Order does not change a sum
a + b + c can be added in any order. Pair the numbers that make tens or round numbers. Each term still carries its sign.
Why it works
Rearranging coins in your hand does not change the total.
Simplifying · Just Numbers · A5
Rearrange & regroup.
Addition can be done in any order. Regroup the terms to add the friendly pairs first — the same mental-math habit, now seen as a property of expressions.
See it simplify.
One step at a time
Do the strongest operation first.
6 + 9 + 4
The idea underneath.
From easy to tricky.
2 + 6 + 2 + 5
1
Step
2 + 6 = 8
2
Step
8 + 2 = 10
3
Step
10 + 5 = 15
8 + 8 + 3 + 7
1
Step
8 + 8 = 16
2
Step
16 + 3 = 19
3
Step
19 + 7 = 26
8 + 8 + 11 + 8
1
Step
8 + 8 = 16
2
Step
16 + 11 = 27
3
Step
27 + 8 = 35
Where students slip.
Trap
Moving a term but dropping its sign.
Fix
A − term stays negative when you move it.
Trap
Thinking subtraction can be freely reordered.
Fix
Reorder by treating each − as adding a negative term.
Test yourself.
The Test
12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.
0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so
t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).Core
Core (4)
C1
2 + 6 + 2 + 5
Need a hint?
- Pair terms that make a round number.
- Keep each sign with its term.
C2
5 + 6 + 2 + 3
Need a hint?
- Pair terms that make a round number.
- Keep each sign with its term.
C3
4 + 2 + 4 + 3
Need a hint?
- Pair terms that make a round number.
- Keep each sign with its term.
C4
4 + 3 + 2 + 4
Need a hint?
- Pair terms that make a round number.
- Keep each sign with its term.
Apply
Apply (4)
A1
8 + 8 + 3 + 7
Need a hint?
- Pair terms that make a round number.
- Keep each sign with its term.
A2
9 + 9 + 3 + 8
Need a hint?
- Pair terms that make a round number.
- Keep each sign with its term.
A3
9 + 8 + 8 + 3
Need a hint?
- Pair terms that make a round number.
- Keep each sign with its term.
A4
3 + 8 + 8 + 8
Need a hint?
- Pair terms that make a round number.
- Keep each sign with its term.
Extension
Extension (4)
E1
8 + 8 + 11 + 8
Need a hint?
- Pair terms that make a round number.
- Keep each sign with its term.
E2
4 + 6 + 11 + 11
Need a hint?
- Pair terms that make a round number.
- Keep each sign with its term.
E3
5 + 7 + 8 + 8
Need a hint?
- Pair terms that make a round number.
- Keep each sign with its term.
E4
5 + 4 + 11 + 10
Need a hint?
- Pair terms that make a round number.
- Keep each sign with its term.