Hello, young mathematician! Multiplication and division become much easier when you can see equal groups, make steady jumps, and check your answer in another way. In this guide, you will build those ideas slowly with drawings, number patterns, and original everyday problems.
Caregiver: Let the learner arrange paper counters or draw quick dots before asking for a number sentence.
This original PrincipalSaab guide follows Chapter 7, Raksha Bandhan, in NCERT’s current Maths Mela book for Class 3. The official chapter sets the learning scope. Every explanation, example, activity, and question below is newly written.
Words to Know
| Word | Simple meaning | Quick picture |
|---|---|---|
| Equal groups | groups with the same number in each | 4 cups with 3 counters in every cup |
| Product | the answer to a multiplication | 4 × 3 = 12, so 12 is the product |
| Array | objects placed in equal rows and columns | 3 rows of 5 dots |
| Share equally | give the same amount to every group | 20 cards shared among 4 teams |
| Remainder | what is left after making all possible equal groups | 17 counters in groups of 5 leave 2 |
| Skip count | count forward or backward in equal steps | 0, 6, 12, 18, 24 |
Your Learning Plan
- Build or draw the groups.
- Name the number of groups and the number in each group.
- Choose multiplication or division.
- Calculate in small, clear steps.
- Check by using the connected operation.
Keep your drawings simple. Circles, tally marks, or small squares are enough. Put a ring around each equal group, then count the rings and the objects inside one ring. This picture helps you choose the correct number sentence. After solving, read the story again and ask, “Does my answer name groups, objects in each group, a total, or a leftover?”
Equal Groups and Multiplication
Multiplication describes equal groups. If six packets hold the same number of pencils, you can multiply. If the packets hold different numbers, first find each amount or add them separately.
The sentence 6 × 4 can be read as six groups of four. It matches repeated addition: 4 + 4 + 4 + 4 + 4 + 4. Both paths reach 24.
Always connect the numbers to the story. The first number can tell how many equal groups there are, while the second tells how many objects are in each group.
- A class makes 7 strips.
- Each strip has 3 paper badges.
- Repeated addition is 3 + 3 + 3 + 3 + 3 + 3 + 3.
- 7 × 3 = 21.
Answer: The class uses 21 paper badges.
Need a number warm-up? What’s in a Name? for Class 3 strengthens counting and number sense before multiplication.
Arrays and Turnaround Facts
An array shows equal groups in rows and columns. It makes a multiplication fact visible. For example, four rows with six dots in each row show 4 × 6.
If you turn the array, you see six rows with four dots. The product is still 24. This is called a turnaround fact: 4 × 6 and 6 × 4 have the same product.
The story words may change, though. Four shelves with six books on each shelf are not described in the same way as six shelves with four books on each shelf, even when both totals are 24.
- A tray has 5 rows.
- Each row holds 8 seed cups.
- 5 × 8 = 40 cups.
- Turning the tray shows 8 × 5 = 40.
Answer: There are 40 seed cups in either view.
Skip Counting and Tables
Skip counting means moving by the same amount each time. Starting at zero and adding 4 gives 0, 4, 8, 12, 16, 20. Five equal jumps of 4 land at 20, so 5 × 4 = 20.
A multiplication table records these equal jumps. You do not need to chant without meaning. Picture each new row as one more equal group.
Patterns make tables easier to check. Products in the 2 table are even. Products in the 5 table end in 0 or 5. Products in the 10 table end in 0. You can also combine known facts: if 6 × 4 = 24 and 2 × 4 = 8, then 8 × 4 = 24 + 8 = 32.
- A counter moves 0, 7, 14, 21, 28, 35.
- Each move adds 7.
- Five jumps of 7 reach 35.
- 5 × 7 = 35.
Answer: The jump size is 7, and the fifth landing number is 35.
Fair Sharing and Grouping
Division answers two connected questions. Sharing asks how many each group receives. Grouping asks how many equal groups can be made.
For 28 counters shared among 4 children, the number of children is known and the size of each share is missing. For 28 counters placed in groups of 4, the group size is known and the number of groups is missing. Both calculations use 28 ÷ 4 = 7, but the sentence answer is different.
Multiplication checks division. If 28 ÷ 4 = 7, then 4 × 7 must rebuild 28.
- There are 42 bookmarks.
- They are shared equally among 6 reading groups.
- 42 ÷ 6 = 7.
- Check: 6 × 7 = 42.
Answer: Each reading group gets 7 bookmarks.
Repeated Subtraction and Leftovers
When you do not know a division fact, repeated subtraction can help. To make groups of 6 from 38, subtract 6 again and again while counting the groups.
Some divisions do not share exactly. After making every complete equal group, a small amount may remain. That amount is the remainder. The remainder must be smaller than the group size; otherwise, another complete group can still be made.
- Pack 38 art cards in bundles of 6.
- Six bundles use 6 × 6 = 36 cards.
- 38 – 36 = 2 cards remain.
- Two is smaller than 6, so no more complete bundle can be made.
Answer: There are 6 complete bundles and 2 cards left.
Larger Products in Easy Parts
You can use facts you know to solve a larger multiplication. Break the number of groups into friendly parts, solve each part, and then join the products.
For 23 × 4, think of 20 groups of 4 and 3 groups of 4. Twenty groups of 4 make 80. Three groups of 4 make 12. Together, 80 + 12 = 92.
Place value helps here. Multiplying by 10 makes ten equal groups. If 7 × 6 = 42, then 70 × 6 means seven tens taken six times, which is 42 tens or 420.
- There are 27 toy carts.
- Each cart has 4 wheels.
- 20 × 4 = 80 and 7 × 4 = 28.
- 80 + 28 = 108.
Answer: The toy carts have 108 wheels altogether.
For more practice with place value before splitting a product, revisit House of Hundreds – I.
Money and Mixed Stories
A story problem may need more than one step. Read it once for the situation and again for the numbers. Ask what must be found first.
Money problems need the rupee symbol or the word rupees in the final answer. If you pay more than the cost, subtract to find the change. When division leaves a remainder, decide what the leftover objects mean in the story.
- One folder costs ₹68.
- Four folders cost 4 × 68.
- 4 × 60 = 240 and 4 × 8 = 32.
- 240 + 32 = ₹272.
- If ₹300 is paid, the change is ₹300 – ₹272 = ₹28.
Answer: The folders cost ₹272, and the change is ₹28.
Arrays, rows, and turns also connect to geometry. Fun with Shapes for Class 3 is a useful next stop when you want to notice organised patterns.
Practice Time
Try these original questions without opening the answer first.
Practice 1. Nine trays hold 4 paint pots each. How many paint pots are there?
Answer: 9 × 4 = 36 paint pots.
Practice 2. Draw or describe an array for 6 × 8. What is its turnaround fact?
Answer: Six rows of 8 make 48. The turnaround fact is 8 × 6 = 48.
Practice 3. Continue the equal jumps: 0, 9, 18, 27, __, __. Write the matching multiplication facts.
Answer: 36 and 45. The facts are 4 × 9 = 36 and 5 × 9 = 45.
Practice 4. Share 56 counters equally among 8 teams.
Answer: 56 ÷ 8 = 7 counters for each team. Check: 8 × 7 = 56.
Practice 5. How many complete groups of 5 can be made from 43 shells? How many are left?
Answer: 8 complete groups use 40 shells, so 3 shells are left.
Practice 6. A number track starts at 47 and moves backward by 6. Write the next five landing numbers.
Answer: 41, 35, 29, 23, 17.
Practice 7. Find 34 × 3 by splitting 34 into 30 and 4.
Answer: 30 × 3 = 90 and 4 × 3 = 12, so 34 × 3 = 102.
Practice 8. One notebook costs ₹46. What is the cost of 5 notebooks?
Answer: 5 × 40 = 200 and 5 × 6 = 30, so the cost is ₹230.
Practice 9. A gardener has 67 seedlings and places 8 in each row. How many complete rows can be made, and how many seedlings remain?
Answer: 8 rows use 64 seedlings, so 3 seedlings remain.
Practice 10. Is 54 ÷ 6 = 8 correct? Show a multiplication check.
Answer: No. Since 6 × 8 = 48, the answer is too small. The correct fact is 6 × 9 = 54, so 54 ÷ 6 = 9.
Quick Self-Check
Open each answer after saying your own answer aloud.
Self-check 1. What must be true before you multiply groups?
Answer: Every group must contain the same number.
Self-check 2. Why do 3 × 8 and 8 × 3 have the same product?
Answer: They are turnaround views of the same rectangular array; both contain 24 objects.
Self-check 3. How can multiplication check a division answer?
Answer: Multiply the number of groups by the amount in each group. It should rebuild the original total when there is no remainder.
Self-check 4. What is wrong if a remainder is equal to or larger than the group size?
Answer: Another complete group can still be made, so the division is not finished.
Self-check 5. What friendly split helps with 26 × 4?
Answer: Split 26 into 20 and 6: 20 × 4 = 80 and 6 × 4 = 24, so the product is 104.
How to Explain Your Work
A clear answer has four parts: name the groups, write the number sentence, show the calculation, and finish with a sentence that names the object.
For division with a remainder, state both parts. For example: “Five complete teams can receive 7 cards each, and 2 cards remain.” Do not hide the leftovers or call them another full team.
When a problem feels large, show the split you used. Writing 32 × 4 as (30 × 4) + (2 × 4) makes the thinking visible and easier to check.
Kaizen step: Build one fact, check it in a second way, and let that small success strengthen the next fact.
Continue Learning
- Browse all Class 3 Mathematics guides
- Next in Maths Mela: continue with the next official chapter after this one.