Scaled Relationships
5 min
Teacher Prep
Setup
Narrative
This is the first Notice and Wonder activity in the course. Students are shown an image and asked: “What do you notice? What do you wonder?”
Students are given time to write down what they notice and wonder about the image and then time to share their thoughts. Their responses are recorded for all to see. Often, the goal is to elicit observations and curiosities about a mathematical idea that students are about to explore. Pondering the two open questions allows students to build interest about and gain entry into an upcoming task.
While students may notice and wonder many things about these figures, the main purpose of this Warm-up is for students to notice that the side lengths of the polygons in this task cannot be easily determined and to wonder how we can tell whether the figures are scaled copies. This will be useful when students examine corresponding distances that are not side lengths in a later activity.
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 with their partner the things they notice and wonder.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- There are 3 figures on a grid.
- Each figure has 4 sides.
- The figures are different sizes.
- The figures are not symmetric.
- All the sides are diagonal.
- Corresponding angles look like they might have the same measures.
- The figures look like they might be scaled copies.
Students may wonder:
- Why did someone draw this shape? Does it represent an actual object?
- How long are the side lengths?
- Why are the figures shown on a grid?
- Do corresponding angles have the same measure?
- Are these figures scaled copies? If so, what is the scale factor?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses 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 observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If these ideas do not come up during the conversation, ask students to discuss:
- The fact that the side lengths are hard to determine given their orientation on the grid.
- The question of whether the figures are scaled copies and how that could be determined.
Standards
- 7.G.1·Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
- 7.G.A.1·Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
10 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Scaled Relationships
5 min
Teacher Prep
Setup
Narrative
This is the first Notice and Wonder activity in the course. Students are shown an image and asked: “What do you notice? What do you wonder?”
Students are given time to write down what they notice and wonder about the image and then time to share their thoughts. Their responses are recorded for all to see. Often, the goal is to elicit observations and curiosities about a mathematical idea that students are about to explore. Pondering the two open questions allows students to build interest about and gain entry into an upcoming task.
While students may notice and wonder many things about these figures, the main purpose of this Warm-up is for students to notice that the side lengths of the polygons in this task cannot be easily determined and to wonder how we can tell whether the figures are scaled copies. This will be useful when students examine corresponding distances that are not side lengths in a later activity.
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 with their partner the things they notice and wonder.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- There are 3 figures on a grid.
- Each figure has 4 sides.
- The figures are different sizes.
- The figures are not symmetric.
- All the sides are diagonal.
- Corresponding angles look like they might have the same measures.
- The figures look like they might be scaled copies.
Students may wonder:
- Why did someone draw this shape? Does it represent an actual object?
- How long are the side lengths?
- Why are the figures shown on a grid?
- Do corresponding angles have the same measure?
- Are these figures scaled copies? If so, what is the scale factor?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses 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 observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.
If these ideas do not come up during the conversation, ask students to discuss:
- The fact that the side lengths are hard to determine given their orientation on the grid.
- The question of whether the figures are scaled copies and how that could be determined.
Standards
- 7.G.1·Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
- 7.G.A.1·Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.