Grade Level: 6-12
Concept: Learn to draw and calculate altitudes
Estimated Duration: 45 minutes
Objectives
Students will be able to:
- draw the altitude of acute, right and obtuse triangles
- calculate the altitude of a triangle using the Pythagorean theorem
Materials
White board
Markers
Math journals/paper
Grid paper
An assortment of different acute, right, and obtuse paper or felt triangles – one of each type of triangle per each student
Differentiation Strategies
These strategies are used to meet the varied needs of all learners:
-
Varying academic levels: uses mixed-ability groups to allow students to learn from one another, uses small- and whole-group discussions to ensure all students participate
-
Visual learners: incorporates illustrations of altitudes
-
Auditory learners: uses direct questioning to categorize triangles, analysis of the difference between everyday and mathematical language, and provides group discussion about the Pythagorean theorem
-
Kinesthetic learners: engages students in drawing triangles and altitudes on grid paper
Key Vocabulary
acute triangle
right triangle
obtuse triangle
altitude
Pythagorean Theorem
Procedures
Warm Up
-
Distribute three felt or paper triangles to each student, an acute, a right, and an obtuse triangle.
-
Have students turn to a partner and take 2 minutes categorize the triangles as acute, right, and obtuse.
-
Ask students to explain how they categorized a triangle.
-
Have them use the corner of a sheet of paper to compare and discuss the angles of each triangle,
Direct Instruction
-
Write and define the term altitude on the white board and ask students to copy the term into their math journal or on a paper.
-
Illustrate the altitude of an acute triangle.
-
Discuss the similarity and difference between the definition of altitude in mathematical terms and in everyday language.
-
Ask non-English speakers to explain whether the word altitude has a meaning in their language.
-
Ask students to draw in their math journals or on paper the three triangles and draw the altitude.
-
Invite students to the white board to draw the altitude.
-
Using the students’ illustrations, point out that the altitude of a right triangle might be one of its sides and that the altitude of an obtuse triangle may lie outside the triangle itself.
-
Have students copy their triangles onto grid paper and find the measure of the altitude.
-
Ask students what other measures they could use to calculate an unknown altitude if they had other measures.
-
Using an illustration on the white board, explain how they can use the Pythagorean theorem to find the altitude.
Practice
-
Create mixed-ability pairs and provide them with a series of problems in which they have to use the Pythagorean theorem to calculate the altitude.
Assessment
-
Ask pairs of students to create a small group with another pair of students and check each other’s work. Tell them that any one of them could be asked to come to the board to share their work, so they need to be prepared.
-
Ask the most challenged student from each group to come to the white board to illustrate how their group used the Pythagorean theorem to find the altitude.
Closure