Decimal Representations of Rational Numbers
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to investigate a representation of rational numbers using zooming number lines, which will be useful when students work with a similar representation in upcoming activities. While students may notice and wonder many things about this image, the fact that each number line zooms in on a specific interval of the previous number line is the important discussion point.
This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is how each number line is partitioned into 10 equal intervals.
Launch
Display the image for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time and then 1 minute to discuss the things they notice and wonder with their partner.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- Each number line zooms in on a specific interval from the previous number line.
- The first number line only shows tenths, the second shows hundredths, and the third shows thousandths.
- These look like the number lines from an earlier activity with scientific notation and very small numbers.
Students may wonder:
- Why does the dot look like it is moving around?
- What number does the dot represent?
- Do all three dots represent the same number?
- Are all three of those points 0.375?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses for all to see without editing or commentary. If possible, record the relevant reasoning on or near the image. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information.
If the idea of what number the dot represents does not come up during the conversation, ask students to discuss this idea, but do not tell them the answer—it will be discussed in a following activity.
Standards
- 8.NS.A·Know that there are numbers that are not rational, and approximate them by rational numbers.
- 8.NS.A·Know that there are numbers that are not rational, and approximate them by rational numbers.
10 min
10 min
10 min
Knowledge Components
All skills for this lesson
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Decimal Representations of Rational Numbers
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to investigate a representation of rational numbers using zooming number lines, which will be useful when students work with a similar representation in upcoming activities. While students may notice and wonder many things about this image, the fact that each number line zooms in on a specific interval of the previous number line is the important discussion point.
This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is how each number line is partitioned into 10 equal intervals.
Launch
Display the image for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time and then 1 minute to discuss the things they notice and wonder with their partner.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- Each number line zooms in on a specific interval from the previous number line.
- The first number line only shows tenths, the second shows hundredths, and the third shows thousandths.
- These look like the number lines from an earlier activity with scientific notation and very small numbers.
Students may wonder:
- Why does the dot look like it is moving around?
- What number does the dot represent?
- Do all three dots represent the same number?
- Are all three of those points 0.375?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses for all to see without editing or commentary. If possible, record the relevant reasoning on or near the image. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information.
If the idea of what number the dot represents does not come up during the conversation, ask students to discuss this idea, but do not tell them the answer—it will be discussed in a following activity.
Standards
- 8.NS.A·Know that there are numbers that are not rational, and approximate them by rational numbers.
- 8.NS.A·Know that there are numbers that are not rational, and approximate them by rational numbers.