CAPS baseline framework
Lesson 31: Subtraction using the column method
H T O H T O
9 1
£
||||| |||||
1 0 5
– 4 6
5 9
0 5 9
• Ask a learner to come up to the board to show the class how they would solve the problem.
• Allow opportunities for discussion, as learners will have different ways of solving the problem and it is important for learners to have time to learn from each other.
• Be aware that learners may be a bit unsure of this problem as it looks a little different to the other problems they have worked on previously. The zero in the tens place of the larger number may make learners feel uncertain of how to solve the problem.
• Make sure you take the time to discuss the steps involved in solving the problem carefully so that learners feel comfortable when calculating numbers containing a zero.
• The first step is to line up the numbers vertically in hundreds, tens and ones.
• We can’t take 6 away from 5, so what should we do? (We borrow or exchange from the tens place)
• But the tens place has a zero. Can we borrow 1 ten from 0 tens? (No because you can’t take 1 away from zero).
• So, where can we borrow from? Make sure that learners know that they cannot swap the numbers around so that they can subtract zero from 1.
• We will borrow from the hundreds column. So, we cross out the 1 in the hundreds column, and then where must we put the 10 tens we have borrowed? Can we put it in the ones place? (No)
• Why not? (Because the 10 tens must go in the tens place / because they’re tens).
• Okay so we now have 10 tens in the tens place instead of zero, but we still haven’t managed to borrow anything for the ones place. What must we do now? (Now we can borrow a ten from the tens place to give to the ones)
• So, we cross out the 10 tens – what are we left with? (9 tens)
• We give 10 ones to the ones place so that we end up with 15 ones.
• So, now we can subtract the ones place: 15 – 6 = 9. Write the 9 in the ones place underneath the line.
• Now go back to the tens place – how many tens were we left with? (9)
• Subtract: 90 – 40 = 50.
• Where must we write the 5? (In the tens place, underneath the line).
• Do we have any hundreds left? (No because we exchanged them for 10 tens and put them in the tens place)
• So, what’s the answer for 105 – 46? (105 – 46 = 59).
• Then write the problem 102 – 9 on the board.
Lesson 31: Subtraction using the column method
WEEK 7
H T O
9 1
1 0 2
– 9
9 3
• Follow the same process, but emphasise that this time we are subtracting a single digit number from a 3-digit number. Learners still need to be aware of what to do when there is a zero in the tens place.
• Also discuss with learners: What happens to the 9 in the tens place because there is no number beneath it? We don’t have anything to subtract from 9 so we just write the 9 in the answer line.
• Then write the problem 100 – 7 on the board.
H T O
9 1
1 0 0
– 7
9 3
• This problem looks a bit different as there is a zero in both the tens and the ones place.
• Ask the same questions as before, for example: Can we take 7 away from 0? (No);
Where should we borrow from? (The hundreds column)
• Finally write 132 – 128 + ---on the board H T O
2 1
1 3 2 – 1 2 8 4
• This problem also looks a bit different as we are subtracting a 3-digit number from a 3-digit number.
• Ask questions as before, for example: Can we take 8 away from 2? (No); Where should we borrow from? (The tens place); What is 2 take away 2? (0) And 1 take away 1? (0) Must we write the zeros in the answer line? (No because 004 still means 4, so we just need to write 4).
Activity 2: Whole class activity
• Repeat Activity 1, using the same numbers again, but this time ask the learners to solve the problems using a number line instead of the column method.
105 – 46
60 105
59 100
– 40 – 5
– 1
101 – 64
40 101
37 100
– 60 – 1
– 3
107 – 78
30 107
29 100
– 70 – 7
– 1
100 – 7
100
93
– 7
132 – 128
10 132
4 130
– 120 – 2
– 6
• Discuss the differences between the methods, getting learners to think about how they break down numbers to help them solve the problems.
• Ask learners: Did you break down the numbers in the same way when you used the column method and the number line? Why / Why not?
Activity 3: Whole class activity
• How do we know if we have answered our subtraction problem correctly? (Learners may say that they will wait for the teacher to mark their work).
• Let learners discuss how to check if the number sentence 8 – 5 = 3 is correct or not. Let them rewrite it in addition (3 + 5 = 8).
• In the same way, let learners discuss how to check 105 – 46 = 59 (in activity 1) is correct.
Let learners check the solution by solving 59 + 46.
H T O
1
+ 5 94 6 1 0 5
• Repeat with the other problems done in Activity 1 and 2.
• Each time, ask the learners which two numbers they need to add together. Make sure learners understand that they add the subtraction problem’s answer to the smaller number.
Lesson 31: Subtraction using the column method
WEEK 7
3 CLASSWORK ACTIVITY AND CORRECTION OF HOMEWORK (25 MINUTES) Solve using the column method:
a 105 – 56 = (49) H T O
9 1
1 0 5
– 5 6
4 9
b 103 – 49 = (54) H T O
9 1
1 0 3
– 4 9
5 4
c 106 – 9 = (97) H T O
9 1
1 0 6
– 9
9 7
d 100 – 4 = (96) H T O
9 1
1 0 0
– 4
9 6
e 142 – 138 = (4) H T O
3 1
1 4 2 – 1 3 8 4
4 HOMEWORK ACTIVITY (5 MINUTES) Solve using the column method:
a 107 – 49 = (58) H T O
9 1
1 0 7
– 4 9
5 8
b 108 – 9 = (99) H T O
9 1
1 0 8
– 9
9 9
c 121 – 116 = (5) H T O
1 1
1 2 1 – 1 1 6 5
5 REFLECTION AND SUMMARY OF LESSON (5 MINUTES)
Call the whole class to attention and summarise the key concepts of the lesson:
Today we have solved subtraction problems, using the column method.
We looked at what happens when there is a zero in the tens or the ones place.