MATHEMATICS SECOND TERM PRIMARY 4 LESSON NOTES / SCHEME OF WORK

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MATHEMATICS SECOND TERM PRIMARY 4 LESSON NOTES / SCHEME OF WORK

SUBJECT: MATHEMATICS

CLASS: BASIC FOUR

WEEK               TOPIC

  1. multiplication of whole number by two digit number

  2. Square of 1 and 2- digit number

  3. Division of 2 digit or 3-digit by number up to 9 with or without a remainder

  4. Common multiples of numbers

  5. Factors of numbers: HCF

  6. Estimation

  7. Money: Addition and subtraction of money

  8. Money: multiplication and division of money by a whole number

  9. Money: division of money by whole number

  • Profit and loss

  • Open sentences

 

WEEK ONE

MULTIPLICATION OF NUMBERS BY 2-DIGIT NUMBERS

Example 1 multiply 25 by 12

Method  1: column form                                             method 2: Expanded form 

                       2    5                                                      25 x 12 = 25 x (10 = 2)

                   x  1    2                                                                        = (25 x 10) = (25 x 2)   

                   2   5   0                    (25 x 10)                                   = 250  + 50

                   +   5   0                    (25 x 2)                                           = 300

                   3   0   0

     5 4                      Step 1: Multiply the units

× 2 6

                                 Regroup

3 2 4     = 54 × 6           Step 2: Multiply the tens

+ 1 0 8 0 = 54 × 20   Regroup

1 4 0 4  =   54 × 26   

 

EXERCIES 1: Multiply the following

  1. 53 x 50    84  x  10

  2. 97 x  10                                        96  x 40

  3. 67 x  50                                        67  x  50

  4. 87 x  20                                       64  x  30

  5. 57 x  40                                       64  x  40

  6. 56 x  10                                       95  x  20

  7. 86 x  20                                       84  x  50

  8. 99 x  50                                                 75  x  10

  9. 89 x  30

  • 75 x 40

 

EXERCISE 2: multiply the following

  1. 89  x 46

  2. 45  x  37 

  3. 56  x  17 

  4. 88  x  32 

  5. 36  x  35

  6. 78  x  18

  7. 76  x  26

  8. 29  x  27

  9. 79  x  49

  10. 75 x  46

Example

25 × 34 = (20 × 34) + (5 × 34)

= 680 + 170

= 850

Exercise 3

Copy and fill the boxes with the correct numerals.

  1. 24 × 33 = ( 20 × 33) + ( 􀁆× 33) = 􀁆2. 35 × 48 = ( 􀁆× 48) + ( 􀁆× 48) = 􀁆

  2. 47 × 18 = ( 􀁆× 18) + ( 􀁆× 18) = 􀁆4. 45 × 35 = (40 × 35) + (5 × 35) = 􀁆

  3. 41 × 25 = (40 × 25) + ( 􀁆× 25) = 􀁆6. 29 × 49 = ( 􀁆× 49) + ( 􀁆× 49) = 􀁆

  4. 57 × 16 = ( 􀁆× 16) + ( 􀁆× 16) = 􀁆8. 61 × 25 = ( 􀁆× 25) + ( 􀁆× 25) = 􀁆

  5. (12 × 7) + (30 × 7) = 􀁆10. 7 × 82 = (7 × 􀁆􀀃) + (7 × 2) 􀁆

  6. (20 × 8) + (2 × 8) = 􀁆12. 8 × 82 = (8 × 􀁆􀀃) + (8 × 2) = 􀁆

  7. 20 × 42 = (20 × 40) + (20 × 2) = 􀁆14. 50 × 28 = (50 × 20) + (50 × 􀁆􀀃) = 􀁆

 

WEEK TWO

BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to

􀁏􀀃 discover what squares and square roots mean

􀁏􀀃 solve problems involving the calculation of squares of numbers.

Exercise 1

Find the value of:

  1. 42 + 62

  2. 52 – 22

  3. 5­­­­­2 + 72     

  4. 102 – 52

  5. 82 + 102

  6. 82 – 62

  7. 22 x 52

  8. 32 x 42

  9. 42 x 32

  10. 52 x 22

  11. 62 x22

  12. 22 x 32 x 52

  13. 22 x 32 x 52

  14. 32 x 22 x 52

 

 

SQUARE OF 2-DIGIT NUMBER

 The squares of two-digit numbers are (in short form) 102, 112, 122, 133, … 992.

To calculate the squares of two digit numbers we may use any of these methods.

  1. a) Multiply the number by itself, i.e. using multiplication method.

  2. b) Find the square from the square table.

  3. c) Count the dots from the square pattern.

(This method may be too cumbersome at a later stage

Examples

Study the workings to find 142.

Solution: (Multiplication method)

142=14×14

(10+4)× (10+4)

10(10+4) + (10+4)

100+40+40+16

=196

Exercise

Solve each of the following:

  1. 42 2. 92 3. 102 4. 122  

  2. 112

  3. 152 7. 172 8. 162  9. 182  10. 202

Unit 2

 

WEEK THREE

DIVISION

BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to

CONTENT

Division of 2-digit and 3-digit numbers by numbers up to 9 without remainder

Example 1: 78 ÷ 6

                      T  U

1    3

                   6  7   8

                  –   6   0   (1 ten x 6)

                       1   8 

  • 1 8  (6 units x 3)

     0

 

Example 2:  82 ÷ 3

                      T  U

                      2   7

               3      8   2

              _       6   0          (2 tens x 3)

                      2   2

                _    2   1            (7 units x 3)

  • (Remainder)

Therefore, 82÷3 = 27 remainder 1

Exercise

  1. Calculate and give the remainder.

  2. 21 ÷ 9 2. 38 ÷ 4 3. 87 ÷ 4    4. 82 ÷ 6

  3. 78 ÷ 7 6. 72 ÷ 7 7. 29 ÷ 9   8. 57 ÷ 7

  4. 68 ÷ 8 10. 73 ÷ 6 11. 35 ÷ 3   12. 64 ÷ 6

  5. 88 ÷ 9 14. 73 ÷ 4 15. 89 ÷ 2   16. 77 ÷ 4

  6. 87 ÷ 9 18. 97 ÷ 8 19. 98 ÷ 6   20. 99 ÷ 5

  7. Solve the following:

  8. 73 nuts are shared among five children. Each child receives the same number of nuts:

  9. a) How many nuts did each child receive? b) How many nuts remain?

  10. Korede shared out 􀎏65 among 8 pupils. Each pupil is given the same amount of money:

  11. a) How much did each pupil receive? b) How much is remaining?

  12. Audu bought a sack of sweet potatoes weighing 50 kg. He divided the potatoes into bags, so that each bag held 3 kg of potatoes.

  13. a) How many complete bags of sweet potatoes did he get from his sack?

  14. b) How many kg of sweet potato remains?

  15. A box contains 87 notebooks. They are given out to 9 pupils equally.

  16. a) How many notebooks did each pupil receive?

  17. b) How many notebooks are remaining

Division of 3-digits numbers without remainder

Example

834 ÷ 3 means ‘how many threes are there in 834? To find 834 ÷ 3 start with the hundreds:

8 (hundreds) ÷ 3 = 2 (hundreds), remainder 2 (hundreds)

Take the remainder, 2 (hundreds), and add to the tens:

2 (hundreds) = 20 (tens); 20 (tens) + 3 (tens) = 23 (tens)

23 (tens) ÷ 3 = 7 (tens), remainder 2 (tens)

Take the remainder, 2 (tens) and add to the units:

2 (tens) = 20 (units); 20 (units) + 4 (units) = 24 units

24 (units) ÷ 3 = 8 units

” 834 ÷ 3 = 278

 

Solution

278

3 834

– 600 􀂪 (2 hundreds × 3)

234

– 210 􀂪 (7 tens × 3)

24

– 24 􀂪 (8 units × 3)

 

Example

Calculate the following:

205 ÷ 5

Solution

2 (hundreds) ÷ 5 = 0 (hundred), remainder 2 (hundreds)

Take the remainder, 2 (hundreds) and add to the tens:

2 hundreds = 20 (tens); 20 (tens) + 0 (ten) = 20 (tens)

20 (tens) ÷ 5 = 4 (tens), remainder 0

5 (units) ÷ 5 = 1 unit, remainder 0

” 205 ÷ 5 = 41

Working

41

5 205

– 200 􀂪 (4 tens × 5)

5

– 5 􀂪 (1 unit × 5)

Exercise

  1. Calculate the following.

  2. 153 ÷ 3 2. 126 ÷ 6  3. 185 ÷ 5     4. 177 ÷ 3     5. 156 ÷ 6

  3. 132 ÷ 4 7. 144 ÷ 4 8. 148 ÷ 4     9. 138 ÷ 6     10. 152 ÷ 4

  4. 171 ÷ 9 12. 224 ÷ 4 13. 105 ÷ 7    14. 102 ÷ 3   15. 465 ÷ 5

  5. 8 984 17. 5 555 18. 9 399 19.       9 981 20.        6 828

  6. 7 777 22. 4 712 23. 2 516 24.     4 636    25.     8 888

  7. Solve the following.

  8. The money contributed by a group of 6 pupils for cake baking is 􀎏426. How much

did each pupil contributes?

  1. Onome is paid 􀎏705 for a five day working week. How much is she paid for each day?

  2. How many 8-litre kegs can be filled from a drum of water containing 928 litres?

  3. A log of wood 522 metres long is sawn into pieces 9 m long. How many such pieces are there?

  4. A book has 312 pages. How many days will it take to read

  5. i) 8 pages a day? ii) 6 pages a day?

 

 

Exercise

  1. Divide 70 by 5

  2. Divide 78 by 6

  3. Divide 304 by 4

  4. Divide 981 by 9

  5. Divide 205 by 3

  6. Divide 420 by 9

  7. A box holds 3o tins. How many boxes can be filled with 810 tins?

  8. One packet contains 10 pencils. How many packets do 470 pencil fill?

  9. How many minutes are there in720 seconds

  • The product of three numbers is 540. The first number is 5 and the second number is 9. What is the third number?

 

 

WEEK FOUR

 

LEAST COMMON MULTIPLES (LCM)

BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to

 

 

􀁏􀀃 find the multiples of numbers

􀁏􀀃 find common multiples of numbers

􀁏􀀃 find the lowest common multiple by listing the multiples of numbers

􀁏􀀃 find the lowest common multiple by calculation.

CONTENT

LEAST COMMON MULTIPLES (LCM)

 

Revision of multiples of numbers

Multiples of a number e.g. 4 are those numbers that 4 can divide without remainder.

Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 etc. The first multiple of a number

is the number itself. Other multiples are obtained by repeated addition of the number.

Every number has unlimited number of multiples.

 

Example 1:

Find the least common multiples of 2 and 3

The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36

Thus the common multiples of 2 and three are 6, 12, 18 and 24

 Examples

Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 …

3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 …

5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 …

We can use repeated addition or multiplication to find the multiples. Here the first five multiples of 6 and 7 are found by using addition. Multiples of 6 are 6, 6 +6,  6 + 6 + 6,  6 + 6 + 6 + 6,   6 + 6 + 6 + 6 + 6

= 6, 12, 18, 24, 30…

Multiples of 7 = 7, 7 +7,    7 + 7 + 7,    7 + 7 + 7 + 7,   7 + 7 + 7 + 7 + 7

= 7, 14, 21, 28, 35…

Here the first five multiples of 6 and 7 are found by using multiplication.

Multiples of 6 = 6 1 6 2 6 3 6 4 6 5

=             6, 12, 18, 24, 30

Multiples of 7 = 7 1 7 2 7 3 7 4 7 5

=           7, 14, 21, 28, 35 …

Here the sixth multiple of 3 and 8 are found by using multiplication.

6th multiple of 3 = 3 6 = 18

6th multiple of 8 = 8 6 = 56

Exercise

  1. Write down the first ten multiples of

  2. 9 2. 10 3. 12 4. 7 5. 14

  3. Find the 5th multiple of

  4. 4 2. 11 3. 6 4. 15 5. 20

  5. Copy and complete the statements with the correct numerals.

  6. 12 is a multiple of 4 and 􀁆􀀃􀀃2. 84 is a multiple of 7 and 􀁆

  7. 90 is a multip2le of 9 and 􀁆4. 108 is a multiple of 9 and 􀁆

  8. 45 is a multiple of 􀁆and 􀁆

 

Example

Here the first three common multiples of 3 and 4 have been found.

Solution

Multiples of:

3 are: 3  6  9  12  15  18  21  24  27  30  33  36

4 are: 4 8 12 16 20 24 28 32 36 40…

The first three common multiples of 3 and 4 are: 12, 24, 36.

 

Exercise 1

Write down the first three common multiples of these series of numbers:

  1. 6 and 9 2. 4 and 8 3. 2, 4 and 6    4. 8 and 16    5. 10 and 15

  2. 7 and 14 7. 3, 6 and 9 8. 5 and 10    9. 4 and 12     10. 5 and 20

Exercise 2

Look at the following numbers in the box.

2    3     4    8    10   12  18    24    27  30   32   36

Which of these numbers are common multiples of:

  1. 2 and 3 2. 3 and 4 3.    3 and 6    4.    4 and 8     5. 5 and 10

LCM of numbers from common multiples

EXAMPLES

 

  1. The LCM of 4 and 6 has been found here.

Multiples of:

4 = 4 8 12 16 20 24 28 32 36…

6 = 6 12 18 24 30 36…

Common multiples of 4 and 6 are 12 24 36…

From 12, 24 and 36, the smallest or least of the common multiple is 12.

Therefore, LCM of 4 and 6 = 12

2    . The LCM of 8 and 12 has been found here.

8 = 8 16 24 32 40 48 56 …

12 = 12 24 36 48 60 …

Common multiple: 24 48…

From 24 and 48, the least of the common multiple is 24

LCM = 24

  1. The LCM of 6 and 9 has been found here.

6 = 6 12 18 24 30 36…

9 = 9 18 27 36…

Common multiples are: 18 36…

From 18 and 36, the least of the common multiple is 18

LCM = 18

 

Exercise

Find the LCM of these pair of numbers by first finding their common multiples.

  1. 3 and 4 2. 4 and 8 3. 3 and 5     4. 2 and 9    5. 4 and 6

  2. 6 and 5 7. 2 and 3 8. 3 and 8     9. 4 and 5    10. 6 and 9

  3. What is the least weight of garri that can be weighed into 3 kg or 5 kg bags without any remainder?

  4. What is the smallest length of a string that can be cut into pieces of 2 cm or 9 cm without any remainder?

The smallest of these multiples (i.e. the least) is 6

We say that the least common multiples of 2 and 3 is 6.

That is L.C.M of 2 and 3 is 6

 

LCM of numbers by calculation (Using Prime Number

Division Method)

What is a prime number? A prime number is a number that has two factors, one and

itself. In other words any number that can be divided by only one and itself is a prime

number.

Prime numbers are: 2 3 5 7 11 13 17 19 …

We will discuss this in detail when we come to factors. Note that 1 is a factor of every

number but not a prime number.

Finding LCM by calculation

Method 1: Prime number division (by prime factors)

Divide the given numbers by prime numbers. If the prime number can divide only one

number, start until the numbers are completely divided without remainder. The LCM is the

product of the prime numbers.

50

Examples

Study how the LCM of the following numbers has been found.

  1. 8 and 12 = 2      8, 12

                            2       4, 6

                            2       2, 3

                            3       1, 3

                                      1, 1

         LCM = 2 2 2 3

                   = 24

  1. 6, 8 and 16 = 2 6, 8, 16

                          2     3, 4, 8

                          2      3, 2, 4

                          2       3, 1, 2

                          3        3, 1, 1

                                    1, 1, 1

                LCM = 2 2 2 2 3

                              = 48

Exercise 1

Find the LCM of:

  1. 12 and 18 2. 10 and 12 3. 12 and 24 4. 6, 8 and 12 5. 12, 18, and 24

  2. 6, 8 and 10 7. 4, 6 and 8 8. 9 and 27 9. 3, 4 and 9 10. 8, 10 and 12

Method 2

Examples

Study how the LCM of the following numbers has been found.

 

  1. 8 and 12

8 =       2     8

            2      4

            2       2

                     1

12 =      2     12

             2      6

             3      3

                     1

8 = 2 ×2 ×2

12 = 2 ×2 ×3

LCM = 2 ×2 ×2 ×3

     = 24

Pick all the prime factors of the first and the second numbers. Find the product.

2 . 8, 9 and 15

 

8 = 2 ×2 ×2

9 = 3 ×3

15 = 3 ×5

LCM = 2 ×2× 2× 3×3 ×5

= 360

 

51

Exercise 2

Find the LCM of:

  1. 10 and 20 2. 5 and 15 3. 14 and 21 4. 8 and 9 5. 8 and 9

  2. 14, 21 and 28 7. 24 and 30 8. 12, 16 and 24 9. 15, 20 and 30 10. 9, 15

 

EXERCISE

Find the by listing the multiples of:

  1. 2 and 5

  2. 3 and 4

  3. 3 and 5

  4. 4, 2 and 6

  5. 2 and 7

  6. 2 and 12

  7. 3 and 7

  8. 3 and 12

  9. 2, 3 and 5

  10. 2 and 10

  • 2, 4 and 6

  • 3 and 15

  • 4 and 7

  • 4 and 7

 

WEEK FIVE

 

HIGHEST COMMON FACTOR (HCF)

BEHAVIOURAL OBJECTIVES: At the end of the lesson, pupils should be able to

􀁏􀀃 find the factors of numbers

􀁏􀀃 identify prime numbers

􀁏􀀃 Work out the common factors and highest common factors of numbers

 

CONTENT

HIGHEST COMMON FACTOR (HCF)

REVISION OF FACTORS OF NUMBERS

Factors are just the numbers that divide into another number exactly without a remainder.

Examples

Factors of 6

To find the factors, begin multiplying two numbers starting with 1.

1 × 6 = 6 nothing else can be multiplied

2 × 3 = 6 to give 6.

$ Factors of 6 are 1, 2, 3, 6

6 can be divided by all the factors exactly without a remainder.

Factors of 12

1 × 12 = 12 2 × 6 = 12 3 × 4 = 12

No other numbers can be multiplied to give you 12. So the factors of 12 are 1, 2, 3, 4, 6, 12.

So 12 can be divided by all the factors exactly without a remainder.

Exercise 1

Write down all the factors of these numbers using the examples to guide you.

  1. 9 2. 10 3. 12     4. 16     5. 18    6. 20

  2. 56 8. 63 9. 70     10. 32   11. 60   12. 96

Common factors of numbers

Study the example carefully.

The factors of 12 are: 1 , 2 , 3 , 4, 6 and 12

The factors of 18 are: 1 , 2 , 3 , 6 , 9 and 18

The common factors are 1, 2, 3, 6 because these factors are

factors of both numbers as you can see.

Exercise

  1. Find all the common factors of both numbers.

  2. a) 25 and 30 b) 18 and 27 c) 12 and 24 d) 9 and 27

  3. Copy and complete this table in your notebook.

Numbers              Common factors

  1. a) 6 and 21

  2. b) 14 and 21

  3. c) 8 and 20

  4. d) 10 and 25

  5. e) 10 and 30

  6. Find the common factors of these numbers.

  7. a) 12 and 15 b) 15 and 25 c) 14 and 28 d) 6, 8 and 10 e) 28, 24 and 30

  8. f) 12 and 28 g) 18, 24 and 42 h) 56, 80, 72 i) 4, 8 and 12 j) 8, 16 and 24

 

54

Unit 3

 HCF of numbers from common factors

Examples

  1. Study the examples to find the HCF of 12 and 16.

12 = 1 × 12         16 = 1 × 16

         2 × 6                    2 × 8

  3 × 4                           4 × 4

 

Factors are 1 , 2 , 3, 4 , 6, 12    Factors are 1 , 2 , 4 , 8, 16

 

Common factors = 1, 2, 4

 

Highest Common Factor is 4 because it is the highest factor among the common factors.

We write HCF = 4

  1. Study the examples to find the HCF of 16 and 24.

16 = 1 × 16      24 = 1 × 24

2 × 8                        2 × 12

4 × 4                        3 × 8

4 × 6

Factors are 1 , 2 , 4 , 8 , 16 Factors are 1 , 2 , 3, 4 , 6, 8

The common factors of these numbers 16 and 24 are 1, 2, 4, 8

The Highest Common Factor (HCF) for 16 and 24 is 8

We write HCF = 8

Exercise

  1. Using the above method find the HCF of each pair of numbers.

  2. a) 8 and 10 b) 12 and 20 c) 25 and 35 d) 20 and 50 e) 18 and 36

  3. f) 60 and 100 g) 18 and 20 h) 25 and 50 i) 27 and 63 j) 20 and 100

 

  1. Find the highest common factors of these pairs of numbers.

  2. a) 9 and 12 b) 5 and 15 c) 12 and 15 d) 12 and 16 e) 16 and 20

  3. f) 10 and 12 g) 16 and 18 h) 5, 10, and 15 i) 4, 5 and 30 j) 18, 21 and 27

 

The product of 2 and 3 is; 2 x 3 = 6

2 and 3 are factors of 6

 

The factors of a number are numbers that divide the number without a remainder

 

EXAMPLE

Find the common factors of 24 and 36

24 =    1 x 24                                       36 =   1 x 36

     =    2 x 12                                                =   2 x 18

    =     3 x 8                                         =   3 x 12

    =     4 x 6                                         =   4 x 9

                                                                      =    6 x 6

Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

Common factors of 24 and 36 are: 1, 2, 3, 4, 6, 12

The highest common factor is 12.

 

EXERCISE

Find the HCF of:

  1. 6 and 9

  2. 6 and 27

  3. 21 and 14

  4. 12 and 18

  5. 6 and 21

  6. 6 and 15

  7. 24 and 60

  8. 18 and 30

  9. 14 and 16

  10. 6 and 10

 

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