Grades 3–5AlgebraPlanned
Expressions, unknowns and rules
Numerical expressions and the order of operations, finding unknown numbers in equations such as 3 × □ = 24, and describing input–output rules.
math.algebra.expressions-and-unknowns
The lesson for this topic has not been written yet. The outline below is part of the curriculum map and has not been reviewed.
Builds on
Required prerequisites, all the way down: 4
You will learn to
- Evaluate expressions using brackets and the conventional order of operations.
- Find the unknown in equations such as 3 × □ = 24 or □ + 17 = 40, explaining the method with inverse operations.
- Describe input–output rules in words and with expressions such as 2 × n + 1, and complete tables from a rule.
Definition
- An expression is a combination of numbers and operations, possibly with brackets, that names a number.
- An equation states that two expressions have the same value.
- An unknown is a number, shown by a box or a letter, whose value we are asked to find.
Theorem
- Brackets group operations; without them, multiplication and division are carried out before addition and subtraction.
- Adding a number is undone by subtracting it, and multiplying by a non-zero number is undone by dividing by it.
Common misconceptions
- Working strictly left to right, so that 2 + 3 × 4 is taken to be 20.
- Thinking an equation must have 'the answer' on the right of the equals sign.
- Believing a letter stands for an object ('a for apples') rather than for a number.
Leads to
Optional discoveries
- One thing after another 'Multiply by 3, then add 1' is a chain of actions; to undo it, subtract 1 first and then divide by 3.
- ← Patterns