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Dear Family,
The next unit in your child's course of study in mathematics class this year is Accentuate the Negative. This unit will introduce students to positive and negative numbers (integers). Your child will work on problems involving many contexts and learn how to compare integers; to add, subtract, multiply, and divide integers; and to use integers to solve problems. The variety of settings will help your child understand positive and negative integers. The class will begin by looking at a game (similar to the game show Jeopardy!®) in which some scores are negative and others are positive. They will work with temperature readings, both above and below 0, on a thermometer. They will also look at business-type situations that speak of being "in the red" or "in the black" and use colored chips to model operations with integers.
Here are some strategies for helping your child work with the ideas in this unit:
  • Ask your child to describe some real-world situations in which integers are used. You can help by noting the daily temperature or talking about changes in temperature during the day If your child talks to you about being "in the red" or "in the black," you may relate this idea to earnings or savings he or she has.
  • Look at your child's mathematics notebook. You may want to read some of the explanations that have been written and, if they aren't clear, talk with your child about why you think they may need more explanation.
  • Encourage your child's efforts in completing all homework assignments. Look over your child's work, and help your child make sure all questions have been answered and that all explanations are clear.
As always, if you have any questions or concerns about this unit or your child's progress in the class, please feel free to call. We are interested in your child's success in mathematics and want to ensure that this year's mathematics experiences are enjoyable.
Sincerely,

Mr. John Hampshire
Topics
Topics:
  • Develop strategies for adding, subtracting, multiplying, and dividing integers
  • Compare and order integers
  • Represent integers on a number line
  • Model situations with integers
  • Use integers to solve problems
  • Explore the use of integersin Real world applications
  • Understand opposites as in 1 and -1
  • Graph in all four quadrants
  • Use of graphing calculator
  • Graph linear equations
  • Observe effects of opposite coefficients and adding constants to y=ax
  • Answer questions using equations, tables and graphs
Big Ideas
Big Ideas:
  • defining and developing understanding of negative integers
  • exploring relationships between positive and negative integers (e.g., interpreting positive integers as a gaim and negative integers as a loss
  • developing understanding of arithemetic operations with positive and negative integers
  • extending the coordinate grid to include negative coordinates
Mathematics
Mathematics:
Mathematical and Problem-Solving Goals
Accentuate the Negative was created to help students:
  • Develop strategies for adding, subtracting, multiplying, and dividing integers
  • Determine whether one integer is greater than, less than, or equal to another integer
  • Represent integers on a number line
  • Model situations with integers
  • Use integers to solve problems
  • Explore the use of integers in real-world applications
  • Compare integers using the symbols =, >, and <
  • Understand that an integer and its inverse are called opposites
  • Graph in four quadrants
  • Set up a coordinate grid on a graphing calculator by naming the scale and maximum and minimum values of x and y
  • Graph linear equations using a graphing calculator
  • Informally observe the effects of opposite coefficients and adding a constant to y = ax
  • Answer questions using equations, tables, and graphs
The overall goal of the Connected Mathematics curriculum is to help students develop sound mathematical habits. Through their work in this and other number units, students learn important questions to ask themselves about any situation that can be represented and modeled mathematically, such as: What situations in daily life can be represented by positive or negative numbers? How can a meaning be found for operations on negative numbers? Where can such operations be modeled? Is it possible to use "less than" or "greater than" concepts with integers? How are the integers different from ordinary whole numbers? How are these two sets of numbers alike? Can the coordinate grid be expanded to include negative numbers? Is it possible to make graphs on such grids using a graphing calculator? What patterns will occur in these graphs? How can these patterns be used to find and understand other patterns?
Tips
Tips:
  • Be sure to read the Mathematical Highlights on page 4. They give you a preview of the activities and problems.
  • As you go through the unit, be thinking about your Unit Project on page 5.
  • I am looking for student suggestions as Tips for this page. If you have any that I can use, there is extra credit available.
  • Get Pages
Games
Games:
Adding Real Numbers - Explorelearning.com
Interactive "Gizmo" illustrating addition of integers on a number line. Comes with exploration guide and assessment questions. By subscription, but has Free 30 day trial account.
Color Chips Addition
The user drags positive/negative chips to the working area, then combines them in pairs to see the sum.
Color Chips Subtraction
Drag positive/negative chips and zero pairs into working area as instructed, then subtract.
Integers: Operations with Signed Numbers
Clear and cute presentations of the rules for integer operations, including The Party in the Mathland for determining the sign of multiplication/division result. Has a link to practice exercises with instant feedback.
Resources
Additional Resources: