In this activity, students will use prime factorization to determine different multiplication statements which reach a given product. This game is a great way to practice multiplication but also can include strategy, allowing students to play around with different values.

Begin by presenting students with a value. A great way to generate a value is to start with the prime factorization you are looking for. For example, if our goal is 2×2×3×3×5, multiply this out to find 180 and announce 180 to students.

Next, give students the factor you are searching for. Start with primes such as 2 or 3, then advance to composite values. The first student to find what times what wins a point.

Not all students thrive in competition-based activities or games. A great way to augment the game for differentiation is to create pairs. Allow students to play in teams. We recommend heterogeneous grouping for this activity (pairing students with different levels of understanding). Structure the game by allowing pairs to work together to find the prime factorization after announcing the number. Encourage students to work together and create a factor tree. For example, with 180, students can find the factorization in many ways. Consider pausing after this step to allow pairs to share their methods with the class. Here are few paths that are great to highlight:

• 180=18×10=(2×9)×(2×5) = 2×3×3×2×5

• 180=2×90=2×9×10=2×3×3×2×5

• 180=2×90=2×2×45=2×2×5×9=2×2×5×3×3

Now, announce the target factor. This can be any factor of your choice. You may ask the class "What times 2 equals 180?". Students who initially halved may find this value quickly, others may need to rearrange their factors and multiply back up. Set a time limit and provide points to all teams who find the correct value, or provide an extra point to the team who is first to solve. Increase the difficulty by asking for composites such as 6 times what is 180 or 15 times what is 180.

The goal here is to help students (1) work with factors, (2) practice multiplication, and (3) see one of the great benefits of prime factorization. Highlight that once we have the prime factorization, we can find what times any factor will produce the target value.

For example, if asking 15 times what is 180, students can use the prime factorization of 2×2×3×3×5 to first make 15 using 3×5; the product of the remaining factors will be the solution. In this case, we have 2×2×3×3×5=2×2×3×(15)=4×3×15=12×15=180. Thus, the solution to what times 15 is 180 is 12! Notice how this is also preparing students for division. A great approach to division is to prime factor the dividend and if taught correctly, this will also allow students to easily deal with remainders as well!

This game can be augmented in many ways. We've made a quick and basic digital activity to aid in random number generation and play. This can be used individually or in groups.

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