(02) Integers 2: Add & Subtract within 100
Topic outline

In this course, students will master every aspect of 1step addition and subtraction of whole numbers from 0 to 100, from meaning to mental math, from pictures and manipulatives to equations and word problems. Fingercounting will be eradicated, confidence will soar, and a very strong foundation will be laid for multiplication, division, and all future math.
Essential Questions
 How do addition and subtraction improve upon counting?
 How do addition and subtraction help us solve problems?
 How are addition and subtraction related?
 How can we use concrete objects, pictures, words, and symbols to represent our thinking? What are the pros and cons of each?
 What is the purpose of automatic recall? Which facts (equations) are worth learning to this level of mastery and which are not?
Whole Course Resources
Games & Puzzles

 TicTacToe Sums
 Fifteen  player vs computer
 Fifteen  player vs player. Materials: Ace through 9 of one suit or any other indicators of 1 through 9.
 Enclosure (Click level 1a, 1b, or 2 on the left panel, then press the green "Recompile" button.)
 Black Hole
 Number Track Game (Click on "0_to_100" on the left panel then recompile.)
 Kenken Puzzles
 Knock Out
 Games for Young Minds explanation
 YouTube video
 Game board printout [coming soon]
Content Sequence
1.11.3 You will learn about the basic Problems and Models of addition and subtraction. You'll learn how to express your ideas in terms of objects, number tracks and bars ten frames, base ten blocks, math words, and math symbols.
2.12.6 You will sharpen your mental addition including automatic recall for all facts within 20 and fluency for all addition within 100.
3.13.3 You will first relate subtraction to addition. You will sharpen your mental subtraction including automatic recall for all facts within 20 and fluency for all subtraction within 100.
4.14.2 You will put it all together, learning to represent and solve all types of problems and equations within 100.

I will...
 Master discrete models of parts, wholes, and changes
 Master linear models of parts, wholes, and changes
 Number Tracks
 From Counters to Bar Models
 Linear Representations of Parts, Wholes, and Changes within 20
 Parts & Wholes with Xs and Os
 Play games
 Auction 35. Best played with 35 counters and a deck of cards, but if online, use the Auction 35 Gameboard Printout.
 Nim
 Crash! [aka Pig]. Can be played with pencil and paper, but beginners should use the Crash gameboard.
 Jack and Jill's Pails [source: Mindtrap's Geometrical Riddles]
 Solve reallife problems with addition and subtraction. [Coming soon.]
So I can...
 Solve all types of parts, wholes, and change word problems.
 Represent my thinking with manipulatives (linear and discrete), words, pictures, and counting.
As assessed now by...
 My ability to create, represent, and solve a variety of practical problems. Detailed instructions & rubric.
 (Mandatory for adult learners, optional for younger learners) Parse every addition and subtraction situation using mathematical vocabulary.
As assessed in the future by...
 My ability to build on this knowledge in Lesson 2 (Equations and Calculation) and Lesson 3 (comparisons).
 My ability to instantly recognize whether to add, subtract, or do neither in the future.

I will...
 Practice on this comparison template.
 [more coming soon]
So I can...
Compare any whole numbers between 0 and 100 using manipulatives, discrete or linear pictures, words, and counting.
As assessed by...
 [coming soon]

I will...
 [coming soon]
So I can...
 Do everything from Lesson 3 and...
 Recognize and explain when to add versus when to subtract. I can generate examples to aid my explanations.
I will...
 Practice solving problems, modeling them with bars, and describing them with fact families.

 Fact Families [under construction]
 Add & Subtract Fact Families & Bar Diagrams

 Do equation drills for fact families.
As assessed by...
 [coming soon]

I will...
 Play KenKen. Focus on the + and , obviously! How big of a square can you beat? And at what level of difficulty?
 Play Black Hole.
 Play TicTacToe Sums
 Master decomposition by playing Knockout. Suggestion: start with two 6sided dice, then two 8 or 10sided dice.

 Games for Young Minds explanation
 YouTube video
 Game board printout [coming soon]

 Master the Doubles by

 Playing The 5 by 5 Game. Gameboard Printout
 Drilling Doubles, Jumbled, All and Doubles, Jumbled, Mostly Harder [coming soon].

 Master the Parts of 10 by

 Doing Greg Tang's "The Tens"
 Playing Squirmy Wormy
 Drilling Partners to 10

 Drill Ten Plus equations.
 Do Rocket Math drills. [Ask Andrew for links to the files.]

 Instructions / Administration
 Addition Diagnostic & Drills
 Addition Answers
 Subtraction Diagnostic & Drills
 Subtraction Answers

So I can...
Demonstrate automatic recall of
 The parts of 5, 6, and 10 (e.g. 3+__=10)
 Addition of 0, 1, 2, and 10 (e.g. 3+10=___)
 All doubles facts (e.g. 8+8=___)
Where "automatic recall" means that correct answers pop into your mind instantly and with no effort. Such recall is easier, more accurate, and faster than counting or modeling.
As assessed by...
[Coming soon]

I will...
 Use Amplify Fluency.
 Practice Making Tens.
 Equation Drills for Ten
 Adjusting Basic Facts Template Use for
 Doubles +1 and +2
 Variants on Partners to 10
 Making tens.
 Equation Drills for Doubles
 Doubles + or  1, Simple
 Doubles, + or  1, Jumbled
 Doubles, Sometimes + or  1, Simple
 Doubles, Sometimes + or  1, Jumbled
 Doubles, + or  2, Simple
 Doubles, + or  2, Jumbled
 Doubles, Sometimes + or  2, Simple
 Doubles, Sometimes + or  2, Jumbled [coming soon]
 All kinds of doubles and variants
 Use incremental flash card practice to solidify my knowledge.
So I can...
Demonstrate automatic recall of all basic facts, plus or minus 1, including
 Doubles Plus or Minus 1 (e.g. 8+7=___ )
 Doubles Plus or Minus 2 (e.g. 8 + 6 = ___ )
 Making 10 with 8 or 9 (e.g. 9 + 6 = ___ )
 Partners to 9 and 11 (e.g. ___ + 6 = 11 or ___ + 3 = 9 )
As assessed by...
 [coming soon]

I will...
 Drill equations to fluency.
 Make a Magic Square from 1 to 9.
So I can...
Demonstrate automatic recall of all addition facts within 20.
As assessed by...
 [coming soon]

I will...
 Learn "Don't Cross 10"
 Concept & Visual Work
 Fluency Practice
 Learn "Cross 10"
 Concept & Visual Work
 Fluency Practice
 Learn "Move Over"
 Concept & Visual Work
 Fluency Practice
 Put it all together
 Drill
 Extend Counting Up or Adjusting.
 Practice demonstrating my thinking in a variety of ways, including equations.
Source of picture: @Howie_Hua's Twitter thread
So I can...
 Extend all previous mental math strategies to 100. Discuss and demonstrate such extensions in a variety of ways.
 Demonstrate fluency in the strategy of dealing with tens and ones separately.
As assessed by...
 [coming soon]
 Learn "Don't Cross 10"

I will...
 Reverse engineer, explain, and perform the "Pick a Number" card trick.
 Play Number Grid TicTacToe.
 Play TicTacToe Sums (using the "Multiples of 10" version).
 Solve and analyze the Magic Triangle.
 Make a bunch of mental math webs.
 Drill Adding Multiples of 10
 Partners to Multiples of 10
So I can...
 Add and subtract multiples of ten fluently, by relating them to singledigit addition facts.
 Determine parts of multiples of ten by comparing them to easier equations and/or counting up.
As assessed by...
 [coming soon]





So I can...
 Demonstrate automatic recall of all addition and subtraction facts within 20, in all forms. If writing speed is a problem, you may have someone else write for you while you state solutions aloud.

I will...
 [coming soon]
So I can...
 Demonstrate either fluency and flexibility with strategies and/or automatic recall for all addition and subtraction within 100.
 Apply the above in pure and applied math contexts.
 Do all of the above without guessing, counting, or modeling.
 Prove my work is right or wrong in a variety of ways.
 Succeed at rich math problems and mini numeracy tasks by myself.
As assessed by...
 [coming soon]