Multiplication/division Flashcards
What is the need for multiplicative thinking?
Adding/subtracting fractions involves common denominators which requires an understanding of factors and multiples
What are some models for multiplication?
3
- sets of objects
- arrays
- skip counting on number lines
What are the multiplication structures?
1) Repeated aggregation structure
2) scaling structure
What is the repeated aggregation structure?
Idea that multiplication means “so many sets of” or “so many lots of”
Multiplication is repeated addition and so the aggregation structure is an extension of the what structure for addition?
Aggregation
What is the scaling structure?
Occurs when multiplication is used to increase a quantity by a certain percentage
Multiplication increases a quality by a what factor?
Scale factor
A scale of 10 means a multiplication by 10.
What is an example of scaling?
Hannah spend $35 on Christmas presents. Geoff spent 3x more than Hannah. How much did Geoff spend
What are the two other properties of multiplication?
1) multiplicative property of zero
2) multiplicative property of one
What are the OG properties of multiplication?
3
1) commutative
2) associative
3) distributive
What is the commutative property of multiplication?
The order in which 2 or more numbers are multiplied does not affect the product
7x5 is 5x7
What is the associative property of multiplication?
Factors may be grouped in any way without affecting the product
(4x3) x 7 is the same as 4 x (3x7)
What is the distributive property of multiplication?
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
What is an application of distributive property?
Partitioning
Multiples are the product of two or more…?
Factors
What is the equal-sharing structure of division?
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
What is the grouping structure of division?
Interprets division in a different way. The question is now “how many groups of 4 marbles are in a set of 20?”
What is repeated subtraction problems in division?
How many sets of 4 can I make from 20?
- removing 4 from 20 until it hits zero
What is repeated addition in division?
How many sets of 4 do you need to make 20?
- adding 4 till reach 20
A number is divisible by another number if there is no ..
Remainder
An even number is a number that is divisible by?
2
What is estimation?
Guessing with some problem solving
Estimation helps to develop
Number sense
What are the three types of estimation?
1) estimating numerical qualities - how many marbles in a jar
2) estimating measurement
3) computational estimation