Grid Moves
10 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to familiarize students with an isometric grid, which will be useful when students transform figures on an isometric grid in a later activity. While students may notice and wonder many things, characteristics such as the measures of the angles in the grid and the diagonal parallel lines are the important discussion points. Students are not expected to know that each angle in an equilateral triangle is 60 degrees, but after previous experience with supplementary angles, circles, and rotations, they may be able to explain why each smaller angle is 60 degrees. Many things they notice may be in comparison to the square grid paper which is likely more familiar.
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 isometric grid 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 with their partner, followed by a whole-class discussion.
Student Task
What do you notice? What do you wonder?
Sample Response
Things students may notice:
- There are three sets of parallel grid lines.
- The line segments form equilateral triangles.
- The individual angles in the equilateral triangles are 60 degrees.
- There are vertical lines but no horizontal lines.
- There are no 90-degree angles made by the grid lines.
- Each vertex has 6 line segments coming from it.
- The grid is made out of equilateral triangles instead of squares.
Things students may wonder:
- Why are there no 90-degree angles?
- Why are there no squares?
- Are we going to use this kind of grid?
- Why would we use this grid instead of the square grid?
- Why are there no horizontal lines?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the image, and show where each of the features students notice is located on the actual grid itself, such as triangles, angles, and line segments. 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 angle measures do not come up during the conversation, ask students to think about how they could figure out the measure of each angle. Some may measure with a protractor, and some may argue that since 6 angles share a vertex where each angle is identical, each angle measures 60∘ because 360÷6=60. Establish that each angle measures 60∘.
Math Community
After the Warm-up, display the class Math Community Chart for all to see and explain that the listed “doing math” actions come from the sticky notes students wrote in the first exercise. Give students 1 minute to review the chart. Then invite students to identify something on the chart they agree with and hope for the class or something they feel is missing from the chart and would like to add. Record any additions on the chart. Tell students that the chart will continue to grow and that they can suggest other additions that they think of throughout today’s lesson during the Cool-down.
Standards
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 8.G.1·Verify experimentally the properties of rotations, reflections, and translations:
- 8.G.A.1·Verify experimentally the properties of rotations, reflections, and translations:
25 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Grid Moves
10 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to familiarize students with an isometric grid, which will be useful when students transform figures on an isometric grid in a later activity. While students may notice and wonder many things, characteristics such as the measures of the angles in the grid and the diagonal parallel lines are the important discussion points. Students are not expected to know that each angle in an equilateral triangle is 60 degrees, but after previous experience with supplementary angles, circles, and rotations, they may be able to explain why each smaller angle is 60 degrees. Many things they notice may be in comparison to the square grid paper which is likely more familiar.
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 isometric grid 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 with their partner, followed by a whole-class discussion.
Student Task
What do you notice? What do you wonder?
Sample Response
Things students may notice:
- There are three sets of parallel grid lines.
- The line segments form equilateral triangles.
- The individual angles in the equilateral triangles are 60 degrees.
- There are vertical lines but no horizontal lines.
- There are no 90-degree angles made by the grid lines.
- Each vertex has 6 line segments coming from it.
- The grid is made out of equilateral triangles instead of squares.
Things students may wonder:
- Why are there no 90-degree angles?
- Why are there no squares?
- Are we going to use this kind of grid?
- Why would we use this grid instead of the square grid?
- Why are there no horizontal lines?
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the image, and show where each of the features students notice is located on the actual grid itself, such as triangles, angles, and line segments. 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 angle measures do not come up during the conversation, ask students to think about how they could figure out the measure of each angle. Some may measure with a protractor, and some may argue that since 6 angles share a vertex where each angle is identical, each angle measures 60∘ because 360÷6=60. Establish that each angle measures 60∘.
Math Community
After the Warm-up, display the class Math Community Chart for all to see and explain that the listed “doing math” actions come from the sticky notes students wrote in the first exercise. Give students 1 minute to review the chart. Then invite students to identify something on the chart they agree with and hope for the class or something they feel is missing from the chart and would like to add. Record any additions on the chart. Tell students that the chart will continue to grow and that they can suggest other additions that they think of throughout today’s lesson during the Cool-down.
Standards
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 8.G.1·Verify experimentally the properties of rotations, reflections, and translations:
- 8.G.A.1·Verify experimentally the properties of rotations, reflections, and translations: