Addition and Subtraction

Question 1

What are the two structures of addition?

Answer 1

1) the aggregation structure

2) the augmentation structure

Question 2

What is the aggregation structure?

Answer 2

• Situations in which two or more quantities are combined into a single quantity

Eg there are 17 peas in one bag and 5 in the other, how many all together?

Question 3

What is the augmentation structure?

Answer 3

Situations in which a quality is increased by some amount

• the $159 bike is increased by $2, how much is it now?

Question 4

The augmentation structure is strongly connected with?

Answer 4

The imagine of moving along a number line

Question 5

What are the three properties of addition?

Answer 5

1) commutative
2) Associative
3) Additive

Question 6

What is the commutative property of addition?

Answer 6

The order in which two or more numbers are added does not affect the sum

Eg 2+5=7, 5+2=7

Question 7

What is the associative property of addition?

Answer 7

The grouping of numbers in an addition does not affect the sum

Eg (2+3) + 4 = 9 and 2 + (3+4) = 9

Question 8

What is the additive property of zero?

Answer 8

Adding zero to any number does not change the original number

Question 9

What is an algorithm?

Answer 9

A step by step procedure performing a calculation

Question 10

What is the standard written algorithm for addition?

Answer 10

Column addition

23
+45
62

Question 11

What is the part-part-whole representation? (Partitioning)

Answer 11

Breaking apart a number to show addition and subtraction

Eg = 7-3=4
7-4=3
3+4=7
4+3=7

Question 12

What are the three structures for subtraction?

Answer 12

1) reduction structure
2) comparison structure
3) the inverse-of-addition structure

Question 13

What is the reduction structure?

Answer 13

• situations where a quantity is reduced by some amount and subtraction is used to find that value

Question 14

What is the comparison structure?

Answer 14

Situations in which subtraction is used to make a comparison between quantities

Eg - how many more blue cards are there to green?

Question 15

What is the inverse of addition structure?

Answer 15

Situations where we must determine what needs to be added to a given quantity to reach a target

This is addition and subtraction
52+28=80 so 80-52=28

Question 16

What is an example of partitioning structure?

Answer 16

Bob and jo had 4 cats between them, bob had 3, how many does Jo have?

Question 17

What is an example of comparison structure?

Answer 17

Bob had 7 balloons, Jo had 4, how many more did Bob have then Jo?

Question 18

What is an example of reduction structure?

Answer 18

Bob had 7 balloons, he gave 4 to his mum, how many were left?

Question 19

What is an example of an inverse-of-addition structure?

Answer 19

Jo had 4 cats, Bob had 7, how many more does jo need to have the same as bob?

Question 20

What is the standard subtraction algorithm called?

Answer 20

Decomposition

Question 21

How can decomposition be illustrated

Answer 21

Place value mat

Question 22

What is the counting forward mental strategy?

Eg for 43+48?

Answer 22

Count the tens, then the ones

48 + 43 = 48, 58, 68, 78, 88, 89, 90, 91
10 10 10 10 10 1 1 1 (43)

Question 23

What is the doubling and compensation mental strategy?

Eg 43+28

Answer 23

Double the first number, add the difference of the first and second number OR
Double the second number, minus the difference of the two numbers

Eg 43+48 =

43+43=86;86+5=91
48+48=96;96-5=91

Question 24

What is adding from the left (Front loading) mental strategy?

Eg 43+48

Answer 24

Adding the tens then adding the ones

Eg 40+40 and then 5+3
80+11=91

Question 25

What is the making tens (bridging tens) mental strategy

Eg 43+48

Answer 25

Add ones to the nearest whole number than add remainder

Eg 43+48=

48+2=50, 50+40=90, 90+1=91

Question 26

What is the making compatibles mental strategy?

Eg 43+48

Answer 26

Same as making tens but with the first number

43+7=50,50+40=91

Question 27

How would you partition 43+48

Answer 27

43+8=51,51+40=91