Problem solving with algebraic manipulation | Maths | Quizalize & Oak National Academy

Starter quiz

Evaluate the expression $\frac{3x}{2x + 5}$ for $x = 5$ .

'1' ✓
Evaluate the expression $\frac{x}{x + 1}$ for $x = 19$ . Give your answer as a decimal.

'0.95' ✓
A book store sells a book for £25, which is 25% more than its cost price. Which of these calculates cost price, $p$ , of the book?

$p = 25 - 0.25 \times 30$

$p = \frac{25}{1.25}$ ✓

$p = 25 + 0.25 \times 100$
Expand and simplify $4(x - 2) - 2(3x + 4)$

$2x - 16$

$-2x - 16$ ✓

$x - 16$
Simplify the expression $\frac{x^2 - 9}{x - 3}$

$x + 3$ ✓

$x - 3$

$x^2 + 3x$
Fully factorise the expression $2x^2 + 12x$

'2x(x+6)' ✓

Exit quiz

A right triangle has area $24 cm^2$ and side lengths $x$ and $x + 2$ . What is the value of $x$ ?

'6' ✓
The sum of two consecutive odd integers is 156. What are the two integers?

'77, 79' ✓
What is the positive value of $x$ where $(x + 4)(x - 2) = 0$ ?

'2' ✓
The difference between the square of a positive integer and the integer itself is 110. What is the integer?

'11' ✓
The sum of the squares of two consecutive positive integers is 365. What is the smallest integer?

'13' ✓
The product of two consecutive integers is 272. What are the two integers?

16 and 17 ✓

14 and 15

17 and 18

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Lesson Details

Key learning points

Quadratic equations can model real-life situations.
Solutions would need to be interpreted in context.
The difference of two squares is not only used in algebra, but can be used to quickly calculate numerical expressions.

Common misconception

Including solutions which are not valid in the context of the question.

Pupils should finish every problem by substituting their solutions back into the original problem. This will help them check their answers but also make them think about whether their solutions are valid in context.

Keywords

Partial product - A partial product refers to any of the multiplication results that lead up to an overall multiplication result.
Binomial - A binomial is an algebraic expression representing the sum or difference of exactly two unlike terms.
Factorise - To factorise is to express a term as the product of its factors.
Solution (equality) - A solution to an equality with one variable is a value for the variable which, when substituted, maintains the equality between the expressions.