Checking and securing understanding of expanding a single bracket | Maths

Starter quiz

Evaluate the expression $\frac{3x}{2x + 5}$ for $x = 3$ . Write your answer as a decimal.

'0.82' ✓
Evaluate the expression $\frac{x}{x + 1}$ for $x = 4$ . Write your answer as a decimal.

'0.8' ✓
A company buys pencils in bulk for £2 per pen and sells them for £3.25 each. If the company sells $x$ pens, which of the following shows the correct expression for the profit, 'p'?

$p = 1.25x$ ✓

$p = 3x$

$p = 3x + 2$
If a taxi charges a £15 base fare plus £2 per mile, which of the following represents the total cost, $c$ , for a trip of $x$ miles?

$c = 15x$

$c = 15x + 2$

$c = 2x + 15$ ✓
A savings account offers 5% annual interest compounded yearly. If $x$ pounds are deposited, which expression represents the amount, $a$ , in the account after one year?

$a = 2x + 0.05x$

$a = 1.05x$ ✓

$a = x(1 + 0.05)^2$
A book store sells a book for £20, which is 20% more than its cost price. What is the cost price, 'p', of the book?

$p = 20 - 0.2 \times 30$

$p = \frac{20}{1.2}$ ✓

$p = 20 + 0.2 \times 30$

Exit quiz

Expand $5(x + 7) + 3(4x + 5)$ and simplify where possible.

$20x + 40$

$17x + 50$ ✓

$23x + 35$

$17x + 35$
Expand $2(3x - 4) - 5(x - 6)$ and simplify where possible.

$x + 22$ ✓

$-x + 22$

$6x - 8$

$x - 30$
Expand $-4(x - 5) + 2(2x + 3)$ and simplify where possible.

$-x - 2$

$-4x + 14$

$26$ ✓

$-4x - 14$
Expand $3(x^2 - 2x) + 4(x - 3)$ and simplify where possible.

$3x^2 - 2x - 12$ ✓

$3x^2 - 6x - 12$

$3x^2 + 2x - 12$

$3x^2 + x - 12$
Expand $-2(x^2 + 3x) - 3(2x - 4)$ and simplify where possible.

$-2x^2 - 12x + 12$ ✓

$-2x^2 - 6x + 12$

$-2x^2 - 6x - 12$

$-2x^2 + 3x - 12$
Expand $4(2x - 3)^2 - 5(3x + 2)$ and simplify where possible.

$16x^2 - 24x + 9 - 15x - 10$

$16x^2 - 24x - 6$

$16x^2 - 63x - 26$

$16x^2 - 63x + 26$ ✓

Worksheet

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Lesson Details

Key learning points

The term could have any form such as fractional or algebraic and may contain exponents.
The expression may be comprised of multiple terms.
If either the term or expression are identical to another term or expression, these can be combined.

Common misconception

Pupils find simplifying expressions which are the difference of two bracketed expressions difficult.

There are two equivalent methods detailed in learning cycle two. Spend time on both, getting pupils to explore their equivalence. If pupils are struggling, considering subtraction as adding the negative value is the easiest to model.

Keywords

Distributive law - The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.