Bio
Laura Frcka has been teaching mathematics for nine years, most recently at William J. Bogan Computer Technical High School, the first 1:1 Chromebook high school in Chicago Public Schools. She focuses on inquiry explorations while incorporating growth mindset. Outside of class, she enjoys spending time with her family and friends and is a novice gardener and cook.
Amazing Lesson
Several summers ago, I taught a pre-calculus course for students entering AP Calculus AB. The students were introduced to trigonometric ratios in previous mathematics courses but had trouble connecting their knowledge in non-traditional settings. My main goal was for students to collaboratively use their critical thinking skills and prior knowledge to determine an unknown, the height of an object. I decided the clinometer lesson would be the perfect avenue to take.
Working in groups, students would venture out of the classroom using their clinometers to measure the heights of several objects around the school, for example: flagpole, light fixture and basketball hoop. Before class, I constructed each clinometer, an instrument used to measure the angle or elevation of slopes from the horizon, using a straw, protractor, string, button and note card.
Students entered class and were immediately curious wondering how they would use the clinometers that I’d constructed. I told the students that they would be working in small groups using the clinometers to find the heights of objects that we are unable to physically measure like a tree. I asked the students how they thought that they could use the clinometers. Several students stated that they wanted to read the overall angle while others wanted to use of the angle of elevation. I allowed the students to discuss with each other and resolve the disparity.
The students drew a diagram and wrote out their calculations to enhance their understanding of trigonometry and see if their answers made sense. At the end of class, we came back together and the students discussed their findings to see if there were any discrepancies. Two groups calculated different heights for the flagpole. Through their discussion, they determined that one group did not add in the height to the observer’s eye while the other group chose the sine ratio instead of tangent. This lesson was successful because the students worked through their own understandings and misconceptions.
This lesson could be easily extended or modified by varying the unit of measurement used and whether the groups use the same or different objects. Students could also use a clinometer app or Google Maps to find the height of landmarks.
Laura Frcka has been teaching mathematics for nine years, most recently at William J. Bogan Computer Technical High School, the first 1:1 Chromebook high school in Chicago Public Schools. She focuses on inquiry explorations while incorporating growth mindset. Outside of class, she enjoys spending time with her family and friends and is a novice gardener and cook.
Amazing Lesson
Several summers ago, I taught a pre-calculus course for students entering AP Calculus AB. The students were introduced to trigonometric ratios in previous mathematics courses but had trouble connecting their knowledge in non-traditional settings. My main goal was for students to collaboratively use their critical thinking skills and prior knowledge to determine an unknown, the height of an object. I decided the clinometer lesson would be the perfect avenue to take.
Working in groups, students would venture out of the classroom using their clinometers to measure the heights of several objects around the school, for example: flagpole, light fixture and basketball hoop. Before class, I constructed each clinometer, an instrument used to measure the angle or elevation of slopes from the horizon, using a straw, protractor, string, button and note card.
Students entered class and were immediately curious wondering how they would use the clinometers that I’d constructed. I told the students that they would be working in small groups using the clinometers to find the heights of objects that we are unable to physically measure like a tree. I asked the students how they thought that they could use the clinometers. Several students stated that they wanted to read the overall angle while others wanted to use of the angle of elevation. I allowed the students to discuss with each other and resolve the disparity.
The students drew a diagram and wrote out their calculations to enhance their understanding of trigonometry and see if their answers made sense. At the end of class, we came back together and the students discussed their findings to see if there were any discrepancies. Two groups calculated different heights for the flagpole. Through their discussion, they determined that one group did not add in the height to the observer’s eye while the other group chose the sine ratio instead of tangent. This lesson was successful because the students worked through their own understandings and misconceptions.
This lesson could be easily extended or modified by varying the unit of measurement used and whether the groups use the same or different objects. Students could also use a clinometer app or Google Maps to find the height of landmarks.
Top 5 Common Themes
After showcasing our amazing lessons, our group developed these 5 common themes throughout each lesson.
Rigorous, cognitively rich tasks
Students are involved in thinking deeply and using various strands of knowledge along with prior learning. The activities reinforce fundamental skills for future applications.
Student engagement and choice
Students actively participate in tasks at hand and are allowed to choose how to solve the problem to develop their understandings. Students own their learning outcomes.
Communication with disciplinary vocabulary
Students work collaboratively and success depends upon effective communication. Students develop and apply content vocabulary.
Safe, supportive place for exploration
Students have a comfortable space to explore the range of their abilities. They are encouraged to take risks with support from their peers and teacher.
Structured environment that celebrates diversity
Teacher systematically creates a classroom that optimizes STEM learning. Lessons balance structure and freedom to explore. Diversity is celebrated in divergent outcomes.
After showcasing our amazing lessons, our group developed these 5 common themes throughout each lesson.
Rigorous, cognitively rich tasks
Students are involved in thinking deeply and using various strands of knowledge along with prior learning. The activities reinforce fundamental skills for future applications.
Student engagement and choice
Students actively participate in tasks at hand and are allowed to choose how to solve the problem to develop their understandings. Students own their learning outcomes.
Communication with disciplinary vocabulary
Students work collaboratively and success depends upon effective communication. Students develop and apply content vocabulary.
Safe, supportive place for exploration
Students have a comfortable space to explore the range of their abilities. They are encouraged to take risks with support from their peers and teacher.
Structured environment that celebrates diversity
Teacher systematically creates a classroom that optimizes STEM learning. Lessons balance structure and freedom to explore. Diversity is celebrated in divergent outcomes.