Monday, July 29, 2019

Making Tens Matters; Play Shut the Box

Math Toys and Games for Young Learners

In this post I highlight toys, games and habits to develop young mathematicians.

Age 0-3

The concepts of cardinality (numbers have quantity) and ordinality (numbers have order) are not obvious. It is one thing to learn a string of words "one, two, three, four..." and another to understand that each of those words represents a quantity, or that the order of those quantities carries meaning. These concepts are reinforced through multiple representations of number and quantity. Have fun. Learn from mistakes. Don't punish children's partial understandings. Build upon them.


Count physical objects with your kids
    Ask "How Many?"
           "How do you know?"
           "How else do you know?"
Play with patterns
    Ask "What comes next?"
           "What else could come next?"

Physical Toys

Be careful of choking hazards.
Check out Frebel's Gifts as a progression of mathy toys to orient a child for future mathematics.

Digital Toys


Age 3-7

Making tens is silly; why wouldn't a young child to rebel against such a mundane task? Memorizing a 12x12 table of numbers is worse yet. Many games reinforce these foundational math facts without the pain of forced repetition.


Ask "How many?" "How far?" "How long?" "How much?"
       "What units?"
       "How do you know?"
       "How else do you know?"
       "What comes next?" 
       "What else could come next?"

Physical Toys

  • Shut the box
  • Board games (Sorry, Candyland, Monopoly, Careers, Katan)
  • Card games
  • Dominos
  • Backgammon
  • Chess
  • Go
  • Cribbage

Digital Toys

Number Sense
  • Dragonbox Numbers
  • Motion Math Zoom
  • Motion Math HD
  • Dragonbox Big Numbers
  • Wuzzit Trouble
Visual Spatial
  • .projekt

Age 8-12

Fractions are daunting. All of the symbols and numbers have new rules that are easily confused. Abstraction seems so irrelevant. How is the letter x going to help me in the real world? The symbol barrier can be overcome when learners are given time to mathematize a concrete experience and use symbols to represent mathematical features of their lived experience. Games like Slice Fractions and Dragonbox Algebra demonstrate this idea.


Cook together. Weigh and measure objects. Cut things in halves, thirds, quarters... Fold clothes together. Demonstrate that math is all around us, don't pressure children into seeing math as right and wrong; and the rules and symbols will come with time.

Digital Toys

  • Slice Fractions
  • Amplify Fractions
  • Refraction
Proportional Reasoning
  • Ratio Rancher
  • Dragonbox Algebra
  • Game over Gopher

In a previous post I discussed resources for high math achievers. That may be relevant for you.

For Teachers

What apps, websites, software programs, etc. do you use with students (or have them use independently) to improve their math skills? Why do you use these tools? What are their strengths and weaknesses?


  • Google – search in class with students to teach searching strategies
  • Wolfram Alpha – use to demonstrate function behavior
  • Wikipedia – search in class and discuss how to validate claims and track sources

Skill Practice

  • Open Middle - open questions provide more practice and engagement
  • Kahoot - gamified knowledge quizzes
  • Motion Math HD - Fractions
  • Motion Math Hungry Fish – Adding positive/negative Integers
  • Motion Math Zoom – Number Line and Place Value
  • Sumdog – basic skills + some metrics to demonstrate gains
  • ST Math – spatial reasoning
  • Khanacademy – Knowledge Graph with Demonstration and Practice
  • IXL - vast range of topics

Conceptual Understanding

  • Desmos - engaging classroom activities to promote mathematical discourse
  • - engaging critical thinking tasks, sequenced into courses
  • Geometer’s Sketchpad/Geogebra - visualize/simulate mathematics
  • NLVM - virtual manipulatives
  • Shodor - interactive activities

Top 3-4 concepts/skills that hold students back

Algebraic expressions: Integers, Fractions, Order of Operations

Functions: Multiple Representations, Relational Reasoning, Inverse Functions

Proportional Reasoning: Scale Factors, Ratios, Percentage

Statistical Reasoning: Randomness, Normal Distribution, Conditional Probability

For more product reviews and tips for raising kids in our digital world, check out Common Sense Media.

This post is just a scratch at the surface. Reach out or follow-up in the comments with more resources to share with parents and teachers.

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