Representing Addition and Subtraction
Represent addition and subtraction using objects, drawings, and mental images
Lesson
Set out your lesson
“We can make addition and subtraction visible. For addition, show the first group, add the second group, and count all. For subtraction, show the start, take some away, and count what is left.”
Bring to the table
- At least 8 large blocks or toys
- Paper and crayons
Extra for the adult
Worked example. 4 animals plus 3 more animals shown side by side make 7. 5 blocks with 2 moved away leave 3.
Optional challenge. Tell a tiny story such as “There were 5 apples and 1 rolled away.” Have your child draw the start, show the change, and count what remains.
What to notice. Save a photo of one addition model and one subtraction model, or a parent note with both equations in words or numbers.
Share and support
Compare teaching approaches
Teaching approaches
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1 approach
We can make addition and subtraction visible. For addition, show the first group, add the second group, and count all. For subtraction, show the start, take some away, and count what is left.
Spend about 10 minutes modeling one put-together addition and one take-away subtraction with objects, then one drawing.
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
Fact Families with Pictures
Before you open · source notes
Picture fact families support representing addition and subtraction relationships. Not every multiplication family.
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 write two addition and two subtraction sentences from the same picture family.
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 2026-11-12 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. “Fact Families with Pictures.” 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
- Use cubes, counters or on-screen counters to show 3 + 2
- Draw a picture to represent a subtraction situation
- Use fingers to model an addition problem
“If your child has 3 apples and you give them 2 more, can they show you how many there are altogether — using their fingers, some small objects, or a drawing?”
Curriculum record
- Type
- Representational
- Subject
- Mathematics
- Domain
- Addition & Subtraction
- Age range
- Ages 4–13
Standards