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February 24, 2016

Teaching Multiplication With the Distributive Property

I love the distributive property! This one little math rule demystifies the steps of long-multiplication, allows me to do multi-digit multiplication in my head (mental math) and alleviates stress about memorizing the “tricky facts” (who doesn’t hate multiplying by 7?!) Given how awesome the distributive property is for making sure that kids actually understand multiplication, it’s sad that it sometimes gets a bad rap as newfangled fuzzy math. The distributive property is logical and straightforward and empowering — yes, empowering! Read on for ideas about teaching the distributive property.

(Want more tips for memorizing the times table? Check out my blog post "Total Recall: Helping Our Students Memorize Multiplication Facts.")

What is the Distributive Property?

The distributive property explains that multiplying two numbers (factors) together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products. It sounds complicated in words, but it’s simple when you see it!

It doesn’t matter how you break up one of the factors. Sometimes, for multi-digit numbers, we prioritize breaking up a factor into its expanded form, but this is not necessary. Students can break up numbers to use their favorite “friendly” numbers. For example, not sure about 6x8? 6x3 added to 6x5 will result in the same answer!

Distributive Property Activities

Drawing the Distributive Property

Just as we first teach multiplication visually with pictures, arrays, and area diagrams, we also use visual models to introduce the distributive property. Dividing up the area of a large rectangle into smaller rectangles clearly demonstrates how the distributive property works. One thing I love about the distributive property is that there isn’t a single correct way to break up the factors. This reinforces the importance of flexibility when thinking about numbers and allows students to personalize their strategies.

Download my Distribute It Again – Area Model Exploration.

Distributive Property Matching Game

Print out these cards onto cardstock, ask a volunteer to cut out the cards and store them in zippered plastic bags, and you have a quick and easy game to help students practice identifying the distributive property. To play, students match the pictorial area model with the corresponding distributive property expression and the expanded form of the distributive property.

Fusible beads (e.g. Perler beads) are a fun “M-Art” (math+art) activity for a math center. Ask students to create rectangles consisting of smaller rectangles. Iron the beads together and then students can take turns finding the total number of beads by adding the area of all of the smaller rectangles. This kinesthetic approach not only explains the distributive property, it also helps some students memorize multiplication facts.

“Break It Up” Chant With Maths Mansion

Maths Mansion is an educational program from the UK with 40 episodes that cover a range of upper elementary math topics, (all available on YouTube.) I love how this program presents math topics in highly visual, mathematically sound yet silly ways. My students are obsessed with this program.

The episode “Breaking Up Is Easy To Do” (#13) covers the distributive property and using known facts to figure out unknown facts. The song/rap portion of the show, "Break It UP" is the best. I replay the song over and over until the kids are chanting the chorus. It really instills a sense of confidence that they can tackle any multiplication problem. Here are the lyrics for the song to share with your students.

Parent Buy-In: The Missing Piece

The way we teach multiplication may look quite different from how our students’ parents learned it. I often contend with parents who are confused by how and why we teach multiplication this “new” way. And I find that if I don’t take the time to explain to parents how we develop multiplication concepts (with arrays, area models, and the distributive property), it’s counterproductive for everybody. Parents are frustrated because they don’t know how to support their children, the kids get frustrated because their parents are showing them different methods than what they are learning in school, and everybody is frustrated with me!

The solution? I host a parent multiplication workshop (in person and with the option to Skype in.) During the workshop, I guide the parents through multiplication activities where they can experience firsthand the ease and benefits of using the distributive property of multiplication. I don’t say that one method is better than another — there’s no need for value judgments! But we discuss the relative merits of different strategies: some are more efficient, others better for mental math, etc.

Download the information packet I share with parents about non-standard multiplication strategies.

What tips or tricks do you have for teaching multiplication to your students? Do you have questions or comments about any of my suggestions? I’d love to hear from you! Reach out on Facebook, Twitter, or in the comments area below.

One year ago: “Women’s History Month for the 21st Century Girl

Two years ago: “Seasonal Reading to Celebrate (and Organize) Our Books

Three years ago: “Get Inspired With Biography Research!

Four years ago: “Five Ideas for Perfectly Bookish Read Across America Celebrations

I love the distributive property! This one little math rule demystifies the steps of long-multiplication, allows me to do multi-digit multiplication in my head (mental math) and alleviates stress about memorizing the “tricky facts” (who doesn’t hate multiplying by 7?!) Given how awesome the distributive property is for making sure that kids actually understand multiplication, it’s sad that it sometimes gets a bad rap as newfangled fuzzy math. The distributive property is logical and straightforward and empowering — yes, empowering! Read on for ideas about teaching the distributive property.

(Want more tips for memorizing the times table? Check out my blog post "Total Recall: Helping Our Students Memorize Multiplication Facts.")

What is the Distributive Property?

The distributive property explains that multiplying two numbers (factors) together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products. It sounds complicated in words, but it’s simple when you see it!

It doesn’t matter how you break up one of the factors. Sometimes, for multi-digit numbers, we prioritize breaking up a factor into its expanded form, but this is not necessary. Students can break up numbers to use their favorite “friendly” numbers. For example, not sure about 6x8? 6x3 added to 6x5 will result in the same answer!

Distributive Property Activities

Drawing the Distributive Property

Just as we first teach multiplication visually with pictures, arrays, and area diagrams, we also use visual models to introduce the distributive property. Dividing up the area of a large rectangle into smaller rectangles clearly demonstrates how the distributive property works. One thing I love about the distributive property is that there isn’t a single correct way to break up the factors. This reinforces the importance of flexibility when thinking about numbers and allows students to personalize their strategies.

Download my Distribute It Again – Area Model Exploration.

Distributive Property Matching Game

Print out these cards onto cardstock, ask a volunteer to cut out the cards and store them in zippered plastic bags, and you have a quick and easy game to help students practice identifying the distributive property. To play, students match the pictorial area model with the corresponding distributive property expression and the expanded form of the distributive property.

Fusible beads (e.g. Perler beads) are a fun “M-Art” (math+art) activity for a math center. Ask students to create rectangles consisting of smaller rectangles. Iron the beads together and then students can take turns finding the total number of beads by adding the area of all of the smaller rectangles. This kinesthetic approach not only explains the distributive property, it also helps some students memorize multiplication facts.

“Break It Up” Chant With Maths Mansion

Maths Mansion is an educational program from the UK with 40 episodes that cover a range of upper elementary math topics, (all available on YouTube.) I love how this program presents math topics in highly visual, mathematically sound yet silly ways. My students are obsessed with this program.

The episode “Breaking Up Is Easy To Do” (#13) covers the distributive property and using known facts to figure out unknown facts. The song/rap portion of the show, "Break It UP" is the best. I replay the song over and over until the kids are chanting the chorus. It really instills a sense of confidence that they can tackle any multiplication problem. Here are the lyrics for the song to share with your students.

Parent Buy-In: The Missing Piece

The way we teach multiplication may look quite different from how our students’ parents learned it. I often contend with parents who are confused by how and why we teach multiplication this “new” way. And I find that if I don’t take the time to explain to parents how we develop multiplication concepts (with arrays, area models, and the distributive property), it’s counterproductive for everybody. Parents are frustrated because they don’t know how to support their children, the kids get frustrated because their parents are showing them different methods than what they are learning in school, and everybody is frustrated with me!

The solution? I host a parent multiplication workshop (in person and with the option to Skype in.) During the workshop, I guide the parents through multiplication activities where they can experience firsthand the ease and benefits of using the distributive property of multiplication. I don’t say that one method is better than another — there’s no need for value judgments! But we discuss the relative merits of different strategies: some are more efficient, others better for mental math, etc.

Download the information packet I share with parents about non-standard multiplication strategies.

What tips or tricks do you have for teaching multiplication to your students? Do you have questions or comments about any of my suggestions? I’d love to hear from you! Reach out on Facebook, Twitter, or in the comments area below.

One year ago: “Women’s History Month for the 21st Century Girl

Two years ago: “Seasonal Reading to Celebrate (and Organize) Our Books

Three years ago: “Get Inspired With Biography Research!

Four years ago: “Five Ideas for Perfectly Bookish Read Across America Celebrations

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