Idea 6of 23Builds onA picture into an expression
Same value, different look
Can two different-looking expressions mean the same thing?
Today you'll discover
- why n + n + n is 3n
- how to test two expressions
- why the order of adding does not matter
Think first3n + 2: three bags and 2 loose
Which says the same as 3n + 2?
Decide first, then press Next. Ask: do both say the same picture?
Three bags marked n and 2 loose squares, with 3n + 2 under them. Then the line n + n + n + 2 is the same as 3n + 2, and with 5 in each bag, 5 + 5 + 5 + 2 = 17 and 3 × 5 + 2 = 17. The last step shows 10 loose cubes and three bags of n.
See the whole ideathe big idea and the key word, in one place
The big idea
Expressions that look different can have the same value for every n.
One picture, three ways
Three ways to write three bags of n and 2 loose.
- addedn + n + n + 2
- grouped3n + 2
- turned round2 + 3n
Easy to get wrongn + n + n is 3n, not n × n × n.
Key word
- equivalent expressions
- expressions that have the same value whatever number the letter stands for
Ready to use it?
- Decide whether two expressions have the same value.