February's Lesson of the Month is on multiplying unit fractions by fractions. Unit fractions are those that have a 1 in the numerator. This lesson shows how to model the multiplication of any unit fraction by any other fraction. It's key to understanding what it actually means to multiply fractions together. The lesson is from Brick Math's Fraction Multiplication Using LEGO® Bricks.
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The lesson starts with a discussion of the term unit fraction, along with a discussion about how to determine which unit fraction is largest: 1/2, 1/3, or 1/4. The lesson then moves on to modeling two multiplication problems.

Most 4th - 6th grade math teachers would agree that multiplying and dividing fractions is a very tricky subject for students to understand. The methods in Brick Math help make clear to students what is actually happening when two fractions are multiplied together -- not simply the process of multiplying the numerators and denominators together. This kind of deep understanding gives students a strong foundation in math that they can build on as they progress into middle school math and beyond.

Brick Math is a K-6 math curriculum that uses LEGO® bricks to model  11 different math subjects: Counting, Addition, Subtraction, Multiplication, Division, Basic Fractions,   Basic Measurement, Fraction Multiplication, Fraction Division, Advanced Measurement and Geometry, and Decimals. This year, the program will expand to include grades 6 - 8, with the additional subjects Data and Statistics, Pre-Algebra, and Ratios and Proportions. Brick Math works in many applications: for homeschooling, math intervention, enrichment, and as a whole-school program. Materials are simple and affordable.
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If you are a math teacher or a parent with a student at home who is learning K - 6th grade math, check brickmath.com. The website includes videos for both teacher training and direct instruction of students. You can learn more about how Brick Math improves students' math test scores and hear what people who are using Brick Math have to say about the program. ​

Knowing fact families is a big step toward learning multiplication facts. In this lesson, students are asked to model the fact families for the numbers 6 and 8 using bricks. The lesson also gives teachers a very clear way to demonstrate the meaning of "4 sets of 2" (4 x 2) versus "2 sets of 4" (2 x 4). Besides showing the commutative property of multiplication, the concept of sets is important in many applications , including engineering, as well as a simple application such as sharing!

I recently had a customer tell me that her son didn’t understand the idea of factors until she tried Brick Math. When he saw the concept of factors made real with LEGO bricks, she said, he knew what they were! It’s exciting to hear when students finally “get it” because modeling with bricks makes all the difference for them.
 
I started to think about that lesson on factors, and I realized it is the perfect way to demonstrate the power of Brick Math as a learning system. Here’s why Brick Math works so well to teach elementary math: it’s tactile (kids touch the bricks and build the models themselves), it’s visual (kids can see exactly what the numbers in a math problem represent), and it’s conceptual (kids understand the underlying idea behind the math when they discover it for themselves in a guided program).

Let me show you how Brick Math works with that lesson on factors:
 
This lesson models all the factors of 16 and demonstrates perfectly the meaning of “factor." Like all Brick Math lessons, it starts with some basic bricks and a baseplate to build on. Begin by placing one brick that has 16 studs on the baseplate (studs are the bumps on LEGO bricks). This can be a 2x8 brick or a 1x16 brick.The model shows 1 brick with 16 studs, so the multiplication fact shown is 1 x 16 = 16. 16 and 1 are factors of 16.

​Next, take two bricks that each have 8 studs and place them next to the brick that’s already on the baseplate. It’s best if those two bricks are two different colors. You’ll use either two 2x4 bricks or two 1x8 bricks. Now the model shows 2 (bricks) x 8 (studs) = 16, and that 2 and 8 are also factors of 16.
 
Now, here’s where the Brick Math program really becomes a powerful learning tool. For the next step, ask the student, “Are there 3 bricks that are all the same size that you can use to build the next row?” Let your students try with different bricks. They will demonstrate to themselves that there are none, so 3 can’t be a factor of 16. It’s so important that students discover for themselves while they are learning. That’s what helps them internalize what the math is all about.
 
When they move on to looking for 4 bricks, they’ll find that four 2x2 bricks or 1x4 bricks do the trick. Now, they have 4 (bricks) x 4 (studs) = 16, so 4 is another factor of 16.

​Dr. Shirley Disseler, developer of the Brick Math method, demonstrates this same lesson in the video below. 

​The concept of factors is key to learning multiplication, division, and fractions, so it’s in all three of the Brick Math books on those subjects: Multiplication, Division, and Basic Fractions. And it (almost) goes without saying: students have fun while they learn!

Whether you're back to school in person or online, or some combination of the two, this free Brick Math Lesson of the Month is a great way to help  students learn math. For September, it's a lesson from Fraction Multiplication Using LEGO® Bricks that shows how the commutative property works when multiplying fractions. Students typically learn about multiplying fractions in grades 4 - 6, but it is sometimes part of the curriculum when students are learning about fractions in grades 2 - 3.

To get the free Lesson of the Month for September 2020, click here.

Students should already understand that a x b = b x a (see Multiplication Using LEGO® Bricks, chapter 5). Now it's time for them to learn that the same commutative property holds when multiplying fractions. This lesson makes it clear to students by using bricks one way to model 1/2 x 6, and a different way to model 6 x 1/2. In both cases, the answer, 3,  is the same.

​This lesson also shows how the two number sentences are used to describe different real-life situations: 1/2 x 6 means "one-half of six," while 6 x 1/2 means "six sets of one-half." So in real-life usage, 1/2 x 6 could describe "half of the six crayons in the box, or three crayons." And 6 x 1/2 could describe "six half-pizzas, or three whole pizzas." Using bricks to model these two scenarios really helps students understand the math.

April's Brick Math Lesson of the Month is about Multiplication. It's a great way to show students exactly what multiplication means, using a bundling technique with bricks.

There are two math problems in this lesson of the month to show how the bundling technique works: first,  2 x 25, and second, 3 x 12. In both problems, the math is modeled to show the sets. The problems also show the difference in modeling if the numbers are reversed; i.e., 25 x 2 or 12 x 3.

This Lesson of the Month shows 4 pages from the Multiplication Teacher Edition first, and then the corresponding pages for students to use from the companion Multiplication Student Edition.

Sign up here to receive a FREE Brick Math Lesson of the Month every month!

Learning multiplication is NOT memorizing times tables! The rote process of repeating multiplication tables over and over, taking speed tests, and writing math facts ten times each— these instructional methods are not supported in educational research.

Students learn the concept of multiplication best through the process of modeling with manipulatives. And that’s where Brick Math can help students learn multiplication. The Brick Math program uses LEGO® or LEGO®-compatible bricks as the manipulatives. With Brick Math, students create models that help them understand the concepts behind multiplication.

Students begin with the basics—understanding the meaning of multiplication as it relates to repeated addition. This understanding usually begins in grade 2 with the introduction of sets and its relationship to skip-counting. Students then learn basic facts of multiplication through modeling, arrays, and word problems, typically in grade 3. They work on one-digit multiplication problems and later learn how to multiply two-digit numbers and beyond in grades 4 and 5.

In Brick Math, students learn multiplication through an integrated program. They create models using the bricks. They then draw the models they’ve created. Finally, they explain in writing how and why they created the models. These three different ways of interacting with bricks lead to a deep understanding of how multiplication works.
When students model the action of multiplication using bricks, they have the opportunity to create multiple solutions to problems instead of looking for the one right answer.

Watch the video below to see a Brick Math lesson in action. This one is about multiplication fact families. Then click here to download a lesson plan about finding factors from the Brick Math book Multiplication Using LEGO® Bricks—Teacher Edition.
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Brick Math is fun! Students love playing with bricks, and Brick Math helps them discover that math can be entertaining. As one Brick Math student said: “Why doesn’t everyone learn math this way?”