23.5-6 Volume of a Cylinder

Step 1
Measure the height (h) of the cylinder. Height is sometimes referred to as the length.

Step 2
Measure the radius (r) of the cylinder. Radius is the distance from the outer edge to the center of the circle.

Step 3
Square the radius. (Multiply the radius by itself.)

Step 4
Mulitply the product (radius squared) from step 3 by pi.
Step 5
Multiply the product from Step 4 by the height

Step 6
Write you answer in the proper cubic unit of measurement.

23.4 volumes of Pyramids

The area of a pyramid can be found by using the following equation:

V= 1/3Bh, where B = l x w

This is read as "volume equals one-third base times height." Watch the following video to see why

23.2 Estimate and find Volume

Things to remember:

• Volume is given in cubic units - a little three above the units
• multiply the area of the base (length times width for rectangles - 1/2 lenght times width f or triangles) times the height to find volume

The robot is back...

23.1 Algebra: Surface Area p.502-505

Here is a video that demonstrates finding surface area of a variety of types of prisms. Please excuse the accent.

This video shows how to find surface area for a cylinder.

22.3 Models of Solid Figures

Go to this link from senteacher.org for printable nets that can be used to construct solid figures.

Please make sure to label your solid figure with the following 5 items:

1. Your name
2. Name of the shape
3. Number of faces
4. Number of edges
5. Number of vertices

22.1 Types of Solid Figures

Polyhedron (Polyhedra - plural): solid figure with flat faces that are polygons

• Prism (named for the shape of its bases): polyhedron with two congruent and parallel bases. - The lateral faces(not bases) are rectangles.
• Pyramid (related to a prism) - has a polygon base and triangular sides

NON POLYHEDRON: curved sides with a circular base

• Cylinder: two flat parallel and congruent sides bases and a curved surface.
• Cone: (related to a cylinder) - has one flat circular base and a curved surface leading to a vertex.

The serious video about circumference

A video about circles from the teacher you wish you had...

Circle Song... another one...

Circle Rap

Enjoy!

Circumference jingle

Don't you wish we did more jingles in class!

20.4 Circumference

borrowed from wikihow.com

Below is an explanation from aaamath.com

The circumference of a circle is the distance around the outside of the circle. It could be called the perimeter of the circle.

How to find the circumference of a circle:

• The circumference of a circle can be found by multiplying pi ( π = 3.14 ) by the diameter of the circle.
• If a circle has a diameter of 4, its circumference is 3.14*4=12.56
• If you know the radius, the diameter is twice as large.

Check your understand with the quiz at the bottom of this tutorial from mathgoodies.com

20.3 Draw a Diagram

The focus of this lesson is to be able to illustrate situations in order to help you find solutions to problems. DRAW A PICTURE

20.2 Perimeter

Find the perimeter by adding up all the external (outside) sides. Watch the video for examples of increasingly difficult problems

19.4 Appropriate Tools and Units (p.428-431)

Precision

• Being very exact and accurate and able reproduce the same measurement over and over again
• Here would be an example of less to more precise units of measurement: miles, yards, feet, inches, 1/2 inches, 1/4 inches... The smaller the unit of measure used, the more precise the measurement.

Try this ruler game from rsinnovative.com to check your understanding of measuring in customary units (inches)

19.3 Relate Customary and Metric

Here are the estimates you need for relating customary and metric

1 in ≈ 2.5 cm

1 ft ≈ 30 cm

1 mi ≈ 1.6 km

1 m ≈ 39 in

1 kg ≈ 2.2 lb

1 oz ≈ 30 g

1 fl oz ≈ 30 ml

1 L ≈ 1 qt

19.1 Customary Conversion

Here is a link that shows nice examples for customary measurement and units for conversion from Mountain City Elementary

Try this matching game made by Harcourt (the people who make our textbooks)

18.4 Symmetry

We will discuss two kinds of symmetry:

1. line symmetry: reflection across a line of symmetry

- the image below has line symmetry, this is shown with the dotted lines

2. rotational symmetry: turning around a center point (point of rotation) and lining up again

-the flowers above also have rotational symmetry because you could turn them and have them line up again.

Check out these links from mathisfun.com for line symmetry and rotational symmetry

• Check out this illustration from innovations learning that shows lines of symmetry in shapes
• Here is game from innovations learning that will check your understanding of lines of symmetry form

18.2 Tessellations (p.397-399)

A tessellation is a design of repeating shapes that fit together without gaps or overlaps.

Shapes that tessellate easily include:

• triangles (three sided)
• quadrilaterals (four sided)
• parallelograms (opposite sides parallel - and congruent)

This link from DIY Tessellations is very helpful for helping you think about how to make your own tessellation.

M. C. Escher is likely the best known artist who used tessellations. Check out this link with some of his tessellations:

Here is a link of "wallpaper patterns" that Escher used as inspiration

18.1 Transformations

Check out these links for more exploration with transformation:

• This link uses shapes to model what we did during story time.
• Link from UTC.edu used during "story time" with examples of transformations.
• http://www.bbc.co.uk/schools/ks3bitesize/maths/shape_space/transformations1/revise1.shtml