Building Number Sense at Home

Yesterday my son came home from school counting by 2’s. He explained how they used a number line in class to start from 0 and then skip a number to land on 2, 4, 6, etc.

He then demonstrated his skip counting for me. William did pretty well counting by 2 up to 20, but it was clear he still needed some practice. Counting backward, he was saying eighty instead of eighteen and sixty instead of sixteen. After 12, he would say ’11’ almost every time. I decided to work with him at home because I know how important it is to help children develop number sense.

The Importance of Number Sense

In the article, Number Sense: the most important mathematical concept in 21st century K-12 education, Stanford Mathematician, Dr. Keith Devlin explains:

“Number sense is important because it encourages students to think flexibly and promotes confidence with numbers.”

“The fact is, students who lack a strong number sense have trouble developing the foundation needed for even simple arithmetic, let alone more complex mathematics.”

Knowing how important building number sense is for children (and even adults like me), I decided to focus on skip counting for the week.

How to Use a Number Line at Home

William asked for a number line to look at as he counted. A quick Google search revealed a fantastic website where you can create your own number lines.

Here it is: Interactive Number Line Generator

On this website, I was able to create a number line up to 30 so William could practice skip counting by 2. When he was ready, I could set the parameters higher so we could go to 40, 50, and even 60. I could also use it for counting by 5’s and 10’s (our next objectives).

Here is a video demonstration:

Using a Number Line for Older Children

When I find an activity for one child, I often look for ways to adapt it for my other child. In this case, I called my 8-year-old in to create his own number lines. He started with fractions. I let him play around with the number line generator.

He wanted to make a number line in tenths. When he typed this in and tried building one from 1 to 10 he realized how much space the tenths took up. All the numbers were scrunched together. I told him he could either make his range smaller or choose bigger intervals. Then, I left him to it. He experimented and found that even going up to five did not allow enough room to display the tenths.

Leaving him to explore, my eldest learned a lot about numbers. He eventually created a nicely spaced number line showing tenths that only went up to 2. Then, he tried a few other fraction number lines as well.

Counting Up the Stairs

Another great number sense building activity is to count up and down the stairs. Grabbing some pink construction paper, I folded it up into 8 equal parts and wrote the numbers 2 to 26 on each rectangle in intervals of 2. I cut them up and put one on each step. Now my 5-year-old counts by 2 each time he goes up the stairs. He counts backward from 26 whenever he goes down the stairs. By the end of the week, he will be a ‘counting by 2’s’ expert.

Here is a video demonstration of William counting up the stairs:

Counting Up the Stairs for Older Children

Once again, I brainstormed ways to use this technique with Ollie, my eldest. Since we were practicing our 6 times tables, I decided to let him count by 6’s up and down the stairs. Using yellow construction paper, to differentiate from his brother’s pink number cards, I wrote numbers in intervals of 6.

Now my eldest counts up and back by 6’s whenever he goes up and down the stairs.

As a surprise extension, Ollie told me he knew what 1/3 of 78 was using the number cards on the stairs. Puzzled, I asked how he did this. Since I had his yellow cards on one side of the stairs across from William’s pink ones, he realized that the pink ones were 1/3 of the yellow cards (the 6’s). On the top step, the yellow card was 78 and the pink one was 26. It was 1/3 of 78. My son’s connection blew me away. My boring adult mind would have never noticed the pattern between the two sets of cards.

Allowing children plenty of opportunities to build number sense at home will not only help them be more confident with numbers, but it may also encourage numerical flexibility that even goes beyond our adult assumptions.