In this post earlier this week, we looked at a math assignment that has gone viral. It’s purpose was to assess children’s ability to subtract using a number line. I promised I’d give some ideas for fun, hands-on ways you can begin exploring number lines with your child.
For many adults, working on a number line to solve a problem feels cumbersome. It’s easy to wonder why they are being used in classrooms today so much. In short, the number line is an important tool that we use to help students develop a strong understanding of numbers (number sense) and relationship between numbers. Using a number line helps students form a visual representation of numbers and their relationships between one another.
Number lines (or some interpretation of a “number line”) are relevant through all grades – starting as young as preschool and certainly through 5th grade. They just evolve as children’s understanding of math concepts does!
There are lots of ways that you can start playing with number lines with your child at home. I say “play” intentionally because this should be fun! When your child hears that you want to play some number games with them they are sure to be more engaged and involved than if this is just more math work. If your child doesn’t seem to be interested, that’s okay. Try again another time.
Preschool through Early Elementary Number Line Play
When my oldest son (Asher) was born, I bought these Eric Carle Number Flash Cards to hang in his room. I loved that they were bright, colorful and had pictures of lots of animals. I loved that they would be a great tool for counting and we do play with them often!
At just 3 years old, Asher and I play with (very rudimentary) number lines a lot. We spend a lot of time looking at the number cards and talking about numbers – how a number like the number six can be represented in different ways. It can be represented by the word six, the number 6, six dots, six animal pictures and more.
I will give Asher a stack of just the cards with dots on them and we will work together to put them in number order. We match the dots with the actual physical number cards. We count the animals on the cards and put them above the dots and numbers on our “number line”.
In order to begin exposing him to math vocabulary, I ask Ash to stand up and run to the card that has the most animals. Then to the least. We practice very early addition and subtraction skills with Asher still running and playing! I ask Ash to run to and stand on the card with 4 dots for example, then say, “Can you jump to the card that has one more dot on it?” “Now jump to the card that has two less dots.”
Sometimes we play this game for 2 minutes, while sometimes Ash is really interested and engaged with numbers and we play for 20 minutes or more. Sometimes he wants to focus on the animals more and our math game turns into pretend play with animals. I always follow Asher’s lead because above all I want him to love math and love learning. We go through phases where he is really interested in numbers and counting and we do games like these daily. And then there are times where he is focused on something else and we talk about numbers very little for weeks. I continue to try to expose him to math games but never pressure him to participate if he’s just not interested.
As your child enters elementary school, your number line play can become more sophisticated. However, it should still feel like fun, be playful, and be driven by their needs and interests.
Yarn Number Line
Students in the early elementary grades will begin using more concrete representations of number lines.
With a child in these grades, you may put a long string on the floor to represent a number line. You can make a stack of index cards (or cut up pieces of paper) with pictures or numbers on them that are appropriate for their current math work. Have your child work toward putting the pictures or numbers in order on your yarn number line.
If you have more than one child, you may make a yarn line for each child and give each child their own stack of cards and have them race. Your kindergartener may have a stack of cards that you draw with different numbers of stars on them, while your 2nd grader may have numbers in the hundreds, and your 5th grader may have fractions and decimals.
To change this game up a little bit, instead of having your child put the cards on the line, you may do it for your child, but put one or two cards in the wrong place. Ask your child to help you find your mistakes and fix the line.
The most valuable piece of these Yarn Number Line games will be the conversations that you have with your child. Resist the urge to give your child directions, and instead ask a lot of questions. If you notice your child put a card in the wrong place on the line, stay silent and give them the space to discover this on their own. Ask your child a lot of questions “Why did you choose to put the number there?” so that they learn to articulate their mathematical thinking.
Paper Number Line
You can also bring number lines to life using just printer paper. Get 5 or 6 pieces of paper and write a number on each one. (Again, an appropriate number for your child’s needs in math.)
For your kindergartener, you may put 0, 5, and 10 on the wall.
For your 1st grader, you may put: 1, 5, 10, 15, 20.
For your 2nd grader, you may put: 0, 100, 200, 300.
For your 3rd grader, you may put: 0, 500, 1,000, 1,500, 2,000.
For your 4th grader, you may put: 0, 10,000, 20,000, 30,000, 40,000, 50,000.
For your 5th grader, you may put: 0, ¼, ½, ¾, 1, 1 ¼.
Have your child help you tape these numbers on a long wall, in order. (You could also tape them on a wall outside, put them in the grass, or write them in sidewalk chalk on a patio or sidewalk!)
After you’ve worked together to tape up the numbers in order, call numbers (not listed on the cards) and have your child run to the spot where they would put that number on their number line. For example, using the 5th grade number choices above, you could call out three-eighths. Your child should run to stand between ¼ and ½. You could also call out six-eighths to see if your child knows this fraction is equivalent to ¾. You could also call out decimals to show your child the relationship between fractions and decimals.
All of these games can be played using different numbers, making the number sets more basic if your child seems frustrated, and more challenging if they need more of a challenge. Remember to have fun and always follow your child's lead!
When you come across challenging "number line" homework problems at home, try turning the problem into one of these games. You may find that the hands-on, kinesthetic nature of these games will translate to a better mathematical understanding by your child of the concepts being covered in their homework assignment. Let me know how it goes!