Kiss those Math Headaches GOODBYE!

Archive for the ‘Place Value’ Category

Everyone Wins When Teachers Listen

Recently I saw something on YouTube that points out how we sometimes miss interesting comments while teaching.

An elementary teacher was teaching about our base 10 number system, and she was showing her first grade students the number 1.

“What do we add to 1 to make 10?” she asked.

A girl answered:  “Zero.”

Instead of listening deeply to what this child said, the teacher plowed ahead,”Well, not quite. Who else has an idea?” And the teacher waited until a student volunteered the answer she was waiting for:  9, saying that 1 + 9 = 10.

(This part of the lesson focused on number pairs that sum to 10.)

What’s sad about this situation is that the girl who said “zero” had a good point that the teacher missed. The girl was saying that a zero, written to the right of a 1, creates the number 10.

This point, had it been explored, could have sparked excitement. The teacher could have pointed out how strange it is that a 1 plus a 0 can create the number 10, when most people would say that 1 + 0 = 1. The teacher could have posed this as a riddle and asked if any student could unravel it. That riddle, in turn, could have helped the whole class ponder how interesting it is that the mere position of a digit affects that digit’s value, in our base 10 system.

Not only did the teacher miss this opportunity, she also inadvertently missed an opportunity to validate the girl. We can’t know for sure, but when a teacher passes over a student, acting like her comment was “incorrect,” the child can feel rejected. Instead, the teacher could have pointed out that this girl’s comment was in fact “right” in a most interesting way.

Of course no teacher is perfect, and as teachers we all miss comments we later wish we had noticed. Still it is helpful to be aware that we might BE missing things. Only then will we be more open to the many surprisingly interesting, unscripted comments that children make every day.


The problem:

It’s your friend’s 73rd birthday. You’ve put together a surprise party and baked a special coconut meringue cake. But at the last minute you realize that — golly gee! — you forgot to get candles.

Rummaging through your drawers with just five minutes before your friend’s scheduled arrival, you find that you do have 14 candles. And being a brilliant mathematician, you realize that you can represent the number 73 with these 14 candles, using every candle. How do you do it?

As a hint, here’s a model showing how to do a problem like this, if you are celebrating someone’s 44th birthday, when you have just 13 candles. Notice that each dot on the top row is one candle.


Note that you may use icing to create the symbols: +, –, x, ÷, and you may also put in exponents, using candles to show the value of the exponent.

Have fun!

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Please include your full name, where you live, and if you don’t mind, describe your connection to math and math education (for example: teacher, tutor, math enthusiast, etc.).

The first person to send in a correct answer receives a $20 gift certificate toward the purchase of any Singing Turtle Press products. I’ll fill the winner in on the details by email.

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Place Value Metaphor

During the summer I get to tutor a lot of elementary age students, remediating them on the basics.

Almost invariably I find that these students are confused about PLACE VALUE, and considering how critical this concept is to all of math, I decided to write this post.

Whenever I have the least suspicion that a student might be confused about place value, I check with a simple test.

I have them write down the number 22, then I ask them if they can tell me the difference between the two 2s. Often they cannot.

Tutoring a girl this past week I came up with a way of understanding place value that really resonated with the student. I want to share it because you may be able to use it, or a modification of it, with your students. First it’s important to know that this student’s mom teaches ballet, and the girl dances at her mom’s studio. 

I asked the girl if she has ever been to a ballet performance, and of course she said yes.

Then I drew a quick diagram of the stage and first few audience rows. I pointed to two seats, one in the front row, another seat several rows back. I asked her if the two seats would cost the same amount. This girl knew that the close seat costs more money because it is closer to the action on stage.

Then I used that idea to explain place value. I showed this girl that just as seats can be more or less valuable because of where they are, so too digits can be more or less value based on where they are in a number. 

She got this idea very quickly, and now she understands place value.

For children with different interests, use whatever makes sense. For example if you’re teaching a boy who loves baseball, make the rows of seats those at a baseball game, and so on.