Inequalities from Situations

At most, at least, and no more than.

11 problems · about 22 minutes · A-CED.A.1

What this lesson teaches

The student writes and solves an inequality modelling a real constraint.

"At most" and "at least" include the endpoint; "more than" and "less than" do not.
A budget is an inequality, not an equation.
Round to what the situation allows, not to what the arithmetic gives.

Straightforward practice. Get the method working first.

4 problems

£60 with books at £7. How many at most?
Answer 8
Why 8.
£25 with items at £5. How many at most?
Answer 5
Why 25 ÷ 5.
£25 with items at £6. How many at most?
Answer 4
Why Round down.
Match each phrase to its symbol.
Answer At most → Less than or equal to; At least → Greater than or equal to; More than → Strictly greater than
Why "At" includes the endpoint.

The same ideas with more to keep track of.

3 problems

5n ≤ 45. Largest whole n?
Answer 9
Why 45 ÷ 5.
3n + 2 ≤ 20. Largest whole n?
Answer 6
Why 3n ≤ 18.
Does "at most 10" include 10? 1 for yes, 0 for no.
Answer 1
Why "At" includes it.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Does "more than 10" include 10? 1 for yes, 0 for no.
Answer 0
Why Strictly greater.
£100 with tickets at £12. How many at most?
Answer 8
Why 100 ÷ 12, rounded down.
The Budget: £40 with pens at £3 each. How many pens at most?
Answer 13
Why 13.
The Minimum: You need at least 50 points and have 32. How many more at minimum?
Answer 18
Why 18.