Using Ten-Frames to Build Multiplication Groups

Multiplication becomes easier to understand when children can see equal groups before they are asked to memorise number facts. A ten-frame provides a simple visual model: ten empty spaces arranged in two rows of five, ready for counters, drawings or small classroom objects.

For a beginning lesson, the aim is to connect repeated addition with multiplication. Three groups of four can be shown as 4 + 4 + 4, then described as 3 groups of 4, or 3 × 4. The ten-frame does not replace concrete materials; it gives those materials an organised structure that helps students notice quantity and pattern.

This approach suits Australian primary classrooms, home learning and tutoring sessions in places such as Melbourne, Brisbane and Perth. It can support the Australian Curriculum’s focus on recognising, representing and solving multiplication problems, while giving children an accessible way to explain their thinking during class discussion or informal practice.

Teachers can use counters, bottle tops, linking cubes or printable circles. Using familiar objects makes the activity practical and inexpensive, whether the lesson takes place in a busy classroom, a library corner or at the kitchen table after school.

Start with one group on a ten-frame

Begin by placing one counter in each space until the chosen quantity is visible. Ask children to describe what they see using everyday language: “There are four counters,” “There are four spaces filled,” or “There are six altogether.” Avoid rushing to the multiplication symbol. The first goal is to build one-to-one correspondence and accurate counting.

Next, place the same number of counters on a second ten-frame. If each frame contains three counters, children can compare the groups and say, “There are two equal groups of three.” Write 3 + 3 beside the frames, followed by 2 × 3. Keep the language consistent: the first number tells how many groups, and the second tells how many are in each group.

Use a short visual grouping guide when preparing cards or prompts for learners who benefit from clear visual routines. Each card can show the frames, the repeated addition sentence and the matching multiplication fact.

Make equal groups visible

Ten-frames are especially useful when children need to distinguish equal groups from random collections. Show two frames with four counters each, then a third frame with five. Ask students to identify which arrangement represents multiplication groups. The unequal example can lead to the important idea that multiplication describes equal quantities in this context.

Have learners build, draw and label several examples. Two groups of five may be recorded as 5 + 5 and 2 × 5. Four groups of two may be represented by four frames, each holding two counters. Encourage children to say the complete sentence aloud: “Four groups of two make eight.” This supports mathematical vocabulary and helps prevent confusion between the number of groups and the number in each group.

For a smaller working area, children can outline sections on a large ten-frame or use coloured counters to mark groups within a row. This is helpful when teaching skip counting by twos or fives, since the arrangement makes regular jumps easier to see.

Connect pictures with equations

Once children can build equal groups, introduce multiplication symbols gradually. Place a number card above the frames to show the number of groups and another beside the frame to show the quantity in each group. Then connect the model to repeated addition and the total.

For example, three frames containing five counters each can be read as 5 + 5 + 5 = 15 and 3 × 5 = 15. Turn the cards around and discuss 5 × 3 only after the original meaning is secure. This creates an opportunity to explain that changing the order can produce the same total, while the story represented by each factor may change.

Use mini whiteboards or printable worksheets for quick checks. A child might draw two groups of seven, write 7 + 7, and then record 2 × 7. Another learner could match a completed set of frames with the correct equation from three choices. These small tasks reveal whether the child understands the groups or is simply guessing from a familiar fact.

Extend the model to arrays and times tables

The two-by-five structure of a ten-frame naturally leads to arrays. A filled frame can be seen as two rows of five or five columns of two. Ask students to count by rows, count by columns and describe both views. This prepares them for rectangular arrays, area models and more efficient calculation strategies.

When several frames are placed side by side, children can explore facts such as 3 × 10, 6 × 5 or 4 × 5. Use Australian coins or supermarket-style price cards in a simple classroom shop: three packs with five items each represent 3 × 5, while a $2 coin repeated five times represents five groups of two dollars. These familiar contexts connect mathematics with everyday Australian habits such as shopping and handling coins.

As recall develops, link the visual work to times-table practice rather than treating memorisation as a separate task. Knowing facts in both directions supports later division and sharing problems; students can explore this connection through backward times tables once they can explain what each factor represents.

Adapt lessons for different learners

Some children will need physical counters for several lessons, while others may move quickly to drawings and equations. Offer a progression: build the groups, sketch the frames, label the repeated addition, write the multiplication fact and explain the answer in words. This gives every learner a clear next step without making the task unnecessarily difficult.

For additional support, use smaller numbers, colour-code each group and provide sentence starters such as “___ groups of ___ make ___.” For extension, ask students to find two different groupings for the same total, such as 12 as three groups of four or four groups of three. They can then discuss why the total stays the same.

In Australian schools, teachers should also consider inclusive classroom routines and responsible use of student information. If photographs of children’s work are shared digitally, follow school policies and relevant requirements under Australia’s Privacy Act 1988. Printable frames are often a practical alternative because they allow assessment evidence to remain in exercise books or learning folders.

Download or draw a set of ten-frames, gather a few counters and begin with one equal group at a time. Use the completed models for partner talk, quick quizzes and short practice sheets so children repeatedly connect concrete quantities with multiplication language.