Subtraction
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Students should be encouraged to estimate answers before attempting to solve problems in concrete or symbolic form. There is still a need to emphasise mental computation even though students can now use a formal written method.
Word problems requiring subtraction usually fall into two types – either ‘take away’ or ‘comparison’. The comparison type of subtraction involves finding how many more need to be added to a group to make it equivalent to a second group, or finding the difference between two groups. Students need
to be able to translate from these different language contexts
into a subtraction calculation. The word ‘difference’ has a specific meaning in a subtraction context. Difficulties could arise for some students with use of the passive voice in relation to subtraction problems eg ‘10 takeaway 9’ will give a different response to ‘10 was taken away from 9’.
Revisit strategies for addition and subtraction using two-, three- and four-digit numbers, including: – the jump strategy eg 23 + 35; 23 + 30 = 53, 53 + 5 = 58
– the split strategy eg 23 + 35; 20 + 30 + 3 + 5 is 58
– the compensation strategy eg 63 + 29; 63 + 30 is 93, subtract 1, to obtain 92
– using patterns to extend number facts eg 5 – 2 = 3, so 500 – 200 is 300
– bridging the decades eg 34 + 17; 34 + 10 is 44, 44 + 7 = 51
– changing the order of addends to form multiples of 10 eg 16 + 8 + 4; add 16 and 4 first Revisit recording strategies
recording mental strategies eg 159 + 22;
‘I added 20 to 159 to get 179, then I added 2 more to
get 181.’
or, on an empty number line
Word problems requiring subtraction usually fall into two types – either ‘take away’ or ‘comparison’. The comparison type of subtraction involves finding how many more need to be added to a group to make it equivalent to a second group, or finding the difference between two groups. Students need
to be able to translate from these different language contexts
into a subtraction calculation. The word ‘difference’ has a specific meaning in a subtraction context. Difficulties could arise for some students with use of the passive voice in relation to subtraction problems eg ‘10 takeaway 9’ will give a different response to ‘10 was taken away from 9’.
Revisit strategies for addition and subtraction using two-, three- and four-digit numbers, including: – the jump strategy eg 23 + 35; 23 + 30 = 53, 53 + 5 = 58
– the split strategy eg 23 + 35; 20 + 30 + 3 + 5 is 58
– the compensation strategy eg 63 + 29; 63 + 30 is 93, subtract 1, to obtain 92
– using patterns to extend number facts eg 5 – 2 = 3, so 500 – 200 is 300
– bridging the decades eg 34 + 17; 34 + 10 is 44, 44 + 7 = 51
– changing the order of addends to form multiples of 10 eg 16 + 8 + 4; add 16 and 4 first Revisit recording strategies
recording mental strategies eg 159 + 22;
‘I added 20 to 159 to get 179, then I added 2 more to
get 181.’
or, on an empty number line
Using the 2008 NAPLAN Year 3 question 15(Jim is 91 years old. Sam is 8 years old.What is the difference in their ages?), ask “What do I know?” Answer: Jim is 91 years old. Sam is 8 years old. What do I want to know? Answer; What is the difference in their ages?
Think aloud: “I know how old Jim is and I know Sam is 8. I know that difference is another word for take away. I will solve this problem using subtraction”
Model the solution of the problem using concrete materials and/or a drawing and writing the appropriate number sentence on the board.eg
Step 1: ‘How many to start with? Jim is 91.’ Put out 91 using tens and ones or draw this.
Step 2: ‘How old is Sam? Answer:8. Move 8 ones away or cross out 8 drawn ones. Write 91-8= ‘How many left?’ Answer: 83. Write 91-8=83
Step 3: ‘What is the difference in their ages?’Answer: 83. Discuss and model other possible solution strategies with the group using counters or drawings.
Guide students to translate the information into a number sentence.91 take away 8 means I subtract so I use the – sign. I want to know many are left so I use the equal sign =. My number sentence is 91-8 =83
Think aloud: “I know how old Jim is and I know Sam is 8. I know that difference is another word for take away. I will solve this problem using subtraction”
Model the solution of the problem using concrete materials and/or a drawing and writing the appropriate number sentence on the board.eg
Step 1: ‘How many to start with? Jim is 91.’ Put out 91 using tens and ones or draw this.
Step 2: ‘How old is Sam? Answer:8. Move 8 ones away or cross out 8 drawn ones. Write 91-8= ‘How many left?’ Answer: 83. Write 91-8=83
Step 3: ‘What is the difference in their ages?’Answer: 83. Discuss and model other possible solution strategies with the group using counters or drawings.
Guide students to translate the information into a number sentence.91 take away 8 means I subtract so I use the – sign. I want to know many are left so I use the equal sign =. My number sentence is 91-8 =83