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.

Look for Multiplication at the Grocery Store

     When you see the multiplication equation 5 x 2 = 10 or 2 x 5 = 10, what picture appears in your mind? You might think of 2 rows of five cupcakes or maybe 5 pairs of socks.

     This week our classes are exploring what it means to multiply, while understanding how multiplication can be an efficient way of counting in certain real-life situations.

     I always remind our kids that they will be counting for the rest of their lives so why not become efficient at it.  We define efficient as doing something in a way that saves you time and energy while achieving your objective. Counting by ones, twos, fives or even tens isn't always the most efficient way for a given situation whether you need 60 apples or 36 eggs at the grocery store. Multiplication is a very efficient way of counting when items are organized into equal groups or arrays. Examples of equal groups include bags that each contain an equal amount of potatoes, say 10. An example of an array would be 24 cupcakes organized in equal rows and columns. Maybe 4 rows that each contain 6 cupcakes.


Multiply at the Grocery Store!

     Next time you go to HEB, Fiesta, Kroger or any other grocery store look for items organized into equal groups or arrays. Have your child count them the way they know how first. They may count by 1s, 2s, 5s or 10s, then ask if they could use multiplication to find the same total. Eventually, as they practice their multiplication facts, they'll just "know" 7 groups/rows of 5 is 35 and won't have to count by 5s. This will come with time and practice.

     You could also give your child an amount of pennies (for example 24) and have them rearrange the coins into different arrays to see different multiplication facts for the same total. For example 24 pennies could be organized into 8 rows of 3, 3 rows of 8, 6 rows of 4, or 4 rows of 6. There's 8 x 3 = 24, 3 x 8 = 24, 6 x 4 = 24 and 4 x 6 = 24. Happy shopping, counting and multiplying.

Estimate At A Best Buy Near You.

     Recently, we turned our classroom into Best Buy. Pictures of electronics such as IPODs, PS3s, and Nintendo DSs decorated our room. My students wrote an estimation story, detailing their "shopping experience." I gave each kid $710 (just pretend :) to spend on two items of their choice. They browsed the "store," wrote the actual price of each item, and then estimated each cost by rounding it to the nearest hundred. They used a strategy we like to call the "Sky to Floor" number line. The goal is to do estimation mentally, however, the number line helps them to "see" the closest hundred in their brain. After finding the estimated costs, they added them to see if they could afford both with just $710. For example, if a PS3 costs about $300 and an IPOD costs around $200, then the total estimated cost would be about $500. You could buy both.

     Through this experience, I want my students to realize that estimating actual amounts like exact prices makes them easier to remember and easier to add. I estimate all of the time when I go shopping, and I hope they do too, the next time you get the itch to spend a few dollars.