Ways to See Multiplication

     Knowing multiplication facts is a tool that will help a person count more efficiently especially when combining equal groups, but you also have to know when to multiply. I learned my facts growing up, but while I was memorizing 7 x 5 = 35, I had know understanding of what that even meant or looked like in everyday life. I didn't know when and how to apply multiplication to solve a mathematical problem.

     While, we want our students to just "know" their multiplication facts by heart,  we strive to build a deep conceptual understanding of what it means to multiply.

     Recently, students have had various experiences "seeing multiplication" by making equal groups and arrays, seeing multiplicative relationships between numbers via paired numbers tables, and making equal jumps on a number line.

     Building a conceptual understanding that multiplication is combining equal amounts to find a product (total) is important for the following reason. Students need to know when multiplication would be the best operation to solve a given problem. If I have to combine one bag of 5 apples and another bag of 6 apples, my best bet would be addition, not multiplication since those two groups are not equal. But if I have to combine 6 bags, each containing 5 apples, then multiplication would be the most efficient way. This is what we want our students to understand.

     Please see the anchor chart to the left, for examples of how students can view multiplication. We have also looked at real world examples of arrays including eggs organized in cartons, cupcakes arranged in rows in a box, and equal groups including bags of apples, bundles of bananas. Help your child look for opportunities to multiply at home and beyond and apply their facts.

Counting Money in Real Life versus on a Paper-based Assignment

     Counting Money under and over a dollar is a skill we have practiced in class recently because it is a skill our kids will practice for the rest of their lives. Performing the skill on a paper-based test or assignment is a bit different than doing it in the real world. For one, you cannot rearrange the pictured coins. We teach our kids that an easier way to count coins and bills is to group them and then skip count from the highest to the lowest value. But if they can't move the coins, then how do they group them? We have used a strategy called "Group, Count and Cross Out" to address this issue. Children group the pictured coins by drawing each coin as a circle with it's corresponding value inside. Then they skip count from the highest to lowest value, while putting the new total under the coin and crossing out the coins already counted. Students sometimes make the mistake of counting a single coin twice or not counting it at all. When we ask kids to show their brain (write their mathematical thinking on paper) this is how we do it. Please see the picture about and look out for this strategy the next time your child has to count coins on a paper-based assignment.