Measurement 4.1
Directly Measuring Area and Volume
Directly Measuring Area and Volume
WATCH: The Challenge of Measuring Area
WATCH: The Challenge of Measuring Area
Measuring area is arguably the most challenging attribute to measure directly. Watch this video as it describes why this is the case and then introduces a tool to make measuring area more bearable.
Measuring area is arguably the most challenging attribute to measure directly. Watch this video as it describes why this is the case and then introduces a tool to make measuring area more bearable.
Discuss
Discuss
Reflect on the ideas in the video and talk about your own experiences of teaching area, including any challenges your students have had with this concept.
Reflect on the ideas in the video and talk about your own experiences of teaching area, including any challenges your students have had with this concept.
TASK: Analyzing Student Work
TASK: Analyzing Student Work
Watch these two videos of Blake, a grade 7 student, as he uses an array to find the area of a rectangle.
Watch these two videos of Blake, a grade 7 student, as he uses an array to find the area of a rectangle.
Discuss
Discuss
What does Blake know about area and what does he still need to learn?
What does Blake know about area and what does he still need to learn?
What is Blake thinking as he sets out the paper tiles?
What is Blake thinking as he sets out the paper tiles?
What focus questions does Blake's teacher use to encourage him to find a shortcut? And how did they nudge Blake's learning forward?
What focus questions does Blake's teacher use to encourage him to find a shortcut? And how did they nudge Blake's learning forward?
Discuss
Discuss
Blake appears to be using the array structure to work out how many squares fit in the rectangle. However he is not able to use the array idea to help him know how many part units he would need across the base.
Blake appears to be using the array structure to work out how many squares fit in the rectangle. However he is not able to use the array idea to help him know how many part units he would need across the base.
Why does Blake have difficulty working out the area of the part units? How does the teacher's prompt help him? What else might you do to help Blake advance?
Why does Blake have difficulty working out the area of the part units? How does the teacher's prompt help him? What else might you do to help Blake advance?
Share
Share
Record highlights from your discussion about Blake and the challenges of directly measuring area in the Collaborative Notebook.
Record highlights from your discussion about Blake and the challenges of directly measuring area in the Collaborative Notebook.
Want to Dig Deeper?
Want to Dig Deeper?
Read more about some of the big ideas involved in measuring area and volume. Use this reading to further clarify some of the challenges around measuring area and volume and some of the instructional moves that can help develop the associated concepts and skills.
Read more about some of the big ideas involved in measuring area and volume. Use this reading to further clarify some of the challenges around measuring area and volume and some of the instructional moves that can help develop the associated concepts and skills.
As a facilitation strategy, you could assign sections of this article to different group members and have each member share a summary of their reading with the group
As a facilitation strategy, you could assign sections of this article to different group members and have each member share a summary of their reading with the group
CONSOLIDATE and SHARE
CONSOLIDATE and SHARE
Watch: Revisiting Blake
Watch: Revisiting Blake
Consider how the deliberate choice of materials can help nudge students away from a "cover and count" approach to directly measuring area to the more practical shortcuts of indirectly measuring area.
Consider how the deliberate choice of materials can help nudge students away from a "cover and count" approach to directly measuring area to the more practical shortcuts of indirectly measuring area.
Discuss and Share
Discuss and Share
Talk with your team about the five tips mentioned in the video on how materials can provoke learning about area. What struck you as being significant? Were there any ideas that you wanted to push back against or new questions that arose? What are some of your own ideas for how to help students advance in their understanding of measuring area?
Talk with your team about the five tips mentioned in the video on how materials can provoke learning about area. What struck you as being significant? Were there any ideas that you wanted to push back against or new questions that arose? What are some of your own ideas for how to help students advance in their understanding of measuring area?
Record your thoughts in the Collaborative Notebook.
Record your thoughts in the Collaborative Notebook.
