Grouping numbers to add
Understand and apply the associative property of addition: when adding three numbers, any two can be added first
Lesson
Set out your lesson
“Grouping numbers to add means that when three numbers are added, you may add any two first and the total stays the same. (2 + 6) + 4 equals 2 + (6 + 4). Choosing a helpful pair—often a make-10—can make the work easier, but the property is about order of grouping, not only make-10. Today we show two groupings for the same three addends, then let the child choose a helpful group.”
Bring to the table
- About 15 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. For 2 + 6 + 4, (2 + 6) + 4 = 8 + 4 = 12 and 2 + (6 + 4) = 2 + 10 = 12. The three addends stay the same; only which pair you add first changes.
Optional challenge. For Grouping numbers to add, solve 9 + 6 + 4 two ways without counters first, then check with counters. Optional: invent one short word story with three small addends and say which pair you grouped first and why.
What to notice. Keep one parent note: triples tried; both groupings or the chosen grouping; totals; whether the child said the total stays the same; support used. A photo of counters alone cannot record the grouping talk. This samples a few triples, not full fluency.
Share and support
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
Grouping numbers to add means that when three numbers are added, you may add any two first and the total stays the same. (2 + 6) + 4 equals 2 + (6 + 4). Choosing a helpful pair—often a make-10—can make the work easier, but the property is about order of grouping, not only make-10. Today we show two groupings for the same three addends, then let the child choose a helpful group.
Spend about 12 minutes adding three one-digit numbers two different ways, writing both groupings, noticing the same total, then choosing a helpful first pair on a fresh triple.
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Domino Addition
Before you open · source notes
Dominoes prompt adding two parts in either order, then combining with a third addend. Use it for grouping addends, not every addition fact.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk the learner to add the two sides of one domino, then add a third number. One round does not prove every make-ten strategy.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-11 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Domino Addition.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
CC BY-NC-SA 4.0 — link only
Check understanding
- Solve 2 + 6 + 4 by first adding 6 + 4 = 10, then 2 + 10 = 12
- Explain that grouping addends differently gives the same total
- Choose which two numbers to add first to make the calculation easier
“If your child needs to add 3 + 7 + 6, can they spot that adding 3 and 7 first (to make 10) is easier — rather than always working left to right?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Addition & Subtraction
- Age range
- Ages 6–8
Standards