Sara’s son, Max, was learning to multiply by 10 at school. He had a homework project to collect 5 groups of 10 objects from nature, like 10 pinecones, 10 leaves, 10 pebbles, and so on. Everybody in the class was assigned a certain type collection with varying numbers of groups between 1 and 10. All the students would share their collections and find the total number of objects in class. The class would then put the collections in order from least to greatest.
Sara thought this seemed like a lot of work to just to learn how to multiply by 10. She thought, “All you have to do is add a zero to the other factor, and that’s your answer.” She showed her son the pattern on a piece of paper.
1 x 10 =10
2 x 10 =20
3 x 10 =30
4 x 10 =40
5 x 10 =50
6 x 10 =60
She wondered why her son’s teacher doing such an elaborate project for such a simple idea.
Why Didn’t Max’s Teacher Teach the Class the Shortcut?
Shortcuts, like the one Sara was teaching Max, help get the right answer quickly. But shortcuts are only helpful to students after the student has totally mastered a concept. For the concept of multiplying by 10, Max’s teacher wanted students to discover this pattern independently. Sara didn’t realize this project wasn’t just teaching how to get the answer to a problems like 8 x 10. The project helped reinforce complex ideas like place value, what multiplication is and concepts of quantity. Once kids have mastered a math concept, showing them a shortcut is appropriate and fun.
What Happens if You Show the Shortcut Too Soon?
Kids who learn the shortcut before fully understanding the concept will likely use the shortcut incorrectly or fail to use it when the problem is presented differently. Another problem is that the kids rely on the shortcut, and fail to understand the concept behind the shortcut. Then the concept skill becomes a learning gap. For Max, he could use the shortcut when he saw the problem as 6 x 10 = __. But failed to use the shortcut when he got this word problem:
Susie and Jessica each bought 3 pieces of gum. Each piece cost a dime. How much money did they spend?
He simply didn’t recognize the problem as the same concept.
Additionally, many short cuts do not apply to all situations. For example: adding the zero to the end when multiplying by 10 only works with whole numbers. Once children start learning decimals, the "rule" no longer holds true. Thus, children incorrectly using the shortcut will get .560 when multiplying .56 x 10, rather than 5.6.
Get the Right Shortcut at the Right Time
At Mathnasium of Littleton we love math shortcuts. We have a whole bag of tricks to make mental math easier. But we don’t introduce the shortcuts until the student has demonstrated understanding of the concept.
Whether your kid is ready for shortcuts or needs to address a learning gap, Mathnasium of Littleton is here to help. We Make Math Make Sense.
This article was written by and owned by Cuttlefish Copywriting, www.cuttlefishcopywriting.com . It is copyright protected. Mathnasium of Littleton has permission to use it. Other Mathnasium locations should contact Heather at [email protected] before using it.
