Topic outline

  • 0.1 Course Outline

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    In this course, students will master every aspect of 1-step addition and subtraction of whole numbers from 0 to 100, from meaning to mental math, from pictures and manipulatives to equations and word problems. Finger-counting will be eradicated, confidence will soar, and a very strong foundation will be laid for multiplication, division, and all future math.

     

    Essential Questions

    1. How do addition and subtraction improve upon counting?
    2. How do addition and subtraction help us solve problems?
    3. How are addition and subtraction related?
    4. How can we use concrete objects, pictures, words, and symbols to represent our thinking? What are the pros and cons of each?
    5. 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

    Addition Table

    Catch & Count

    Games & Puzzles

     

    Content Sequence

    1.1-1.3 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.

    2.1-2.6 You will sharpen your mental addition including automatic recall for all facts within 20 and fluency for all addition within 100.

    3.1-3.3 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.

    4.1-4.2 You will put it all together, learning to represent and solve all types of problems and equations within 100.

  • 1.1 Parts, Wholes & Changes

    I will...

    1. Master discrete models of parts, wholes, and changes
      1. Splat
      2. Start, Change, Final [template] exercises
      3. Hidden, Visible, Total [template]
      4. Ten Frames
    2. Master linear models of parts, wholes, and changes
      1. Number Tracks
      2. From Counters to Bar Models
      3. Linear Representations of Parts, Wholes, and Changes within 20
      4. Parts & Wholes with Xs and Os
        1. Level 1
        2. Level 2
        3. Level 3
        4. Level 4
        5. Level 5
    3. Play games
      1. Auction 35. Best played with 35 counters and a deck of cards, but if online, use the Auction 35 Gameboard Printout.
      2. Nim
      3. Crash! [aka Pig]. Can be played with pencil and paper, but beginners should use the Crash gameboard.
      4. Jack and Jill's Pails [source: Mindtrap's Geometrical Riddles]
    4. Solve real-life problems with addition and subtraction. [Coming soon.]

     

    So I can...

    1. Solve all types of parts, wholes, and change word problems.
    2. 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...

    1. My ability to build on this knowledge in Lesson 2 (Equations and Calculation) and Lesson 3 (comparisons).
    2. My ability to instantly recognize whether to add, subtract, or do neither in the future.

  • 1.2 Comparisons

    I will...

    1. Practice on this comparison template.
    2. [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...

    1. [coming soon]

  • 1.3 Equations & Calculations

    I will...

    1. [coming soon]

     

    So I can...

    1. Do everything from Lesson 3 and...
    2. Recognize and explain when to add versus when to subtract. I can generate examples to aid my explanations.

    I will...

    1. Practice solving problems, modeling them with bars, and describing them with fact families.
    2. Do equation drills for fact families.

    As assessed by...

    1. [coming soon]

  • 2.1 Basic Addition Facts

    I will...

    1. Play KenKen. Focus on the + and -, obviously! How big of a square can you beat? And at what level of difficulty?
    2. Play Black Hole.
    3. Play Tic-Tac-Toe Sums
    4. Master decomposition by playing Knockout. Suggestion: start with two 6-sided dice, then two 8- or 10-sided dice.
    5. Master the Doubles by
    6. Master the Parts of 10 by
    7. Drill Ten Plus equations.
    8. Do Rocket Math drills. [Ask Andrew for links to the files.]

     

    So I can...

    Demonstrate automatic recall of

    1. The parts of 5, 6, and 10 (e.g. 3+__=10)
    2. Addition of 0, 1, 2, and 10 (e.g. 3+10=___)
    3. 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]

  • 2.2 Basic Addition Facts Plus or Minus 1 or 2

    I will...

    1. Practice Making Tens.
    2. Equation Drills for Ten
      1. Compare to Partners to 10
        1. Simple
        2. Jumbled
      2. Make Ten
    3. Adjusting Basic Facts Template Use for
      1. Doubles +1 and +2
      2. Variants on Partners to 10
      3. Making tens.
    4. Equation Drills for Doubles
      1. Doubles + or - 1, Simple
      2. Doubles, + or - 1, Jumbled
      3. Doubles, Sometimes + or - 1, Simple
      4. Doubles, Sometimes + or - 1, Jumbled
      5. Doubles, + or - 2, Simple
      6. Doubles, + or - 2, Jumbled
      7. Doubles, Sometimes + or - 2, Simple
      8. Doubles, Sometimes + or - 2, Jumbled [coming soon]
      9. All kinds of doubles and variants
        1. Simple
        2. Jumbled
      10. Use incremental flash card practice to solidify my knowledge.

     

    So I can...

    Demonstrate automatic recall of all basic facts, plus or minus 1, including

    1. Doubles Plus or Minus 1 (e.g. 8+7=___ )
    2. Doubles Plus or Minus 2 (e.g. 8 + 6 = ___ )
    3. Making 10 with 8 or 9 (e.g. 9 + 6 = ___ )
    4. Partners to 9 and 11 (e.g. ___ + 6 = 11 or  ___ + 3 = 9 )

     

    As assessed by...

    1. [coming soon]

  • 2.3 Extending Single-Digit Addition Facts to 20

    I will...

    1. Drill equations to fluency.
      1. Simple
      2. Jumbled
    2. Make a Magic Square from 1 to 9.

     

    So I can...

    Demonstrate automatic recall of all addition facts within 20.

     

    As assessed by...

    1. [coming soon]

  • 2.4 Extending Single-Digit Addition Facts to 100

    I will...

    1. Learn "Don't Cross 10" 
      1. Concept & Visual Work
      2. Fluency Practice
    2. Learn "Cross 10"
      1. Concept & Visual Work
      2. Fluency Practice
    3. Learn "Move Over"
      1. Concept & Visual Work
      2. Fluency Practice
    4. Put it all together
    5.  Drill
      1. Extend Single Digit Addition
      2. Add and Subtract within 100, 1 part single-digit
      3. Separate Tens and Ones - Simple
      4. Separate Tens and Ones - Jumbled
    6. Extend Counting Up or Adjusting.
    7. Practice demonstrating my thinking in a variety of ways, including equations.

     

    Source of picture: @Howie_Hua's Twitter thread

     

    So I can...

    1. Extend all previous mental math strategies to 100. Discuss and demonstrate such extensions in a variety of ways.
    2. Demonstrate fluency in the strategy of dealing with tens and ones separately.

     

    As assessed by...

    1. [coming soon]

  • 2.5 Addition Within 100 - Multiples of 10 (and + or - 1 or 2)

    I will...

    1. Reverse engineer, explain, and perform the "Pick a Number" card trick.
    2. Play Number Grid Tic-Tac-Toe.
    3. Play Tic-Tac-Toe Sums (using the "Multiples of 10" version).
    4. Solve and analyze the Magic Triangle.
    5. Make a bunch of mental math webs.
    6. Drill Adding Multiples of 10
      1. Simple
      2. Jumbled
    7. Partners to Multiples of 10
      1. Just 100
      2. All Multiples of 10

     

    So I can...

    1. Add and subtract multiples of ten fluently, by relating them to single-digit addition facts.
    2. Determine parts of multiples of ten by comparing them to easier equations and/or counting up.

     

    As assessed by...

    1. [coming soon]

  • 2.6 Addition Within 100

  • 3.1 Solving Addition Equations

  • 3.2 Basic Subtraction Facts within 20

  • 3.3 Subtraction within 100

  • 4.1 Addition & Subtraction within 100

     

     

    So I can...

    1. 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.
      1. Simple Equations
      2. Jumbled Equations

  • 4.2 Putting it All Together

    I will...

    1. [coming soon]

     

    So I can...

    1. Demonstrate either fluency and flexibility with strategies and/or automatic recall for all addition and subtraction within 100.
    2. Apply the above in pure and applied math contexts.
    3. Do all of the above without guessing, counting, or modeling.
    4. Prove my work is right or wrong in a variety of ways.
    5. Succeed at rich math problems and mini numeracy tasks by myself.

     

    As assessed by...

    1. [coming soon]