TEACHER EDITION

Order of Operations — Expressions and Equations

Grade 6 · Lesson 1 · Dimensions 6A p.2
Math Book 6 · sheet 1
Warm-up — yesterday: Grade 5 — multiplying by tens
Work out 7 × 400.
2,800

What we are learning

An EXPRESSION is a calculation with no equals sign. An EQUATION states that two expressions are equal.

How it is done — keep this beside you

These steps stay on your page while you work. If you get stuck, find the step you are on and read it again before you put your hand up.

1
Here is a calculation.
3 + 4 × 2
2
It has no equals sign, so it is an expression. It has a value.
3 + 4 × 2 expression → value
3
Now I claim its value is 11.
3 + 4 × 2 expression → value 3 + 4 × 2 = 11
4
An equals sign has appeared. This is now an equation.
3 + 4 × 2 expression → value 3 + 4 × 2 = 11 equation
5
An equation can be TRUE or FALSE. An expression can only be evaluated.
3 + 4 × 2 expression → value 3 + 4 × 2 = 11 equation expression: evaluate · equation: judge

Practice

I DOteacher builds it, nothing erased
Is 5 × 3 − 2 an expression or an equation? Evaluate it.
  1. No equals sign, so it is an expression.
  2. Multiplication first: 15 − 2.
  3. 13
WE DO 1together, on whiteboards
Is 12 ÷ 4 = 3 an expression or an equation? Is it true?
Look for the equals sign first. Boards up.
  1. Equals sign, so an equation.
  2. 12 ÷ 4 = 3, so TRUE.
WE DO 2together, on whiteboards
Is 8 + 2 × 5 = 50 an expression or an equation? Is it true?
Careful — evaluate properly before you judge it.
  1. Equation.
  2. 8 + 10 = 18, not 50.
  3. FALSE
YOU DOindependent, from the book
Book 6A p.2 — the Do section, clipped onto the slide
the book page
Ask yourself: “Is there an equals sign?”
Watch for
8 + 2 × 5 = 50 is true only if you work left to right, which is what most of the class will do. Do not correct it yet — this is the problem the next three lessons exist to solve, and letting them feel it is worth more than telling them.