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CBSE Class 2 · Mathematics

Grouping and Sharing (Multiplication and Division)

Official NCERT chapter from Joyful Mathematics (English) (book code bejm1). ExamMaster notes are original teaching at CBSE Class 2 depth.

This lesson follows the official chapter “Grouping and Sharing (Multiplication and Division)” in Joyful Mathematics (English). The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 2
  • Easy level
  • 8 concepts

1Wheels of autos and bicycles are equal groups

A bicycle has 2 wheels. An auto has 3. Those are equal groups of wheels. Four bicycles are four groups of 2.

A broken auto with 2 wheels is not a full auto-group.

Figure. A bicycle is a group of 2 wheels. An auto is a group of 3. Four bicycles are four groups of 2. Two wheels on a broken auto are not a full auto-group.

How it works

  1. Name the vehicleBicycle, or auto.
  2. Lock the group size2, or 3.
  3. Count full vehiclesHow many groups.

22+2+2+2 is four groups of two

Repeated 2 four times is 4 × 2. It is not 2 + 4. The addends must match.

If one addend is 3, it is not this equal-group sentence.

Figure. Repeating 2 four times is 4 × 2. It is not 2 + 4. Every addend must be the same size or it is not this equal-group sentence.

How it works

  1. Write the repeated add2 + 2 + 2 + 2.
  2. Count the addendsFour groups.
  3. Read 8Four times two.

3Multiplication names those equal groups

× is a short name for adding the same number again. 4 × 2 means four groups of two.

The first number counts groups. The second names the size.

Figure. × is the short name for adding the same number again. The first factor counts groups; the second is the size. 4 × 2 is four pairs, eight wheels — not 4 + 2.

How it works

  1. Draw the groupsFour pairs of wheels.
  2. Join2 + 2 + 2 + 2.
  3. Write 4 × 2 = 8Times is the short name.

Four bicycles

4 bicycles, 2 wheels each. How many wheels?

  • Group size2
  • Four groups2 + 2 + 2 + 2
  • Total8

Pro tip. 4 \times 2 is repeated 2, not 4 + 2.

4Division is sharing into equal groups

12 wheels shared into groups of 2 make 6 bicycles. Division asks how many groups, or how many in each group.

The story must say which ask. Do not swap them.

Figure. 12 wheels shared into groups of 2 make 6 bicycles. Division asks how many groups, or how many in each group. The story must say which ask.

How it works

  1. Name the total12 wheels.
  2. Name the group size2.
  3. Count the groups6. That is 12 \div 2.

5An array shows both readings

3 rows of 4 dots is 3 × 4 and also 4 columns of 3. Same dots, two times-sentences.

A messy scatter is not an array.

Figure. 3 rows of 4 is 3 × 4 and also 4 columns of 3. Same twelve boxes, two times-sentences. A messy scatter is not an array.

How it works

  1. See a rowOne equal group.
  2. Count the rowsOne reading.
  3. Count the columnsThe other reading.

6A leftover in sharing is a remainder

13 wheels shared into 2s leave 1 leftover. That leftover is a remainder, not a bicycle.

Forcing the leftover into a group of 2 makes 7 a lie.

Figure. 13 wheels in groups of 2 fill six bicycles (12) and leave 1. That leftover is a remainder, not a seventh bicycle. Forcing it into a pair of 2 makes 7 a lie.

How it works

  1. Fill full groups of 2Six bicycles, 12 wheels.
  2. See the leftover1 wheel.
  3. Keep it as remainderNot a seventh bicycle.

8A moving car is still four wheels — the group did not change

Motion does not add a wheel. Four wheels parked or moving are still one group of 4.

The story of driving is not a new times.

Figure. Motion does not add a wheel. Four wheels parked or moving are still one group of 4. The story of driving is not a new times.

How it works

  1. Count the wheelsFour.
  2. See it moveStill four.
  3. Keep the group sizeMotion is not a fifth wheel.
4 \times 2 = 8. Then 8 \div 2 is
  1. 4
  2. 16
  3. 6

Fact family: the same three numbers.

Notes

  • The official chapter title is “Grouping and Sharing (Multiplication and Division)”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • a \times b is a groups of b.
  • If a \times b = c, then c \div b = a.

Recap

Hold these pegs from the official chapter “Grouping and Sharing (Multiplication and Division)”. The wording is ExamMaster’s teaching, not a textbook recap.

Wheels of autos and bicycles are equal groups
A bicycle has 2 wheels. An auto has 3. Those are equal groups of wheels. Four bicycles are four groups of 2.
2+2+2+2 is four groups of two
Repeated 2 four times is 4 × 2. It is not 2 + 4. The addends must match.
Multiplication names those equal groups
× is a short name for adding the same number again.
Division is sharing into equal groups
12 wheels shared into groups of 2 make 6 bicycles.
An array shows both readings
3 rows of 4 dots is 3 × 4 and also 4 columns of 3.
A leftover in sharing is a remainder
13 wheels shared into 2s leave 1 leftover.

Practise Grouping and Sharing (Multiplication and Division)

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