 # Fractions and Decimals on a Number Line

• 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?