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A free printable book

Maths for classes 3 to 5

4 lessons, each with worked examples, a try-at-home activity and a practice sheet. The practice sheets are together after the lessons, and the answer keys are at the very back.

  • Maths
  • Classes 3-5
  • 4 lessons
  • 40 practice questions
  • Free to print

Contents

Free learning for kids, Gurukul Technicals Institute. Printed from engineergurukul.com/resources/kids/books/maths-3-5/

Contents

What is in this book

  1. 1Multiplication tables made easyUnderstand multiplication as repeated addition and learn tricks and patterns that make tables easy to remember.4 min
  2. 2Division: sharing equallyLearn division as equal sharing and equal grouping, see how it links to multiplication, and handle remainders.3 min
  3. 3Fractions: parts of a wholeLearn what numerators and denominators mean, compare fractions, find equal fractions and take fractions of a group.3 min
  4. 4Perimeter and areaFind the distance around a shape (perimeter) and the space inside it (area) for rectangles, squares and triangles.3 min

Every lesson here can also be read on its own page, with links to related lessons. All printable books.

Lesson 1 of 4

Multiplication tables made easy

Understand multiplication as repeated addition and learn tricks and patterns that make tables easy to remember.

Open this lesson on its own page · Practice sheet · Answer key · Contents

Let us begin

The big idea

Multiplication is a quick way to add the same number again and again. Once you see the patterns, tables become fun and easy to remember.

Multiplication means groups of equal size. 4 × 6 means 4 groups of 6, which is 6 + 6 + 6 + 6 = 24.

The order does not matter. 4 × 6 = 6 × 4. This halves the tables you need to learn.

There are patterns. The table of 2 gives even numbers. The table of 5 ends in 0 or 5. The table of 10 adds a zero at the end.

For the table of 4, double the number and then double again. For 9, the digits of each answer up to 9 × 10 add up to 9: 18, 27, 36, 45 and so on.

To find a harder fact, use an easy one. 6 × 8 is 5 × 8 plus one more 8: 40 + 8 = 48.

An array for 4 × 6Twenty-four dots arranged in 4 rows with 6 dots in each row. Next to it, the working shows 4 rows of 6, which is 6 + 6 + 6 + 6, which is 24. 4 rows of 6 6 + 6 + 6 + 6 = 24 4 × 6 = 24 and 6 × 4 = 24
4 rows of 6 dots make 24 dots. Turn it sideways and you get 6 rows of 4.

Worked examples

See how it works

  1. Repeated addition: 7 × 4

    7 × 4 means 4 groups of 7. 7 + 7 = 14, 14 + 7 = 21, 21 + 7 = 28. So 7 × 4 = 28.

  2. A trick for 9 times: 9 × 7

    Take 1 less than 7. That is 6, and it is the tens digit. Then find what adds with 6 to make 9. That is 3, the ones digit. So 9 × 7 = 63. Check: 6 + 3 = 9.

  3. Build from 5: 6 × 8

    5 × 8 = 40. One more group of 8 is 8. So 6 × 8 = 40 + 8 = 48.

  4. Double and double: 4 × 7

    Double 7 to get 14. Double 14 to get 28. So 4 × 7 = 28.

Try it at home

Stone arrays

You will need

  • 24 small stones, beans or buttons
  • Paper and a pencil

What to do

  1. Put the 24 stones in 4 rows of 6. Write 4 × 6 = 24.
  2. Turn the paper around. Now there are 6 rows of 4. Write 6 × 4 = 24.
  3. Try 3 rows of 8, 2 rows of 12 and 1 row of 24.
  4. Write all the multiplication facts you found.
  5. Try again with 18 stones. How many different arrays can you make?

Ask a grown-up: Keep small stones and beans away from younger children who might put them in their mouths.

Fun fact

In the 9 times table, the digits of every answer from 9 × 1 to 9 × 10 add up to 9.

Lesson 2 of 4

Division: sharing equally

Learn division as equal sharing and equal grouping, see how it links to multiplication, and handle remainders.

Open this lesson on its own page · Practice sheet · Answer key · Contents

Let us begin

The big idea

Whenever you share sweets with your friends so that everyone gets the same, you are dividing. Let us see how division works and how to do it fast.

Division means sharing equally or making equal groups. 12 ÷ 3 = 4 means 12 things shared among 3 gives 4 each.

Division is the opposite of multiplication. Because 3 × 4 = 12, we know 12 ÷ 3 = 4 and 12 ÷ 4 = 3.

In 12 ÷ 3 = 4, the number 12 is the dividend, 3 is the divisor and 4 is the quotient.

Sometimes things cannot be shared equally. What is left over is called the remainder. The remainder is always smaller than the divisor.

To check a division, multiply the quotient by the divisor and add the remainder. You should get the dividend back.

12 laddoos shared among 3 platesThree plates, each with 4 laddoos on it. Twelve laddoos have been shared equally. Below the plates it says 12 divided by 3 equals 4.12 laddoos shared equally among 3 plates Plate 1: 4 Plate 2: 4 Plate 3: 4 12 ÷ 3 = 4
Sharing 12 equally among 3 plates gives 4 on each plate.

Worked examples

See how it works

  1. Equal groups: 20 ÷ 4

    Ask: 4 times what is 20? 4 × 5 = 20. So 20 ÷ 4 = 5.

  2. With a remainder: 15 ÷ 4

    4 × 3 = 12, and 4 × 4 = 16 is too big. So the quotient is 3. 15 − 12 = 3 is left over. So 15 ÷ 4 = 3 remainder 3. Check: 4 × 3 + 3 = 15.

  3. A story: 56 mangoes in 7 baskets

    Share 56 mangoes equally into 7 baskets. 7 × 8 = 56. So each basket gets 8 mangoes.

  4. Two-digit number: 84 ÷ 4

    84 is 8 tens and 4 ones. 8 tens ÷ 4 = 2 tens. 4 ones ÷ 4 = 1 one. So 84 ÷ 4 = 21. Check: 21 × 4 = 84.

Try it at home

Share the beans

You will need

  • 25 beans, stones or buttons
  • 6 small bowls or cups
  • Paper and a pencil

What to do

  1. Share 24 beans equally into 2 bowls. How many in each? Write 24 ÷ 2 = 12.
  2. Now share 24 into 3 bowls, then 4 bowls, then 6 bowls. Write each division fact.
  3. Take 25 beans and share them among 4 bowls. What is left over?
  4. Write the answer as a quotient and a remainder.
  5. Check by multiplying and adding the remainder.

Ask a grown-up: Keep beans and small stones away from little children who might put them in their mouths.

Lesson 3 of 4

Fractions: parts of a whole

Learn what numerators and denominators mean, compare fractions, find equal fractions and take fractions of a group.

Open this lesson on its own page · Practice sheet · Answer key · Contents

Let us begin

The big idea

If you cut a roti into 4 equal pieces and eat 1 piece, you have eaten a fraction of it. Fractions help us talk about parts of a whole.

A fraction shows equal parts of a whole. The bottom number is the denominator. It tells how many equal parts the whole is cut into. The top number is the numerator. It tells how many parts we take.

In 3/4, the whole is cut into 4 equal parts and we take 3 of them. The parts must be equal in size.

When the denominators are the same, the bigger numerator means the bigger fraction. 4/5 is bigger than 2/5.

When the numerators are the same, the bigger denominator means smaller pieces. So 1/4 is smaller than 1/2.

Different fractions can show the same amount. 1/2 = 2/4 = 3/6. These are called equivalent fractions. We get them by multiplying the top and bottom by the same number.

Half, quarter and three quartersThree bars of equal length. The first is cut into 2 equal parts with 1 shaded, showing one half. The second is cut into 4 equal parts with 1 shaded, showing one quarter. The third is cut into 4 equal parts with 3 shaded, showing three quarters.½ 1 of 2 parts ¼ 1 of 4 parts ¾ 3 of 4 parts Equal parts: every part is the same size.
Equal parts make fractions: 1/2, 1/4 and 3/4.

Worked examples

See how it works

  1. A paratha cut into 4

    A paratha is cut into 4 equal pieces. Ravi eats 3 pieces. He ate 3/4 of it. 1/4 is left because 3/4 + 1/4 = 4/4, which is the whole.

  2. Comparing fractions

    Compare 2/5 and 4/5. Both have the same denominator, 5. The bigger numerator is 4, so 4/5 is greater than 2/5.

  3. Equivalent fractions

    Multiply the top and bottom of 1/2 by 2: 1 × 2 = 2 and 2 × 2 = 4. So 1/2 = 2/4. Multiply by 3: 1/2 = 3/6.

  4. Fraction of a group: 3/4 of 12 mangoes

    First find 1/4 of 12. 12 ÷ 4 = 3. Then 3/4 is 3 × 3 = 9. So 3/4 of 12 mangoes is 9 mangoes.

Try it at home

Fold a paper into fractions

You will need

  • Two or three sheets of paper
  • Crayons or a pencil

What to do

  1. Fold the first sheet into two equal halves and open it. Shade one half. Write 1/2.
  2. Take a new sheet. Fold it in half and then in half again. Open it. You have 4 equal parts. Shade 1 part. Write 1/4.
  3. On a third sheet folded into 4, shade 3 parts and write 3/4.
  4. Compare your sheets. Which shaded part is biggest?
  5. Try folding a sheet into 8 equal parts.

Ask a grown-up: An adult can help make the folds neat so the parts are really equal.

Lesson 4 of 4

Perimeter and area

Find the distance around a shape (perimeter) and the space inside it (area) for rectangles, squares and triangles.

Open this lesson on its own page · Practice sheet · Answer key · Contents

Let us begin

The big idea

If you walk around a cricket ground, you cover its perimeter. If you cover the whole ground with grass, you cover its area. Let us measure both.

Perimeter is the total length of the boundary of a shape. To find it, add the lengths of all the sides. It is measured in cm or m.

For a rectangle, the perimeter is length + breadth + length + breadth, or 2 × (length + breadth). For a square with side s, it is 4 × s.

Area is the amount of flat space inside a shape. It is measured in square units such as square cm (sq cm) or square m (sq m).

For a rectangle, area = length × breadth. For a square, area = side × side. Count the unit squares to see why: 6 rows of 4 squares is 24 squares.

A rectangle 6 cm by 4 cmA rectangle drawn on a grid of unit squares. It is 6 squares long and 4 squares wide. Under the picture the perimeter is worked out as 20 cm and the area as 24 square cm. 6 cm 4 cm Perimeter = 6 + 4 + 6 + 4 = 20 cm Area = 6 × 4 = 24 sq cm
Each small square is 1 cm by 1 cm. Perimeter is the distance round; area is the number of squares inside.

Worked examples

See how it works

  1. Perimeter of a rectangle

    A rectangle is 8 cm long and 5 cm wide. Perimeter = 8 + 5 + 8 + 5 = 26 cm. Or 2 × (8 + 5) = 2 × 13 = 26 cm.

  2. Area of a rectangle

    The same rectangle has area 8 × 5 = 40 sq cm.

  3. A square

    A square has side 7 m. Perimeter = 4 × 7 = 28 m. Area = 7 × 7 = 49 sq m.

  4. A triangle and a fence

    A triangle has sides 5 cm, 6 cm and 7 cm. Perimeter = 5 + 6 + 7 = 18 cm. A rectangular park is 30 m by 20 m. Fence all round: 2 × (30 + 20) = 100 m.

Try it at home

Squares on a page

You will need

  • A squared notebook page (or paper with a grid drawn on it)
  • A pencil
  • A ruler

What to do

  1. Draw a rectangle that is 5 squares long and 3 squares wide.
  2. Count the squares inside. That is the area. 5 × 3 = 15.
  3. Count the edges of squares along the outside. That is the perimeter. 5 + 3 + 5 + 3 = 16.
  4. Draw two more rectangles and find their area and perimeter.
  5. Can two rectangles have the same area but different perimeters? Try 2 by 6 and 3 by 4.

Ask a grown-up: No special help is needed. An adult can check the counting and the multiplication.

Part two

Practice sheets

One sheet for each of the 4 lessons. Write your name and the date at the top, answer in the spaces, then check with the answer keys at the back.

Practice sheet

Multiplication tables made easy

Practice sheet: Multiplication tables made easy (Classes 3-5, Maths)

  1. 3 × 5 = ?
  2. 6 × 7 = ?
  3. 8 × 4 = ?
  4. 9 × 6 = ?
  5. 7 × 8 = ?
  6. Which is bigger, 6 × 9 or 7 × 8?
  7. A packet has 6 laddoos. How many laddoos are in 8 packets?
  8. Fill in the blank: 5, 10, ___, 20, 25.
  9. Use 5 × 8 = 40 to find 6 × 8.
  10. An auto-rickshaw carries 3 passengers. How many passengers can 9 autos carry?

Practice sheet

Division: sharing equally

Practice sheet: Division: sharing equally (Classes 3-5, Maths)

  1. 18 ÷ 3 = ?
  2. 24 ÷ 6 = ?
  3. 40 ÷ 8 = ?
  4. 63 ÷ 9 = ?
  5. 48 pencils are shared equally among 6 children. How many does each child get?
  6. If 7 × 6 = 42, what is 42 ÷ 7?
  7. 17 ÷ 5 = ? (give the quotient and the remainder)
  8. 29 ÷ 4 = ? (give the quotient and the remainder)
  9. 96 ÷ 3 = ?
  10. Rs 250 is shared equally among 5 children. How many rupees does each child get?

Practice sheet

Fractions: parts of a whole

Practice sheet: Fractions: parts of a whole (Classes 3-5, Maths)

  1. In the fraction 3/8, which number is the numerator?
  2. A paratha is cut into 8 equal pieces. Ravi eats 3. What fraction did he eat?
  3. What fraction of that paratha is left?
  4. Which is bigger, 3/7 or 5/7?
  5. Fill in the blank: 1/2 = ___/4.
  6. Which is smaller, 1/2 or 1/4?
  7. What is 1/3 of 12?
  8. What is 3/5 of 20?
  9. Write 3/4 in words.
  10. Put in order from smallest to biggest: 1/2, 1/8, 1/4.

Practice sheet

Perimeter and area

Practice sheet: Perimeter and area (Classes 3-5, Maths)

  1. What does perimeter measure?
  2. A square has side 5 cm. What is its perimeter?
  3. A rectangle is 9 cm long and 4 cm wide. What is its perimeter?
  4. A rectangle is 6 cm long and 3 cm wide. What is its area?
  5. A square has side 8 cm. What is its area?
  6. A triangle has sides 7 cm, 8 cm and 9 cm. What is its perimeter?
  7. A garden is 12 m long and 8 m wide. How much fencing is needed to go all round it?
  8. What is the area of the same garden?
  9. A rectangle has area 36 sq cm and length 9 cm. What is its width?
  10. A square has perimeter 36 cm. What is the length of one side?

Part three

Answer keys

The answers to every practice sheet, in the same order as the lessons. Parents and teachers may like to keep these pages separately.

Answer key

Answers: Multiplication tables made easy

  1. 15
  2. 42
  3. 32
  4. 54
  5. 56
  6. 7 × 8, because 56 is bigger than 54.
  7. 48 laddoos (6 × 8).
  8. 15
  9. 48 (40 + 8).
  10. 27 passengers (3 × 9).

Answer key

Answers: Division: sharing equally

  1. 6
  2. 4
  3. 5
  4. 7
  5. 8 pencils (48 ÷ 6).
  6. 6
  7. Quotient 3, remainder 2 (5 × 3 = 15, 17 − 15 = 2).
  8. Quotient 7, remainder 1 (4 × 7 = 28, 29 − 28 = 1).
  9. 32 (9 tens ÷ 3 = 3 tens, 6 ones ÷ 3 = 2 ones). Check: 32 × 3 = 96.
  10. Rs 50 each (250 ÷ 5 = 50).

Answer key

Answers: Fractions: parts of a whole

  1. 3 (the denominator is 8).
  2. 3/8
  3. 5/8 (8/8 − 3/8).
  4. 5/7
  5. 2 (1/2 = 2/4).
  6. 1/4. When the whole is cut into more parts, each part is smaller.
  7. 4 (12 ÷ 3).
  8. 12 (20 ÷ 5 = 4, then 4 × 3 = 12).
  9. Three quarters (or three-fourths).
  10. 1/8, 1/4, 1/2.

Answer key

Answers: Perimeter and area

  1. The distance all round the edge of a shape.
  2. 20 cm (4 × 5).
  3. 26 cm (2 × (9 + 4)).
  4. 18 sq cm (6 × 3).
  5. 64 sq cm (8 × 8).
  6. 24 cm (7 + 8 + 9).
  7. 40 m (2 × (12 + 8)).
  8. 96 sq m (12 × 8).
  9. 4 cm (36 ÷ 9).
  10. 9 cm (36 ÷ 4).

The end

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