How do I get this kid to internalize the number line?

[Kanin]

Hi all,

 

Thanks to your help over the past months, and Ronit Bird's books, my formerly math-illiterate student (11) can now tell me the "numbers inside" 1-10, add (and starting to subtract) within 10, identify hundreds, tens, and ones in a number, and add 2-digit numbers with no regrouping. He still makes mistakes, but if I ask him to "picture the dots!" he corrects quickly. Yeah! He also says he loves math. Woo hoo!

 

Our next order of business is solidifying the number line in his mind. I keep thinking it's in there and then realizing it's not. He can tell me hundreds, tens, and ones, he still doesn't have a good mental picture of the number line. He can count forwards but not backwards, and has a heck of a time putting random numbers (say 48, 49, 50, 51, 51) in order. He puts them in order by ones (50, 51, 52, 48, 49). I could have him memorize that you always go by tens first, and then ones... but I'm not sure that's the best idea. I want him to understand what's happening. The trouble is, I've never taught "regular" kids before so I don't know how regular teachers do it! Do kids memorize? Get the concept? Or is the concept natural to most kids so it's not even an issue?

 

I'd like to do something fun like build a gigantic number line on the wall, or some other big project. We use c-rods to build numbers, but apparently that hasn't translated to seeing that 52 is bigger than 49. Anyone have any ideas for a fun project? The bigger the better!

 

Thanks so much! You guys are awesome!

[Heathermomster]

Can he build two numbers with c-rods and see which pile is bigger?  When you are comparing two, two digit numbers, you are supposed to look at the 10s place first.  Determine which is larger based upon 10s.  If the 10s are the same, move over to the units and determine which is larger.  

 

Prior to focusing on a number line, work on comparing two numbers first.  Maybe teach him to visualize the blocks.  He needs to get into the habit of looking at the 10s first.  Maybe once he is solid comparing two numbers, slowly work up to three numbers.

[Kanin]

Teaching him to visualize the blocks is a great idea, thank you!

[aaplank]

Make a huge number line for the floor. Have him walk it out. For example - how many steps from 4 to 10?

[Heathermomster]

I have been thinking about this more. You have taught your student to perceive numbers within 10. Now maybe play a game of building numbers to help him perceive numbers above 10 and go slowly. The next step would be to work within numbers to 20. C-rods make the larger number very evident. It is just completely evident that you look at the 10 rods first when determine which number is bigger.

A friend on mine used McRuffy math k and 1 st grade materials, and they are supposed to be very explicit. Parts of it you would likely skip over. There are some top and side views of isometric shapes that could be complicated. The materials used an interesting layout for money and counting. There was also a number line provided. If you can, maybe look at the materials and determine if there is something you could use.

It seems like the number line work should come after your student has familiarized himself with place value and what exactly the units and tens place really mean.

About the visualizing. Visualizing is a new skill that needs to be encouraged. I can see now that I should have actively encouraged that when DS was younger. I read an article earlier this year about math and faulty heuristic thinking. Student brains are still immature so they are prone to jumping to an answer without thinking the problem through. As dyslexics must be taught to not guess when reading, kids with maths issues need to be taught to not jump to conclusions without thinking the answer through. The problem remains that using faulty thinking is easier. Besides visualizing, your student could also draw a rods picture..

[geodob]

The mental number line, is actually something that is concieved of with Spacial thinking.

Which uses our left and right Parietal lobes, just behind our ears.

Where it uses them to locate opposing points.

With zero at the mid-point between them.

 

With this mid-point, it then use the Left to concieve of 'less than', and the Right to concieve of 'greater than'.

It also uses these sides to locate the past and the future.

It also uses these opposing points, to create and concieve of division within them.

Such as with minutes, hours, days, weeks, months, years.

As well as our base 10 number system.

 

The words and symbols that we use for numbers, or time or weight, etc?

Are just ways to represent these different increments.

But if we can't spacially concieve of these increments?

It is rather like someone his is born without vision, learning the order of colors on a color wheel.

[Kanin]

Thanks, you've given me a lot to mull over. It's evident that the number line is not something that comes naturally to him. I wish I could understand how he sees numbers!

 

Today we started bridging through 10. The problem was 7+4, and we were building the dot patterns with buttons.  "Ok, what goes with 7 to make 10?" I ask. "9?" he guesses. "Picture our Make 10 game!" I remind him. "Oh, 3!" he says instantly.

 

For one thing, he thought it was reasonable that 7+9 could be 10. Or, maybe, he just said the first number that occurred to him. But when visualizing, he got it! I like the idea of visualizing c-rods. 

 

Perhaps he can practice visualizing for getting better at reading, too.

[merry gardens]

It may help to "internalize" the number line if he first "externalizes" it. As the weather turns warmer, I suggest using a modified form of something like hopscotch with sidewalk chalk on the driveway. Draw 10 big boxes in a line, numbering the boxes from 1-10. Show him first, by hopping on one foot, from box to box, saying the numbers as you land on them. Turn around at ten, then count backwards. Have him try. If he can do in on the right leg, switch next to the left leg. If he can't hop on one foot, then have him jump with both feet. The point isn't so much to hop or jump, but to give him an activity that uses the number line with his whole body. Once he has the jumping down, the game could be played more an old-fashioned game of hopscotch with a stone as a marker thrown, with each of you taking turns and having to throw the marker in each box from 1-10. 

 

The sidewalk chalk game could be modified in all kinds of ways. You could practice skip counting by landing just on even. You could count by tens, (with boxes marked, 10, 20, 30....). If your driveway or sidewalk area is big enough, you could write the number line from 1-100+ and hop around counting. 

[Heathermomster]

http://www.math-salamanders.com/image-files/free-printable-math-sheets-counting-on-in-1s-to-10-1.gif

Have you tried something like this first?  My DD is a 1st grader and the number lines start simply.  Because of the student's age and grade, the temptation would be to jump to ordering higher numbers; however, I would resist that urge and stick to numbers that he has mastered.  

[wapiti]

You might also try a variety of number lines that are oriented differently in space.  For example, I visualize the number line much better vertically than horizontally (really, at a slight angle, with different colors for different numbers, and with a few curves in places getting up over a thousand, but we don't have to go there LOL).  Maybe make a vertical number line up the wall (like a thermometer, a line with hash marks with numbers to the right).  Consider including a good deal of negative numbers as well.

 

Better yet, have him help you make the number line.  Put a vertical strip of paper on the wall with lines, write a zero someplace, and have him write the numbers, using colors if he wants.

[fairfarmhand]

sidewalk chalk on the driveway for one. Then you can also use popsicle stick math.  I had my student create bundles of 10 popsicle sticks rubber banded together. So when we talked about 21, she had to grab 2 bundles and 1 individual stick. That was different from 12, which was ONE bundle and two plain sticks. (She could not understand why there wasn't a "two teen" and I never thought we'd get 12 and 21 straight)

 

This helped her understand place value and comparisons. She knew that each bundle was ten, and corresponded with the tens place in the written representation of numbers. For some reason this stuck with her better than rod type things because she knew that if she pulled the rubber band off of the bundle there would be ten separate sticks in there.

 

Also, we spread number cards all over the living room and had her hop from one to another as she counted. This also worked on the driveway with sidewalk chalk."stand on 7....now hop UP three numbers. This is like 7 plus 3. What number are you now? So 7 plus 3 more equals 10!"