Transcript Session 3 aug19_v2 - GAINS

Trigonometric Functions
Session #3
Continued…
• Finish CLIPS Presentations
Consolidate Debrief (continued)
• Demonstration of screen captures on the
Interactive White Board
Consolidate Debrief (continued)
Going Deeper
– What kind of question(s) can be posed to see
if students have developed the understanding
of this big idea OR what scaffolding questions
can be created to help support students?
• Few examples chosen from the
Mathematical Processes Booklet:
– Reasoning & Proving: How can we show …?
– Reflecting: What do you notice about…?
– Connecting: What are the connections
between…?
Consolidate Debrief (continued)
Going Deeper
• Turn and Talk Share question(s) with
another pair
Learning Goals: Session 2
• Identify common misunderstandings that
students have about trigonometric functions
• Build awareness of Trig CLIPS
• Make connections between CLIPS, the
misunderstandings, and the big ideas of trig
• Practice posing questions based on the big
ideas
• Build content knowledge of trigonometry
Learning Goals
• Build content knowledge of radian
measure
• Develop understanding of the rates of
change of trigonometric functions through
a parallel task
• Develop a parallel task based on a specific
learning goal
Action!
• Parallel Task: Walk the Walk Talk the Talk
Action: (continued)
Record your thinking on your handout
Action! (continued)
• Form teams of three (walker, calculator
operator, CBR manager)
• Select one of the walks pictured or
create your own on
• Discuss and record how you will “Walk
the Walk” to make the graph and use
this knowledge to create a similar
graph with a graphing calculator and a
CBR
Action! (continued)
Action: Consolidate the Parallel
Task
• How did you decide which graph you
wanted to do?
• What’s are some of the things you thought
of when you were first trying to make your
graph
• What’s adjustments did you have to make
for your walk to get closer to your graph
• What was most challenging about creating
your graph?
Consolidate (continued)
• Whole group share…
– Why is this a parallel/open task???
– Scaffolding questions???
– Concepts covered???
• Rates of change, periodic nature of walk,
maximum, minimum, intervals of increase and
decrease, points of inflection….
– Connection to big ideas???
– Talk the Talk???
Action! (continued)
• Our turn to share
– Anecdotal observations
• How we opened up the task…
– Started with an existing task (Hula Hoop
Activity from TIPS)
– Thinking about student struggles/choice
– Developed learning goals based on the
overall/specific expectations
– Focus on the big ideas
Action! (continued)
Expectations: MHF4U D1.2, D1.3
• Recognize that the rate of change for a function is a
comparison of changes in the dependent variable to changes
in the independent variable, and distinguish situations in
which the rate of change is zero, constant or changing,…
• Sketch a graph that represents a relationship involving rate of
change, as described in words, and verify with technology
Learning Goal:
• When you’re analyzing rates of change for periodic functions
you need to consider intervals of increase and decrease, and
when the rate is zero, constant or changing
Action: (continued, parking lot connection)
• So why radians?
– It’s about the scale y=sin x where x is an
angle measured in degrees, y = sin x where x
is a real number (radians are real numbers)
– Real contexts
– Graphing compositions of functions
(e.g. y = x sin x)
Action! (continued)
• Demonstration: Radian Wheel Activity
– How to make a radian wheel
– Complete steps 3 through 7 and explore the
relationships
– Connect to real world phenomena
Action! (continued)
• What did you think?
•
•
•
•
A look at a future clip:
What is a radian?
Understanding the unit circle?
Graphing in Radians
Action! (continued)
• Creating your own parallel task (small
group)
– Select a big idea and an overall expectation
from a Trig Functions strand (include
appropriate specific expectations)
– Consider the connected potential
misconceptions/struggles/partial
understandings that students have (posted)
– Create a learning goal and an appropriate
parallel task that addresses the area of
difficulty
Consolidate Debrief
• Share
Consolidate Debrief (continued)
Consolidate Debrief (continued)
• Record your understandings of today’s
activities in your “What’s Important Book”
• Consider:
– What’s the most important thing about a
radian? about an angle? about periodic
functions? about any concept focussed on trig
functions? …
– What’s the most important thing about
creating a parallel task? An open question?...
Learning Goals
• Build content knowledge of radian
measure, as well as the characteristics
and rates of change of trigonometric
functions through a parallel task
• Develop a parallel task based on a specific
learning goal
Consolidate Debrief (continued)
BLM 1.4, Trigonometric Functions Session – Reflection Template
Use this template to record your reflections related to your new learning, potential shifts in practice, and implications for student learning.
Trigonometric
Functions
Focus Activity
CLIPS
Parallel Task:
Walking the
Periodic Curve
Radian Wheel
Visualizing
Graphs: Using
the IWB
Spotlight
Open Task:
World Climate
The Big Ideas of
Trigonometric Functions
The Mathematical Processes
(problem solving, reasoning, reflecting, selecting
tools and computational strategies, representing,
connecting, communicating)
Establishing Math Talk
Learning Communities
Assessment for / as / of
Learning
Further Consolidation
• Based on today’s session, complete your
Trigonometric Functions journal, focusing
on the prompts that are most meaningful
to you.
– Given what I have learned today, what ideas
are challenging my belief about teaching
trigonometric functions? Why?
– What new learning do I believe has helped
me shift my practice?
– The new ideas that I am prepared to
implement upon my return to the classroom /
board are…
Session Three: The End
Parking Lot: Applications
• In groups of four record on a placemat
different real phenomena which involve
trigonometric functions
• Summarize
• Add as we go, volunteer to type
Minds On…(continued)
• Let’s Share:
Tides
Sonar
Ferris Wheel
• Anticipation
Minds On…(continued)
Radar
Pendulum
Radio Waves
Session Three: Minds On…(continued)
astronomy
Sound Waves
• Modelling real phenomena with trig functions
requires radians