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Once children are comfortable with multiplying two-digit numbers by one-digit numbers, they can go on to learn the multiplication of two-digit numbers by two-digit numbers.
There are a number of ways in which teachers can help children become fluent in performing two-digit number multiplications. This article describes simple strategies to do so. Read on to learn more.
How to Explain Multiplying Two-Digit Numbers by Two-Digit Numbers
Review Multiplying Two-Digit Numbers by One-Digit Numbers
Before teaching about multiplying two-digit numbers by two-digit numbers, you may want to review your students’ knowledge of multiplying two-digit by one-digit numbers. This can be done through a simple activity that will let you identify whether some children require more attention in this area.
For instance, you can use a simple game, such as this online basketball game. It’s not necessary to download an app for the game and students can simply play it on their iPads, laptops, or phones.
Each student plays the game individually and takes turns playing the role of two teams, for instance, a red team and a blue team. Alternatively, if there aren’t enough devices for all students in the class – you can also decide to pair students up.
One student then plays the role of one team and the other one takes over when it’s the other team’s turn. Have fun playing and let the best team win!
Introduce Partial Product Multiplication
For starters, explain that you’ll be using a simple strategy called ‘partial product multiplication’ in order to learn how to multiply two-digit numbers by two-digit numbers.
Explaining partial product multiplication means that you look at each of the factors in a given multiplication equation and then break them down into their parts. In other words, each factor will be written in its expanded form.
Provide a multiplication equation as an example, such as 37 x 26. Now ask students how the two factors, 37 and 26, can be presented in an expanded form. This is something that they already know from earlier units on place value and should be able to answer easily.
After someone explains that 37 breaks down into 30 + 7 and and 26 breaks down into 20 + 6, point out that 37 x 26 = (30 + 7) x (20 + 6). Then remind kids of the distributive property of multiplication, i.e. a x (b + c) = a x b + a x c.
Explain that in our case, by applying the distributive property of multiplication we have to multiply each digit of one factor by each digit of the other factor, taking into consideration their place value. Thus, we’ll get four different partial products.
That is, 30 x 20 = 600; 30 x 6 = 180; 7 x 20 = 140; 7 x 6 = 42. Tell kids that the last step is to simply add all of the partial products: 600 + 180 + 140 + 42 = 962. In other words, 37 x 26 = 962. So our total product is 962.
Additional Multiplication Models and Resources
Now students are familiar with one of the easiest ways to multiply two-digit numbers by two-digit numbers, particle product multiplication. There are of course other ways as well, such as the area model.
Download our Guided Notes Worksheet (Members Only) to further explore partial product multiplication, as well as explore other multiplication models. Print out a number of copies and hand them out to each student so that they read them. Then, discuss the guided notes together in class.
Practice multiplying two-digit numbers by two-digits with the exercises in our Bell-Work Worksheet (Members Only) as well as with the equations in our Assignment Worksheet (Members Only). You can also use these resources for individual practice even if you’re a homeschooling parent.
If you’re teaching in a school, at the end of the class, organize one or two fun games to further hone children’s multiplication skills! Check out our recommended activities in the next paragraphs.
Activities to Practice Two-Digit by Two-Digit Number Multiplication
Group Work
Group work is arguably the simplest and yet one of the most effective ways to practice a new math concept. Print out our Interactive Notebook Worksheet (Members Only). It contains a variety of two two-digit multiplication problems, including simple word problems, such as:
“Alex went for a walk every day for three weeks. He walked 35 km every day. How many km did he walk altogether?”
- Divide students into groups of two and hand out one copy per group.
- Explain to students that they’re supposed to work together to solve the multiplication problems.
- As soon as a group is done, they present their results in front of the class.
- Encourage students to explain how they got the results they did and have them explain each step of the multiplication process. This way, you’ll make sure they grasp two two-digit multiplication properly and don’t sneak in a calculator to do the job for them!
Snakes and Ladders Multiplication
To play the snakes and ladders multiplication game, you’ll need to bring several snakes and ladders game boards, as well as a number of dice and counters according to the number of players. You’ll also need to bring a few calculators.
You can simply download a free, blank snakes and ladders template (there are plenty of beautifully illustrated versions online). Print out several copies according to the size of your class.
Alternatively, you can even draw one yourself and make copies accordingly. To draw a snakes and ladders game board, you’ll need to draw a square and divide it into twenty-five equal squares inside (five in each row and five in each column).
Mark the square in the lower-left corner with ‘start’ and the square in the upper. Mark all other squares with numbers from one to twenty-three, one being the square to the right of the ‘start’ square and twenty-three being the square to the left of the ‘finish’ square.
Draw several ladders and snakes (ex: five ladders and 7 snakes) that connect any two adjacent squares (such as squares six and seven). It should be visible which part is the bottom of each ladder and snake.
Finally, make sure that in each square there’s a different multiplication problem consisting of two two-digit numbers, such as 34 x 87, 69 x 54, etc.
Start playing!
- Divide children into groups of three. In each group, there are two players that compete against each other, and one ‘checker’ that checks their answers.
- Place one dice and one game board on the table of each group. Provide one counter to each player. Provide one calculator to each checker.
- Explain to children that the goal of the game is to be the first that reaches the ‘finish’ square with their counter.
- Explain the rules of the game to the students. Each player’s counter is on the ‘start’ square. Player one rolls the dice and moves up their counter as many squares as the number of the dice indicates. For example, if they’re on square four and they get a five when they roll the dice, they move up to square nine.
- Once they land on a particular square, they must solve the multiplication problem. If they answer correctly, the play continues and the other player repeats the same.
- If they answer incorrectly, they miss a go, that is, the other player gets to roll the dice two times in a row.
- The checker checks each answer provided on a calculator but makes sure that the players can’t see the result on their calculator. This way, they prevent players from seeing the right answer if they happen to do a calculation incorrectly.
- Players should also make sure to reveal their answer only to the checker and not to each other. This way, they prevent the other player from copying their answer if they land on the same square.
- Point out to children that if they land on a square that has a snake’s head – their counter slides down to the square where the snake’s tail is. For example, let’s say square one and seven are connected by a snake diagonally, with the snake’s head being in square seven. If a player lands on square seven, they have to slide down to square one and solve the multiplication problem of square one.
- If they land on a square that has the bottom of a ladder, they slide their counter up to the square where the top of the ladder is.
- The person that reaches the ‘finish’ square first, wins the game.
- Another game starts, this time, the winner is the checker and the other two kids are players.
Two-Digit by Two-Digit Number Multiplication Dice Game
This is an easy game that requires very little prep work. The only materials needed are dice, a number of markers, and individual whiteboards for every student. If you lack individual whiteboards, you can also use empty sheets of paper.
- Divide students into pairs of two.
- Hand out two dice to each pair, two markers, and two individual whiteboards.
- Explain the rules of the game: each student rolls the two dice twice to get two two-digit numbers. They write them down on their whiteboard and multiply them.
- The other student then checks their answer (they can use a calculator to check it if needed). If their answer is correct, they score one point. If their answer is incorrect they lose one point.
- The second player repeats the same process.
- This goes on for as many rounds as time allows.
- In the end, the player that has the most points wins the game.
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This article is based on:
Unit 3 – Multi-Digit Whole Number Multiplication