Erika's Math 251 (Unit 2) Map

Models of Multiplication

Repeated addition

Example: Ryan has 4 plates of cookies, with 7 coookies on each plate. How many cookies does Ryan have all together.

Similar to sets, but in mulitplication, the sets have to be the same size (add them all)

Area Model

Example: In the classroom, there are desks lined up in 4 rows with 7 desks in each row. How many total desks are there in the classroom?

Very Efficient because it ALWAYS elicits columns/rows

Tree/Combinations

Example: Adam has 4 pairs of pants and 7 different skirts. How many different outfits can he make?

One of the last versions we want to introduce to kids

Website with picture EXAMPLES!

Properties of Multiplication

Communative Property

3 x 2 = 2 x 3

Associative Property

3 x 6 x 5

3 X (6 x 5)

3 x 30 = 90

Identity Property

6 x 1 = 6 or 1,215,365 x 1= 1,215,365

6 x 0 = 0 or 1,215,364 = 0

Distributive Property

a x (b+c) = (a x b) + (A x c)

Models of Divisioin

Rpeated Subtraction (or Addition)

Example: Megan has $48. She wants to give $6 to needy kids for school supplies. How many kids can she give supplies to?

Here you would seperate the money into 8 groups of 6 because you know that the groups need to be in 6, then count up till you get to $48

Partition (Groups)

Example: Megan has $48. She wants to give an equal amount of money to 6 needy kids for school supplies. How much can she give to each kid?

Here you would know that there are 6 kids that need supplies, so you could draw the 6 kids and distribute the $48 evenly to each kid.

242 x 309

Area Model

Ratio Table

Partial Producats

Expanded Notation

347,568

300,000 + 40,000+7,000+500+ 60+ 8

A number gets broken down into each, different value (1000s, 100s, 10s, etc.)

Scientific Notation

347, 568

(3 x 10^5) (4 x 10^4) (7 x 10^3) (5 x 10^2) (6 x 10^1) (8 x 10^1)

This is a way that you can write down numbers that may be too big or too small to write out completely. You always multiply a number that is less than 10 by 10 to an exponent

The exponent is related to how many place values the number has. For example, kids will find out that the exponent is the number of 0s the number has when it is written out in expanded notation.

Displaying them on Number Lines

Subtracting

Distance between numbers can also be displayed on a number line

Multiplying

Example: After Andrews Middle School is built, it will hold 609 students. Each classroom will have 29 students. How many classrooms does the school have?

How to solve this:

Partial Quotients

Area Model

Ratio Table