Ged geometry - from start to finish
I. Identification and properties of common shapes - planar
(shapes found on the formula sheet for GED)
- Circle (radius, diameter, pi)
- Square (all sides equal and perpendicular to each other)
- Rectangle (opposite sides equal in length and sides perpendicular)
- Parallelogram (opposite sides parallel but not perpendicular, height is perpendicular)
- Triangle (right, isosceles, equilateral and scalene, height perpendicular to base)
- Trapezoid (parallel sides are bases, height must be perpendicular to base)
Emphasis suggestions:
- Understanding relationship between pi, radius and diameter
- The height of an object is always perpendicular to the base and not necessarily the length of the side
- meaning of perpendicular
https://www.oercommons.org/courses/geometry-basic-student-s-edition/view
https://www.oercommons.org/courses/geometry-basic-teacher-s-edition/view
http://www.letspracticegeometry.com/free-geometry-worksheets/
II. Perimeter of common shapes
- Perimeter always involves addition (exception of circle)
a. Fancy word for perimeter of a circle is circumference
2. Key words
-distance around, revolution (circle), laps, enclose, surround, outline, encircle, border
3. Finding perimeter with lengths given in different units
a. All units of measure must be the same
b. Convert to same units before you add (1’ + 1” in does not equal 2’)
4. Perimeter word problems
a. Simple perimeter problems
b. Finding length of a side given the perimeter
5. Perimeter problems where the word perimeter is not used
6. Perimeter of compound shapes
Emphasis suggestions:
- real life examples of perimeter - laps, interior design,
- no need for formula! Perimeter always involves addition (exception of circle)
- perimeter is always a unit of length
III. Pythagorean Theorem
1. How to solve for a, b, or c. C is always the longest side. Shortest side corresponds to lowest angle. Knowing the difference between leg and hypotenuse
Emphasis suggestions:
- do not get bogged down in the formula - two sides of a triangle NEVER add up to the third side. have students try to make a triangle with a two 2 inch sticks and a 4 inch stick. can they do it?
- Pythagorean in life - ladder leaning against a building, handicap ramp, construction
- Pythagorean triples (3-4-5, 5-12-13, 7-24-25, 8-15-17)
http://stemsheets.com/math/pythagorean-theorem-worksheet
IV. Area of common shapes
- Area always involves multiplication
1. Introduce area formulas for shapes
2. Define what height is (always perpendicular to base)
2. Key words
- Cover, square units, paint, carpet, tile, glass
3. Finding area with different units (introduces conversions)
- Cannot multiply feet by yards etc, convert before you do calculation
4. Area word problems
1. Simple area problems (finding area given dimensions)
2. Finding missing dimension given area
5. Area word problems where the word area is not used
6. Area of compound shapes (adding areas)
1. Finding area of two of the same shape
2. Finding area of an L shaped object where you have to draw in rectangles
3. Finding area of two different shapes (basketball court)
7. Area of compound shapes (subtracting areas)
1. Finding area of shaded region
a. Rectangle or square within a rectangle (picture frame for example)
b. Circle within a circle (mirror with wood frame/ tablecloth hanging down)
Emphasis Suggestions:
-Area is always in square units and the units must match (inches and inches)
- Real life area problems such as cost of carpeting or painting a room
- Bring out formula sheet for ged and start going over it
V. Identification and properties of 3-dimensional shapes/solids
- Rectangular prism (fancy word for a box) and cube
- Right prism
1. A right prism is any polygon bases with sides perpendicular to that base
a. Triangular tube, hexagonal tube (have a handout with pictures perhaps or an actual triangular tube)
3. Cylinder - height and radius, examples of cylinders - soup can, pipe, tube
4. Cone - Height and radius, examples of cones - ice cream cone, party hats, tee pees
5. Square pyramid - the base is a square so the sides of the base are equal
6. Sphere - only measurement needed is radius or diameter -ball, orb, marble
Emphasis Suggestions:
- Able to identify the above given shapes in the world around you
VI. Surface area of 3-dimensional shapes/solids
- What is surface area? (square units) - sum of the area of all the sides of a solid
- Key words (material, wrapping paper, cardboard for a box)
- Formulas and where they come from
- Finding the surface area
- Surface area in word problems
- Finding missing dimensions given surface area
Emphasis Suggestions:
-Surface area is like the area of a 3 dimensional object
- Difference between area and surface area
- surface area being in square units
- Show where formula for surface area of rectangular prism and cube comes from - perhaps derive it
- Don’t forget ged formula sheet
https://www.oercommons.org/courses/difference-between-volume-and-surface-area/view
VII. Volume of solids
- What is volume (cubic units)
- Key words (fill, capacity, space, hold)
- Formulas and where they come from (Volume is the area of the base (B) times the height)
- Calculating volumes of different solids
- Volume word problems
- Finding missing dimensions given the volume
Emphasis Suggestions:
-Volume always in cubic units and units must match
-Volume in real life (pool, air in a balloon, concrete)
- Difference between B (area of the base) and b (length of the base) as given on GED formula sheet
- Show how V=Bh is evident in the volume of a cylinder formula and rectangular prism formula (from the GED formula sheet)
https://www.oercommons.org/courses/geometry-solid-geometry-volume