Area of a Circle

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


Field

6 y

d

4 y

dS

HE

D

GR

AS

S


Sample Response to Discuss: Kadu

1. Try to explain what Kadu has done.

2. Do you agree with his conclusion? Why / Why not?


Sample Response to Discuss: Shifa

1. Try to explain what Shifa has done.

2. Do you agree with her conclusion? Why / Why not?


Sample Response to Discuss: Alice

1. Try to explain what Alice has done.

2. Do you agree with her conclusion? Why / Why not?


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

The Area of a Circle Projector Resources

Field

P-1


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


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!


Sample Student Work: Kadu

P-4


Sample Student Work: Shifa

P-5


Sample Student Work: Alice

P-6

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

Area of a Circle

Documents

Transcript of Area of a Circle