Grades 6-8
Constellations: looking at triangles. Grade 6.
Activity contributed by Judy Dussiaume, Sudbury and Susan Stuart, Nipissing.
The task requires students to classify triangles according to angle and side properties.
Students use Geometer's Sketchpad to manipulate triangles to see that constructed triangles
have imposed restrictions whereas drawn triangles can be freely dragged to change properties.
Students will use mathematical language to describe geometric concepts as they explore,
manipulate, and hypothesize about the classifications of triangles.
Students will use geometry to find a hidden constellation in a group of "stars".
This activity includes teacher notes, rubrics, a quiz, a recording sheet and four
sketches.
Curriculum links: 6m64. identify, describe, compare, and
classify geometric figures
6m69. use mathematical language effectively to describe
geometric concepts,
reasoning, and investigations, and coordinate systems
Squares around a triangle. Gary Flewelling
This is a rich task that involves investigating various configurations of squares around
triangles (and then triangles around squares...).
This activity includes an introduction to the task with some ideas for possible
investigations.
Curriculum links: 6m64. identify, describe, compare, and
classify geometric figures
6m69. use mathematical language effectively to describe
geometric concepts,
reasoning, and investigations, and coordinate systems;
formulate conjectures and generalizations about geometric relationships involving
two-dimensional figures, through investigations facilitated by dynamic geometry software,
where appropriate.
Grades 9-10
Polygons and their Offspring (Draft). Gary Flewelling and
Nathalie Sinclair
Investigation of polygons that can be formed using special lines. The first investigation,
for example, looks at the "offspring" triangle formed by the medians of a triangle.
Curriculum links: Investigating Geometric Relationships, Grade
9
- determine the properties of angle bisectors, medians, and altitudes in various types of
triangles through investigation;
- formulate conjectures and generalizations about geometric relationships involving
two-dimensional figures, through investigations facilitated by dynamic geometry software,
where appropriate.
Perambulating Polygons (Draft). Gary Flewelling and
Nathalie Sinclair
Investigation of the relationship between perimeter and "diagonals" of the family of
regular polygons and the circle.
Curriculum links: Measurement, Grade 8
- Solve problems related to the calculation of the radius, diameter, and circumference of a
circle
- measure the radius, diameter, and circumference of a circle using concrete material
- recognize there is a constant relationship between the radius, diameter, and
circumference of a circle and approximate its value through investigation
- develop the formula for finding the circumference of a circle
- estimate and calculate the radius, diameter, and circumference of a circle, using a
formula in a problem-solving context
- · define radius, diameter, and circumference and explain the relationship between them
Painting Polygons (Draft). Gary Flewelling and Nathalie
Sinclair
Investigation of relationships between height and area of circular, triangular and
rectangular painting areas. Linear and non-linear relationships.
Curriculum links: Investigating Geometric Relationships, Grade
9
- determine the properties of angle bisectors, medians, and altitudes in various types of
triangles through investigation;
- formulate conjectures and generalizations about geometric relationships involving
two-dimensional figures, through investigations facilitated by dynamic geometry software,
where appropriate.
Curriculum links: Relationships, Grade 9
- pose problems, identify variables, and formulate hypotheses associated with relationships
- demonstrate an understanding of some principles of sampling and surveying (e.g.,
randomization, representivity, the use of multiple trials) and apply the principles in
designing and carrying out experiments to investigate the relationships between variables
- collect data, using appropriate equipment and/or technology (e.g., measuring tools,
graphing calculators, scientific probes, the Internet)
- organize and analyse data, using appropriate techniques (e.g., making tables and graphs,
calculating measures of central tendency) and technology
- describe trends and relationships observed in data, make inferences from data, compare the
inferences with hypotheses about the data, and explain the differences between the inferences
and the hypotheses
- communicate the findings of an experiment clearly and concisely, using appropriate
mathematical forms (e.g., written explanations, formulas, charts, tables, graphs), and justify
the conclusions reached;
- solve and/or pose problems related to an experiment, using the findings of the experiment.
- construct tables of values, graphs, and formulas to represent linear and non-linear relations derived
from descriptions of realistic situations
Grades 11-12
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