Using the iPod Touch to Develop Number Sense

I have the distinct pleasure of working with Bate Middle School in Danville, Kentucky with their iPod Touch Literacy Program. They are piloting for the second semester the use of iPods with middle school students to increase opportunities in classroom instruction to have students reading/writing/speaking & listening about content.

read write speak triangle

I’ve been very interested in working with the teachers to develop instructional routines for use with students that take advantage of the multiple tools available to students with an iPod Touch. Students have access to so many different media, games, processing tools, and they have an equal opportunity to create information as they do to consume information.

In a post on this blog, I discussed using games to engage students to help them learn facts that might not otherwise be memorized or that need extra practice by students. The two cases I discussed are geography and multiplication tables, but this concept isn’t limited to those categories. It is limited by the teachers’ imagination and access to games students’ might find enjoyable. Luckily with the iPod Touch there are lots of math games that deal with number sense and number relations (computation), understanding of estimation, relationships between number forms, and applying strategies for computation to large/complex problems.

A second set of goals that we think are critical to success of mathematics students is to help students be aware of their skills and strategies, and to work at getting better at these skills. It is the ideas of meta-cognition and perseverance in problem solving that we know are now part of the new Common Core Academic Standards in mathematics that we want to begin to instill in students.

The question becomes how do we achieve these goals with the students?


  • is more than just practice/memorization,
  • has built in identification and monitoring of goals and progress,
  • is fun as well as educational,
  • addresses several skill sets during the course to meet the needs of multiple students, and
  • is developmental and provides students opportunities to address specific strategy development as well as reinforcement.

Here is my initial take on a Rational Number Improvement Plan:
The routine has three components: Monitoring and Goal Setting, Practice and Formative Assessment, and Strategy/Skill Development

Part 1: Monitoring and goal setting- Students:

  • Set goals based on their strengths/weaknesses and performance over the course of the year
  • Monitor their progress/scores using Google Forms and create broken line graph to represent their performance
  • As part of the Google Form students reflect on their performance on the game, identifying specific problems they thought were easy, had difficulty in answering, or were not sure about how to answer.

Part 2: Practice and formative assessment- I identified an initial five games on the iPod Touch to help students work on their rational number development:

  • Number line by Todd Bowden- ordering rational numbers
  • number line app

    (Students move the numbers into the correct order on the number line; if they move the numbers incorrectly the numbers turn red; indicating the need to reorder the number)

    number line app 2

  • Fraction Factory by Radford University, Games Lab– estimating values of fractions in decimal number form and on a number line
  • fraction factory app

    (Note that students move the fraction from the assembly line to the appropriate spot on the number line; in the second image you see that students are provided an accuracy score to reinforce their skill in estimating the value of the fraction)

    fraction factory app 2

  • Freddy Fraction by Radford University, Games Lab– finding equivalent number forms for  fractions, decimals, percentsfreddy fraction app(Players start in the upper left hand corner and have to identify the correct number that relates to the value in the upper right hand corner of the game; in this case the number 0.70 is related to 7/10)
  • Pearl Diver by New Mexico State University, Learning Games Lab- Equality and order on the number line, Number line propertiespearl diver app(In this game players are asked to identify the correct value for the integer given and dive to get the pearl; if successful without being electrocuted by the eel the diver is given another number to dive for until four pearls have been collected moving on to a new level)pearl diver app 2
  • Alien Equation by funnerlabs– number relationships that form computation equations

    alien equation

    (Players slide numbers and operators up/down and left/right to form relationships that make equations; when a correct equation is formed it disappears providing new numbers for the player to turn into new relationships; the game progresses in difficulty and operators as it progresses)

Part 3: Strategy/skill development- Students identify one or two problems they struggled with during the day’s practice/game session and create a model of the problem that utilizes multiple representations and/or models a strategy that students could have brought to bear on that problem. This allows students to learn to identify problems that they realize are harder for them, have practice with specific strategies that help them to solve related problems, learn to apply strategies to a variety of problem types, and uses multiple representations to deepen student understanding of rational number.

skill development 1

(This is an example of what a student analysis of one problem might look like; in this case the student is learning to estimate values of fractions using an upper and lower benchark; additionally the student is using multiple models for representing the value)

skill development 2(In this example a student is using a chunking strategy or distributive property to learn to turn multiplication facts into easier problems, using a verbal description, a model, and a symbolic representation. It is likely that the student will need some support, but in future analysis the student will return to this strategy until they feel comfortable with doing it on their own during the game.)

In a future post, I will describe what  typical week of classroom activities entails.

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