One of the most important ways we can teach math to students is to use the progression of "Concrete, Pictorial, and Abstract" during instruction. Concrete refers to using hands-on manipulatives to demonstrate strategies. Pictorial means making a representation on paper of the math in picture form. When you get to the abstract stage, you are taking the same information from your concrete and pictorial representations and assigning numbers (or, in the case of algebra, letters) in a number sentence to the math.
This is exactly what I saw in action today as fourth graders were working on multiplication. They used foam chips to make arrays of multiplication sentences, then they drew a picture of their arrays, and then completed the number sentence.
| Building Arrays |
| Here is the chart they made to use as a guide in the classroom. |
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