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Lesson Plans > Mathematics > Grades 6 - 8 > Exploring Altitudes in Math
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Kinesthetic Learner
Kinesthetic Learner
Visual Learner
Visual Learner
Auditory Learner
Auditory Learner
Technology Integration
Technology Integration

Exploring Altitudes in Math

Draw and calculate altitudes

 

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:
  • for various grade levelsVarying 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
  • for visual learnersVisual learners: incorporates illustrations of altitudes
  • for auditory learnersAuditory learners: uses direct questioning to categorize triangles, analysis of the difference between everyday and mathematical language, and provides group discussion about the Pythagorean theorem
  • for kinesthetic learnersKinesthetic 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
  • for kinesthetic learners 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.
  • for auditory learners 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
  • for visual learners 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.
  • for visual learners Illustrate the altitude of an acute triangle.
  • for auditory learners 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.
  • for visual learners 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.
  • for visual learners 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.
  • for auditory learners Using an illustration on the white board, explain how they can use the Pythagorean theorem to find the altitude.
Practice
  • for various grade levels 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
  • for kinesthetic learners 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.
  • for kinesthetic learners 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
  • for auditory learners Remind students that the measure of altitude of a triangle is used to calculate area.
  • Applied learning: Ask students to think about real-world situations that would require them to use or calculate the measure of the altitude of a triangle.
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