Tag / place value

by Beyond Traditional Math

Teen Numbers are Early Place Value

Teen numbers in English are STRANGE. I mean, look at these weirdos in the first half of the numbers:

11 – eleven (not one teen)

12 – twelve (not two teen)

13 – thirteen (not three teen)

14 – fourteen

15– fifteen (not five teen)

16 – sixteen

17 – seventeen

18 – eighteen

19 – nineteen

When we start teaching these numbers to our youngest learners, we often take for granted the strangeness of the names of these numbers.We are used to the names and counting with them…we don’t even question or notice how strange they are. The first half of them don’t even follow a logical pattern! In addition, I often hear videos being played where the singer is saying “Teen numbers start with a 1!” Actually, teen numbers are written with a 1 first yes, but that one in the teen number does NOT have a value of “one”.

Teen numbers are the basis of place value. I still work with third graders who will see 10+6 and start counting on their fingers to figure it out! How they don’t know that shortcut always shocks me. I think somewhere we failed them in understanding the value of the 1 in the teen number.

Beginning to learn about place value for our early learners needs to include some key things. We have to spend a lot of time letting them play with the numbers, get comfortable with different representations of those numbers, including finding the ten that is hiding in the number. In many state standards teen numbers are expected to be thought of/written as a group of 10 and some more ones. YES, this is key! In the photo below you’ll see some of these various representations with fingers and numbers. In future posts, I’ll show some other representations and tools that work AWESOME.

In addition concrete tools should also be incorporated as much as possible! Here we are using units of one and ten to make it match the fingers. Very powerful for them to connect a tool from their body (fingers) to a more abstract tool (base ten blocks).

Never skimp on those teen numbers kindergarten teachers! Future grade levels depend on you to explore these concepts deeply with your students.

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by Beyond Traditional Math

I Am Obsessed With Visuals

I can’t stop using visuals in elementary math. They are on every anchor chat, every lesson plan, every assignment if possible. It started last year when I noticed students were having trouble understanding place value until I made a visual 100 chart.

When students have a visual to connect mathematics to, it’s like something magical starts to happen. Students who excel want to make their own visuals, students who struggle start to understand…it’s truly remarkable.

You might be wondering more about what I mean by visuals. I’m going to introduce you to Berkeley Everett at Math Visuals. He is a K-5 Math Specialist out in California that has been working on making math come to life with visual animation. It’s truly remarkable the amount of hours he has put into this task, and it’s all FREE.

Need to learn to count in kindergarten? There’s a visual for that.

Need to see different types of division? There’s a visual for that.

Need to understand the concept behind compensation in addition? There’s a visual for that.

Need to work on different ways to represent two digit numbers using place value concepts? Theres a visual for that, too.

Go to this site and you’ll be lost for hours. Better yet, it will inspire you to create your own visuals on your math anchor charts. It will inspire your students to connect those very abstract math concepts to something that they can hold in their brain.

Thank you Berkeley, you’ve made me a better math teacher, and helped a whole lot of students at our school.

by Beyond Traditional Math

1 and 2 is NOT 12!

place-value-misconceptions

I know you see it all the time, when you ask a student what a number is made of, and they instantly throw place value out the window. That is why so many of us are doing this “Squashing Misconceptions” blog hop about place value.

I was working with a second grader that was struggling to add some two digit numbers (12 and 24).  I was thinking that if we could split the 12 she could add a ten and 2 more to 24.  So I asked her: “What two numbers go together to make 12?”

“1 and 2!”

Now you might be thinking that I tricked her with the question or that it was a matter of not understanding what I was asking, so I posed the question in a few different ways (“What is 12 made of? What two numbers can you add to get 12?”).  Each time, she maintained that 12 is 1 and 2 put together.

So, what do you do when there is a struggle with place value? Get out the MATERIALS.  ALWAYS. Don’t waste time or think that this will make it more difficult or confuse them. Just get out manipulatives, counters or cubes.  I love cubes because you can group and ungroup them at any time.

I gave her some unifix cubes and told her to prove to me that 1 and 2 make twelve. The second she pulled out those cubes her face lit up.  “That’s only 3!”

So I asked her again what makes 12.  Do you know what that little cutie did? She pulled out a ten and 2 cubes without even having to count the ten.  She was so used to seeing those concrete tools that it was a no brainer.  We had to have those materials out to make it concrete, she was not ready for bare numbers yet.

place-value-misconceptions

We constantly make those leaps too soon, and then time and time again (myself included!) it doesn’t occur to us to pull out tools, manipulatives or materials.  Our young learners need this, as they are very concrete and it can help them make the connection to number sentences.

So let them have those materials! Have them out for ALL students, so that no student ever feels “babyish” having to use them.  This is essential for students to understand place value conceptually.

Want to read some more about misconceptions in place value? Check out the next stop in the blog hop: