What do you call a shape which is created using two or more basic shapes?
an irregular shape
a parallelogram
a polygon
a trapezium
Q2.
Which of these is an expression for the area of this rectangle?
$$2x + 10$$
$$4x + 20$$
$$x^2 + 24$$
$$x^2 + 10x + 10$$
Correct answer: $$x^2 + 10x + 24$$
Q3.
Which of these is an expression for the area of this triangle?
$$x^2 + 6x + 8$$
$$2x^2 + 6x + 16$$
$$2x^2 + 10x + 16$$
Correct answer: $$2x^2 + 12x + 16$$
$$4x^2 +24x + 32$$
Q4.
Find an expression for the horizontal length marked with a '?' on this compound shape.
$$x + 7$$
$$x + 9$$
Correct answer: $$2x + 1$$
$$2x + 11$$
$$4x + 11$$
Q5.
Which of these is an expression for the area of this compound shape?
$$5x^2 +19x + 41$$
$$7x^2 +13x + 12$$
Correct answer: $$7x^2 + 23x + 39$$
$$7x^2 +33x + 53$$
$$7x^2 +61x + 57$$
Q6.
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 .
Correct Answer: 5, 5 cm, 5cm