Recently I’ve been a little obsessed with the area model as a way to represent multiplication. So much so that I created my own set of area model cards (see attachment below). Why the area model? It’s one of the problem types that third graders are responsible for being able to solve (see Table 2 here on p. 89). Also, it’s used heavily in the fourth grade standards in multiplication (4.NBT.2.5) and division (4.NBT.2.6). Because of this I’ve been thinking about how important it is that third grade students get lots of experience with this model throughout the year, not just in the “area unit.” There are tons of connections within third grade depending on the question you ask:
- Interpreting multiplication (3.OA.1.1) What multiplication expression would match/represent this model? How do you know?
- Interpreting division (3.OA.1.2) What division expression would match/represent this model? How do you know?
- Solving multiplication and division word problems (3.OA.1.3) What is a math story you could tell about this model? What would the solution be and where do we see it in the model?
- Applying properties of multiplication as strategies (3.OA.2.5) What multiplication expression would represent the whole rectangle? What expression would represent the shaded squares? The non-shaded squares? How could we use this to figure out the total?
- Relating multiplication and division (3.OA.2.6) What are the related multiplication and division expressions that would represent this model? Explain how you see the relationship in the area model?
- Fluency with multiplication (3.OA.3.7) (All this multiplication work around the area model is leading towards fluency)
- Recognize area as an attribute of a figure (3.MD.3.5)
- Measure area by counting unit squares (3.MD.3.6)
- Relate area to the operations of multiplication and addition (3.MD.3.7)
With all of these connections you can truly be addressing multiple standards with one tool. These are just the standards that have explicit connections to the area model in third grade. There are others, but they would require some specific constraints. Still though, this is 9 third grade standards… out of 25. That’s more than a third of the grade level standards. This is definitely a high yield representation for third grade. The cards are shaded after 5 to help students see the smaller facts within the larger facts (similar to a rekenrek) and I’ve included links to the cards below in PDF format.
If you use them with your students let me know how it goes. Have other connections or questions you would ask with the area model cards? Reply in the comments or @zack_hill on Twitter.