The goal of this activity is to provide students with more practice finding products using smaller values.

To set up the game, place about a dozen numbers in a jar or other container. We recommend using values with 4 or more prime factors (you can use the table above to identify them). Group students into two teams. In each round, one student from each team will go head-to-head in a bidding product battle.

Call up a student from each team and select a number from the jar. Alternate which team member bids first (in round 1, the player from team 1 bids first while in round 2 the player from team 2 bids first, etc.). Each player makes a declaration on the length of the multiplicative statement they can write. The bidding continues back and forth, each player bidding more than the previous declaration, until they cannot bid higher.

When a player cannot bid any higher they announce for their competitor to "make that product". If the opposing student can successfully make the product in the stated number of factors, their team earns a point. An incorrect answer gives the opposing team the chance to steal. If the opposing team can make the product in the number of factors bid, they earn the point. If neither team can make the product, the round ends.

Play continues by selecting a new member of each team to go head-to-head. Play as time permits or set a number of rounds at the start of play. For larger classes, students can be broken into groups to play simultaneously as teachers rotate around the room.

Example Game

Josie is selected from team 1 and Armand is selected from team 2. The number selected from the jar is 16.

Josie: I can write this as a product of 2 numbers

Armand: Well, I can write this as a product of 4 numbers

Josie: Okay Armand, make that product

Armand: 16=8×2=4×2×2=2×2×2×2

Since Armand successfully created an expression, team 2 earns a point. Note students need not increase their bid by only 1 each time. In addition, students do not need to achieve the maximum number of factors. If Armand instead bid 3 and Josie could not think of a way to write 16 with more than 3 factors, Armand's team could still win the point with 4×2×2.

Conclude with a whole group discussion. Ask students why it can be helpful to think of the multiplication facts as the product of more than 2 numbers. Demonstrate to students how this can help us with some of the trickier facts, and with facts larger than 100 as well.

For instance, if you are not sure what 7×8 is, you can break 8 into 4×2. This changes the question to 7×4×2. You may be able to more easily determine 7×4=28 to know 7×8 is the same as 28×2. By doubling 28 (28+28) you can arrive at the correct product of 56. Allow students to give additional examples. By sharing the values they have trouble with, not only are we creating new strategies, but also finding connections and realizing that other students share in our struggles. This models perseverance and problem-solving which can help with motivation and confidence.