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.
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: