Connect Fraction Strips and Number Lines. It is important that students understand that fractions are numbers. Just as 2 and 100 are numbers that have places on the number line, fractions have places on the number line, too. Display the Showing Fractions on Number Lines Master to help students connect representations on fraction strips and number lines.
Suggest that students use their fraction strips and ask:
- Example A shows a fraction strip and a matching number line. Into how many equal parts is the fraction strip divided? (4)
- Into how many equal parts is the number line divided? (Also 4)
A common mistake students make is to count the number of marks between 0 and 1, so they might incorrectly think the marks should be labeled with thirds.
Point out that the number of parts should be counted instead of the number of marks using the following prompt:
- How should I label the fractional parts on each? (The number line is divided into four equal parts so they should be labeled with fourths.)
Label the parts of both the fraction strip and number line as shown in Figure 8.
- Is there another label possible for 2/4? (Yes, it shows half of the strip or number line, so you could use 1/2.)
- How are the fraction strip and the number line alike? (Both are divided into the same number of equal parts. The ends of each part of the fraction strip match the ends of each part of the number line.)
- How are they different? (The parts of the fraction strip are all labeled the same. Each is labeled 1/4. But on the number line, the labels count up 0/4, 1/4, 2/4, 3/4, 4/4.)
- Fold your yellow fourths fraction strip to show 2/4. Where is 2/4 located on the number line? (When I lay the strip onto the number line, 2/4 is where the fraction strip ends.)
- Fold your pink halves fraction strip to show 1/2. Where is 1/2 located on this number line? (1/2 is located where the fraction strip ends and is the same place 2/4 is located.)
- How can two fractions mark the same location on the number line? (The fractions are the same size and are therefore equivalent.)
Locate Fractions on a Number Line. Focus students' attention on Example B on the Showing Fractions on Number Lines Master.
- In Example B, into how many equal parts are the fraction strip and the number line divided? (8)
- How should I label the fraction strip? (Write 1/8 in each section of the fraction strip.)
- Fold your blue fraction strip to show 3/8. Line up the fraction strip on the number line. Where is 3/8 located on the number line? (Where the fraction strip ends when the strip is folded to show 3/8.)
- Fold your blue fraction strip to show 6/8. Where is 6/8 located on the number line?
Show students how to fold the blue fraction strip to show each of the other fractions and label them appropriately on the number line.
Ask students to use their fraction strip to show 3/2. Students may partner with a neighbor and put together one pink strip and show 1/2 on the other. Other students may show 1 whole with one of the other color strips and show 1/2 with the pink strip.
- Where is 3/2 on the number line?
On a display or board, show students how to draw a line and then use the fraction strips to mark and label 0, 1/2, 2/2, 3/2, and 4/2 on the line.
- Where is 11/2 on this number line? (The same place as 3/2.)
- Where is 13/4 on this number line?
- Where is 3/4 on this number line?
Encourage students to show 13/4 with their fraction strips and then use the folds in the strip to mark 13/4 on the line they have drawn.
Ask students to complete Questions 1–4 on the Fractions on Number Lines pages in the Student Activity Book. These questions guide students to use the fraction strips to label fractions on the number line. Students can use their fraction strips to show a fraction and then use it to locate the fraction on the number line since these are at the same scale as the fraction strips they made earlier. Circulate among the students helping them use the fraction strips to locate fractions on the number line.
- How many parts are in one-whole fraction strip?
- Use your fraction strip to show [fractional part].
- How many parts are in one-whole of the number line?
- One part is what part of the fraction strip?
- How far is that mark from zero?
- Look at Questions 1–2. What do you notice about the fractions 1/2 and 2/4? (They represent the same part of the whole fraction strip and they are both located in the same place on the number line.)
- Look at Question 4F. What is different about this number line and fraction strip? (More than 1 whole is represented. You cannot use your fraction strips to line up on the number line because the whole is a different size.)
Ask students to complete Questions 5–7 on the Fractions on Number Lines pages in the Student Activity Book. These questions guide students to show specific fractions with the fraction strips and on the number line. Again, students can use their fraction strips to show the fraction since the scale of the fraction strips and the number lines are the same. Circulate among students helping them use their fraction strips to locate fractions on the number line and compare fractions.
- Look at Questions 5A–5B. What do you notice about 2/8 and 1/4? (They represent the same part of the whole fraction strip and they are both located in the same place on the number line.)
- Look for other pairs of fractions that show the same part of the whole and share the same point on the number line. (Answers will vary. A possible response: 4/8, 1/2, 3/6 are all equal and 2/3 and 4/6 are equal as well.)
Ask students to look at Question 8A.
- Is 1/2 equal to 2/4? (Yes)
- How do you know? (They show the same part of the whole and are located on the same place on the number line.)
Have students answer Questions 8A–8H. Encourage students to use their fraction strips and their answers to Questions 1–7 to answer the new questions. Identify a few students to share their responses to Question 8H with the class. Use the following prompts to listen to student strategies as they are working.
- Which fractions are you comparing?
- Do you think these fractions are equal?
- Show how to use the number sentence to compare the fractions.
- Show how to use the fraction strips to compare the fractions.
- If the statement is false, show how to change the statement so it is true.
Assign Questions 8I–P. These questions ask students to compare fractions with inequalities. Again, students should be able to use their fraction strips and their responses to Questions 1–7 to compare these fractions. Again, identify a few students to share their reasoning as they compare fractions.
- Which fractions are you comparing?
- Is the statement true or false?
- How do you know?
- Write a number sentence to compare the fractions.
- Show how to use the fraction strips to compare the fractions.
- If the statement is false, show how to change the statement so it is true.
Use the Fractions on Number Lines pages with Feedback Box in the Student Activity Book to assess students' abilities to partition a fraction strip and number line [E6]; make connections among fraction strips and number lines [E8]; represent fractions with fraction strips and locate fraction on number lines [E1]; find equivalent fractions using area models [E9]; and compare and order fraction models [E10].
