When I taught fifth grade, it always seemed as though it was the first time my students encountered the distributive property of multiplication.
This was true of so many concepts I taught in math at the fifth grade level. My students looked at me as if they had never encountered the concepts we were learning about. Teaching these concepts felt overwhelming at the time. However, having taught fifth, fourth, and third grade, I can tell you that SO many math concepts are recycled year after year and build on one another.
That’s why I feel confident in sharing with you about the distributive property. We don’t always have time to look back and forwards in the math standards. Knowing what students “should” have learned in previous grades allows you to build on that foundation.
Here’s what students learn in Grades 3 – 5 about the distributive property of multiplication.
What is the distributive property of multiplication?
The distributive property of multiplication states that when a number is multiplied by the sum of two addends, the product is equivalent if we first multiply each addend by the given factor and THEN add.
How is the distributive property of multiplication used in Third Grade?
Third grade is when this concept is first introduced. When learning multiplication, third graders build arrays. They arrange objects into rows with the same number in each row. This builds on what they learned in grade two about repeated addition.
As a way of supporting third graders in determining the total amount in an array, they break apart arrays.
They select to either break apart the number of rows, or the number in each row. They should NOT be breaking apart both factors at the same time when learning about the distributive property of multiplication.
To do this in my own classroom, we always use hands on materials. We love using tiles, I also like using table scatters from Hobby Lobby, or objects like corn kernels. I find varying our manipulatives makes math learning more engaging throughout the year.
This year, because it was fall when we were working on this task, we used corn kernels and had a corny day of math fun. They were especially surprised that they got to eat popcorn as they built their arrays.
To represent their models, they had to write two math expressions that represented their array and how they divided them.
For an 8 x 3 array, they decided to break apart the number in each row. This created two arrays: 8 rows of 1 ( 8 x 1 ) and 8 rows of 2 ( 8 x 2 ). Their final expression for the array was ( 8 x 1 ) + ( 8 x 2 ).
This is the beginning of their journey with the distributive property. In later grades, they learn that because both factors are being multiplied by 8, they can write the expression as follows: 8 x (1 + 2).
Both expressions create the same product, whether they multiply each individual addend by 8 first, or find the sum or the two factors and then multiply it by 8.
Distributive Property of Multiplication in Fourth Grade
In fourth grade, students use the distributive property of multiplication when they multiply larger numbers. First it begins in the area model of multiplication. Then, as students move onto the place value sections model and the algebraic notation method, they rely heavily on the understanding that they are distributing the parts of each factor to find the final product.
For students needing more hands on strategies, I used area and perimeter thinking mats from my third grade materials that were designed to hold the 1 cm cubes commonly used as base ten blocks.
We used these to build the numbers and distribute the single digit factor we were multiplying by to each place value of the larger number.
What about fifth grade?
In fifth grade, many of the properties come together. Students refine their understanding of how they work and become more effecient at solving problems.
Again, we see the distributive property of multiplication being used in the multiplication of larger numbers and more complex numbers.
Fifth graders multiply factors that include both multi-digit whole numbers, mixed numbers and decimals. Breaking apart numbers into their whole and their parts really serves students well when they have to multiply a mixed number or decimals.
My fifth graders always felt like these were magical powers somehow, but I wanted them to understand that it wasn’t math magic. These were superpowers that they could use to help them be more fluent in computing numbers.
In Conclusion
The distributive property of multiplication comes back time and again in grades 3 – 5. As a third grade teacher, I want my students to understand how this math property works and how they can use it to make multiplication at a conceptual level easier.
If your fourth and fifth graders are looking at you as if you are introducing something completely new to them, you may just need to remind them of what they learned in third grade. Of course, it is possible that their previous teacher did not teach the concept. It could have been a crunch on time or because they didn’t see the value of it at the time.
That’s the beauty of teaching multiple grade levels over the years. You get the opportunity to see how important those basic conceptual learning experiences are to build a firm math foundation for students.
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