Checking and securing understanding of the distributive law with algebraic terms | Maths

Starter quiz

What does the symbol $\equiv$ represent in the identity $x + x + x \equiv 3x$ ?

There is a value for $x$ which makes both sides equal.

Both sides are equivalent expressions. ✓

The left hand side does not equal the right hand side.

The identity can be solved to find the value of $x$
Which of these examples show two like terms?

$2x$ and $0.4x$ ✓

$x^2$ and $x$

$5xy$ and $5y$

$3xy$ and $3yx$ ✓

$8x$ and $4$
Which of these bar models represents 3 lots of the expression $2x + 1$ ?
Match the product of two terms with its simplified expression.

$3 \times 2x$

⇔

$6x$ ✓

$3 \times -2x$

⇔

$-6x$ ✓

$-3 \times -x$

⇔

$3x$ ✓

$x \times 2x$

⇔

$2x^2$ ✓

$-x \times 2x$

⇔

$-2x^2$ ✓

$-3x \times -2x$

⇔

$6x^2$ ✓
Which of these is an equivalent calculation to $44\times 12$ ?

$(11\times 3) + (4\times 4)$

$(44\times 6) + (44\times 2)$

$(44\times 8) + (44\times 4)$ ✓

$(40\times 10) + (4\times 2)$

$(44\times 10) + (44\times 2)$ ✓
Match each product of two terms with its simplified expression.

$-x \times -x$

⇔

$x^2$ ✓

$2x \times x$

⇔

$2x^2$ ✓

$2x \times y$

⇔

$2xy$ ✓

$-2y \times x$

⇔

$-2xy$ ✓

$x \times -y$

⇔

$-xy$ ✓

Exit quiz

Use the area model to select the correct expanded form for the expression $5(3x + 4)$ .

$8x + 4$

$8x + 20$

$15x + 4$

$15x + 20$ ✓

$20 - 15x$
Use the area model to select the correct expanded form for the expression $-3(4x - 6)$ .

$-12x - 18$

$-12x - 6$

$-12x + 18$ ✓

$12x - 18$

$12x + 6$
Use the area model to select the correct expanded form for the expression $x(x - 1)$ .

$x$

$2x - 1$

$x^2 + x$

$x^2 - x$ ✓

$2x^2 - x$
Match up each bracketed expression with its equivalent expression in expanded form.

$4x(x - 6)$

⇔

$4x^2 - 24x$ ✓

$4x(x + 6)$

⇔

$4x^2 + 24x$ ✓

$-4x(x - 6)$

⇔

$-4x^2 + 24x$ ✓

$-2x(-2x + 3)$

⇔

$4x^2 -6x$ ✓

$-2x(2x - 3)$

⇔

$-4x^2 + 6x$ ✓

$2x(2x+ 3)$

⇔

$4x^2 + 6x$ ✓
Select the correct expanded and simplified form of the expression $3(2x + 4) + 7(x - 6).$

$10x - 30$

$10x + 6$

$13x - 30$ ✓

$13x - 2$

$13x + 54$
Select the correct expanded and simplified form of the expression $8(5x - 3) - 6(5x - 3).$

$2x - 6$

$10x - 6$ ✓

$10x - 42$

$70x - 42$

$70x + 42$

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

The distributive law can be understood using an area model.
The distributive law can help us multiply an expression by a term.
The expression may contain any number of terms.

Common misconception

Pupils forget to multiply every term in the bracket by the term outside the bracket.

Remind pupils about the distributive law with numerical examples, e.g. 4(3 + 7) and show that this is not equivalent to 12 + 7. Using algebra tiles can also help pupils to make sense of this skill.

Keywords

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