Games for Learning to Multiply: Grades 3-5
Updated: Apr 21, 2020
Everyone can learn math! But one thing that can get in the way of learning is anxiety. Math anxiety can start as early as grade 1! Learning through playing games can be fun and keep that anxiety at bay.
This post will show you how to use a few terrific games to help your child develop a sound understanding of multiplication and their multiplication facts. Check out Multiply Around the House too for ideas to get your youngster doing multiplication by helping around the house.
Race to 100: This is one of my favourite multiplication games. It’s fun and packs in a lot of learning. There are also lots of ways to adapt it as your child learns. This game comes from Jo Boaler's article, Fluency Without Fear.
You will need a marker and two dice. Download and print copies of this 100 grid game board or make your own.
You and your child work together to play this game. Take turns rolling the dice and using the numbers on the dice to make and fill the game board with rectangular arrays.
An array is a rectangle or square that is made up of rows and columns. Below is an example of an array. Since the game board is also an array, you can fill it with smaller arrays. That's the goal of the game - to see how close you can come. to filling the whole game board with smaller arrays,
The numbers that you roll on the 2 dice tell you how big to make the array you are going to draw on the board. You would draw the array above if you rolled a 3 and 6 because this array has three rows with six in each row. One dice tells you how big the row is and the other dice tells you how many rows are in the array.
Here's what a roll of 5 and 3 could look like on the game board. Notice that rolling 5 and 3 allows us to create two different arrays. The first one has 5 rows with 3 squares in each row. The second has 3 rows with 5 squares in each row. You decide which way you want to orient your array.
You can draw the array anywhere on the game board as long as it doesn’t overlap another array. It also needs to be fully on the game board.
Let your child figure out the total number of squares in your array and write the total inside the array.
Here's what a partially completed game could look like:
There will come a time when the numbers you roll will not create an array that fits anywhere on the game board. This ends the game. For example, rolling 4 & 4 would end the game shown above. The goal is to fill as much of the board as you can. How close can you get to 100?
As you can see, arrays represent multiplication facts. An array with 3 rows of 5 gives us 15. Later children will learn to write this as 3 x 5 = 15. But don't rush into writing equations until your child can easily create and describe arrays.
Tips for helping children who find it hard to draw the arrays:
Difficulty with learning arrays is a normal part of math development. A thorough understanding of the array is a big achievement and is developed over time. Some children might need more experience building physical models of arrays with blocks and objects before being able to draw arrays and play this game. See the article Multiply around the House for ideas to do this..
As your child is learning how to use the numbers on the dice to draw arrays, avoid naming the array by its dimensions (e.g. 2 by 4 array). This way of thinking about arrays is much further along in development. At first, kids need to be thinking of the repeated rows or columns, so use language something like this:
“We rolled a 3 and 5. We need to make three rows with five squares in each row.”
In the early stages of learning to draw arrays, it helps to have children colour in or place dots to make the first row and then build up one row at a time.
It helps some children to use two different colour dice at first. Roll one dice to tell you how long the row is. Once you have the row drawn, roll the other dice to determine how many rows to create. Have your child do the drawing. Physically making the rows and replicating them helps develop understanding of the array structure.
Tips for helping your child figure out how many squares are in the array:
Your child will likely start out counting by ones to find out how many squares there are in an array. Look for opportunities to gently move them beyond counting by ones.
Here are some examples of how you might do that:
If your child has drawn the array below and you know they can count by 2’s or 5’s, prompt them to do that by asking “Is there another way you could count these squares rather than by ones?” If they say, I could count by 2's ask "Where do you see the groups of twos?" This reinforces the meaning of skip counting.
In the picture below, the child needs to find out how many squares are in the array shown on the left. You might point to the smaller one that is already known and say “You know this one is 4. Could that help you figure out how many are in the bigger one?”
Once your child gets used to using known arrays to figure out unknown arrays, you could ask the question more generally: “Is there another array on the board that could help you?”
This thinking helps children build part/whole relationships and notice important relationships between number facts. For example, 2 x 4 is double 2 x 2.
You can also model these ways of thinking by occasionally doing a think-aloud on your turn. Here are some examples:
“Hm… I see some groups of two in here (point to each group of two). So I know I can count by 2’s.... 2, 4, 6, 8'
“Hm… I see that this little array (point to 2 by 2 array) fits in this bigger one (point to 2 by 4 array) two times. So it must have double the number of squares. 4 plus 4 is 8”.
Boxed Out: Boxed out is a competitive version of Race to 100. In this version, each player has a different colour marker. Players take turns rolling and putting arrays on the grid. The goal is to capture more of the grid space than the other player. A player's game is finished when they have rolled the dice three times in a row without being able to add an array to the grid. We call this being ‘boxed out’. The other player continues to roll and add arrays until they too are boxed out. Tally up your scores to see who wins.
A New Twist: You can add this twist to either Boxed Out or Race to 100. In this version, players can create a different array that will fit on the board, as long as it has the same value as the array defined by the roll of the dice.
For example, if a player rolls a 2 and 6, they can make the following arrays:
So if you can't find room for a 2 by 6, you can build a 4 by 3 array as shown below. Two arrays that cover the same number of squares are called equivalent arrays.
For this version, you may want to use the 12 by 12 game board.
This version helps students begin to build understanding of equivalence and additional relationships between multiplication problems. Make sure your child is very comfortable playing the basic version before adding this twist.
Enjoy learning and playing with your child!