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# Integer Chips

## by gabbymancilla on Feb 11, 2009

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## Integer ChipsPresentation Transcript

• Integer Representations History
• Integer Representations Taken together, these chips add to zero. Think of a red chip as positive one and a blue chip as negative one. Example +1 -1 Red Blue
• Represent a positive three:
• Representation There are many ways to represent any integer. But the representation below will be referred to as the Distinguished Representation.
• Representation This is an example of a Distinguished Representation. This is not an example of a Distinguished Representation.
• Representation Example Non Example What is the definition of a Distinguished Representation?
• Integer Representations
• Represent each of these numerals physically (with collections of red and blue markers). For each numeral make 3 different representations, including the distinguished representation.
• a) -4 b) +5
• c) 0 d) -1
• Addition of Integers To add 3 + 4. To add two numbers, model each number and take the union of the models. Then find the distinguished representation.
• Addition of Integers To add two numbers, model each number and take the union of the models. Then find the distinguished representation. To add 3 + -4. -1
• Addition Practice. Use the Set Model to find the sums.
• a) +3 + (+4)
• b) -3 + (-4)
• c) 3 + (-4)
• d) -4 + (5)
• Addition of integers 5 + -3 = ?? 2 + 3 + -3 = ?? How can we approach addition of integers by their symbols? For example: What are two numbers that add to 5? 2 + 0 = 2 2 2
• 5 + 5=
• 5 + 4 =
• 5 + 3 =
• 5 + 2 =
• 5 + 1 =
• 5 + 0 =
• 5 + -1 =
• 5 + -2=
• 5 + - 3=
• 5 + - 4=
• 5 + - 5=
• 5 + - 6=
• 5 + - 7=
• 5 + - 8=
10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3
• Subtraction of Integers
• Subtraction of Integers To subtract two numbers, model the first number and take-away the second number. Then find the distinguished representation. To subtract 5 - 3.
• Subtraction of Integers 2 To subtract two numbers, model the first number and take-away the second number. Then find the distinguished representation. To subtract 5 - 3.
• Subtraction of Integers To subtract two numbers, model the first number and take-away the second number. Then find the distinguished representation. Example: 5 - - 3. But there are no blue chips to take-away! What is another representation for 5?
• Subtraction of Integers 8 To subtract two numbers, model the first number and take-away the second number. Then find the distinguished representation. Example: 5 - -3.
• Subtraction of Integers
• Use the Take-away Model.
• a) +5 - (+4)
• b) -5 - (-4)
• c) +4 - (+5)
• d) +4 - (-5)
• e) -4 - (+5)
• f) -4 - (-5)
-1 1 9 -9 -1 1
• Subtraction of Integers
• 5 - -4 =
• 5 - -3=
• 5 - -2 =
• 5 - -1=
• 5 - 0 =
• 5 - 1 =
• 5 - 2 =
• 5 - 3=
• 5 - 4=
• 5 - 5=
• 5 - 6=
• 5 - 7=
• 5 - 8=
9 8 7 6 5 4 3 2 1 0 -1 -2 -3