Download MAFS.912.G-SRT.3.6-3.8 MAFS-FSA Resource

Florida MAFS-FSA Resource
Purpose: Teachers should utilize the ExploreLearning published Teacher Guide and Student Exploration
Sheet to teach the content of this standard. This document is a supplemental resource designed to help
support teachers in preparing students for content and various computer-based question mechanisms
on the Florida Standards Assessment.
Guidelines: Below are select sample item stems from various sources, such as the Florida Department of
Education (DOE). Teachers are encouraged to teach the standard/benchmark as recommended by their
school district. Teacher may utilize the “Suggested Lesson Sequence” section in the ExploreLearning
Teacher Guide and accompanying Student Exploration Sheet in teaching the content/concept.
In providing practice for MAFS FSA, teachers can use the question stems and facilitate the use of the
Gizmo through various modes. Gizmo suggestions have been made for each question stem for wholeclass facilitation. Contact your Project Manager or Sales Executive for professional development
opportunities, such as classroom modeling.
FL MAFS Content Standard
MAFS.912.G.-SRT.3.8 Use trigonometric ratios
and the Pythagorean Theorem to solve right
triangles in applied problems.
MAFS.912.G.-SRT.3.6 Understand that by
similarity, side ratios in right triangles are
properties of the angles in the triangle, leading
to definitions of trigonometric ratios for acute
angles.
ExploreLearning Gizmo
MAFS.912.G.-SRT.3.7 Explain and use the
relationship between the sine and cosine of
complementary angles.
Sine, Cosine, Tangent Ratios
Sample Item Stem
Response Mechanism
1. Lars rides a chairlift to the top of a
Equation Editor
mountain. The chairlift rises at a
Response
constant angle of 37°. If the length of the
chairlift ride is 1,392 m, what is the
elevation gain from the base of the
chairlift to the top?
Draw a right triangle to model this
problem and use the Gizmo to find sin
37°. Show your work.
_______________
To solve the problem, make a sketch,
write an equation involving cosine, find
the cosine value you need in the Gizmo,
and solve for the unknown height. Show
your work below.
Introduce the concepts of Sine,
Cosine, Tangent by showcasing
the Gizmo during whole class
instruction. Build student
understanding for the mnemonic
device “SOH-CAH-TOA” found in
the Teacher Guide – see suggested
lesson sequence section, Gizmo
activity ELL adaptation.
Complete activity A found in the
Student Exploration Sheet by
facilitating student usage of the
Gizmo using a wireless mouse or
interactive whiteboard, if
available. Students may also
complete the activity 1:1 or 2:1
using laptop carts, a computer lab,
or BYOD.
Elevation gain:
2. A 12-foot ladder leans against a
building. The top of the ladder forms an
angle of 19° with the top of the building,
as shown. How high is the top of the
ladder?
Gizmo Suggestions
Equation Editor
Response
Debrief the answer to question 6
of Student Exploration Sheet
activity A using the Student
Exploration Sheet Answer Key.
Extend student learning (previous
Gizmo experience - activity A of
the student exploration sheet) by
completing activity B of the
student exploration sheet. Upon
completion, allow time for
students to review answers from
activities A and B in pairs.
Emphasize the use of the length
and angle measurement tools of
the Gizmo.
Debrief the answer to question 5
of Student Exploration Sheet
activity B using the Student
Exploration Sheet Answer Key.
Height of the top of the ladder:
______________________
Use the Gizmo during a whole
class mini-lesson/review on Sine
and Cosine. Have students create
a triple Venn Diagram – Sine,
Cosine, Tangent. At the conclusion
of the mini-lesson, provide time
3. Gabriella and her friends are going
camping. She is helping her friend pitch
the tent. The support wire needs to be
at a 45° to the ground, and it is 8 ft long.
How far away from the base of the tent
does she need to place the stake for the
support wire? Choose the appropriate
trigonometric ratio to solve the problem
and justify your answer with an
explanation.
Open Response
4. Joseph is measuring a tree. He walks
15.3 m from the base of the tree, lies on
his stomach, and measures a 25° angle
of elevation. What is the height of the
tree?
Multiple Choice
Response
To solve the problem, write an equation
using the correct trigonometric ratio,
use the Gizmo to find the value you
need, and solve for the unknown height.
A.
B.
C.
D.
X ≈ 6.47
X ≈ 13.86
X ≈ 7.13
X ≈ 8.35
for students to evaluate Sine and
Cosine and fill in as much as they
can on the Venn Diagram.
Allow time for students to work
independently or in pairs to
problem solve the question stem.
Once students have problem
solved on paper, students can use
the Gizmo to recreate the problem
and check their work. Start by
selecting the “Cosine” Gizmo tab.
Then use the angle slider to set
the appropriate angle degrees.
Click and drag point C to make the
“support wire” as close to 8 units
as possible (8.01). Select the
“Show side lengths” and “Show
cosine computation” Gizmo
options to extend the learning
opportunity. Use the
measurement tools when possible
and associated color coding of the
Gizmo (adjacent = green,
hypotenuse = purple, opposite =
red).
Extend student learning (previous
Gizmo experiences - activities A
and B of the student exploration
sheet) by completing activity C of
the student exploration sheet.
Upon completion, allow time for
students to review answers in
pairs. Emphasize the use of the
length and angle measurement
tools of the Gizmo.
Debrief the answer to question 5
of Student Exploration Sheet
activity C using the Student
Exploration Sheet Answer Key.
As an informal assessment,
provide time for students to ad
onto and complete the triple Venn
Diagram they previously created.
Name: ______________________________________
Date: __________________
Period # ___________
MAFS-FSA Student Task
Sine, Cosine, Tangent Ratios
MAFS.912.G.-SRT.3.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in
applied problems.
MAFS.912.G.-SRT.3.6 Understand that by similarity, side ratios in right triangles are properties of the
angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
MAFS.912.G.-SRT.3.7 Explain and use the relationship between the sine and cosine of complementary
angles.
Math Tasks (Begin by exploring the Gizmo. Utilize the Gizmo to answer questions below.)
1. Lars rides a chairlift to the top of a mountain. The chairlift
rises at a constant angle of 37°. If the length of the
chairlift ride is 1,392 m, what is the elevation gain from
the base of the chairlift to the top?
Draw a right triangle to model this problem and use the
Gizmo to find sin 37°. Show your work.
Elevation gain:
2. A 12-foot ladder leans against a building. The top of the
ladder forms an angle of 19° with the top of the building,
as shown. How high is the top of the ladder?
To solve the problem, make a sketch, write an equation
involving cosine, find the cosine value you need in the
Gizmo, and solve for the unknown height. Show your
work below.
Height of the top of the ladder: ___________
3. Gabriella and her friends are going camping. She is
helping her friend pitch the tent. The support wire needs
to be at a 45° to the ground, and it is 8 ft long. How far
away from the base of the tent does she need to place
the stake for the support wire? Choose the appropriate
trigonometric ratio to solve the problem and justify your
answer with an explanation.
4. Joseph is measuring a tree. He walks 15.3 m from the
base of the tree, lies on his stomach, and measures a 25°
angle of elevation. What is the height of the tree?
To solve the problem, write an equation using the correct
trigonometric ratio, use the Gizmo to find the value you
need, and solve for the unknown height.
A.
B.
C.
D.
X ≈ 6.47
X ≈ 13.86
X ≈ 7.13
X ≈ 8.35