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MathBait™ Multiplication

Build It!

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This activity introduces students intuitively to prime numbers. The goal is not to perfect, know, or list prime numbers, but rather to explore how numbers can be built and what numbers we need to build values of every size.


Resource Type


Primary Topic

Dual Processing







The purpose of this activity is to introduce students to the word prime. We have multiple activities to build a deep understanding of prime numbers both later in the MathBait™ Multiplication series and within The Kryptografima. For now, we are only exposing students to the idea and not worried about mastery of the concept.

Provide students with 5-6 sheets of graph paper and colored pencils. Explain their goal will be to build towers of a given height. Since any height can be made with one-blocks, we won't have one-blocks. Our first block size will be a two-block. Have students label the top of one sheet of their graph paper "My Blocks". On the page, select a color for their two-blocks, draw it out, and label it.

On another piece of graph paper have students draw out towers using their two blocks. Note, the width doesn't matter. A common LEGO is 2×2 but making all blocks have length 1 will save space. Ask students to label their towers by their height; what do they notice? Highlight that with blocks that are 2 units tall, we can make towers of size 2, 4, 6, 8, 10, ..., exactly our multiples of 2 or the numbers we say when skip counting by 2's.

My Blocks showing the towers build with blocks of size 2

Ask students for tower heights they were not able to build with 2 blocks (3, 5, 7, 9, 11, 12, ...). We should notice many sizes are multiples of 3, so let's make a 3 block. Allow students to select a design for their 3 block and add it to their My Blocks page. Then, draw out the first few tower sizes they can make using only 3 blocks.

Emphasize to students that in building our towers, we cannot combine block sizes. We are looking to build only using one size of block.

My Blocks with sizes 2 and 3 and towers created by 2 and 3 blocks

Ask students what they notice. Some key ideas are the towers we can build with 3 blocks are the multiples of 3 and some blocks can be built with 2 blocks or 3 blocks, such as 6 and 12. Connect back to previous activities when we learned that we can count by 6's by skip-skip counting by 3's or skip-skip-skip counting by 2's.

Now ask students what is the next size block we need. Students may suggest 4 (as logically we have 2, 3, 4). Explain we don't need a 4 block because we can make it using 2's! We already have a tower of size 4. Students should settle on 5 and design their 5 block on their My Blocks sheet and draw a few towers of size 5.

If time permits continue up to 10. Students will find they only need a 2, 3, 5, and 7 block as the other sizes have already been completed.

Explain that we call numbers like 2, 3, 5, and 7 prime because they are needed to build towers, or other numbers. These numbers are super powerful and we will continue to learn more about them later. For now, we just want to be introduced to what prime means.

Conclude by asking students to each give a number larger than 10 that they think is prime. Have a short discussion about their choices and how we might be able to test if a number is prime. Here are some strategies:

  • If we know a number is a multiple, or a number we say when skip counting, it can't be prime because it can be built with smaller blocks.

  • If a number is on our multiplication table (other than the first row and columns, as everything can be built with ones), it can't be prime.

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