A correct total is only the beginning
A student looks at two displays and says, “They both show 12.” The total is correct, but it does not yet show whether the student has noticed the size of each group or can explain what an expression represents. Year 2 guidance describes the possibility of students finding an answer without being able to explain its meaning or represent the multiplication involved, so this brief activity gives you an opportunity to watch, listen and choose a useful next step. See the Mathematics Hub Year 2 multiplication and division planning guidance.
The key question is not simply “How many altogether?” It is “Does each addend record one whole displayed group?”
Prepare two displays with the same total
Prepare six clearly bounded mats—three for each display—and 24 counters, divided into two sets of 12. Keep every counter visible.
- Display A: place 4 counters on each mat, giving group sizes of 4, 4 and 4.
- Display B: place 2 counters on the first mat, 4 on the second and 6 on the third.
Both displays contain three groups and 12 counters altogether. Holding the number of groups and the total constant makes the group sizes the important difference.
Before beginning, check that students can count these small collections and recognise which objects belong within each mat. Individual counting, pointing and oral answers are all suitable; fluent skip counting and recalled multiplication facts are not required.
Ask about the groups before counting altogether
Invite students to count the counters on each mat. Then ask:
- How many groups are in this display?
- How many counters are in each group?
- Are the groups equal? How do you know?
- How many counters are there altogether?
For this activity, equal groups are groups containing the same number of objects. The counters do not need identical spacing or arrangements. Display A has equal groups because every mat contains four counters. Display B has unequal groups because its mats contain different numbers.
Using physical collections alongside equal-group and repeated-addition representations is consistent with the Mathematics Hub Year 2 planning guidance. It also helps distinguish the number of groups from the group size. A group can be treated as one countable unit containing several objects—an idea reflected in the NSW Department of Education’s guidance on sharing and forming groups. Students do not need to learn the term composite unit to make this distinction.
Match one addend to one mat
Show the expression 4 + 4 + 4 and ask: “Which display matches 4 + 4 + 4 when each addend must describe one whole mat? Explain by pointing.”
For Display A, point to each mat while saying:
There are three groups. Each has four counters. Each 4 in 4 + 4 + 4 records one group.
Write 4 + 4 + 4 = 12. Then point to the mats in Display B and record their actual sizes: 2 + 4 + 6 = 12.
Both expressions have the value 12, but they record different displayed group structures. The expression 4 + 4 + 4 represents Display A one mat at a time; it does not record the individual mat sizes in Display B.
If you introduce multiplication notation, label the factors in context: 3 × 4 means three groups of four in this example, and its product is 12.
Make the unequal groups equal
Ask students to make Display B’s groups equal without adding counters to the display or taking any away.
Move two counters from the mat containing six to the mat containing two. The first group changes according to 2 + 2 = 4, while the last changes according to 6 − 2 = 4. The middle group remains at four, producing group sizes of 4, 4 and 4.
Ask students to describe what changed and what stayed the same. The group sizes changed, but the display still has three groups and a total of 12. Students can now point to the three mats as they read 4 + 4 + 4 = 12.
Record the reasoning in separate parts
A response of “12” answers only the total question. Ask the student to point to the mat represented by each addend so you can hear how they connect the groups and notation. This follows the distinction in the Year 2 planning guidance between giving an answer and explaining or representing its meaning.
| What to notice | Quick record | Possible next prompt |
|---|---|---|
| Counts the objects on each mat | Accurate, recounts or needs support | “Touch each counter once as you count.” |
| Judges whether the groups are equal | Compares quantities or relies on appearance | “How many are on each mat?” |
| Matches one addend to each group | Points consistently or matches only the total | “Which mat does this addend describe?” |
| Explains the total | Uses objects, words or notation | “How do the three groups make 12?” |
If notation is getting in the way, let the student describe or rebuild the groups before returning to the symbols. Follow an uncertain response with another example. A single response is useful evidence for the next teaching decision, but it cannot establish mastery or explain why an error occurred.
Try the idea with four baskets
Draw one display of four baskets containing 3, 3, 3 and 3 objects. Beside it, draw another four baskets containing 2, 3, 3 and 4 objects. Both displays total 12.
Before showing the expressions, ask students to point to each basket, state its quantity and decide whether the groups are equal. Then ask which display matches 3 + 3 + 3 + 3 when one addend represents one basket.
The first display matches: 3 + 3 + 3 + 3 = 12. The second display is recorded basket by basket as 2 + 3 + 3 + 4 = 12. Again, a matching total does not establish a matching group structure.
On a later attempt, vary the spacing or arrangement of the three objects within the equal groups. Keep every object visible and ask students to base their decision on the quantity in each basket rather than its appearance.
Place the check in the learning sequence
The Year 2 curriculum description reproduced by the Mathematics Hub connects multiplication and division by one-digit numbers with repeated addition, equal grouping, arrays and partitioning. This activity addresses the equal-grouping and repeated-addition parts of that description; it does not cover the complete descriptor. Read the AC9M2N05 curriculum alignment reproduced with The array.
Equal-group repeated addition is one useful model for multiplication, but it is not a definition of every multiplicative situation. The NSW Department of Education’s multiplicative-strategies guidance also identifies contexts involving comparison, scale, rate, combinations and area. Those contexts need not be introduced during this short check; the important point is to keep the language specific to the example in front of the student.
Continue with more representations if useful
The free activity above is complete with counters, mats and something to write on. For broader follow-up work, the optional Multiplication as Repeated Addition — Year 2 resource is relevant to equal groups and several connected representations.
Its catalogue description says:
Make the meaning of multiplication visible before students begin memorising facts. Multiplication as Repeated Addition — Year 2 develops the concept through equal groups, arrays, repeated addition, multiplication sentences, bar models, number lines and skip counting.
The counter-and-mat check in this article is a separate suggested activity and is not presented as an included task in that resource.
Finish by checking every basket
Exit prompt: “Point to each basket as you read its addend. How do you know the groups are equal?”
Use the response to decide whether to revisit the quantities within each group or practise connecting groups to notation. The lasting classroom habit is simple: before accepting a correct total, check that every addend accounts for its corresponding group.