Addition in any order
Understand and apply the commutative property of addition: addends can be added in any order
Lesson
Set out your lesson
“Addition in any order means the addends can switch places and the total stays the same. 3 + 8 gives the same answer as 8 + 3. When you count on, start from the larger number so there is less to count. Subtraction is different: 5 − 3 is not the same as 3 − 5. Today we only check addition order, then one quick subtraction contrast.”
Bring to the table
- About 12 large counters, blocks, or dried beans (parent keeps any small pieces away from mouths)
- Paper and pencil
- Clear table space
Extra for the adult
Worked example. 3 counters and 8 counters make 11 either way: 3 + 8 = 11 and 8 + 3 = 11. Counting on from 9 for 2 + 9 goes 10, 11. For subtraction, 5 − 3 = 2, but 3 − 5 is not the same story with these counters.
Optional challenge. For Addition in any order, give 8 + 7 without counters first. Ask for both orders and the shared total, then which order is easier to count on from. Optional stretch: invent one word story for 4 + 9 and retell it with the addends swapped, keeping the same total.
What to notice. Keep one parent note: pairs tried (for example 3+8/8+3 and 7+5/5+7); both totals; whether the child chose the larger start when counting on; the subtraction contrast (5−3 vs 3−5 or 6−2 vs 2−6); and support used. A photo of equations alone does not record the explanation. This session samples these pairs, not every commutative fact.
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Teaching approaches
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1 approach
Addition in any order means the addends can switch places and the total stays the same. 3 + 8 gives the same answer as 8 + 3. When you count on, start from the larger number so there is less to count. Subtraction is different: 5 − 3 is not the same as 3 − 5. Today we only check addition order, then one quick subtraction contrast.
Spend about 12 minutes building matching addition pairs with counters, writing both orders, choosing the larger start when counting on, and contrasting one subtraction pair that does not commute.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Visnos · Practice link — not the full lesson
Addition & Subtraction Facts
Before you open · source notes
Move parts while the equation updates to show addition can be done in either order (commutativity) for the same total.
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Before you openSave screenshots of a fact and its turned-around partner (for example 3+5 and 5+3) with the same total.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Unknown — link only
Topmarks · Practice link — not the full lesson
Robot Addition
Before you open · source notes
Match addition equations to totals. After two matches, ask the learner to swap the addends and predict the same total.
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Before you openSave a matched screenshot plus a parent note that the learner stated a turn-around fact with the same sum.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Unknown — link only
Check understanding
- Explain that 3 + 8 gives the same answer as 8 + 3
- Use commutativity to choose the larger number to count on from
- Demonstrate that subtraction is not commutative (5 − 3 ≠ 3 − 5)
“Does your child know that 6 + 4 gives the same answer as 4 + 6, so they can always choose whichever order makes the adding easier?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Addition & Subtraction
- Age range
- Ages 6–12
Standards