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Another thing that I learned that using a chart in multiplication is helpful to show students the pattern of repeated addition when doing the operation.

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I learned that using a chart is a helpful way to help students see that with multiplication the numbers are being added each time. For example under one, 6 would be under within the chart. Then under two, 12 would be under within the chart and so on.

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Representing patterns in a chart is a good way to help students recognize them

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We can see the 3 blue balls equals 12 as a division problem, as the balls are the same size and shape. 12 divided by 3 is 4. Now that we know the blue ball is 4, we can subtract that from the total, 8, so that leave 4 for the 2 red cubes, making each cube worth 2, because 4 divided by 2 is 2

2 red cubes + 1 blue ball = 3 blue balls

2 x + 1 y = 3 y

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I learned that students need to learn the early steps of alegbra before then can begin to do highlevel math.

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One thing I learned was that when multiplying two even numbers and an odd and even number when visually representing the problem there are going to be even pairs. However, when multiplying two odd numbers there is going to be and uneven amount of pairs and there will be one left over.

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I learned that there generalizing in algebra is basically taking a topic that you're learning about and summarizing it into the main idea, which helps for students to understand what the main point of the lessons are.

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I learned that the early steps to algebra involve recognizing patterns

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A great demonstration of patterns is by showing the way they change and can be added onto. This shows the importance of variables.