area of a circle
DESCRIPTION
AreaTRANSCRIPT
-
CONCEPT DEVELOPMENT
Mathematics Assessment Project
CLASSROOM CHALLENGES A Formative Assessment Lesson
The Area of a Circle
Mathematics Assessment Resource Service
University of Nottingham & UC Berkeley
Beta Version
For more details, visit: http://map.mathshell.org 2014 MARS, Shell Center, University of Nottingham May be reproduced, unmodified, for non-commercial purposes under the Creative Commons license detailed at http://creativecommons.org/licenses/by-nc-nd/3.0/ - all other rights reserved
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Student Materials The Area of a Circle S-1 2014 MARS, Shell Center, University of Nottingham
The Goat and the Grass
A goat is tied to the corner of a rectangular shed in a large field full of grass. The rope is 3 yards long and a plan view (from above) of the shed and field is shown below.
1. Sketch the area of grass the goat can eat. Your sketch does not have to be accurate.
2. Calculate the area of grass that the goat can eat. Show all your reasoning.
3. What length of rope would enable the goat to eat 10 square yards of grass? Show all your reasoning.
6 yd
4 yd SHED
GRASS
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Student Materials The Area of a Circle S-2 2014 MARS, Shell Center, University of Nottingham
Field
6 y
d
4 y
dS
HE
D
GR
AS
S
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Student Materials The Area of a Circle S-3 2014 MARS, Shell Center, University of Nottingham
Sample Response to Discuss: Kadu
1. Try to explain what Kadu has done.
2. Do you agree with his conclusion? Why / Why not?
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Student Materials The Area of a Circle S-4 2014 MARS, Shell Center, University of Nottingham
Sample Response to Discuss: Shifa
1. Try to explain what Shifa has done.
2. Do you agree with her conclusion? Why / Why not?
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Student Materials The Area of a Circle S-5 2014 MARS, Shell Center, University of Nottingham
Sample Response to Discuss: Alice
1. Try to explain what Alice has done.
2. Do you agree with her conclusion? Why / Why not?
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Student Materials The Area of a Circle S-6 2014 MARS, Shell Center, University of Nottingham
The Goat and the Grass (Revisited)
A goat is tied to the corner of a rectangular shed in a large field full of grass. The rope is 8 yards long and a plan view (from above) of the shed and field is shown below.
1. Sketch the area of grass the goat can eat. Your sketch does not have to be accurate.
2. Calculate the area of grass that the goat can eat. Show all your reasoning.
3. What length of rope would enable the goat to eat 25 square yards of grass? Show all your reasoning.
6 yd
4 yd SHED
GRASS
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The Area of a Circle Projector Resources
Field
P-1
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The Area of a Circle Projector Resources
The Problem
The farmer is going to leave the goat for a day and wants it
to have access to an area of exactly 20 square yards of
grass.
How long should he make the rope?
On another occasion, he wants to leave the goat for longer,
so he might want the goat to have 50 square yards of
grass.
Your task is to find out how long he should make the rope
to give the goat access to different areas of grass.
P-2
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The Area of a Circle Projector Resources
Sample Responses to Discuss
P-3
1. Take turns to explain to the rest of the group what the
student in your sample response has done and what
your answers are to the questions on the sheet.
2. Listen carefully to the explanations.
Ask questions if you dont understand.
3. When everyone is satisfied with the explanations,
you may want to change some of your own ideas!
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The Area of a Circle Projector Resources
Sample Student Work: Kadu
P-4
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The Area of a Circle Projector Resources
Sample Student Work: Shifa
P-5
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The Area of a Circle Projector Resources
Sample Student Work: Alice
P-6
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Mathematics Assessment Project
CLASSROOM CHALLENGES
This lesson was designed and developed by the
Shell Center Team
at the
University of Nottingham
Malcolm Swan, Clare Dawson, Sheila Evans,
Marie Joubert and Colin Foster
with
Hugh Burkhardt, Rita Crust, Andy Noyes, and Daniel Pead
It was refined on the basis of reports from teams of observers led by
David Foster, Mary Bouck, and Diane Schaefer
based on their observation of trials in US classrooms
along with comments from teachers and other users.
This project was conceived and directed for
MARS: Mathematics Assessment Resource Service
by
Alan Schoenfeld, Hugh Burkhardt, Daniel Pead, and Malcolm Swan
and based at the University of California, Berkeley
We are grateful to the many teachers, in the UK and the US, who trialed earlier versions
of these materials in their classrooms, to their students, and to
Judith Mills, Mathew Crosier, Nick Orchard and Alvaro Villanueva who contributed to the design.
This development would not have been possible without the support of
Bill & Melinda Gates Foundation
We are particularly grateful to
Carina Wong, Melissa Chabran, and Jamie McKee
2014 MARS, Shell Center, University of Nottingham This material may be reproduced and distributed, without modification, for non-commercial purposes, under the Creative Commons License detailed at http://creativecommons.org/licenses/by-nc-nd/3.0/
All other rights reserved. Please contact [email protected] if this license does not meet your needs.
Teacher's GuideIntroductionBefore The LessonSuggested Lesson OutlineSolutions
Student MaterialsThe Goat and the GrassFieldSample Response to Discuss: KaduSample Response to Discuss: ShifaSample Response to Discuss: AliceThe Goat and the Grass (Revisited)
Projector ResourcesFieldThe ProblemSample Responses to DiscussSample Student Work: KaduSample Student Work: ShifaSample Student Work: Alice
Credits