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Multiplication and Division are the last operations that students learn. Look below to see some activities and tips for learning multiplication/division, mastering basic facts, and how this skill is expanded on in upper grades.
Early Multiplication and Division Models:
Did you know the foundation of multiplication begins in 2nd grade?
In a very conceptual way, students begin to practice with arrays and repeated addition. When students get to 3rd grade they begin to really work with multiplying and dividing within 100. By 4th grade, students are multiplying greater numbers by expanding on these models. Helping your kiddo demonstrate their multiplication by drawing some of these models, helps to build understanding, accuracy, and fluency with basic facts. Here are some of the Early Multiplication & Division Models:
Equal Groups: One of the first ways students learn multiplication is with equal groups. The problem 4 x 3 means “4 groups of 3”. Students can model the problem by drawing 4 circles and putting 3 objects inside them. This model also shows multiplication as repeated addition.
4 x 3 = 3 + 3 + 3 + 3 = 12
Arrays/Grids: For this model, objects can be arranged into rows and columns to show the equal groups. This method is a precursor to multiplying greater numbers using area models. Each row and column tells how many groups and how many are in each group. To the left is an example from our math curriculum, ReadyMath, that shows how a student might demonstrate multiplication using an array.
Skip Counting (Number Lines): This model shows yet another way to show the equal groups, this time by skip counting on a number line. You can see the 3 groups (the jumps on the number line) and 4 in each group (skipping 4 numbers every jump) to make 12 (where the last jump ends).
** Remember, division is the opposite, or inverse, of multiplication. These models can be done “in reverse” to show division.**
Multiplication and Division Basic Facts:
Here are some ideas to help your kiddo practice (and master!) their Multiplication & Division Skills (Basic Facts):
Multiplication War: Play this game similar to the card game “War.” Deal out a standard deck of cards, face down to each player. Players each flip a card and the first person to call out the correct product of the two cards wins that round. The game continues until someone has all the cards. Aces = 1, and Face Cards = 10
Kaboom!: Get some wood craft sticks and write basic multiplication facts on them, except for a few sticks on which you write “Kaboom!” Then put the sticks into a container, so you can’t see the fact. One at a time, pull sticks from the can. If you get the fact correct, you keep the stick. If you get the fact wrong, you put it back in the can. If you pull a “Kaboom!” stick, you have to put all your sticks back in the can.
Multiplication Salute: This game requires 3 players. Two of the players pick a card from a deck of cards without looking and hold it up to their foreheads. The third player can see both cards and tells the product of the two cards. By looking at your opponent's card and knowing the product of the two cards, you need to figure out what is on your card. The first person to call out their number correctly wins the two cards. Play can rotate between players. (Aces = 1, Face Cards = 10)
Ways to Multiply & Divide:
Did you know that the standard algorithm for multiplication isn’t mastered until 5th grade? And the standard algorithm for division isn’t mastered until 6th grade?
Prior to learning the standard algorithm for these operations the students learn different strategies to solve problems, beginning in 4th grade. The strategies they learn help students build number sense around numbers and be able to really understand what is happening when we multiply or divide with the traditional method. Here are some ways that your kiddo may be practicing how to multiply or divide before the standard algorithm:
Multiplication Area Model: This model breaks apart the numbers you’re multiplying into their place value, to make easier numbers to multiply. Doing this actually shows the “steps” to do when solving with the standard algorithm broken down. Once you’ve multiplied each product, add those together to get the answer. Here is a filled-in example from our Ready Math curriculum for 25 x 32:
Multiplication Partial Products: Once students have worked with the area model, they are ready to move towards the standard algorithm. Students will still use partial products; now they can do it without drawing all the boxes. See the example from our Ready Math curriculum that shows the four partial products and how it closely resembles the standard algorithm. This method really prepares students to move to the standard algorithm in 5th grade.
Division Area Model: This model breaks apart the problem into smaller parts and uses repeated subtraction to find the answer. Estimation is also a very important skill to use for this model and knowing facts can help make that very easy. This model also resembles the division “house” we use when using the standard algorithm, so transitioning to that is easier. See the example below, with some notes/directions, to understand how to use this model.
Two-Digit Division: 2-Digit Division can be VERY difficult! Not many people have fluency with 2-digit multiples. While it may be a little longer, here is a strategy that uses easier numbers to divide. Start off by writing the multiples of 10 times your divisor on the side. Use the product that makes the most sense and keep subtracting that number from the dividend - make sure to keep track on the side. When you can’t subtract that anymore, you need to move to a smaller product. Once you can’t divide anymore, the numbers on the side become your quotient. Add the tens and ones and put them on the top of the division “house” for your answer. If your kiddo is able to flexibly think of numbers, they may begin to recognize that you don’t have to subtract groups of tens or ones separately. This can be used with even greater numbers.
If students are able to, they can also list some multiples of the 2-digit divisor on the side to help them figure out their quotient and what to subtract from the dividend.
Beyond Whole Numbers:
Once your student has mastered multiplying and dividing whole numbers, they’ll continue to expand on that learning in 5th and 6th grades. Students will learn how to multiply and divide decimal numbers and fractions and mixed numbers. 6th graders will also begin to use multiplication and division in expressions and balancing equations. Here are some tips to help them when solving these kinds of problems.
Decimal Numbers: Once students have multiplied and divided whole numbers, they move to doing the same with decimal numbers. When multiplying decimal numbers, you can “ignore” the decimal and multiply the numbers as if they were whole numbers. Once you’ve found the product, you put the decimal back into the answer, depending on the number of places after the decimal in the factors. Estimating can be a great tool to help figure out where the decimal point goes back into the product. Dividing decimals can get a little trickier, as we don’t want to leave remainders anymore. We can find an exact answer by bringing the place value out as far as is needed. Remember, adding a zero in decimal place values to the right won’t change the value of the number! Check out these videos to help you understand the different dividing decimal situations.
Fractions & Mixed Numbers: Once adding and subtracting fractions has been taught, 5th and 6th graders will also begin working with multiplying and dividing fractions and mixed numbers. Khan academy is a great resource to understand what goes on when multiplying and dividing fractions.
Pre-Algebra: Students in 6th grade will begin to work with algebraic expressions and balancing equations. Students will use all four operations, including multiplying and dividing to find the value of a variable. Khan Academy has some great videos and explanations to watch and help students understand what is happening when we balance an equation.
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