Dilations on a Square Grid
5 min
Teacher Prep
Setup
Required Preparation
Narrative
In this Warm-up, students estimate a scale factor based on a picture showing the center of the dilation, a point, and its image under the dilation.
Launch
Provide access to geometry toolkits. Clarify that “estimate” doesn’t mean “guess” and encourage students to use any tools available to make a precise estimate (MP5). Give students 2 minutes of quiet work time followed by a whole-class discussion.
Student Task
Point C is the dilation of point B with center of dilation A and scale factor s.
Estimate s. Be prepared to explain your reasoning.
Sample Response
Sample response: The scale factor s is about 2.3 because the distance from A to C is a little more than twice the distance from A to B.
Activity Synthesis (Teacher Notes)
The goal of this discussion is to review different ways to determine scale factor. Discuss with students:
-
“How did you measure distances?” (I used a ruler. I used an index card and marked off the distances.)
-
“Is the scale factor greater than 1?” (Yes.) “How do you know?” (The point C is further from A than B.)
-
“Is the scale factor greater than 2?” (Yes.) “How do you know?” (The distance from C to A is more than twice the distance from B to A.)
-
“Is the scale factor greater than 3?” (No.) “How do you know?” (The distance from C to A is less than 3 times the distance from B to A.)
- “Is the scale factor greater or less than 2.5?” (Less than.) “How do you know?” (The distance from C to A is less than 2.5 times the distance from B to A.)
Standards
- 8.G.A·Understand congruence and similarity using physical models, transparencies, or geometry software.
- 8.G.A·Understand congruence and similarity using physical models, transparencies, or geometry software.
10 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Dilations on a Square Grid
5 min
Teacher Prep
Setup
Required Preparation
Narrative
In this Warm-up, students estimate a scale factor based on a picture showing the center of the dilation, a point, and its image under the dilation.
Launch
Provide access to geometry toolkits. Clarify that “estimate” doesn’t mean “guess” and encourage students to use any tools available to make a precise estimate (MP5). Give students 2 minutes of quiet work time followed by a whole-class discussion.
Student Task
Point C is the dilation of point B with center of dilation A and scale factor s.
Estimate s. Be prepared to explain your reasoning.
Sample Response
Sample response: The scale factor s is about 2.3 because the distance from A to C is a little more than twice the distance from A to B.
Activity Synthesis (Teacher Notes)
The goal of this discussion is to review different ways to determine scale factor. Discuss with students:
-
“How did you measure distances?” (I used a ruler. I used an index card and marked off the distances.)
-
“Is the scale factor greater than 1?” (Yes.) “How do you know?” (The point C is further from A than B.)
-
“Is the scale factor greater than 2?” (Yes.) “How do you know?” (The distance from C to A is more than twice the distance from B to A.)
-
“Is the scale factor greater than 3?” (No.) “How do you know?” (The distance from C to A is less than 3 times the distance from B to A.)
- “Is the scale factor greater or less than 2.5?” (Less than.) “How do you know?” (The distance from C to A is less than 2.5 times the distance from B to A.)
Standards
- 8.G.A·Understand congruence and similarity using physical models, transparencies, or geometry software.
- 8.G.A·Understand congruence and similarity using physical models, transparencies, or geometry software.