Download 4.G.2 A Look at Triangles

4th Grade
A Look at Triangles
Unit 4
Standards addressed by this lesson experience:
o 4.G.2. Classify two-dimensional figures based on the presence or absence of parallel or
perpendicular lines, or the presence or absence of angles of a specified size. Recognize right
triangles as a category, and identify right triangles.
Goal: Students will classify triangles based on their properties.
Materials Needed:
Geoboards and geobands (rubber bands)
Geodot paper (in unit)
Paper, pencils, and crayons for recording in their math notebooks
Vocabulary:
Polygon- a closed plane figure formed by three or more line segments called sides. Each side intersects
exactly two other sides, but only at their end points. Sides that have common end points are part of the
same line.
Right angle- angle measuring exactly 90 degrees
Acute angle- angle measuring more than 0, but less than 90 degrees
Obtuse angle- angle measuring more than 90 degrees
Lesson 1:
Define polygon with students and have them record the definition in their notebooks. (If students are
unfamiliar with the term- you may need to show them examples and non-examples of polygons before
the lesson)
Review the angle types and have students record the definitions and an example of each in their math
notebooks.
Show students some different triangles and ask them to identify them as triangles. Brainstorm as a class
what properties they have in common (3 sides, 3 angles, etc).
Put students in groups of 3-4 and give students geoboards and bands. Pose the following question:
 Is it possible to make a 3 sided polygon that is not a triangle?
o Have the students first decide and record their decisions on the board (votes for yes and
no).
o Then have students use their geoboards to explore possibilities and come to a
consensus in their group.
o If students construct shapes that are not polygons, bring them back to the definition of
a polygon and ask them if their shape meets the definition of the polygon.
o If students construct a triangle, but do not identify it as a triangle, bring them back to
the definition of a triangle.
 Make an anchor chart that lists the properties of a triangle (3 sides, 3 angles, a polygon)
 Have student record the anchor chart in their math notebooks.
Last revised 5-4-12
1
Rogers Public Schools
Adapted from Navigating Through Geometry, NCTM publication
4th Grade
A Look at Triangles
Unit 4

Pose the next question: Is it possible for a triangle to have more than 1 right angle?
o Again have the students answer the question individually and then tally the class’s
responses.
o Have them test their ideas on the geoboard and come to consensus in their small
groups. Follow up with whole class discussion.
 If a student construct a figure with 2 right angles, but is not a triangle, ask
him/her if the figure has all the properties of a triangle.
o When students reach the consensus that a triangle can have only 1 right angle- add this
idea to your anchor chart. Define that triangle as a right triangle. Have students do the
same in their math notebooks.

Extension question: How many different right triangles can be made on the geoboard?
o Again have the students answer the question individually and then tally the class’s
responses. Discuss what different means (if a triangle can be flipped or turned to match
one that is already made, then it is not different).
o Have them test their ideas on the geoboard and record their findings on the geodot
paper. (There are fourteen different right triangles that can be made). If students only
find a few, challenge them to find them all. Ask them what strategy they are using to
make sure they are finding them all.
 (Try this yourself before you give this task to your students- this will enable you
to ask the right questions and scaffold students’ thinking. You might share with
student that you could start with a right triangle that has a base of one unit and
a height of one unit. You could keep the base the same and try to find how
many more right triangles you could make. Then you could make one with a
base of two units…)
o Share their findings in a whole group- did any group find all the right triangles? Have
them record the ones they didn’t find on their geodot paper.
Assess
During each exploration, circulate among the groups, observing and attending to students’ ideas and the
reasoning behind their ideas. This would be a great time to use your scoring guide to score students to
the standards.
To conclude the lesson, have students write a reflection in their math notebooks. Here are some
prompts you may give students to respond to.
 What have you learned about a triangle from this investigation?
 If you could make a triangle that was as large as you wanted, would you be able to make one
that had two right angles? Explain your thinking.
 Write everything you know is true about all right triangles.
 Finish each sentence with as many different answers as possible.
o All triangles have…
o Some triangles have …
Last revised 5-4-12
2
Rogers Public Schools
Adapted from Navigating Through Geometry, NCTM publication
4th Grade
A Look at Triangles
Unit 4
*Note:
You could continue this lesson by asking some of the following questions:
 Can you make a triangle with more than one obtuse angle?
 How many different types of triangles can you make?
You could also use this same format when discussing squares and other rectangles. Design the activity in
the same way, but ask these questions instead:
 How many different squares can you make on your geoboard?
 How many different rectangles can you make on your geoboard?
 How do you know that you have found them all?
 How do you know they are all different?
 How are a rectangle and a square alike? How are they different?
 Could a square be considered a special kind of rectangle? In what way?
 Could a square be considered a special type of parallelogram?
A Venn Diagram can then be developed to show the relationship among the three types of
quadrilaterals.
Parallelograms
Rectangles
Squares
Last revised 5-4-12
3
Rogers Public Schools
Adapted from Navigating Through Geometry, NCTM publication