Multiplication/division

Question 1

What is the need for multiplicative thinking?

Answer 1

Adding/subtracting fractions involves common denominators which requires an understanding of factors and multiples

Question 2

What are some models for multiplication?

3

Answer 2

• sets of objects
• arrays
• skip counting on number lines

Question 3

What are the multiplication structures?

Answer 3

1) Repeated aggregation structure

2) scaling structure

Question 4

What is the repeated aggregation structure?

Answer 4

Idea that multiplication means “so many sets of” or “so many lots of”

Question 5

Multiplication is repeated addition and so the aggregation structure is an extension of the what structure for addition?

Answer 5

Aggregation

Question 6

What is the scaling structure?

Answer 6

Occurs when multiplication is used to increase a quantity by a certain percentage

Question 7

Multiplication increases a quality by a what factor?

Answer 7

Scale factor

A scale of 10 means a multiplication by 10.

Question 8

What is an example of scaling?

Answer 8

Hannah spend $35 on Christmas presents. Geoff spent 3x more than Hannah. How much did Geoff spend

Question 9

What are the two other properties of multiplication?

Answer 9

1) multiplicative property of zero

2) multiplicative property of one

Question 10

What are the OG properties of multiplication?

3

Answer 10

1) commutative
2) associative
3) distributive

Question 11

What is the commutative property of multiplication?

Answer 11

The order in which 2 or more numbers are multiplied does not affect the product

7x5 is 5x7

Question 12

What is the associative property of multiplication?

Answer 12

Factors may be grouped in any way without affecting the product

(4x3) x 7 is the same as 4 x (3x7)

Question 13

What is the distributive property of multiplication?

Answer 13

Multiplication can be distributed across addition and subtraction

3x (2+4) is the same as 3 x 2 + 3x4

• ••••• = •• ••••
• ••••• •• + ••••
  * • ••••

Can be the same with minus

Question 14

What is an application of distributive property?

Answer 14

Partitioning

Question 15

Multiples are the product of two or more…?

Answer 15

Factors

Question 16

What is the equal-sharing structure of division?

Answer 16

Situations where a quantity is shared out equally into a given number of portions and we are asked to determine how many are in each portion

Question 17

What is the grouping structure of division?

Answer 17

Interprets division in a different way. The question is now “how many groups of 4 marbles are in a set of 20?”

Question 18

What is repeated subtraction problems in division?

Answer 18

How many sets of 4 can I make from 20?

• removing 4 from 20 until it hits zero

Question 19

What is repeated addition in division?

Answer 19

How many sets of 4 do you need to make 20?

• adding 4 till reach 20

Question 20

A number is divisible by another number if there is no ..

Answer 20

Remainder

Question 21

An even number is a number that is divisible by?

Answer 21

2

Question 22

What is estimation?

Answer 22

Guessing with some problem solving

Question 23

Estimation helps to develop

Answer 23

Number sense

Question 24

What are the three types of estimation?

Answer 24

1) estimating numerical qualities - how many marbles in a jar
2) estimating measurement
3) computational estimation

Question 25

What is the importance of estimation through relevance?

Answer 25

1) relevance - shows more number sense, estimation is used more than exact quantity. $45.43 to paint is not showing number sense, 42,000 at a footy game is more user friendly

Question 26

Why does estimation help concept development?

Answer 26

Students who estimate when measuring get a quicker development of an understanding of how heavy a kilo is or how long a meter is.

Question 27

Estimations of computation develop students number sense because of?

Answer 27

The mental strategies it demands

Question 28

Is division commutative?

Answer 28

No, the order of the numbers matters