This post is part of the Math Games for Young Mathematicians series! Check out these previous posts for more on the following topics:
In this post, I will dive into number path games.
The math behind number path games deals with one of the most fascinating aspects of how children develop math concepts. If you’ve been looking for the perfect fun fact to tell your family over Thanksgiving, look no further.
The number line is the foundation of number path games. When you think of a number line, you probably think of something like this:
However, research shows that children (and humans for that matter) start with a number line that looks like this:
See anything odd about the second number line?
The difference between the above number lines is that the first one is a linear number line and the second is a logarithmic number line.
At the most basic level, the difference has to do with the distance between each number. On the linear number line, the distance between each number is the same. On the logarithmic number line, the distance between each number is different.
What we’re dealing with here is the concept of magnitude, which has two parts. First is the understanding that the order of numbers relates to the size of numbers. For example, 4 is more than 2 because it comes after 2 in the counting sequence and on the number line. Second is the understanding that the distance between each number is the same. For example, 5 is one more than 4 just like 2 is one more than 1.
The number line is an important mental tool that helps structure children’s understanding of number. The transition from a logarithmic to a linear number line is an essential step in early math learning.
How to Play
Number path games are simple: players move a token across a line of numbered squares. Players take turns rolling a die or using a spinner to determine how many spaces they get to move each turn. The first player to get to the end of the number path wins.
Connecting the Math
Number path games are great for developing a linear mental number line and the concepts of magnitude. As children move across the board, each space takes them one space away from the start. Moving one space at a time enforces the idea that each number gets bigger by one. Moving away from the start also emphasizes that numbers come before and after each other and that numbers later in the game are greater than numbers earlier in the game.
Studies by Romani and Siegler (2008) have shown that number path games are highly effective in building children’s mental number line. Interestingly, they found that games that used colored squares without numbers did not have the same positive impact on children’s understanding of magnitude.
Number path games also help children develop one-to-correspondence as they count one square per number, and they encourage numeral recognition as children recognize the space they’re token lands on.
Bring out the Math
To get the most out of playing number path games, set the following ground rules:
- After rolling the die, count and clap the number you roll: 3, one (clap), two (clap) , three (clap)
- When moving a token, touch each space and count out loud, one number per space.
Extend the math learning by asking questions:
- How far away are you from the end?
- Who is the closest to the end?
Once your child can confidently play with the above ground rules in place, build in the strategy of counting on. Instead of starting to count from one, start counting from the number of the space you are on. For example, if you are on space 3 and you roll a three, you would count on from three- “four, five, six” instead of “one, two, three.”
Note that this skill is challenging and will most likely require patience and practice. What a great opportunity to build perseverance and model how to learn from mistakes!
- Create your number path board and dice or spinner! Use the links in the section below to find the resources you need. Involve your child in the creation process for extra investment and fun.
- Commit to playing your number path game for 15 minutes at least once per week.
- Share the number path board you make with the Counting Fingers and Toes community! Email it to me or post it in Instagram and tag me (@countingfingersandtoes), and I’ll add it to this post.
- Questions about how to make or play the game? Email me at firstname.lastname@example.org.
How to Make a Number Path Game
One of the great things about number path games is that you can make the materials for the game yourself.
Board: Start with numbers 1-5 and work your way up to numbers 1-20. If you choose to make your own, they key is for each number to be equally spaced apart.
- Use this template to make your own. Have your child choose a theme and decorate it!
- Use these printable version from Young Mathematicians. You can combine them to create longer boards as your child learns more numbers: 1-10, 11-20, 21-30, 31-40, and 41-50.
- Make your own with sticky notes, notecards, or pieces of paper.
- Make it life size. Use some chalk to create a board on your sidewalk or a dry erase marker to make a board on the kitchen tile.
Die: Use a die or spinner with numbers 1-3. This increases game play because it prevents a player from moving halfway across the board with just one roll. If possible, use the dot representations of 1-3 to encourage subitizing (recognizing the amount without counting each dot).
- Make your own dice. Use a blank six-sided cube and mark the sides with numbers 1-3 twice.
- Use an online die simulator.
- Make your own spinner.
- Use an online spinner simulator. I created this one by repeating the number 1-3.
If you’re looking for an option you can buy, Chutes and Ladders is an excellent option and a classic.
NAEYC and NCTM. 2010) Early Childhood Mathematics: Promoting Good Beginnings. NAEYC/NTCTM Joint Position Statement.
Number Path Games. Young Mathematicians. Retrieved from https://youngmathematicians.edc.org/jumping-on-the-lily-pads/.
Reed, K. and Young, J. (2018). Math Games to Excite Young Minds. Development and Research in Early Math Education. Retrieved from https://dreme.stanford.edu/news/math-games-excite-young-minds.
Reed, K. and Young, J. (2017). Play Games, Learn Math! Number Path Games. Teaching Young Children 11(1). Retrieved from https://www.naeyc.org/resources/pubs/tyc/apr2019/number-path-games.
Romani, G. and Siegler, R. (2008) Playing linear numerical board games promotes low-income children’s numerical development. Developmental Science. Retrieved from this website.