Shifty Subtraction

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Purpose

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

A PDF of the student activity is included. 

Achievement Objectives
NA4-2: Understand addition and subtraction of fractions, decimals, and integers.
Student Activity

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Specific Learning Outcomes

subtraction with integers

Required Resource Materials

FIO, Link, Number, Book Four, Shifty Subtraction, page 15

A calculator

Activity

Activity One

Questions b and c in this activity are open ended so that the students can explore the process of subtracting a larger number from a smaller number. Some students may choose to use the additive reverse to solve question a, that is, -3 + =  17.

Activity Two

Students who have been encouraged to think through subtraction using part-whole knowledge of numbers and place value should find the novel method of subtraction in this activity an interesting investigation. Your challenge is to help your students make sense of this method so that they can apply it to the expressions that they are asked to find answers for.

Anyone who says “You can’t do 4 take away 7” is actually wrong. So the overall discussion needs to centre round the question: “What is happening here?” This is a method of subtraction that doesn’t adjust the sum above the answer line. If used in a more traditional working form, the algorithm would look like this:

equation.

You could put this question up on the board: “Lefu has used this method to find the answer, but he cannot explain how he did it. How can Lefu explain this method of subtraction so that the teacher understands what he did?” The students could discuss it in small groups.

Another possible strategy to help your students make sense of and use this method of subtraction is to cover part of the working and see if they can complete the missing part. For example, with "80= -40" hidden:

equation.

Answers to Activity

Activity One
a. 20
b. Any two numbers, as long as the first number is 3 less than the second number, for example: 0 – 3, 1 – 4, 2 – 5, 3 – 6, -8 – -5, …
c. Any two numbers, as long as the first number is 5 less than the second number, for example: 0 – 5, 1 – 6, 2 – 7, 3 – 8, -10 – -5, …
Activity Two
a. 5 – 6 = -1
80 – 40 = 40
-1 + 40 = 39
b. 5 – 7 = -2
100 – 60 = 40
-2 + 40 = 38
c. 2 – 8 = -6
80 – 60 = 20
400 – 200 = 200
-6 + 20 + 200 = 214

d. 0 – 8 = -8
90 – 60 = 30
500 – 400 = 100
-8 + 30 + 100 = 122
e. 7 – 4 = 3
40 – 60 = -20
200 – 100 = 100
3 + -20 + 100 = 83
f. 9 – 3 = 6
10 – 60 = -50
800 – 400 = 400
6 + -50 + 400 = 356

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Level Four