Two expressions are equivalent when they always give the same value. To test that, you substitute a number into each and check they match. So this lesson runs on plugging a number into a box and on knowing order doesn't change a sum or product. Warm those up first.
Answer these 3, then press Show my path. No grade — this just points you to the right level.
1. If ▢ = 2, what is ▢ + 3?
2. If ▢ = 2, what is 3 + ▢?
3. Do 2 + 3 and 3 + 2 give the same value?
Two expressions are equivalent if they give the same value for every number you try. A quick check: pick a number, put it in both, and see if the results are equal.
Your quick check picks one for you, but you can switch any time:
Level 0 Put the number in the box, one step at a time.
A. ▢ = 4. What is ▢ + 1?
Put 4 in: 4 + 1 = 5.
B. ▢ = 4. What is 1 + ▢?
Put 4 in: 1 + 4 = 5 — same as before.
C. ▢ = 3. What is ▢ + ▢?
Put 3 in both: 3 + 3 = 6.
Level 1 Plug in and compare both sides.
A. x = 5. What is x + 2?
5 + 2 = 7.
B. x = 5. What is 2 + x?
2 + 5 = 7 — matches part A, so x+2 and 2+x are equivalent.
C. Since both gave 7, are x + 2 and 2 + x equivalent?
Same value, so yes — equivalent.
Level 2 Warm up straight into testing equivalence.
A. x = 4. What is x + x?
4 + 4 = 8.
B. x = 4 gives x + x = 8 and 2 × x = 8. Are x + x and 2x equivalent?
Both give 8, so yes — equivalent.
1. x = 6. What is x + 3?
6 + 3 = 9.
2. Do 3 + x and x + 3 give the same value?
Adding in any order gives the same total, so yes.
You've practiced exactly what Lesson 6-6 uses. Time to dive in.
Start Lesson 6-6 →