Topic outline

  • Essential Questions

    1. How does arithmetic change when a fraction is involved? 
    2. How does arithmetic stay the same when a fraction is involved?
    3. How should I represent my thinking for whole & fraction arithmetic?

     

    Course Sequence

    [coming soon]

     

    Whole Course Resources

    Mathigon Polypad

  • Lesson 1: Add & Subtract with Drawings & Reasoning

    I will...

    1. Master the Prior Knowledge / New Knowledge Pairs for addition and subtraction with fractions.
    2. Add & Subtract Fractions on Number Lines [under construction]
    3. Sketch and reason when exact values are too difficult to draw. Fraction & Wholes, Sketching & Calculations 
    4. Practice Multiple Representations of Whole & Fraction Addition & Subtraction.

     

    So I can...

    1. Compare and contrast addition and subtraction of two whole numbers vs one whole number and one fraction, given quantities are easy to draw and visualize.
    2. Do simple calculations in my head and check them with a calculator or software.
    3. Solve word problems and represent my thinking in a variety of ways, including visuals and equations.
    4. Infer exact values of solutions when drawing and visualizing are too difficult. [Standard algorithms not intended yet.]
    5. Sketch reasonably to show my thinking.

     

    As assessed by...

    [coming soon]

  • Lesson 2: Multiply & Divide with Drawings

    I will...

    1. JUMP Multiply Fractions & Wholes
    2. Wholes to Fractions
      1. Multiply & Divide, Wholes & Fractions
      2. Multiply & Divide: Wholes to Fractions
      3. Whole & Fractions, Mult & Div
    3. Games
      1. Halves and Quarters
      2. Halves and Thirds
    4. Payroll
      1. 3 Clocks Per Page
      1. Hourly Payroll
    5. Fraction & Whole, Direction of Multiplication and Division
    6. The Coffee Cake Recipe
    7. The Green Tile Supply
    8. Coming soon: Garden Plots & Freezie Pricing

     

    I can...

    1. Compare and contrast multiplication and division with two whole numbers vs one whole number and one fractional number, as long as the quantities are easy to draw and visualize. This includes equal groups, areas and arrays, comparisons. Optional: Ratios and rates.
    2. Reasonably interpret situations involving remainders or fractional quotients.
    3. Create examples to show when order matters and when it does not.

     

    As assessed by...

    [coming soon]

  • Lesson 3: Multiply & Divide with Reasoning

    I will...

    [coming soon]

     

    So I can...

    1. Explain in a variety of ways why 
      1. multiplying by 1/n is equivalent to dividing by n. 
      2. dividing by 1/n is equivalent to multiplying by n.
    2. Explain my reasoning for both of the above using common English and math symbols. E.g. “One third of 60 is 60 divided by 3.”
    3. Do simple calculations in my head and check them with a calculator or software.
    4. Generate examples with stories and pictures to show when “multiply” and “divide” do or do not mean “increase” vs “decrease”.

     

    As assessed by...

    [coming soon]

  • Lesson 4: Multiply & Divide with Estimating

    I will...

    [coming soon]

     

    So I can...

    1. Estimate solutions when drawing and visualizing are too difficult. [Standard algorithms not intended yet.]

     

    As assessed by...

    [coming soon]

  • Lesson 5: All Operations, 1-step SSDDs

    I will...

    1. All Fraction & Whole Operations
    2. Whole & Fraction SSDD
    3. Rectangles with Fractional Dimensions

     

    I can...

    1. Select appropriate operations and representations of single-step SSDDs.

     

    As assessed by...

    [coming soon]

     

  • Lesson 6: All Operations, Multi-step SSDDs

    I will...

    [coming soon]

     

    So I can...

    1. Select appropriate operations and representations of multi-step SSDDs.
    2. Generate my own examples to demonstrate my learning.

     

    As assessed by...

    [coming soon]

  • Lesson 7: Rich Tasks

    I will...

    [coming soon]

     

    So I can...

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

     

    As assessed by...

    [coming soon]