Multiplying and Dividing with Algebra

November 16, 2021

Differentiated Learning Objectives

• All students should be able to simplify algebraic products.
• Most students should be able to simplify expressions with multiplications and divisions.
• Some students should be able to simplify algebraic expressions involving powers and brackets.

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Starter/Introduction

Students recap simplifying expressions by collecting like terms using the algebra pyramids.  It may be necessary to remind students that the sign to the left of a term determines whether it is positive or negative. For instance, 3x – 2y has a +3x term and a -2y term. Understanding this early on makes it much easier when expanding brackets with a negative on the outside.

 Prompts / Questions to consider

• Which terms are alike and can be collected together?
• Do I need to add the terms or find their difference?

Multiplying and Dividing with Algebra

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When simplifying algebraic expressions, students should be taught:

• Not to include the multiplication sign as it can be confused with x. For instance, 5 × y -> 5y
• Write divisions as fractions. For instance, 5 ÷ m -> ⁵/_y
• Write numbers before the letters. For instance, m × 3 × 2 -> 6y
• Write letters in alphabetical order. For instance, m × 4 × p × 3 × r -> 12mpr

When students are comfortable applying the rules to simplify traditional questions, they should move on to connecting this to other areas of mathematics, such as finding factors of algebraic expressions, the area or volume of shapes, and for the more able students, compound measures.

 Prompts / Questions to consider

• What are the different terms?
• Does e² have any factors?
• Is 36e²wy the same as 36ywe²?
• Can the expression be broken up into more than four ways?

Plenary

The plenary challenges students to consider the different ways of writing the same expression. This activity takes between 5 and 8 minutes and is best completed on mini-whiteboards so the teacher can assess progress.

 Prompts / Questions to consider

• Which expressions follow the four rules for algebraic notation?
• Is there another way to write these expressions?

Differentiation

More able students could use index notation to simplify powers and roots. Less Able students should avoid questions with powers and brackets.