(06) Integers 6: Negativity

Topic outline

• Course Outline

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  Essential Questions

  1. Why did mathematicians invent negative numbers? How are negative numbers used in the real world?
  2. How is arithmetic with negative numbers similar to arithmetic with positive numbers? How is it different?

   

  Resources

  • Negative Integers Diagnostic
  • Enclosure. Documents 3, 4, and 5 in the left panel are relevant.
  • Number Lines: -50 to 50 &-100 to 0
  • Number Tracks (click on the files that start with "neg" on the left panel, then click "Recompile".)
  • Number Hives

• Lesson 1: Count & Compare

  I will...

  1. Compare temperatures using a thermometer and contexts.
  2. Play Crash!
     1. Crash Game Board from -30 to 30
     2. Crash Game Board from -60 to 30
  3. Play Target! Number Tracks are the game board. Go to document (C) in the left-panel then press the recompile button. To make the board in a big line, you'll need to print the papers and cut them into strip with scissors. You will need a deck of cards and two tokens of different colors.
  4. Apply my knowledge of counting and comparing to negative integers in Integer Notation Made Explicit
     
     1. Temperatures and Thermometers
     2. Banks and Balances
     3. [more coming soon.]
  5. Compare integers using number lines and inequalities
      in JUMP Compare Integers

   

  So I can...

  1. Extend my understanding of counting and comparing numbers to negative integers.

   

  As assessed by...

  [coming soon]

• Lesson 2: Add & Subtract

  I will...

  1. Play
     1. Enclosure. Documents 3, 4, and 5 in the left panel are relevant.
     2. The Number Track game. Game board (click on "-50 to 50" in the left panel then press "recompile").  Rules.
  2. Play Auction 35!
     1. Auction 35 Card Values
     2. Auction 35 Printout with Negative Integers
     3. Auction Variations
  3. Do leveled integers drills
     • Level 1a: Add & Subtract, Describe the Vector
     • Level 1b: Add & Subtract, Draw the Vector to Answer
     • Level 1c: Add & Subtract, Draw the Vector to Answer, Jumbled
     • Level 2a: Signs Only
     • Level 2b: Picture Mentally, Magnitudes within 20
     • Level 2c: Picture Mentally, Magnitudes within 20 - Jumbled
     • Level 2d: Picture Mentally, Varied Magnitudes
     • JUMP Gains and Losses
     • 
  4. Represent my thinking from the last unit using equations. [More details coming soon.]

   

  So I can...

  1. Demonstrate my understanding of adding and subtracting below zero through number lines, counters, and applications.

   

  As assessed by...

  [coming soon]

• Lesson 3: Signs & Brackets

  I will...

  1. Do leveled drills to mastery
     1. JUMP Signs and Operations
     2. Level 3a: Operation & Sign Interpretation
     3. Level 3b: Operation, Sign, & Magnitude Interpretation
     4. Level 3c: Simplifying it All
     5. Level 4a: Simplify then Calculate
     6. Level 4b: Add & Subtract, Jumbled
     7. Add & Subtract Integers with Bigger Magnitudes (link might not be working)
  2. Translate applications and Enclosure moves into the above notation. [More coming soon.]

   

  So I can...

  1. Simplify and interpret signs and brackets appropriately and in a way that makes sense to me.

   

  As assessed by...

  [coming soon]

• Checkpoint 1

• Lesson 4: Properties of Multiplication & Division

  I will...

  1. Investigate properties of mulitiplication and division with negative numbers.
     1. Understanding Multiplication & Division with Negatives
     2. JUMP Mult & Div Properties
  2. Do leveled integer drills.
     1. Level 5 - Number Lines. Exercises and Solutions.
     2. Level 6 - Fact Families
        
        • Exercises
        • Solutions
     3. Level 7: Determine Sign for × & ÷

   

  So I can...

  1. State the properties of multiplication and division with negative integers.
  2. Create story problems and patterns to explain why the properties make sense.

   

  As assessed by...

  [coming soon]

• Lesson 5: Fluency & Zero

  I will...

  1. Represent multiplication and division involving zero in a variety of ways, including: stories, pictures and diagrams, fact families, equations, fractions, and words. [More details coming soon.]
  2. Do Leveled Integer Drills
     1. Level 8: Simple × & ÷
     2. Level 9: Jumbled × & ÷
     3. Factor Pairs

   

  So I can...

  1. Explain in a variety of ways why the properties of multiplying and dividing involving zero make sense.
  2. Solve multiplication and division equations fluently. 

   

  As assessed by...

  [coming soon]

• Lesson 6: All Operations

  I will...

  1. Do leveled integer drills.
     1. Level 10: All Operations, Simple
     2. Level 11: All Operations, Jumbled
     3. Mandatory for grade 10 students and above, optional for the rest
        1. Level 12a: Systems, × & +, Small Magnitudes
        2. Level 12b: Systems, × & +, All Magnitudes
        3. Level 13: Systems, ÷ & -
        4. Level 14: Systems, All Operations
  2. Practice and mark my own SSDD problem sets. 

   

  So I can...

  1. Fluently solve all 1-step integer equations.
  2. Select appropriate operations and representations for 1-step SSDD problem sets.

   

  As assessed by...

  [coming soon]

• Lesson 7: Grouping & Calculating

  I will...

  1. Explore this Twitter thread on banning BEDMAS. [Details coming soon.]
  2. Go deep into leveled drills. Each level can be done as a beginner, intermediate, or advanced. 
     1. Beginner: Do calculations in roughly the same order as the answer key.
     2. Intermediate: Ensure you can also rearrange the given expressions into equivalent expressions. Check your work with a calculator. Recommendation: A fancy physical scientific calculator or the Desmos Scientific Calculator.
     3. Advanced
        1. How early can you determine the sign of the final answer?
        2. How early can you reasonably estimate the final answer?
        3. When and where can we combine steps from the answer key? Does that or does that not break the acronym PEMDAS? Explain.
     4. The Drills themselves. You do NOT have to do all of the exercises provided. Level up as soon as you've reached mastery.
        1. 2-step equation drills
        2. 3-step equation drills
        3. 4-step equation drills
        4. 5-step equation drills
        5. 6-step equation drills
  3. JUMP Integer Concepts
  4. Do multi-step SSDD sets. [Details coming soon.]

   

  So I can...

  1. Solve multi-step integer equations fluently.
  2. Select appropriate operations and representations of multi-step SSDD problem sets.

   

  As assessed by...

  [coming soon]

• Lesson 8: Rich Tasks

  I will...

  [coming soon]

   

  So I can...

  1. Succeed at rich problems and numeracy tasks by myself.

   

  As assessed by...

  [coming soon]

• Exit Assessment

  [coming soon]