Math Leadership Support Network 08-09 Developing Formulas for Perimeter and Area

Math Leadership Support Network ’08-’09

Developing Formulas Developing Formulas for for

Perimeter and AreaPerimeter and Area


With your talking With your talking partner(s), partner(s), discuss…discuss…

Why do our Why do our students struggle students struggle with finding with finding Perimeter and Perimeter and Area?Area?


Prancer

the Perimeter Pony


x


Arnie, the Area Aardvark



Classroom Practice:Classroom Practice:

1.1. How many steps will it take for How many steps will it take for

Prancer to prance around the Prancer to prance around the

perimeter of…. perimeter of….

- an index card?- an index card?

- your binder?- your binder?

- your desk?- your desk?

- the poster on the wall?- the poster on the wall?


Classroom Practice:Classroom Practice:

1.1. How many Arnies will it take How many Arnies will it take to cover…to cover…

- an index card?- an index card?

- your binder?- your binder?

- your desk?- your desk?

- the poster on the wall?- the poster on the wall?


Use your 5 one inch Use your 5 one inch square tiles to create square tiles to create oneone field for Arnie and field for Arnie and

Prancer.Prancer.

**Sides must be connected, Sides must be connected,

not just vertices…not just vertices…

NOT


Compare your field to the Compare your field to the fields of your table fields of your table partners…partners…

Did we all get the same Did we all get the same field?field?

If we prance Prancer around If we prance Prancer around our fields, would we all our fields, would we all get the same perimeter?get the same perimeter?


How many times can Arnie How many times can Arnie plop on your field? plop on your field?

Compare your answer to Compare your answer to your table mates…your table mates…


We all used 5 square tiles…We all used 5 square tiles…

Did we get the same Did we get the same perimeter with Prancer?perimeter with Prancer?

Did we get the same area Did we get the same area with Arnie? with Arnie?

How can this happen?How can this happen?


Continue to use 5 Continue to use 5 square tiles, but this square tiles, but this time record your time record your fields on the geo fields on the geo paper and FIND AS paper and FIND AS MANY FIELDS AS MANY FIELDS AS YOU CAN…YOU CAN…


What are we building with What are we building with the 5 squares?the 5 squares?

WHY are we using 5 square WHY are we using 5 square tiles and not 4?tiles and not 4?

Why are we going from Why are we going from using tiles to geo-board using tiles to geo-board paper?paper?


How many How many differentdifferent fields did you come up fields did you come up with?with?


Try different sizes Try different sizes of fields with your of fields with your partner…. (see partner…. (see fields 1-11)fields 1-11)


Dig Dig Deeper…Deeper…

What if I have 24 feet of What if I have 24 feet of fencing? Will the same 24 fencing? Will the same 24 feet, regardless of how I lay it feet, regardless of how I lay it out, yield the same pen?out, yield the same pen?



If I know that I have an If I know that I have an AREA of 8 square units, AREA of 8 square units, can you draw me a shape? can you draw me a shape?



If I know that I have a If I know that I have a perimenter of 8 units, can perimenter of 8 units, can you draw me a shape? you draw me a shape?


When we just give our When we just give our students a formula up students a formula up front, we give them front, we give them permission to permission to quit quit thinkingthinking…. ….

Additionally, we assume Additionally, we assume that students can identify that students can identify basebase and and height height and and plug-plug-and-chug and-chug those values into those values into a formula….a formula….


What is the formula What is the formula that we give our that we give our students for finding students for finding the area of the area of rectangles?rectangles?

Documents

Math Leadership Support Network 08-09 Developing Formulas for Perimeter and Area