**Single-Digit Multiplication**

**Mathematical Landscape Project**

Single-Digit Multiplication

Multiplying (repeated addition) of two or more whole numbers that are less than ten.

**Theresa Dominguez and Cheyenne Evans**

EDUC*220

EDUC*220

Prerequisites

Essential Understanding

Understandings, Knowledge, Skills

Models and Meanings of the Concept

Common Difficulties & Misconceptions

Other Information

Properties/Strategies

Thinking Strategies

Connections

Repeated Addition

Ex: 4*2 is the same as 4+4

Ex: 4*3 is the same as 4+4+4

Inverse of Division

4*2=8 and 8/2=4

3*4=12 and 12/4=3

Example: (n<10) x (n<10)

What Should Students Know:

Number Sense

Symbols for Multiplication and Addition

Understand Single Digit Addition

Terms for Multiplication

Application:

Story Problems

Money

Repeated Addition Problems

Division

Set Models

Equal size sets

Measurement

Number line

Arrays

Rows of Equal Size

Cartesian Product

Tables and Tree Diagrams

Multiplicative Compare

Distributive Property

Symbols:

a

(

b

+

c

)=(

a

*

b

)+(

a

*

c

)

Ex:

3

(

4

+

2

)= (

3

*

4

)+(

3

*

2

)

Multiplying the sum or difference by a number gives the same result as multiplying each addend by the number and then adding/subtracting the products together

Associative Property

Symbols:

(a*b)

*c=a*

(b*c)

Ex:

(3*4)

*5=3*

(4*5)

Grouping doesn't matter when we multiply several numbers. The product is still the same.

Commutative Property

Symbols: a*b=b*a

Ex: 3*4=4*3

When we multiply any two numbers, we get the same product regardless of the order

Closure Property

Symbols: Real Number 1* Real Number 2= Real Number 3

Ex: 5*6=30

For any real number, the product of any two real numbers equals another real number

Identity Property

Symbols: A*1=A

Ex: 4*1=4

When we multiply any number by one, we get the same number

Zero Property

Symbols: A*0=0

Ex: 4*0=0

When we multiply any number by zero, the product is zero

Addition and Multiplication

Multiplication is repeated addition

Division and Multiplication

Multiplication is the inverse of division

Square Numbers

Ex: 2*2=4

2's Double

Ex:2*4=4+4=8

Four Structure

Ex: 4*7=2(2*7)

9's Pattern

Ex: 9*7=7*9=63

Finger Pattern

6+3=9

5's Pattern

Ex: 5*6=30

Half then Double

Ex:6*7=(3*7)=21*2

7's Structure

Ex:7*8=(5+2)*8

8's Structure

Ex: 8*5=[(5*2)*2]*2

Number Sense

Counting

Skip Counting

Single Digit Addition

Joe has 5 trucks. Kade has 3 times as many.

How many does Kade have?

5

5

5

5

http://www.math-play.com/multiplication-games.html

http://www.coolmath-games.com/numbermonster/mult25.htm

http://www.multiplication.com/games/all-games

Counting from one to find product

Does not understand vocabulary

ex: groups of, multiply by

Do not connect ideas

Does not focus on rows or columns

Only sees arrays as a collection of 'ones'

Cannot apply knowledge of doubles

Does understand adding groups