Performance Stations in Math
Geometry/Measurement
Grade 9
by
Liliane Gauthier
Teacher / Educational Consultant
Saskatoon Board of Education

1. Geometry/Measurement
Angles, Lines & Line Segments: Grade 9
G/M-1e

Materials:
  small rectangle or square of colored paper
  mira
  Geometry Set
  cardboard strips

Your friend call you over the telephone and says,
"How can you draw complementary angles".

You reply, "Get your ______________________ and
follow these steps."

1.	Choose a manipulative to replace the above blank and write the rest the conversation.
2.	Draw your construction according to your reply.
3.	You have completed the instructions and your friend says, "Yes, but how do you know that they are complementary?" Write what you could answer your friend.
4.	Is it possible to draw the following angles? If yes, draw them. If no, explain why it is not possible.
	a)	Two adjacent obtuse angles that are complementary.
	b)	Two adjacent angles, one acute and one obtuse that are complementary.
	c)	Two adjacent reflex angles that are complementary.
	d)	Two adjacent congruent angles that are complementary.
	e)	Three adjacent angles that are complementary angles.
	f)	Two complementary angles who together are congruent to a reflex angle.

2. Geometry/Measurement
Angles, Lines & Line Segments: Grade 9
G/M-1e

Materials:
  small rectangle or square of colored paper
  mira
  Geometry Set
  cardboard strips

1.	Use one or more of the above materials to draw three adjacent angles that are supplementary.
2.	How do you know that angles are complementary?
3.	Is it possible to draw the following angles? If yes, draw them. If no, explain why it is not possible.
	a)	Two adjacent angles, one acute and one obtuse that are supplementary.
	b)	Three adjacent obtuse angles that are supplementary.
	c)	Two adjacent acute angles that are supplementary.
	d)	Two adjacent congruent angles that are supplementary.
	e)	Two adjacent angles, one reflex and the other acute that are supplementary.

4. Geometry/Measurement
Angles, Lines & Line Segments: Grade 9
G/M-1f, G/M-3

Materials:
  mira
  protractor
  Geometry Set
  ruler

1.	Use the mira or the instruments in your geometry set to draw two horizontal parallel lines that are about 6 cm long and 2 cm apart.
2.	Use a ruler and the instruments in your geometry set to draw two horizontal nonparallel lines that are about 6 cm long and 2 cm apart.
3.	Draw a transversal in each of your above constructions. Label the angles that are formed by the transversal. Use different labels for each angle.
4.	Use the chart below to compare your two constructions.

	Parallel Lines	Nonparallel Lines
alternate interior angles
alternate exterior angles
corresponding angles
same side interior angles

9. Geometry/Measurement
Angles, Lines & Line Segments: Grade 9
G/M-9, G/M-10
G/M-13, G/M-15

Materials:
mira

1.	Using a mira draw the following:
	a)	a square
	b)	a rectangle
	c)	a parallelogram
	d)	a isosceles trapezoid
	e)	a rhombus
	f)	a kite
2.	Each of the above polygons is called ________________.
3.	Use what you know about diagonals of polygons and the sum of the angles in a triangle to write a rule about the sum of the angles in each of the above.
4.	a)	Draw a non-isosceles trapezoid and an irregular quadrilateral.
	b)	Does the rule that you wrote in #3 apply to these quadrilaterals as well. Use the diagrams in your explanation.
5.	Use the scientific method (Problem, Materials, Procedure, Observation and Conclusion) to answer the following question. "Does the rule about the sum of the angles of quadrilaterals apply to concave quadrilaterals?"

14. Geometry/Measurement
Angles, Lines & Line Segments: Grade 9
G/M-12

Materials:
  compass
  paper for folding
  ruler or tape measure

1.	Draw a square using a compass. Explain your work.
2.	What would you do differently to draw a rectangle?
3.	Show how you can use paper folding to cut a square out of a rectangular piece of paper.
4.	Are you a rectangle or a square? Check the length of your arms from tip to tip and your height from head to toe.

19. Geometry/Measurement
Polygons: Grade 9
G/M-20, G/M-23

Materials:
  board
  rubber bands
  thumb tacks
  grid paper
  draw program on the computer

1.	Draw a polygon.
2.	Make polygons similar to the one you drew using a
	a)	grid
	b)	pantograph
	c)	computer drawing program if available
3.	Record the scale factor for each drawing.

25. Geometry/Measurement
Plane-Space: Grade 9
G/M-40

Materials:
  pentominoes shapes
  paper pentominoes
  scissors
  tape
  recycling paper
  construction paper

1.	Carefully examine the pentomino shapes. Which ones do you think could be folded to form open boxes. Record by writing the letters under a yes and a no column.
2.	Cut the paper pentominoes to check your predictions.
3.	Report your findings.
4.	Take the object provided at the station and create a net to make a box to store the object. You may choose to have a bottom and a lid or have it all in one piece. Do not forget to leave tabs for gluing. Use the recycling paper to experiment, the draw your net on your answer sheet and build the box with construction paper.

29. Geometry/Measurement
Area: Grade 9
G/M-73

Materials:
  two sizes of packages
  of Toblerone chocolate
  Calculator

1.	Calculate the surface area of each of the boxes.
2.	Calculate the volume of each box.
3.	Copy and complete this chart.

	dimensions	surface area	volume	mass of chocolate
Box 1
Box 2

4.	Compare the mass of the chocolate in the boxes to the surface areas of the two boxes. Is the ratio the same?
5.	Compare the mass of the chocolate in the boxes to the volume of the two boxes. Is the ratio the same?

31. Geometry/Measurement
Area: Grade 9
G/M-64

Materials:
paper
Calculator

Suppose you have the choice of square shaped pizza and circular pizza. The sides of the square pizza are equal to the diameter of the circular pizza.
  Design an investigation to see which shape, if any, gives you more pizza. (All other factors remain the same such as thickness)
  If there is a difference, is the difference proportionately different for different sizes? Approximate the difference in percentage.
  Apply what you have discovered to square and circular meat patties for hamburgers. Which ones provide more meat? How could you compensate so that you could make it look like more meat but indeed have the same amount in each case.

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