Lots of Flags
5 min
Teacher Prep
Setup
Narrative
In this Warm-up students reason about figures on a grid and determine which are scaled copies. This reminds students of proportional reasoning in a geometric context, which was done earlier in the course.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time and another 1–2 minutes to share their solutions with their partner. Ask students to make sure they have the same objects identified in the first question. If one partner is missing a set of scaled objects, they should add them to their list during their partner discussion.
As students discuss their answers with their partner, select students to share their answers to the second question during the whole-class discussion. Select students so that different sets of objects and their scale factors are represented in the discussion.
Student Task
-
Which of the geometric objects are scaled versions of each other?
12 shapes on a grid. Shape A, triangle with base 5 units and height 4 units. Shape B, traingle with base 3 units and height 2 units. Shape C, square with sides 5 units. Shape D, rectangle with length 4 units and width 2 units. Shape E, square with sides 2 units. Shape F, rectangle with length 6 units and width 2 units. Shape G, circle with diameter 6 units. Shape H, triangle with base 5 units and height 3 units. Shape I, rectangle with length 6 units and width 3 units. Shape J, circle with diameter a little over 2 units. Shape K, square with sides 3 units. Shape L, circle with diameter a little over 4 units. - Pick two of the objects that are scaled copies, and find the scale factor.
Sample Response
-
- A and B
- C, E, and K
- D and I
- G, J, and L
- Sample response: A is 2 times the size of B. The height of A is 4, and the length of its base is 6. The height of B is 2, and the length of its base is 3.
Activity Synthesis (Teacher Notes)
Invite previously selected students to share their answers to the second question. Ask the rest of the class whether they agree or disagree with the responses.
If time permits, ask students, “Were there any figures that you initially believed were scaled versions of one another but later decided that they weren't? How did you know?”
Anticipated Misconceptions
Students might think H is a scaled version of A or B. Suggest that they consider possible scale factors to get from, for example, A to H.
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.
- 7.RP.2.a·Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
- 7.RP.A.2.a·Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Lots of Flags
5 min
Teacher Prep
Setup
Narrative
In this Warm-up students reason about figures on a grid and determine which are scaled copies. This reminds students of proportional reasoning in a geometric context, which was done earlier in the course.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time and another 1–2 minutes to share their solutions with their partner. Ask students to make sure they have the same objects identified in the first question. If one partner is missing a set of scaled objects, they should add them to their list during their partner discussion.
As students discuss their answers with their partner, select students to share their answers to the second question during the whole-class discussion. Select students so that different sets of objects and their scale factors are represented in the discussion.
Student Task
-
Which of the geometric objects are scaled versions of each other?
12 shapes on a grid. Shape A, triangle with base 5 units and height 4 units. Shape B, traingle with base 3 units and height 2 units. Shape C, square with sides 5 units. Shape D, rectangle with length 4 units and width 2 units. Shape E, square with sides 2 units. Shape F, rectangle with length 6 units and width 2 units. Shape G, circle with diameter 6 units. Shape H, triangle with base 5 units and height 3 units. Shape I, rectangle with length 6 units and width 3 units. Shape J, circle with diameter a little over 2 units. Shape K, square with sides 3 units. Shape L, circle with diameter a little over 4 units. - Pick two of the objects that are scaled copies, and find the scale factor.
Sample Response
-
- A and B
- C, E, and K
- D and I
- G, J, and L
- Sample response: A is 2 times the size of B. The height of A is 4, and the length of its base is 6. The height of B is 2, and the length of its base is 3.
Activity Synthesis (Teacher Notes)
Invite previously selected students to share their answers to the second question. Ask the rest of the class whether they agree or disagree with the responses.
If time permits, ask students, “Were there any figures that you initially believed were scaled versions of one another but later decided that they weren't? How did you know?”
Anticipated Misconceptions
Students might think H is a scaled version of A or B. Suggest that they consider possible scale factors to get from, for example, A to H.
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.
- 7.RP.2.a·Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
- 7.RP.A.2.a·Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.