Topic outline

  • Essential Questions

    1. Why did mathematicians invent fractions? i.e. What can we do with fractions that cannot be done with whole numbers?
    2. How many ways can I represent the need for fractions?
    3. How are fractions similar to whole numbers? How are they different?
  • Lesson 1: Fractional Counting

    I will...

    1. Create a Fractional Freezie Menu.
    2. Count by fractions and mixed numbers.
      1. Video example
      2. Picture example
      3. Exercises
      4. Solutions
    3. Make sure I can state both names for any randomly selected point on fractional number lines.
      1. Number Lines with Space for Written Counting
      2. Visual Reference Pages
      3. Drills: Identify Fractional Points on Number Lines. Every time you recompile this link, you will get new exercises and solutions.
      4. "Answer key" (fractional number lines with counting provided)
    4. Play on the Fractions Racing Board. Use Fraction Strips to determine equivalent fractions. This has both letter and legal size options in left panel. Challenge. In writing, answer the following. Provide examples to aid your explanation. How should a player think about:
      1. Which dice to roll?
      2. Which token on which number line to move?
      3. Deciding between 3/4 and 4/3 when rolling a 3 and a 4?

     

    So I can...

    1. Identify and name denominators in number line and area diagrams.
    2. Use those denominators to count by fractions and by mixed numbers.
    3. Explain why every fractional value has two names and how the name corresponds to a visual.
    4. State the purpose of fractions and support my statement with examples of my own creation.

     

    As assessed by...

    [coming soon]

  • Lesson 2: Conversions with Visuals

    I will...

    1. Name Mixed and Improper Numbers
      1. Name & Draw, Mixed & Improper Numbers (from JUMP Math Confidence Builder) and then I will mark my work with the answer key.
      2. Common Core Sheets (coming soon: Name the numbers in both fraction and improper ways.
    2. Practice representing a single fractional value in a variety of ways.
      1. Example
      2. Exercises & Solutions
    3. Generate my own examples of representing a single fractional value in a variety of ways. Optional: Do my work on this Template.
    4. Place a Set of Fractions on a Single Number Line

     

    I can...

    1. Fluently translate representations of fractions between words, math symbols, area diagrams, and number lines.
    2. Recognize and define: whole number, mixed number, improper fraction, and proper fraction.
    3. Generate examples and non-examples of each and state and represent key properties of each.

     

    As assessed by...

    [coming soon]

  • Lesson 3: Conversions without Visuals

    I will...

    1. Practice conversion drills to mastery. 
      1. Level 1 - Mixed & Improper
      2. Level 2 - All Kinds of Numbers
    2. Create my own guides for converting mixed, whole, and improper numbers. [To be done with a teacher or tutor.] Optional template: Mixed & Improper Conversion
    3. Practice teaching another student (real or pretend) how to do the conversions. I will provide a visual, either a drawing or physical objects, to help explain why the conversion method works.

     

    So I can...

    1. Fluently convert whole, proper, improper, and mixed numbers, without counting by ones or by fractions. 
    2. Show my reasoning using number lines, area diagrams, and math vocabulary.

     

    As assessed by...

    [coming soon]

  • Lesson 4: Estimating Fractional Magnitudes

    I will...

    1. After doing a column of these conversions, I know which numbers are equal, which are far apart, and which are close together. I can verify my work on these number lines.
    2. Estimate Fractional Points on Number Lines
      1. Exercises with solutions
      2. Exercises only
    3. Do Fraction Comparison Exercises.

     

    So I can...

    1. Estimate the magnitude of fractions when precise drawings are too difficult.
    2. Show my thinking using equations, approximations, number lines, and area diagrams.

     

    As assessed by...

    [coming soon]

  • Lesson 5: Benchmarks, Tops and Bottoms

    I will...

    1. Comparing Fractions Worksheet . (Close the tab and click on this link again to get new numbers.)
    2. Find 4 Between
    3. Fraction Comparison Exercises

     

    I can...

    1. Use estimates, benchmarks, and reasoning with numerators and denominators to:
      1. Order all types of numbers.
      2. Estimate their magnitudes in area diagrams and on number lines.
    2. Identify fraction pairs that are so close that they require a more precise method to compare.
    3. Represent the comparison with appropriate use of the symbol ≈.

     

    As assessed by...

    [coming soon]

  • Lesson 6: Equivalent Fractions

    I will...

    1. Investigate JUMP Math Equivalent Fractions.
    2. Generate my own equivalent fractions and describe them with equations.
      1. Number Line Only Template
      2. Number Line & Areas TEMPLATE
      3. Scales
    3. Do Fraction Comparison Exercises
    4. Practice Simplifying Fractions to fluency.
    5. Simplify Fractions by Cancelling GCF [coming soon]
    6. Generate fraction pairs that are best suited to each method of comparison. Fraction Comparison Methods Reference
     
     

    So I can...

    1. Explain the principle of equivalent fractions using stories, examples, visuals, and manipulatives.
    2. Use equivalent fractions to compare and order fractions when previous methods are insufficient.
    3. Explain the following falsehoods using examples and visuals.
    4. Fluently generate equivalent fractions and fluently simplify them.
    5. Explain all of the above using math vocabulary.

     

    As assessed by...

    [coming soon]