Lesson 1
Estimation Explorations with Fractions
Warm-up: Which One Doesn’t Belong: Fractions (10 minutes)
Narrative
This warm-up prompts students to compare four images. It gives students a reason to use language precisely. It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another. During the synthesis, ask students to explain the meaning of any terminology they use, such as parts, pieces, whole, shapes, triangle, quadrilateral, or halves.
Launch
- Groups of 2
- Display the image.
- “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
- 1 minute: quiet think time
Activity
- “Discuss your thinking with your partner.”
- 2–3 minutes: partner discussion
- Share and record responses.
Student Facing
Which one doesn’t belong?
Student Response
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Activity Synthesis
- “Let’s find at least one reason why each one doesn’t belong.”
Activity 1: Estimation Exploration: Diagram (15 minutes)
Narrative
The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information. In this activity, students estimate what fraction of a square is shaded to revisit area diagrams.
Advances: Conversing, Reading
Launch
- Groups of 2
- Display the image.
- “What is an estimate that’s too high? Too low? About right?”
- 1 minute: quiet think time
Activity
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Record responses.
Student Facing
What fraction of the square is shaded?
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
| \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) | \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) | \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) |
Student Response
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Activity Synthesis
- Consider asking:
- “Is anyone’s estimate less than _____? Is anyone’s estimate greater than _____?”
- “Based on this discussion does anyone want to revise their estimate?”
- “If you wanted to find out exactly what fraction of the square is shaded, how would you go about doing that?” (Try to partition the square into equal parts and see how many of the parts are shaded.)
- 2 minutes: partner discussion
- Share and record responses.
- Optional: Have students find the exact fraction shaded. (\(\frac{5}{8}\))
Activity 2: Estimation Exploration: Fraction Strip (10 minutes)
Narrative
The purpose of this activity is for students to use their experience with fraction strips and tape diagrams to estimate what fraction of a strip is shaded.
Supports accessibility for: Social-Emotional Functioning
Launch
- Groups of 2
- Display the image.
- “What is an estimate that’s too high? Too low? About right?”
- 1 minute: quiet think time
Activity
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Record responses.
Student Facing
What fraction of the strip is shaded?
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
| \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) | \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) | \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) |
Student Response
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Activity Synthesis
- “If you wanted to find out exactly what fraction of the strip is shaded, how would you go about doing that?” (See how many copies of the shaded part can fit into the whole strip. Partition the strip into fractions we know and see what fraction the end of the shaded part lines up with.)
- 2 minutes: partner discussion
- Share and record responses.
- Optional: Have students find the exact fraction shaded. (\(\frac{1}{3}\))
Activity 3: Estimation Exploration: Number Line (10 minutes)
Narrative
Launch
- Groups of 2
- Display the image.
- “What is an estimate that’s too high? Too low? About right?”
- 1 minute: quiet think time
Activity
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Record responses.
Student Facing
What number does the point represent?
Record an estimate that is:
| too low | about right | too high |
|---|---|---|
| \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) | \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) | \(\phantom{\hspace{2.2cm} \\ \hspace{2.2cm}}\) |
Student Response
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Activity Synthesis
- “If you wanted to find out exactly what fraction is at that point on the number line, how would you go about doing that?” (Partition the number line into fractions we know and see what fraction the point lines up with.)
- 2 minutes: partner discussion
- Share and record responses.
- Optional: Have students find the exact location marked on the number line. (\(\frac{4}{3}\))
Lesson Synthesis
Lesson Synthesis
Display the number line from the last activity.
“Today we practiced our estimation skills with fractions shown in different ways. When you were estimating the location of this point on the number line, what were some things you knew right away?” (The fraction would be greater than 1 and less than 2. The numerator had to be larger than the denominator. I could write it as 1 and a fraction. It would be closer to 1 than 2.)
“What did you have to work a little harder to think about?” (What denominator to use in my estimate because no parts are marked on the number line. What fraction would be greater than 1 but less than \(1\frac{1}{2}\).)
Cool-down: Fraction Representations (5 minutes)
Cool-Down
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