L2 · Many Expressions, One Number

Learning goal

“I can build many different expressions that all have the same value, and I can check whether two expressions really are worth the same number.”

Value — the number an expression works out to (review from L1).

Equal value — two expressions have equal value when they work out to the same number, even if they look completely different.

Worked example

The target number is 12. Build expressions worth 12. Road 1 (addition): 6 + 6 = 12. Road 2 (multiplication): 3 x 4 = 12. Road 3 (subtraction): 20 - 8 = 12. Road 4 (division): 24 / 2 = 12. Road 5 (two operations - use L1's rule): 2 x 3 + 6. Multiplication first: 2 x 3 = 6, then 6 + 6 = 12. Say it plainly: there are infinitely many expressions for the same number. Changing the operations and the numbers does not change the value - and the value is the only thing that decides whether two expressions match.

Check yourself — explain it

Why do 3 x 4 and 20 - 8 count as expressions for the same number?

Paired problem — example still visible

Build an expression worth 15 that uses division -> sample: 30 / 2 (accept any expression whose value is 15 and that uses division)

Faded completion — last step is yours

"An expression worth 20 that uses x: 5 x ___" -> 4

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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