Measurement 1.1
What does it Mean to Measure?
What does it Mean to Measure?
Returning Spatial Reasoning to the Realm of Measurement
Returning Spatial Reasoning to the Realm of Measurement
WATCH: Presenting the Envelope Task
WATCH: Presenting the Envelope Task
TASK: Exploring Measurement
TASK: Exploring Measurement
What can you say about the shaded part of this envelope?
What can you say about the shaded part of this envelope?
Individually, take a moment to visualize relationships and form hypotheses.
Individually, take a moment to visualize relationships and form hypotheses.
Verbalize your ideas with your table group.
Verbalize your ideas with your table group.
Download and print the envelope. With a partner, verify your ideas. Record your thoughts. Pay attention to any connections to spatial reasoning.
Download and print the envelope. With a partner, verify your ideas. Record your thoughts. Pay attention to any connections to spatial reasoning.
Discuss and Share
Discuss and Share
Talk about the strategies you used to find the area of the envelope flap.
Talk about the strategies you used to find the area of the envelope flap.
How did you draw on spatial reasoning to solve this task? Review the Paying Attention to Spatial Reasoning document and record. How did you also use Proportional reasoning? Fractions? Algebraic reasoning? Be explicit. Were there any types of reasoning that you and your group didn’t draw on? If so, how might you attack the task from that perspective?
How did you draw on spatial reasoning to solve this task? Review the Paying Attention to Spatial Reasoning document and record. How did you also use Proportional reasoning? Fractions? Algebraic reasoning? Be explicit. Were there any types of reasoning that you and your group didn’t draw on? If so, how might you attack the task from that perspective?
What attributes of this shape did you describe? What other ones could you have described? What other attributes might have been highlighted if you were given this envelope.
What attributes of this shape did you describe? What other ones could you have described? What other attributes might have been highlighted if you were given this envelope.
What was the impact of visualizing and verbalizing, before verifying a solution to the problem? Discuss the impact of this spatial reasoning strategy and talk about how you could apply it in your own teaching. Listen as Sharon and the Learning Team share their thoughts.
What was the impact of visualizing and verbalizing, before verifying a solution to the problem? Discuss the impact of this spatial reasoning strategy and talk about how you could apply it in your own teaching. Listen as Sharon and the Learning Team share their thoughts.
Optional: Want to Go Deeper?
Optional: Want to Go Deeper?
1. Consider Different Envelopes.
1. Consider Different Envelopes.
How would the task have changed if you were given any of these envelopes? All these questions are adaptations of an EQAO grade 6 question that asked students to use a ruler to calculate the area. Discuss the impact each of these instructional decisions would have on a lesson and the learning goal.
How would the task have changed if you were given any of these envelopes? All these questions are adaptations of an EQAO grade 6 question that asked students to use a ruler to calculate the area. Discuss the impact each of these instructional decisions would have on a lesson and the learning goal.
2. Consider Different Rectangles.
2. Consider Different Rectangles.
You found that the shaded part of the envelope was an eighth of the whole. And you probably did so by proving that it was “a fourth of a half.” But is it true that the diagonals of a rectangle always create fourths?
You found that the shaded part of the envelope was an eighth of the whole. And you probably did so by proving that it was “a fourth of a half.” But is it true that the diagonals of a rectangle always create fourths?
Develop your “proofs” and talk about them as a group. Share your thinking on the Collaborative Notebook.
Develop your “proofs” and talk about them as a group. Share your thinking on the Collaborative Notebook.
Listen to the strategies of the Learning Team. How do their strategies compare with yours? Which ones do you find particularly persuasive?
Listen to the strategies of the Learning Team. How do their strategies compare with yours? Which ones do you find particularly persuasive?
Reflect on the teaching and learning interactions in this video section What do you notice? Which facilitative moves were helpful? Which ones might you do differently? Are there questions you wished had been asked that weren’t?
Reflect on the teaching and learning interactions in this video section What do you notice? Which facilitative moves were helpful? Which ones might you do differently? Are there questions you wished had been asked that weren’t?
They say brilliance is often transcribed on the back of a napkin. Check out Wayne’s algebraic proof (constructed at home with his son) and talk about the power of algebra for generalizing principles.
They say brilliance is often transcribed on the back of a napkin. Check out Wayne’s algebraic proof (constructed at home with his son) and talk about the power of algebra for generalizing principles.
CONSOLIDATE
CONSOLIDATE
What Do You Think?
What Do You Think?
Is the envelope task a measurement task? Why or why not? What are the essential ideas that make something a measurement task? What does measuring require?
Is the envelope task a measurement task? Why or why not? What are the essential ideas that make something a measurement task? What does measuring require?
Watch
Watch
Listen to Helene and Scott from the Learning Team share their reflections on measurement.
Listen to Helene and Scott from the Learning Team share their reflections on measurement.
Share
Share
Record your insights, questions and conclusions in the Collaborative Notebook. Take some time to read through the thoughts of others and comment on any similarities and differences.
Record your insights, questions and conclusions in the Collaborative Notebook. Take some time to read through the thoughts of others and comment on any similarities and differences.
