Comparing Relationships with Equations
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to elicit comparisons of lengths and areas, which will be useful when students decide whether such relationships are proportional in a later activity. While students may notice and wonder many things about these images, the important discussion points are the way that the side lengths, perimeter, and area are increasing.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
Arrange students in groups of 2. 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:
- There are three rectangles on the grid.
- The rectangles are scaled copies.
- The rectangles increase in size from top to bottom.
- The width increases by 3 each time.
- The height increases by 1 each time.
- The small rectangle could fit into the medium rectangle 4 times, and it could fit into the large rectangle 9 times.
Students may wonder:
- By how much does the area increase each time?
- By how much does the perimeter increase each time?
- Why are the rectangles getting larger?
- Does this pattern keep going?
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 continuing the pattern does not come up during the conversation, ask students to discuss this idea: “What predictions can you make about future rectangles in the set if the pattern continues?”
Standards
- 4.OA.5·Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. <em>For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.</em>
- 4.OA.C.5·Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. <span>For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.</span>
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Comparing Relationships with Equations
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to elicit comparisons of lengths and areas, which will be useful when students decide whether such relationships are proportional in a later activity. While students may notice and wonder many things about these images, the important discussion points are the way that the side lengths, perimeter, and area are increasing.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
Arrange students in groups of 2. 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:
- There are three rectangles on the grid.
- The rectangles are scaled copies.
- The rectangles increase in size from top to bottom.
- The width increases by 3 each time.
- The height increases by 1 each time.
- The small rectangle could fit into the medium rectangle 4 times, and it could fit into the large rectangle 9 times.
Students may wonder:
- By how much does the area increase each time?
- By how much does the perimeter increase each time?
- Why are the rectangles getting larger?
- Does this pattern keep going?
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 continuing the pattern does not come up during the conversation, ask students to discuss this idea: “What predictions can you make about future rectangles in the set if the pattern continues?”
Standards
- 4.OA.5·Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. <em>For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.</em>
- 4.OA.C.5·Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. <span>For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.</span>