Number Sense

I have taught math to elementary-aged students for more than 20 years. I have seen math methods come and go, watched students make progress and get stuck in the muck, and tried many "new" things... and I've learned some things. Things that are very much affecting how I teach Joy.

One of the things I know is that kids who just get numbers do much better in math. But how do I teach "getting numbers"?? Because Joy is at an early stage of development in math, and because she has no peers with whom to compare herself (which she would definitely DO if she had them), I can teach her in a way to develop that elusive number sense. So math in Stealth Kindergarten isn't so much about adding and subtracting and comparing numbers, as it is about understanding numbers.

For example, taking the number rolled on two dice, in this case: 56, and making the visual picture of 56 using Base Ten Blocks. These are commercially-made cubes that are in ones, tens, hundreds, and thousands. Fifty-six looks like 5 "longs" (bars of 10 cubes) and 6 "little cubes" (single small cubes). Then Joy counts them, "10, 20, 30, 40, 50, 51, 52, 53, 54, 55, 56." This is not easy! Transitioning from counting by 10s to counting by 1s without losing your place is a sophisticated skill. I have known 4th and 5th graders who could not model numbers in this way. Joy has some difficulty with the transitions sometimes, but she is definitely improving her true understanding of what the numbers mean.

Base Ten Blocks are a wonderful tool, and I use them quite often with Joy and with students I tutor in math. They can be used to model numbers through 1,999 and decimals through the thousandths. They are only one tool, though, and one of the other tools I frequently use costs nothing, so I really like it, too!

Egg cartons are a great way to make ten-frames! A ten-frame is simply a rectangle with two rows of five spaces, equaling 10, of course. We have used ten-frames to learn to identify numbers of objects up to ten.

For these ten-frames, I cut off the lid and one set of the egg-holes so there are ten holes in two rows of five. I use small glass beads that are sold for use in plant vases. You could use anything from buttons to pennies to marbles to fill the ten-frames. You can see that we have quite a number of these egg-carton ten-frames!

I have collected egg cartons for about a year now, and we have more than 20 of them. I bundled up a stack of ten to make one "hundred." Now Joy can make numbers up to 199! We sometimes roll the dice to select a number. Sometimes, I write a number on a whiteboard for Joy to create, and sometimes I model a number and she writes it down. Understanding that 38 is much smaller than 83 is an important goal of these kinds of activities. Place value is an essential skill to understanding how numbers work.

 

Another way to model numbers is with visual patterns. A ten-frame is one visual pattern for kids to use. Dice arrange the numbers 1-6 in different ways that are good to recognize. These cards are an extension on some visual patterns.  We are playing "War" with them in this picture, comparing the number of dots on each card.

After becoming familiar with many different visual models of numbers, I had Joy make her own set of ladybug cards, putting various visual models on ladybugs. To the right, she put a dice-shaped 6, plus one. Below, she used the 10-frame model to make the same 7. Joy had a great time creating ladybugs with various dot patterns. We use them to play games and she loves it!

We've even found visual models for numbers in making cookies!!!!
Joy recognized this "nine" right away.

These pipe cleaner bracelets are also part of Joy's number sense instruction. Each one has a different number of buttons on it and is labeled with that number. The idea behind these is that you can divide the buttons into two groups, modeling part-part-whole.

For example, the 8 bracelet identifies the whole (8). In this picture, the two parts are 4 and 4. So this model shows the following:  4+4=8 and 8-4=4. We use these frequently to tell stories and model the number facts.

This 10 bracelet models 7+3=10, 3+7=10, 10-3=7 and 10-7=3. We might tell a story like this: There were 10 children at the playground; three went home. How many children are left at the park? Joy tells stories for me, and I tell stories for her. This is important because it helps her understand the stories better than simply answering "story problems."

We just recently added triangular flash cards to our number sense instruction. These are cards that show the whole number family, not just a simple problem. I absolutely believe that children need to develop automaticity with basic math facts, but this will be far more meaningful if they have a strong number sense before they try to memorize. These cards are a great transition; under Joy's hand is the "whole" (5). Each card shows "part-part-whole," and the "whole" is red. So you can use this card to model 5+0=5, 0+5=5, 5-0=5, or 5-5=0. Using these cards will help Joy move toward numerical representations of the number sense she is developing.


A good resource if you are looking to work on number sense with your little one is Building Number Sense by Catherine Jones Kuhns. It has great activities for K-1 students!