Checking and securing understanding of the distributive law with algebraic terms
I can use the distributive law to multiply an expression by a term.
- Year 9
Checking and securing understanding of the distributive law with algebraic terms
I can use the distributive law to multiply an expression by a term.
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.
Keywords
Distributive law - The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.
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.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.What does the symbol $$\equiv$$ represent in the identity $$x + x + x \equiv 3x$$ ?
Q2.Which of these examples show two like terms?
Q3.Which of these bar models represents 3 lots of the expression $$2x + 1$$ ?
Q4.Match the product of two terms with its simplified expression.
$$3 \times 2x$$ -Â $$6x$$
$$3 \times -2x$$ -Â $$-6x$$
$$-3 \times -x$$ -Â $$3x$$
$$x \times 2x$$ -Â $$2x^2$$
$$-x \times 2x$$ -Â $$-2x^2$$
$$-3x \times -2x$$ -Â $$6x^2$$
Q5.Which of these is an equivalent calculation to $$44\times 12$$ ?
Q6.Match each product of two terms with its simplified expression.
$$-x \times -x$$ -Â $$x^2$$
$$2x \times x$$ -Â $$2x^2$$
$$2x \times y$$ -Â $$2xy$$
$$-2y \times x$$ -Â $$-2xy$$
$$x \times -y$$ -Â $$-xy$$
Assessment exit quiz
6 Questions
Q1.Use the area model to select the correct expanded form for the expression $$5(3x + 4)$$.
Q2.Use the area model to select the correct expanded form for the expression $$-3(4x - 6)$$.
Q3.Use the area model to select the correct expanded form for the expression $$x(x - 1)$$.
Q4.Match up each bracketed expression with its equivalent expression in expanded form.
$$4x(x - 6)$$ -Â $$4x^2 - 24x$$
$$4x(x + 6)$$ -Â $$4x^2 + 24x$$
$$-4x(x - 6)$$ -Â $$-4x^2 + 24x$$
$$-2x(-2x + 3)$$ -Â $$4x^2 -6x$$
$$-2x(2x - 3)$$ -Â $$-4x^2 + 6x$$
$$2x(2x+ 3)$$ -Â $$4x^2 + 6x$$
Q5.Select the correct expanded and simplified form of the expression $$3(2x + 4) + 7(x - 6).$$
Q6.Select the correct expanded and simplified form of the expression $$8(5x - 3) - 6(5x - 3).$$
