## 1. Number Sense

## 2. Interpretations of Multiplication

### 2.1. Repeated Addition

2.1.1. 2 x 10 would be seen as 2 groups of 10 and be solved by adding one number at a time (2+2+2+2+2+2+2+2+2+2)

### 2.2. Array Concept

### 2.3. Area Concept

### 2.4. Cartesian Products

## 3. Multiplication Chart and Associated Strategies

### 3.1. 1’s, 2’s, 3’s

### 3.2. Commutative Law

3.2.1. If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.)

### 3.3. 5’s, 10’s, 4’s

### 3.4. Doubles

### 3.5. Near Facts (example, if you know 5 x 2 = 10, you can use it to answer 5 x 3 = 5 x 2 + 5 = 10 + 5

### 3.6. 9’s, 11’s,

### 3.7. 6’s, 7’s, 8’s

### 3.8. Squares (1, 4, 9, 16, etc. --do visually with tiles)

## 4. Looking at Factors, Products, and Multiples in Different Ways

### 4.1. Multiplication Stacks

### 4.2. Using Tiles to Create Arrays to Show All Factors of a Number

## 5. Helping Children Memorize and Understand Even the Most Difficult Facts

### 5.1. Making Connections

5.1.1. Your students need to make connections among these entry-level strategies and multiplication by making the links to multiplication clear (Parrish, 2014).

## 6. Teaching Strategies

### 6.1. Procedural

6.1.1. Describing the Rule

6.1.2. Using Lined Paper

6.1.3. Using Placeholders

### 6.2. Conceptual

6.2.1. Explaining the Rationale in terms of Number Sense: What does 123 x 645 mean?

6.2.2. Separating the Problem into Three Subproblems (123 x 600) + (123 x 40) + (123 x 5)

## 7. Box Model

### 7.1. Break factors into Smaller factors: Example 49 into 40 and 9. Label both sides of draw rectangle with decomposed factors then divide into regions. Multiple the four partial products. Then add the four numbers to receive the solution.

## 8. Multiples of 9 Hand Trick

## 9. Inverse Operation is Division

## 10. Multiplication Chart

## 11. 3rd Grade

## 12. Any Number Multiplied by 1 is that Number

## 13. Any Number Multiplied by 0 is 0

## 14. Any Number Multiplied by 2 is that Numbered Doubled

## 15. Fast Pased games

### 15.1. Multiplication Baseball or Flash Cards

## 16. Word Problems

### 16.1. Example: Mr. John's new car gets him 50 miles per gallons.If Mr John get a full tank with 14 gallons of gas, How far can Mr John go?

## 17. Memorization

## 18. Any Number Multiplied by 10 is that Number with a zero attached to the End

### 18.1. Activities that Support Learning of the Multiplication Facts

18.1.1. Using Grid Paper to make lists and draw sets to answer these questions

18.1.2. Using Unifix Trains

18.1.3. Array Cards and Frames

## 19. Time Assessments

## 20. Number Talks

### 20.1. Repeated Additon or Skip Counting

### 20.2. Making Friendly Numbers

20.2.1. adjust forty-nine to reach the nearest multiple of ten, which would be fifty

### 20.3. Partial Products

### 20.4. Doubling and Halving

### 20.5. Breaking Factors into Smaller Factors

20.5.1. Example 49 into 40 and 9

## 21. Five Number Talk Goals

### 21.1. Place Value

### 21.2. Fluency

### 21.3. Properties

21.3.1. If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)