The Number System

Apply and extend previous understandings of numbers to the system of rational numbers.

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Resource | Resource Type Grade Level | Rating |
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This interactive Java applet game has a user adding positive and negative integers to arrive at a sum of zero. Seven overlapping circles form a ring similar to a Venn diagram. Five blue numbers are in position when the game begins. The remaining nine numbers (from -6 through 7) must be placed in the empty spaces to produce a sum of zero in each circle. There is a unique solution for each puzzle. Instructions for users and teacher information are available through links at the top of the page. | Activity, Interactive Media Grade Level: 5, 6+ | |

This interactive Java applet helps the learner conceptualize the addition of signed numbers. The user clicks and drags red and black colored chips to a circle to represent a problem and then simplifies by placing a red negative chip on top of a positive black chip. The student actually sees the opposite pair disappear. Users may practice problems generated by the computer, themselves or free play with the chips. There are separate tabs to access information for the learner, the instructor and to seek help. | Activity, Interactive Media Grade Level: 5, 6+ | |

This virtual manipulative is designed to help conceptualize the subtraction of integers. Positive integers are black chips and negative integers are red chips. Dragging a single black on top of a red chip together makes the pair disappear (visually emphasizing that the sum is 0). Users may practice problems generated by the computer, themselves or free play with the chips. There are separate tabs to access information for the user, the teacher and to seek help with instructions. | Activity, Interactive Media Grade Level: 5, 6+ | |

This open-ended interactive Flash applet can be used in many ways to develop numeracy concepts and skills. It provides three highlight colors, a hide or reveal feature, and the ability to vary the start number and the increment size. | Activity, Interactive Media Grade Level: K, 1, 2, 3, 4, 5, 6+ | |

This lesson plan based on a Cyberchase activity, first addresses a common misconception: starting measurement from 1 instead of 0. Then, it introduces negative numbers by extending a number line beyond 0 in the negative (left) direction. It is motivated by the Cyber Squad’s mission to find the captured Cyberchase Council on a particular floor of a tall building as seen in two quicktime videos: “Importance of the Origin" and "Inventing Negative Numbers" (each are cataloged separately). In addition to the learning activity, other support materials are included: handouts, assessments and answer keys. | Lesson Plans, Video Grade Level: 4, 5, 6+ | |

In this quick time video segment from Cyberchase, viewers learn about extending a vertical number line below zero as they watch the CyberSquad rescue the Cyberspace Council, which is being held captive by Hacker in a tall building. This video is also featured in the lesson plan: "Introducing Negative Numbers" (cataloged separately). Teaching Tips and a transcript are included. | Video Grade Level: 4, 5, 6+ | |

The authors of this website have identified 8 common misconceptions that lead to errors in mathematics (and promise to add more as time permits). Topics include: Rounding Numbers, Multiplication can Increase or Decrease a Number, Multiplying Decimals, Decimals and their Equivalent Fractions, Dividing Whole Numbers by Fractions, Adding with Negative Numbers, Calculations with Negative Numbers, and Calculations with Hundreds and Thousands. Each misconception is described in a pdf document which explains how the misconception arises, the rationale for the correct concept, and exercises aimed at reinforcing the correction. | Problem Set, Tutorial Grade Level: 4, 5, 6+ | |

In this activity from the Mixing in Math collection, learners rate something on a scale from -2 to 2. The leader starts by choosing something the group will rate, such as a book, the weather or how the day is going so far and makes sure to explain to the group the scale, including what negative numbers and 0 mean. Then, everyone takes turns giving their ratings and explaining their thinking. Modifications and extensions are included at the bottom of this activity. Available as a web page and downloadable pdf. | Activity Grade Level: 3, 4, 5, 6+ | |

This interactive Java applet allows users to visualize and practice multiplying integers using an area representation. The user drags sliders to adjust the two factors and then observes the resulting changes in the rectangular array. The color of the array shows the sign of the product. Instructions for users and teacher information are available through links at the top of the page. | Activity, Interactive Media Grade Level: 5, 6+ | |

This Technology Problem of the Week (tPoW) challenges students to add and subtract quantities of small temperature changes near freezing, and model those positive and negative changes with red (hot) and blue (cold) chips, respectively. It links to the Java applet "Color Chips." Solve and explain your solution; download hints and answer checks. Free registration is required. | Model, Problem Set Grade Level: 3, 4, 5, 6+ |