Transcript Perimeter, Area, and Volume

Measure Up with Common
Core: Hands-on Perimeter,
Area, and Volume
Elizabeth Berman Appelbaum
Slide 1
Area and Perimeter
1 Inch Grid, No Formulas
A=
sq in
P=
in
Slide 2
Area and Perimeter with
Fractions, 1 Inch Grid
A=
P=
sq in
in
Slide 3
Area and Perimeter with
Fractions, 1 Inch Grid, Con.
Do Page 1 of
Worksheet
Slide 4
Area and Perimeter with
Formulas
• Measure the sides first.
Slide 5
Area with Formula, Con.
Sides are w and d inches
𝐴 = 𝒘 × 𝑑 sq in
𝟏
=𝟑 ×𝟐
𝟐
𝟏
= 𝟑 ×𝟐+ 𝟑 ×
𝟐
𝟑
=𝟔+
𝟐
𝟏
=𝟔+𝟏
𝟐
1
= 7 square inches
2
Slide 6
Perimeter with Formula
Sides are w and d inches
𝑃 = 𝟐 𝒘 + 𝒅 𝐢𝐧
𝟏
= 𝟐 3+𝟐
𝟐
Slide 7
Mixed Numbers are Better than
Improper Fractions
• Do not use improper fractions when
– multiplying a mixed number and a whole
number
– Adding a set of mixed numbers
– Adding a set of mixed numbers and
whole numbers
• Reasons: efficiency and usefulness.
• Do page 2 of worksheet.
• I will pass out rulers.
Slide 8
Volume of a Rectangular Prism
• Students must handle actual cubes
• First, find volume and lateral (side)
area without formulas
• Then use formulas.
• Furniture and appliances are
commonly described with width,
depth, and height. So I use w, d, and
h. The formula for volume is
𝑉 = 𝑤𝑑ℎ
Slide 9
SurfaceArea of a Prism
• This formula applies to right prisms (top and bottom
aligned) and right cylinders, with height h.
• First find the perimeter P of the base.
• Then use this formula for lateral area.
𝐿 = 𝑃ℎ
• Fold paper to motivate the formula.
• Best way to measure walls for paint or wallpaper.
• To find total surface area, find lateral area first. Then find top
area, double it, and add that number to lateral area.
• Do page 3 of worksheet.
Slide 10
Playacting
• Work in groups of 2 or 3.
• Each group makes up a show about
area, perimeter, volume, lateral area,
or total surface area.
• Give your show to another group.
• Then watch their show.
Slide 11
Contact Information
Elizabeth Berman Appelbaum, Ph.D.
8275 W 116 Ter
Overland Park KS 66210
Telephone 913.339.9407
E-mail [email protected]
I do private tutoring of mathematics, all
levels.
Materials will be posted at
http://katm.org/wp/common-core/
Slide 12