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Image by Chris Liverani

MathBait™ Multiplication

Playing with Blocks

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Introduce students to factoring with this easy to understand visual representation. As students work to create rectangles with a specified number of blocks, they find all the factors of a given value.


Resource Type

Warm Up

Primary Topic

Primes & Factoring







The goal of this activity is to encourage students to play and explore in order to find and identify patterns.

Provide students with 24 blocks. We recommend stacking blocks such as Math Link Cubes. These cubes are great for building number sense and have many applications. Alternatively, small squares may be cut from paper. If using paper squares we highly recommend using card stock/thick paper to help students more easily manipulate the pieces. We encourage the use of an item students can physically manipulate but if this is not available, students can use graph paper to simply draw their rectangles.

Begin by asking students to organize their 24 blocks/squares into rows. Explain the only rule is each row must contain the same number of blocks. After giving students a few minutes, invite them to share the rectangle they made. We picked 24 as it is a number rich in factors. Once students have determined one configuration, encourage them to find another!

Display all the possible combinations for students to see.

All possible rectangles made up of 24 blocks

While students have previously been exposed to the commutative property of multiplication, the goal here is to build fluency with factors and thus we encourage students to find all possible rectangles, even if they are a rotation of an existing rectangle.

Highlight how our rectangles look like a multiplication table. In fact, we could find many of these rectangles on the table. For instance, if we drew a rectangle from the top-left corner measuring 3 squares wide and 8 squares high, we'd have the same 8×3 rectangle we just made! If possible, demonstrate for students how the number 24 would end appear in the bottom-right corner when constructing this rectangle on a multiplication table. The image below is from a previous activity in MathBait™ Multiplication and demonstrates how a 3 by 4 rectangle would align with the product, 3×4, in the bottom-right corner.

image showing how a 3 by 4 rectangle on the multiplication table corresponds to the value of 12

Ask students which of the rectangle they created with 24 blocks would not appear on our multiplication table? (Those with side lengths greater than 10 are not on our table as it only reaches 10).

Remind students we call the solution to a multiplication problem a product. For each of these rectangles, the product, or total squares, is 24. We call the numbers we are multiplying factors. Over the next few lessons students will learn how to find all the factors of a number.

Allow students to practice identifying the factors of 24 shown by each rectangle. For instance, the factors of the 6×4 rectangle are 6 and 4. Ask students if they can name all the factors of 24 (1, 2, 3, 4, 6, 8, 12, and 24).

Conclude by explaining how knowing the factors of a number will help us to very quickly find the product, or solve tricky multiplication problems.

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