Fractions and Decimals on a Number Line

 

Curriculum Goals Grade 5/6

  • Determine and explain the relationship between fractions and their equivalent decimal forms.
  • Comparing and ordering fractional amounts with unlike denominators.
  • Relating simple fractions (proper, improper, mixed numbers), decimals, and percentages.

Context

  • Area close to the board for the lesson.
  • Carpet area, floor, or a long desk for the activity.
  • Students should know simple fractions (½, 1/3, ¼, 1/5) and equivalent decimals and percentages.
  • Students should understand that percentages are directly related to decimals
    (example: 0.45 is the same as 45%).

Materials

  • Blackboard/Whiteboard/Smartboard
  • Paper and pencils
  • Several sets of fraction cards (include mixed numbers, improper fractions, equivalent fractions) (Appendix A)
  • Several sets of decimal cards (decimals should relate to the simple fractions) (Appendix B)

Lesson

  1. Using the board, write down some simple fractions one at a time.
    Examples: ½ , ¾ , 1/3
  2. Have students state the name of the fraction (“one half, three fourths, one third”).
  3. Ask students what these are in decimals or percentages (50% or 0.5, 75% or 0.75, 33.3% or 0.33). Ensure that students understand that decimals and percentages are directly related to each other.
  4. Start providing examples of fractions that are more difficult.
    Examples: 5/10, 1/25, 3/5
  5. Ask students if they have strategies to determine what the equivalent decimal or percentage is.
    Examples of strategies include: reducing the fraction into its simplest form, changing the denominator to be 100 and changing the numerator accordingly

Activity

  1. Explain to students that they will be given a set of fraction cards (15 cards per pair; Set 1), and the task is to order them on an imaginary number line with a partner.
    – Simple fractions should be provided first
    – Review that a number line goes from left to right: smallest to largest
  2. Provide an example to get students started.
    – Example: putting ½ in the middle of their work area, and then putting 1/8 on the far left
  3. Have students work together to finish arranging the rest of the cards.
    – Encourage students to use a paper and pencil to change the fractions if necessary (referring back to the strategies discussed earlier)
  4. Once a pair finishes, provide the decimal cards and have students determine which decimal card matches with the fractions on the number line (15 cards per pair; Set 2).
  5. When a pair is done, provide the mixed number/improper fraction/more difficult fractions/equivalent fractions cards (30 cards per pair; Set 3).
  6. When pairs finish, go through the number line with them, starting from zero. Encourage students to explain their reasoning and thinking.

Note: Not all pairs will finish arranging all 60 cards. The last set of cards is for fast finishers.

Questions to Extend Student Thinking

  • What were some of the strategies you used to match the decimal to the fraction?
  • How about when ordering the more difficult fraction cards?
  • How do you know that 1/25 is the same as 4/100?
  • What was your strategy for working with improper and mixed fractions?

Look Fors/Assessing the Learning

  • Are students using strategies discussed earlier in the class?
  • What is common knowledge to the students?
    For example, do students automatically know that 6/10 is 0.6?
  • Where are students hesitating or getting stuck?