Twelve objects, three drawn groups and the number sentence 3 × 4 = 12 can describe the same relationship. The learning happens when a child can explain the connection, not simply move quickly from a picture to an answer.
For families exploring schools around Novena, hands-on Mathematics is a useful point of discussion. Objects can make an idea visible, while drawings and symbols help a learner represent it in different ways.
This guide uses SJI Junior’s published Mathematics approach as local context, followed by an independent equal-groups activity. It does not reproduce school lessons or promise examination results.
eduKateSG · Neighbourhood education
Choose your next learning step
Explore the school context, try a small task or review the learning.
1. Understand the context · 2. Try the activity · 3. Check and continue
Contents
Explore, practise and connect · Four chapters
CHAPTER 1 OF 4
1. Understand the published approach
St. Joseph’s Institution Junior’s Mathematics Department page identifies the transition from concrete to abstract concepts, reasoning and problem-solving as part of its mission. It lists activity-based learning for Primary 1 to Primary 5.
That gives families a specific question to ask: how do classroom activities help pupils explain the mathematical relationship they are representing?
Use the school’s current information for programme details. The task below is a family example, not a statement about the school’s precise sequence of teaching or the expectations for every year level.
CHAPTER 2 OF 4
2. Build equal groups with objects
Use twelve large paper squares on a clear surface. Ask the child to arrange them into three equal groups. Large paper pieces avoid the need for small counters; choose materials suitable for the child and supervise where necessary.
Count the number in each group. There should be four. Then count the total to check that no pieces were lost or added. Say the relationship aloud: three groups, four in each group, twelve altogether.
If one group has more pieces, pause before writing a number sentence. Ask how to make the groups equal. The arrangement needs to match the intended relationship.
Keep the first task narrow. A child does not need several operations and a lengthy story problem at once to explain equal groups clearly.
CHAPTER 3 OF 4
3. Draw the arrangement and name the symbols
Next, draw three circles with four marks in each circle. Ask which part of the drawing stands for the groups, which stands for the number in each group and which shows the total.
For this example, write 3 × 4 = 12 and explain it as three groups of four. Connect each number to the drawing. Follow the notation and wording used by the child’s teacher if they differ.
Cover the paper squares briefly. Can the child use the drawing to explain the same idea? If not, return to the objects and compare them side by side rather than treating the drawing as a test of speed.
Symbols are a concise representation, not a separate trick. A correct answer is more informative when the learner can say what the numbers represent.
CHAPTER 4 OF 4
4. Check understanding by changing the arrangement
Rearrange the same twelve squares into four equal groups. Now there are three in each group. Compare the two arrangements: the total stayed twelve, but the number of groups and the amount in each group changed.
Ask the child to draw the new arrangement and explain it before writing another number sentence. This checks whether the representation follows the objects rather than a memorised picture.
A useful parent prompt is “Show me where that number is in your drawing.” Avoid removing the objects merely because a learner has reached a particular age. Use the representation that makes the current idea understandable.
Finish with one clear explanation. If the child is tired or uncertain, stop and return another day. A short discussion that connects objects, drawings and symbols can be more useful than a long page completed without meaning.
Sources and scope
School information checked on 13 October 2026 (Singapore time): SJI Junior: Mathematics Department. Programmes may change. Suggested family activities are independently written by eduKateSG, not official school tasks. This article does not imply school endorsement, rank schools or guarantee admission or learning results.