Multiplication Strategies

Repeated Addition

As students begin learning multiplication, they see the connection between multiplication and repeated addition. 
3 x 4 = 4 + 4 + 4
6 x 5 = 5 + 5 + 5 + 5 + 5 + 5
 

Zero Property (x0)

The product of any number and 0 is 0. 
4 x 0 = 0       0 x 65 = 0

Times Ten (x 10)

Focus on the base ten aspect of our number system. Discuss moving a place.
 6 x 10 = 60       45 x 10 = 450
 

Doubles (x 2)

To multiply by 2, double the other number or think of the addition doubles.
2 x 5 = 5 + 5 = 10                   14 x 2 = 14 + 14 = 28
 

Double-Double-Double (x8)

To multiply by 8, double the other number, double the result and double it again.
8 = 2 x 2 x 2
8 x 6 = ((6x2) x2) x 2 = (12x2)x2= 24 x2= 48
8 x 43 = ((43x2) x2) x 2 = (86 x 2) x 2= 172 x 2 = 344
 

Double Plus a Set (x 3)

To multiply by 3, double the other number than add one more set of that number.

3 = 2 + 1
3 x 6 = (2 x 6) + 6
3 x 15 = (2 x 15) + 15
 

Visualizing Arrays

The array provides a visual model for multiplication. The numbers being multiplied correspond to the dimensions of the rectangle and the product of those numbers correspond to the area of the rectangle. 

Identity Property (x1)

The product of any number and 1 is that number.
5 x 1 = 5         1 x 43 = 43

Half Ten (x 5)

To multiply by 5, multiply by 10 and then divide the result in half. 5 = 10 ÷ 2
5 x 3= (10 x 3) ÷ 2 = 30 ÷ 2 = 15 
5 x 18 = (10 x 18) ÷2 = 180 ÷ 2 = 90
 

Double-Double (x 4)

To multiply by 4, double the other number and then double the result. 4 = 2 + 2
4 x 6 = 2 x (2 x 6) = 2 x 12 = 24
4 x 24 = 2 x(2x24) = 2 x 48= 96
 

Ten Minus a Set (x 9)

To multiply by 9, multiply the number first by ten and then subtract a set of that number.

9 = 10 - 1
9 x 6 = (10 x 6) – 6= 60 – 6 = 54
9 x 45 = (10 x 45) – 45 = 450 – 45 = 405
 

Half Ten Plus a Set (x 6)

To multiply by 6, carry out the steps for multiplying by 5 and then add a set. 

6= 5 + 1
6 x 7 = ((10 x 7) ÷ 2) + 7 = 42
6 x 42 = ((10 x 42) ÷2) + 42= (420÷2) + 42= 210 + 42 = 252
 

Fact Fluency Games: Multiplication

Multiplication War

Matches or pairs are made by matching products. On a player’s turn, he or she asks another player for a product that would make a match with a card in his or her hand. Otherwise, the player is told to “Go Fish.”
 

Multiplication “Go Fish”

Materials: Flashcards or index cards with subtraction facts written on them but no answers

Each player is dealt 7 cards. Matches or pairs are made by matching differences. Thus 12 - 9 and 8 - 5 can be a match. On a player’s turn, he or she asks another player for a difference that would make a match with a card in his or her hand. Thus if the player has 18 -9 in his hand, he would ask another player for a 9.  If that player has 12 - 3 or any other card equaling 9, a match has been made. Otherwise, the player is told to “Go Fish.”
 

Multiplication “Memory”

As with other Memory games, players take turns flipping two cards. If the products are equal, the player has made a match and keeps the cards. If products are not equal, the cards are turned back over. 
 

Array Games

 

Materials: graph paper

Make rectangular arrays for the multiplication facts, and cut them out. Then, label the dimensions on one side and the answer on the other side. For example:
Front                                      Back
 

You can then use the arrays to look at the dimensions and give the total or, given the total, state the dimensions. Another variation could be a game of “big array, small array” in which you lay 5 large arrays out for each player. Take turns finding two arrays that can cover a big array completely for a “match”.  

Draw the Array Game

Materials: graph paper, pair of dice


Each player gets a piece of graph paper. On a player’s turn, he rolls the dice. The dice will tell the player the dimensions of a rectangle to draw on the graph paper. So, if the player rolls a 3 and a 4, the player draws a 3 by 4 rectangle on the graph paper. Inside the rectangle, the player records 3 X 4 = 12. Then, the next player rolls. Play continues until one of the players can’t place a rectangle on the graph paper because there is no room left. Each player figures out the total number of squares covered on the graph paper. The winner has covered the most squares.  
 

Multiplication Baseball

Materials: pair of dice, coins or small markers to use as players around the bases.  

Decide who will be up to bat first.  The other player will be the pitcher.  The pitcher rolls the dice.  The player up to bat must find the product of the dice rolled.  Use the following game board to move your game pieces around the bases.  After 3 outs, players switch rolls.  
 

worksheet for multiplication baseball game