Same Size, Related Sizes
10 min
Narrative
The purpose of this Warm-up is to revisit the idea from IM Grade 3 that tape diagrams and number lines are related, which will be useful later in the lesson, when students transition from using fraction strips to using the number line to represent fractions and reason about their size.
While students may notice and wonder many things about these representations, the connections between the tape diagram and number line (the number and size of the parts in relation to 1) are important to note.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Sample Response
Student may notice:
- The number line is partitioned into fourths.
- There are 12 parts (or 12 twelfths) in the entire fraction strip.
- The entire length of the fraction strip is 1.
- There are 3 parts of 121 for each tick mark on the number line.
Student may wonder:
- Why is the number line only partitioned into fourths?
- Why is the fraction strip partitioned into twelfths but the number line is not?
- Where is 0 on the fraction strip?
- Can we add tick marks to the number line to show twelfths?
Activity Synthesis (Teacher Notes)
- “How are these representations alike? How are they different?”
- “Some tick marks on the number line are not labeled. What labels do you think would be appropriate for them?” (41, 42, 43, or 41, 21, 43, or 123, 126, 129)
Standards
- 3.NF.2·Understand a fraction as a number on the number line; represent fractions on a number line diagram.
- 3.NF.A.2·Understand a fraction as a number on the number line; represent fractions on a number line diagram.
- 4.NF.1·Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
- 4.NF.A.1·Explain why a fraction <span class="math">\(a/b\)</span> is equivalent to a fraction <span class="math">\((n \times a)/(n \times b)\)</span> by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
20 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Same Size, Related Sizes
10 min
Narrative
The purpose of this Warm-up is to revisit the idea from IM Grade 3 that tape diagrams and number lines are related, which will be useful later in the lesson, when students transition from using fraction strips to using the number line to represent fractions and reason about their size.
While students may notice and wonder many things about these representations, the connections between the tape diagram and number line (the number and size of the parts in relation to 1) are important to note.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Sample Response
Student may notice:
- The number line is partitioned into fourths.
- There are 12 parts (or 12 twelfths) in the entire fraction strip.
- The entire length of the fraction strip is 1.
- There are 3 parts of 121 for each tick mark on the number line.
Student may wonder:
- Why is the number line only partitioned into fourths?
- Why is the fraction strip partitioned into twelfths but the number line is not?
- Where is 0 on the fraction strip?
- Can we add tick marks to the number line to show twelfths?
Activity Synthesis (Teacher Notes)
- “How are these representations alike? How are they different?”
- “Some tick marks on the number line are not labeled. What labels do you think would be appropriate for them?” (41, 42, 43, or 41, 21, 43, or 123, 126, 129)
Standards
- 3.NF.2·Understand a fraction as a number on the number line; represent fractions on a number line diagram.
- 3.NF.A.2·Understand a fraction as a number on the number line; represent fractions on a number line diagram.
- 4.NF.1·Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
- 4.NF.A.1·Explain why a fraction <span class="math">\(a/b\)</span> is equivalent to a fraction <span class="math">\((n \times a)/(n \times b)\)</span> by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.