Lesson 21 Expressions and equations

# Episode 3

Reasoning Resources: Worksheets 2 and 3
This episode can be carried out in two mini-episodes, first on the questions on Worksheet 2, then on Worksheet 3.
Whole class preparation
Seeing how the splitting method can be used when the unknown is on both sides. Write an example on the board: 2x + 4=7 +12. As a class, solve using both methods from Episode 2.
Pair and group work
Practising the methods on given equations. Struggling with Q2 — how to achieve 6 on the right hand side of the equation? Give out Worksheet 2. Which method works best for different equations?

Depending on the needs of the class decide whether to stop and have a class discussion after these or to let pupils continue with Worksheet 3. This could either be tackled in pairs/groups and then discussed or, if time is short, worked through as a whole class.
Whole class sharing/discussion
Exploring a practical use of equations to solve a problem on Worksheet 3. How did you solve the first question on Worksheet 2 using the splitting up method?

If there were problems with multiplying out the brackets in question 3, give a simple example of a bracketed expression multiplied by a number and expand it intuitively. For example: Three friends each had the same amount of money m plus £2 each. How much money do they have in total? How did you go about solving the problem on Worksheet 3?
Extension- constructing equations
Any two linear expressions can be made into an equation with a unique value for the unknown. But the context may disallow negative or fractional values. Ask pupils to create equations where the unknown appears on both sides. This can be in context, such as a number of ‘rods of unknown lengths’ on straight lines or polygons. You may wish to offer questions such as:

Suppose two friends at a fair win prizes (P) that can be exchanged at the door for a standard amount of cash. The first wins 2P and has £13 of her own; the other wins 7P and has no money extra. But they both ended up having the same amount. How much is P? Suppose the second ended up twice as rich as the first. What is the value of P in that case?
NOTE
Reflecting on the different methods used and the meanings of the equals sign.

Acknowledging the power of algebra in solving problems where there are unknowns.
There is likely to be more instruction content in this lesson than in most other Thinking Maths lessons, This lesson takes the pupils one step further in algebra, and builds on vocabulary and writing conventions used in TM2:Text ‘n’ talk and TM7: Which offer shall | take?

The agenda is to make explicit some basic reasoning steps that underlie algebraic manipulations. These logical reasoning steps are normally short-circuited and summarised in rules needed for solving equations and simplifying expressions such as ‘change the side and change the sign’ and the mnemonics of BODMAS for the order of carrying out operations. While such devices are harmless in revision for exams, they are likely to be premature and harmful at the formative stage of algebraic skills at lower secondary years.
End of Lesson Reflection

• What have we learnt about solving equations today?
• What does ‘=’ mean?
• How was algebra useful in the problem about the square and the rectangle?