(06) Integers 6: Negativity
Topic outline

Essential Questions
 Why did mathematicians invent negative numbers? How are negative numbers used in the real world?
 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".)

I will...
 Compare temperatures using a thermometer and contexts.
 Play Crash!
 Play Target! Number Tracks are the game board. Go to document (C) in the leftpanel 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.
 Apply my knowledge of counting and comparing to negative integers in Integer Notation Made Explicit
 Temperatures and Thermometers
 Banks and Balances
 [more coming soon.]
 Compare integers using number lines and inequalities
So I can...
 Extend my understanding of counting and comparing numbers to negative integers.
As assessed by...
[coming soon]

I will...
 Play Enclosure. Documents 3, 4, and 5 in the left panel are relevant.
 Play Auction 35!
 Play Target ... with bonuses. For the game board, use the Number Tracks. Click on "50 to 50" in the left panel.
 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 (under construction)
 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
 Represent my thinking from the last unit using equations. [More details coming soon.]
So I can...
 Demonstrate my understanding of adding and subtracting below zero through number lines, counters, and applications.
As assessed by...
[coming soon]

I will...
 Do leveled drills to mastery
 Translate applications and Enclosure moves into the above notation. [More coming soon.]
So I can...
 Simplify and interpret signs and brackets appropriately and in a way that makes sense to me.
As assessed by...
[coming soon]


I will...
 Investigate properties of mulitiplication and division with negative numbers.
 Do leveled integer drills.
 Level 5  Number Lines. Exercises and Solutions.
 Level 6  Fact Families
 Level 7: Determine Sign for × & ÷
So I can...
 State the properties of multiplication and division with negative integers.
 Create story problems and patterns to explain why the properties make sense.
As assessed by...
[coming soon]

I will...
 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.]
 Do Leveled Integer Drills
So I can...
 Explain in a variety of ways why the properties of multiplying and dividing involving zero make sense.
 Solve multiplication and division equations fluently.
As assessed by...
[coming soon]

I will...
 Do leveled integer drills.
 Level 11: All Operations, Simple
 Level 12: All Operations, Jumbled
 Mandatory for grade 10 students and above, optional for the rest
 Level 15: Systems, All Operations
 Practice and mark my own SSDD problem sets.
So I can...
 Fluently solve all 1step integer equations.
 Select appropriate operations and representations for 1step SSDD problem sets.
As assessed by...
[coming soon]
 Do leveled integer drills.

I will...
 Explore this Twitter thread on banning BEDMAS. [Details coming soon.]
 Go deep into leveled drills. Each level can be done as a beginner, intermediate, or advanced.
 Beginner: Do calculations in roughly the same order as the answer key.
 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.
 Advanced
 How early can you determine the sign of the final answer?
 How early can you reasonably estimate the final answer?
 When and where can we combine steps from the answer key? Does that or does that not break the acronym PEMDAS? Explain.
 The Drills themselves. You do NOT have to do all of the exercises provided. Level up as soon as you've reached mastery.
 JUMP Integer Concepts
 Do multistep SSDD sets. [Details coming soon.]
So I can...
 Solve multistep integer equations fluently.
 Select appropriate operations and representations of multistep SSDD problem sets.
As assessed by...
[coming soon]

I will...
[coming soon]
So I can...
 Succeed at rich problems and numeracy tasks by myself.
As assessed by...
[coming soon]

[coming soon]