A starting point
Choose where to start
Pick the part that matches the task in front of you. You do not need to work through every activity in one sitting.
| If this is the sticking point | Start here | A question to ask |
|---|---|---|
| The multiplication sign has no clear meaning yet. | Make equal groups. | “How many groups? How many in each?” |
| Your child can count the picture but is unsure what to write. | Connect the picture to addition and multiplication. | “Which number tells us how many groups there are?” |
| Your child understands the groups but does not recall a fact. | Build from a familiar fact. | “Is there a fact you know that is close to this one?” |
These are ways to choose an example, not a test or a score. Leave the paper visible while you talk.
Activity 1
Make three equal groups
Draw three circles. Put four dots inside each, or use twelve pencils arranged in three groups of four.
- Ask your child to check that every group has the same number.
- Count the total together in whichever way they choose. Then point to each group as you say “four, plus four, plus four”.
- Write 4 + 4 + 4 = 12 beneath the picture.
- Write 3 × 4 = 12 and read it as “three groups of four make twelve”.
In this guide, the first number counts the groups and the second tells us how many are in each group. A teacher may describe the factors in a different order; follow that convention for schoolwork. What matters in this picture is being able to explain both numbers.
Now change the picture: add a fifth dot to each circle. Ask what changed. There are still three groups, but now each has five, so 5 + 5 + 5 = 15 and 3 × 5 = 15.
If your child writes 3 + 4 = 7 for the first picture, return to the groups: “Does the picture show three dots and four dots, or three groups of four?” Let them point before changing the equation.
Activity 2
Turn the groups into an array
An array is a rectangular arrangement in rows and columns. Arrange twelve dots in four rows of three:
Reading across, there are four rows with three dots in each: 4 × 3 = 12. Reading down, there are three columns with four dots in each: 3 × 4 = 12.
Ask your child to trace one row, then one column. The total has not changed; the grouping description has. In this example, four groups of three and three groups of four both make twelve, even though “four groups” and “three groups” describe different groupings.
Try drawing an array for 2 × 5. Can your child also find five columns of two? Keep the drawing beside the equations so the two ways of describing it stay visible.
Activity 3
Build a new fact from one you know
Suppose your child knows 5 × 7 = 35 but is working out 6 × 7. There is no need to start counting from one.
Draw five rows of seven, then add one more row. That extra row contains seven, so:
6 × 7 = 35 + 7 = 42.
Ask, “What stayed the same, and what did we add?” Each row still has seven; there is one more row. Adding one row means adding seven, not adding one to the total.
For a separate example, use doubling to work out 4 × 7. If 2 × 7 = 14, make another two rows of seven. Now there are four rows:
4 × 7 = 14 + 14 = 28.
Doubling the number of groups has doubled the total. Use this route when 2 × 7 is a fact your child can already explain; otherwise, draw and count it first.
NCERT's mathematics assessment guidance discusses deriving multiplication facts from known facts and patterns rather than relying only on rote recitation (§5.4, printed pages 223–224).
A parent prompt
When a table is easy to recite but a separate question is not
Imagine your child has just recited the seven-times table but pauses when you ask “What is 6 × 7?” Give them room to work it out rather than immediately repeating the question faster.
Here is one possible exchange:
- Parent: “Which multiplication by seven do you know?”
- Child: “Five sevens are thirty-five.”
- Parent: “How could we use that to find six sevens?”
If the next step is unclear, return to the drawing and add the sixth row. If the child chooses a different correct route, ask them to show it. The point of the question is to hear their reasoning, not to insist on your preferred shortcut.
If they do not have a familiar fact to start from, make a smaller example together. A pause on one question does not, by itself, tell you why the answer is difficult or what your child understands.
Paper practice
A small multiplication practice sheet
Copy this mini-sheet onto paper, or keep it beside you and write the answers separately. There is no timer or pass mark. Drawings, repeated addition and words are welcome; you can choose one question rather than complete the whole sheet.
Optional home practice
Multiplication at home
Use the spaces on paper. The explained answers follow in a separate section.
Keep the sheet at home. It needs no name or school identifier. Do not enter, upload or share student information, credentials, payment details or confidential family information on this public resource.
After trying a question
Practice answers and explanations
Keep these answers separate from the questions while your child tries a drawing or explanation. Then compare how you worked it out, not only the final number.
| Question | Answer | Why |
|---|---|---|
| 1. Three groups of four | 4 + 4 + 4 = 12; 3 × 4 = 12 | There are three equal groups, with four dots in each. |
| 2. Rows and columns | Rows: 4 × 3 = 12. Columns: 3 × 4 = 12. | Four rows of three are also three columns of four; both descriptions count the same twelve dots. |
| 3. One more group | 35 + 7 = 42; 6 × 7 = 42 | The extra group contains seven, so add seven to 35. |
| 4. Double the groups | 14 + 14 = 28; 4 × 7 = 28 | Two groups plus another two groups make four groups. |
| 5. Unequal groups | 3 + 3 + 4 = 10. No: the last group has four, not three. | Three equal groups of three would contain nine dots. These groups are not all the same size. |
The multiplication statements above use the group-count-first convention introduced in Activity 1. If your child's class writes the factors the other way round, ask them to explain their notation rather than mark it wrong for that reason.
Another example or a question
What to try next or ask the teacher
For another example, change just one thing: add a group, change the number in each group, or draw the same total in rows and columns. Ask your child what changed and what stayed the same. You can stop after one useful explanation and return another day.
If the school method is unclear, bring the teacher a specific question. For example: “We drew three groups of four at home. Which way are you writing the multiplication in class?” Or: “My child can say the table, but we are unsure how to use a known fact for a separate question. What example should we try?”
Use the school's usual communication route. You do not need to finish this sheet before asking. For a scheduled meeting, the PTM questions guide can help you choose what else to discuss.
Frequently asked questions
Frequently asked questions
Should my child memorise tables or work them out?
You can practise recall and still ask what a fact means. Use groups or a drawing to explain it, then try recalling it on another occasion. When recall is uncertain, return to a known fact or the picture rather than treating working out the answer as a mistake. Follow the teacher's expectations for assigned tables practice.
Which multiplication table should we start with?
Begin with the table being taught at school or a fact your child can explain. For these home activities, a small group you can draw is enough. This guide does not require learning every table in a fixed order before trying an unfamiliar fact.
Is multiplication the same as repeated addition?
For the positive whole-number equal groups used here, repeated addition describes the total: three groups of four can be written as 4 + 4 + 4. Multiplication records that relationship as 3 × 4. This is an introduction, not an explanation of every kind of multiplication your child will meet later.
What if my child does not want to do the practice sheet?
You can use one drawing or an everyday grouping question instead. The sheet is optional home practice, not a condition for moving on or a substitute for school assignments. If you are unsure what support is expected at home, ask the teacher.