We know that flexibility is an essential part of fluency, but it can be hard to wrap our heads around how to teach it. Number tiles can help students actually SEE the computation. Students can manipulate the numbers in different ways to see relationships between operations and think flexibly. Math confidence increases because students see that they can break problems down into manageable parts, making it possible to solve any problem.
Using Number Tiles for Basic Multiplication
We know that we want students to build an understanding of multiplication and division rather than rely on memorization. But it can be difficult to know how to do this.
For the x3 facts, we can use the “double plus one more group” strategy. For example, for 3×8, we can think of the double of 8 (16) plus one more group of 8 to make 24. Some kids can understand this when we explain it verbally, but we can reach more kids, and allow them to build deeper understanding when we provide concrete practice with the concept. Here’s an example of what this might look like with number tiles.
Building these equations conceptually gives students a deeper understanding of what they are actually doing when they are computing using this strategy.
GET YOUR OWN SET OF NUMBER TILES HERE.
The x9 facts are another set that we can easily relate to something kids already know – in this case, the x10 facts. This can be conceptualized easily with number tiles. We can start with a ten, and then just cover up a group to build the understanding of the relationship between the x10 and x9 facts. This understanding easily transfers to muliplying bigger numbers like 19.
Once students work concretely with this concept, they’ll build the understanding that to multiply by 8, they could start with x10 and then subtract TWO groups. Or when multiplying x18, they can start with x20 and subtract two groups.
We can also help kids build flexibility by seeing that they can break basic facts up into smaller parts. Of course, automaticity is the goal for basic facts, but understanding is the way we get there. If a fact is forgotten there is always a way to figure it out. Here’s an example of how we could use 5 groups of 9 and 2 groups of 9 to figure out 7 groups of 9.
Using Number Tiles for Multi-Digit Multiplication and Division
We can also use number tiles to show students that they are capable of solving big problems in their heads. On the left, we see how we could solve 28×4 by breaking it up into 10 fours, another 10 fours, and then 8 more fours. On the right, we could think about 34×4 as 30×4 and 4×4. There are many ways to think about problems. This is a key piece to building number flexibilty.
These manipulatives also work beautifully for division. Not only do they make division visual, but the relationship between multiplication and division becomes clear.
What other concepts could you use number tiles for? I’d love to hear in the comments below!
