Open Sentences : Addition, Subtraction, Multiplication and Division
SECOND TERM E NOTES FOR PRIMARY 4 MATHEMATICS
SUBJECT: MATHEMATICS
CLASS: BASIC FOUR / / PRIMARY 4
WEEK 10
TOPIC : Open Sentences involving Addition, Subtraction, Multiplication and Division
Learning Objectives
Pupils should be able to:
- illustrate and explain the
term open sentence. - predict the missing numbers 8
in an open sentence.
tell stories on open
sentence, - write and solve
the equations.
solve quantitative reasoning
involving open sentence
Learning Activities
Pupils:
-respond to the following questions with TRUE or FALSE
- 8+4=5+7
- 6X8= 25+23
- 5-4 =7+7
- predict missing numbers in these open
sentences:
e.g. (a)
+ 5 = 12
= 9
(b) 20 - -tell stories on open sentences, write the
equations and solve them.
Embedded Core Skills
- Critical thinking and problem solving skills
- Communication and Collaboration
- Student Leadership skills and Personal Development skills
- Problem solving skills and Personal Development
Audio Visual Resource
- Flash cards
Content
The mathematical statements above are called closed number sentences.
Closed number sentences can either be true or false.
Examples
15 + 7 = 22 (True mathematical statement) 18 + 3 = 19 (False mathematical statement)
3 × 6 = 12 (False mathematical statement) 42 ÷ 6 = 7 (True mathematical statement)
Study each of the following mathematical statements:
- {}+ 9 = 13
- 11 +{} = 25
- {}− 4 = 11
- 20 –{} = 7
- {}× 5 = 15
- 4 ×{} = 24
- {} ÷ 6 = 5
- 48 ÷{} = 12
In each of the statement above, there is a missing number called unknown represented by box. They are called open sentences.
An open sentence is a mathematical statement that involves equality signs and a missing
quantity represented by that the four arithmetic operations of addition, subtraction,
multiplication and division can be applied to solve.
Open sentences can either be true or false depending on the value .
Exercise
A. Write True (T) or False (F) for each of the following closed number sentences.
- 15 + 16 = 31
-
54 + 4 = 68
-
18 + 10 = 38
-
51 + 47 = 98
-
29 + 60 = 82
-
42 + 54 = 84
-
55 − 23 = 33
-
54 − 11 = 43
-
64 − 43 = 21
-
98 − 45 = 53
B. Write True (T) or False (F) for each of the following open sentences if is replaced by 4.
-
- 2 = 9
-
- 3 = 7
-
- 7 = 12
- − 3 = 1
-
12 − = 7
-
8 − = 4
-
4 × = 16
-
× 2 = 10
-
÷ 2 = 2
Unit 2 Operation of addition and subtraction involving open
sentences (Revision)
Examples
Here the number represented by in each of the following has been found.
1. + 14 = 36
2. 12 + = 8
3. − 4 = 30
4. 15 − = 9
Solution
1. + 14 = 36 can be interpreted as “what can be added to 14 to get 36?”
+ 14 = 20 + 16
+ 14 = 20 + 2 + 14
+ 14 = 22 + 14
= 22
Check:
22 + 14 = 36
Short method
If + 14 = 36
then = 36 − 14
= 22
$ = 22
Check:
22 + 14 = 36
Exercise
1. When 79 is added to a number, we get 124. Find the number.
2. When 71 is added to a number, we get 214. Find the number.
3. When I subtract 19 12 from a certain number, the result is 9 12 . What is the number?
4. When 31 kg of meat is removed from the part of the cow, there is 25 kg left. What is the weight of the cow?
5. A poultry farmer took four crates of eggs to the market. He had 45 eggs left after market hour. How many eggs were sold?
6. When 564 is added to a certain number, the result is 801. Find the number.
7. 6 times an unknown number gives 72. Find the number.
8. When a number is multiplied by 12, we get 108. Find the number.
9. I think of a number, divide it by 8 and get 32. Find the number.
10. A certain number of oranges was shared equally among 6 children. Each child received 14 oranges. How many oranges were shared?
Open sentences are math equations that have at least one unknown value. This means that some part of the equation is missing and we need to solve for it. Let’s take a look at some examples for each operation:
Addition: An open sentence for addition might look like this: 5 + __ = 12. We know that 5 plus some number equals 12, but we don’t know what that number is. To solve the equation, we need to find the missing number that would make the equation true. In this case, the missing number is 7, because 5 + 7 = 12.
Subtraction: An open sentence for subtraction might look like this: __ – 8 = 3. We know that some number minus 8 equals 3, but we don’t know what that number is. To solve the equation, we need to find the missing number that would make the equation true. In this case, the missing number is 11, because 11 – 8 = 3.
Multiplication: An open sentence for multiplication might look like this: 4 x __ = 16. We know that 4 times some number equals 16, but we don’t know what that number is. To solve the equation, we need to find the missing number that would make the equation true. In this case, the missing number is 4, because 4 x 4 = 16.
Division: An open sentence for division might look like this: 20 ÷ __ = 4. We know that 20 divided by some number equals 4, but we don’t know what that number is. To solve the equation, we need to find the missing number that would make the equation true. In this case, the missing number is 5, because 20 ÷ 5 = 4.
Evaluation
- What is the missing number in the equation 7 + __ = 14? a) 7 b) 14 c) 21 d) 6
- What is the missing number in the equation 12 – __ = 5? a) 17 b) 7 c) 5 d) 6
- What is the missing number in the equation 6 x __ = 30? a) 6 b) 5 c) 36 d) 25
- What is the missing number in the equation 18 ÷ __ = 3? a) 3 b) 6 c) 9 d) 18
- What is the missing number in the equation 8 + __ = 11? a) 11 b) 19 c) 3 d) 4
- What is the missing number in the equation 15 – __ = 6? a) 9 b) 6 c) 21 d) 15
- What is the missing number in the equation 3 x __ = 9? a) 6 b) 3 c) 9 d) 27
- What is the missing number in the equation 24 ÷ __ = 4? a) 6 b) 8 c) 4 d) 12
- What is the missing number in the equation 11 + __ = 16? a) 16 b) 27 c) 5 d) 6
- What is the missing number in the equation 30 – __ = 18? a) 48 b) 12 c) 18 d) 8
Lesson Presentation
Introduction:
- Begin the lesson by asking students if they have ever seen a math problem with a blank space instead of a number.
- Explain that this is called an open sentence, and it means that we don’t know the missing number and need to figure it out.
Body:
- Start with addition open sentences, using the example 4 + __ = 10. Explain that we need to figure out what number makes the equation true, and ask for student volunteers to share their answers. Write the correct answer (6) on the board.
- Move on to subtraction open sentences, using the example __ – 8 = 5. Ask students to solve for the missing number, and write the correct answer (13) on the board.
- Next, cover multiplication open sentences, using the example 3 x __ = 15. Encourage students to share how they solved for the missing number, and write the correct answer (5) on the board.
- Finally, discuss division open sentences, using the example 20 ÷ __ = 4. Ask students to solve for the missing number, and write the correct answer (5) on the board.
Closure:
- Provide students with worksheets to practice solving open sentences on their own.
- Have students share their answers with a partner or in small groups.
- Review the concepts covered in the lesson and remind students of the importance of understanding open sentences in math.
Assessment:
- Observe students as they work on the worksheets to ensure they understand the concepts.
- Use informal questioning to check for understanding throughout the lesson.
Weekly Assessment /Test
- 3 + __ = 10 The missing number is _________.
- __ – 5 = 12 The missing number is _________.
- 6 x __ = 36 The missing number is _________.
- 100 ÷ __ = 10 The missing number is _________.
- 8 + __ = 17 The missing number is _________.
- __ – 10 = 20 The missing number is _________.
- 5 x __ = 35 The missing number is _________.
- 60 ÷ __ = 6 The missing number is _________.
- 9 + __ = 15 The missing number is _________.
- __ – 4 = 7 The missing number is _________
