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Category: Problem-Solving

Math Tricks

Math Tricks

I hired my youngest son, Ryan, for the summer. When your kids get older they don’t hang out with you as much so we have to find ways to keep them around. I find money works. :-)But hiring him was really a win/win. He needed a job and I needed help. So he’s been keeping track of the hours he’s worked and every couple of weeks we square things up.

Yesterday he reminded me that I owe him $100 for rent. We help him with his rent while he’s in college and he was able to sub-let his room for the summer for a fraction of what he usually pays.

“Just add it to what I already owe you,” I told him. About five seconds later he said, “Okay, that’s 6 hours and 40 minutes of work.”

Now, I do not subscribe to the idea that the faster someone can do math, the smarter they are. Math is not about speed. It’s about thinking. But that said, I was pretty impressed with how quickly he came up with the number of hours and minutes he needed to earn $100. So I asked him how he figured it out so quickly.

“I get $15 an hour. So $15 times 6 hours is $90. I had $10 left so I had to figure out how many minutes $10 of $15 per hour is so I thought how long it would take to make $10. 10 divided by 15 simplified is 2/3. And 2/3 of 60 minutes is 40 minutes. So, $100 is 6 hours and 40 minutes of work.”

I so badly wanted to be in a classroom and have him explain to the group how he solved the problem. This is exactly the type of thinking and sharing out that is encouraged in the Common Core and NCTM* Standards.

But that’s not what this newsletter is about. It’s about what happened next.

My son continued, “I found this really cool app called Math Tricks. I have to solve problems in a certain amount of time. But what I really like about it is that it shows me tricks that can help.”

He pulled it up on his cell phone and solved a problem within seconds. 111 x 105 = 11655. “Look, here’s how it works. Subtract 100 from 111 and add the 11 to 105 to get 116. Add two zeros after 116 to get 11600. Then multiply the 11 by the 5 and add the result to get the final answer of 11655.” He then showed me how he learned the “trick” by accessing the training mode where the trick is described.

So this started an argument, uh, discussion on math “tricks”. I insisted they not be called tricks. These tricks, I told him, are not tricks. A trick is intended to create mystery and that’s exactly what we don’t want to do in math. These are strategies based on mathematical structure (MP7). Some of them may be pretty complicated and difficult to understand but, regardless, they’re not tricks.

“Well, it doesn’t make sense but it works. It’s not like I really know what I’m doing but I know how to get the answer,” he argued.

So to illustrate my point I showed him how he could find the answer to 5 + 7 by simply finding the number in between 5 and 7 and doubling it. In other words, 6 – the number in between 5 and 7 – doubled is 12 so the answer to 5 + 7 is 12. A young child may call this a trick because they simply haven’t had the experience yet in working with numbers. But it can be easily modeled by taking 5 beans on one side and 7 beans on the other side, moving one bean from the 7 over to the 5 side so both sides have 6. So now it’s easy to see how this “trick” works.

He seemed impressed but I wasn’t done. “Let’s take 8 times 6,” I told him. “If you can’t remember 8 x 6, but you do know 4 x 6 then how about breaking it up into (4 x 6) + (4 x 6). Is that a trick or a strategy?” I was about to gather my inch tiles so I could create an array to prove that it would work when he acquiesced.

What I find so exciting about the Common Core State Standards in Mathematics is the push towards getting our students to understand – really understand – the math they are doing. When this happens, math will no longer be full of tricks. Students will begin to develop confidence in their ability to do math and we’ll move away from generations of I’m not good at math to generations of I can do math. And part of that comes from taking away the math tricks and replacing them with the math strategies they are.

I am happy to say that none of our Family Math Night kits include tricks. Just lots of fun. So if you haven’t calendared your Family Math Night event, there’s still time. As you know, our number one priority is to help you host the best event of the school year!

Family Math Night Make-N-Take Kit

Family Math Night Make-N-Take Kit

maketakekit_fullkit

We all know that when parents get involved in their child’s education, student learning increases.  What better way to get parents actively involved in important skills than through fun and engaging games that reinforce classroom learning?  That’s the idea behind the newest addition to our Family Math Night kit series:  Make-N-Take Station Kit.

Designed to give students practice in important number skills, our Make-N-Take Kit is the perfect way to make sure your K-5 students continue the learning at home.

Similar to our Play-N-Take Station Kit, families will go home with game boards and the game pieces needed to play the games over and over.  And all games come INDIVIDUALLY packaged saving you a lot of time and effort!

What’s fun and unique about our Make-N-Take Kit is that families play a role in making their game boards and game pieces!  They love that!  And teachers and parents love the extra skills practice kids will receive in a fun and creative way – all aligned to the Common Core State Standards in Mathematics.

I invite you to check out this short video where I describe the kit contents and the mathematical learning involved.  As always, if you have any questions please do not hesitate to contact me.  Our number one priority is to help you host a fun and successful event.

 

Beginning Level

Balloon Bunch Capture and Go 4 the Win reinforce beginning place value, addition and subtraction to 20, and making a 10.CCSSM:  K.NBT.A.1; K.OA.A.1; K.OA.A.2; K.OA.A.4; K.OA.A.5; 1.OA.A.1; 1.OA.B.4; 1.OA.C.5; 1.OA.C.6; 1.NBT.B.2

Intermediate Level

Place Value Shuffle and Number Shuffle reinforce place value to the hundreds place, greater than/less than, even/odd numbers, and basic addition and subtraction skills.CCSSM:  2.NBT.A.1; 2.NBT.A.3; 2.NBT.A.4; 2.OA.B.2

Advanced level

Number Shuffle and Cake Walk reinforce place value to the hundreds place, even/odd numbers, multiples, factors, prime and composite numbers, 1- and 2-digit multiplication, division facts, and fractions on a number line.CCSSM:  4.OA.B.4; 4.NBT.A.1; 4.NBT.A.2; 4.NBT.A.3;4.NBT.B.5; 4.NBT.B.6; 4.NF.A.1; 4.NF.A.2; 4.NF.B.3; 5.NBT.A.1

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Embedded Instruction

Embedded Instruction

When my oldest son was entering Kindergarten, he had an appointment with his teacher before the school year started so that she could assess where he was academically.  I remember sitting in the back of the room and listening to the two of them chat about his interests, his summer activities and his thoughts about being in Kindergarten.

She then asked him if he could count to 100 for her.  Without skipping a beat, my son asked if she wanted him to count by ones, twos, fives or tens.

I remember her shooting me a glance as she told him she was going to move on to a different topic.

My son had a little bit of an advantage.  His mom is someone who happens to be passionate about education – specifically elementary math education.  But if you’d asked him back then if he studied math at home, he would have most likely answered ‘no’.

That’s because most of the math he learned was embedded in whatever we happened to be doing at the time.  You’ve heard about embedded assessment – assessing students while they’re engaged in the lesson. It’s sort of like that only with instruction.  I like to think of it as the stealthy way to teach.

My son learned to count by  twos, fives, and tens because we happened to be counting large quantities of legos or goldfish crackers or Halloween candy and skip counting was more efficient.  So that’s what we did.  And over time, he learned.

Now we can’t possibly teach all of our lessons in the classroom this way.  It would take too long waiting for the appropriate moments.  Besides, there’s a lot of value in direct teaching.  But that said, we can still sneak in some stealthy teaching along the way.  A super easy way to do this non-direct teaching is to share your thinking out loud when solving problems that come up throughout the day.

I just got a notice in my teacher’s box that the assembly begins at 11:00 today.  Let’s see, we should probably be in the multi-use room at 10:50 and it takes about 7 minutes for us to get organized and walk there.  So that’s 10:50 minus 5 minutes which is 10:45 minus another 2 minutes means we need to begin getting ready at 10:43.

And don’t assume that you have to stick with problems that are in your current curriculum.  Beginning Kindergartners aren’t supposed to be able to skip count by twos, fives and tens but my son learned by hearing me do it over and over.

By the way, did you notice how the teacher above shared a notice that was in her teacher’s box?  Kids are so curious about how the adult world works, and sharing things like teacher’s boxes and special notes piques their interest.  They’re nosy that way.  So let’s use it to our advantage.

Here’s a short video of another stealthy way to reinforce learning if your students are studying their multiplication (and division!) facts.

How to Use Transition Times to Reinforce Multiplication and Division Facts - Grades 2-4
How to Use Transition Times to Reinforce Multiplication and Division Facts – Grades 2-4

There are times when direct teaching is the way to go.  And there are other times when indirect teaching works well.  Together, they make for a very powerful learning environment!