When I learned my basic multiplication facts, it was totally through rote memorization. I might have memorized 6 x 6, knowing immediately that the product is 36, yet when asked about 6 x 7, I would see no connection. I had not memorized that one yet. Fast forward. Our goal for basic facts has not changed—we still want our students to have automaticity with basic facts. What’s changed is our approach. We now know that a better way to teach basic facts is through a strategy-based approach. So if a student knows 6 x 6 = 36, they can reason that 6 x 7 must be 42, because it’s just one more group of 6. Students learn their squares facts (2 x 2, 5 x 5, etc.) quite easily, so they can use those facts to reason about “near squares” like 6 x 7.
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A couple of great resources for teaching facts with a strategy-based approach are Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention and Mastering the Basic Math Facts in Multiplication and Division: Strategies, Activities & Interventions to Move Students Beyond Memorization. Both include many games that students can play to practice their facts.
And I’ve got a free game you can download and use in your classroom tomorrow for practicing the squares facts! This game requires strategy, which brings a little problem-solving into the activity.
Ideally, math games should be played with pairs of students. Two students working together, rather than 3 or 4, allows the game to move more quickly and encourages mathematical discussion.
Each player needs a Squares Squeeze recording sheet and one die is needed for the pair. Using a regular die allows players to practice facts up to 6 x 6. Using a ten-sided die allows practice for facts up to 9 x 9. The Squares Squeeze recording sheet has room for players to play five rounds of the game. A multiplication/division chart is provided for support.
Player 1 rolls the die. In the example shown, an 8 is rolled. The player states the squares fact—8 x 8 = 64. Now comes the strategy! The player must put their number in one of the squares on the number line. Once placed, it can’t be moved. The five numbers must be in order from least to greatest, so it’s important to think carefully about where to place each number. As with all strategy games, let students figure out the strategy on their own! That’s how you bring problem-solving into the activity.
Since 64 is one of the larger numbers—only 9 would result in a larger product—Player 1 decides to put the 64 in the next-to-the-last square. Keep in mind that the only roll this player can get to fill that last square is a 9. Good strategy? Maybe. If they had put the 64 in the last square and then they rolled a 9, they would not be able to place the squares product, 81, on the number line.