Transcript Mathematical Kids

Mathematical Kids
About the Educator
Mr Azhar Sheik Dawood
Educator Mathematics
School: SARM State Secondary School
Educational Profile: Bsc Mathematics from University of Mauritius
Technology profile: Conversant with Office365, Sharepoint, Azure.
Career Profile: Started teaching in 2010. Currently teaches age group 11 to 18 years. Has been
awarded MIE expert in 2014.
Objectives of the project
“Mathematical Kids" is about applying what we learn in the classroom on simple
mathematical concepts in everyday life to become a 21st century learner.
Students would be requested to work in groups and come up with a PowerPoint
presentation as well as dynamic excel files on angles, triangulation and
trigonometry. They would peer tutor using interactive whiteboard. students
would then prepare a mouse mischief and carry out fun self-evaluation with
MCQs, drawing & matching.
Xbox with Kinect will then be used for the same topic. Dr Kawashima's Body and
Brain game will be used to develop the student's logic, critical thinking, problem
solving skills, fast thinking skills, spatial orientation and knowledge building skills.
Students engage in Fun learning to develop twenty first century skills by using
Kodu and its pre-loaded games for math calculations.
Star chart is used to calculate angles through triangulation to understand how
astronomy is related to simple math concepts. students would use Ms Excel to
create a dynamic report on angles between the stars.They would collaborate
among themselves even outside the classroom using Skype as a communication
tool to remain always connected while preparing their assignments.
After peer tutoring with their own classmates, they would share their knowledge
with other classes of the school. The project will also be shared with students of
two other secondary schools and one primary school.
Bing in the classroom is used as the search engine in inquiry based learning. All
research work is carried out using this tool to sharpen their search results.
LESSON PLANNING - A
LESSON PLAN (A. Sheik Dawood)
Lesson Title: Angle Attributes and Measures
Course: Math
Level: Form 3
Ministry of Education Syllabus:
4.1c Draw label and describe attributes of angles, 4.2b Measure angles
Lesson Objective(s):
Students will describe angle attributes and will be able to measure and estimate measures for
angles.
Enduring Understanding (Big Ideas): Essential Questions:
Angles are a basic idea in geometric
 Where are examples of angles found in the
thought and measurement
real-world?
 How can I describe the attributes for an angle?
 What is the measure for a given angle?
Skill Focus:
Vocabulary Focus:
Recognize attributes of angles
angle, vertex, protractor, degree, acute, right,
Measure angles
obtuse
Estimate angle measures
Materials:
 Angle Sort paper
 Measuring Angles worksheets
 Measuring angles quiz
 Classifying Angles song overhead
 Scissors
 Protractors
 Two-Colored Circular manipulative (made with small plastic plates)
 Paper for foldable
 Win 8 Device
 Starchart App
 Mouse Mischief
 Kinect
Assessment (Traditional/Authentic): Student performance tasks, question responses,
Quiz, MCQ with mouse mischief
Ways to Gain/Maintain Attention (Primacy): sorting, cooperative learning, manipulative,
movement, virtual manipulative skills, kinesthetic and sensory skills
Written Assignment:
Measuring Angles
Angles Foldable
LESSON PLANNING - B
Measuring Distances with Triangulation
Theme: Scale and Structure
Grade Level: Form 3
Group size: 2 - 4 students
Setting: Classroom and outdoors
Approximate Time Required: 3 class periods
Objectives:
Students will:
1. Determine the distance to the object by sighting a distant object from 2 different locations and knowing
the distance between those locations (parallax).
2. Use trigonometry to determine an unknown distance.
Major Concepts:
1. By sighting a distant object from 2 different locations and knowing the distance between those locations
(called the line of position), we can determine the distance to the object.
2. A carefully drawn scale model can be used to determine an unknown distance.
3. Trigonometry can be used to determine the unknown distance.
4. The farther an object is from an observer, the smaller its parallax.
Processes: Measuring, Modeling, Interpreting Data
Vocabulary:
1. Line of Position: The distance between the two measured angles (line AB).
2. Parallax: The angle subtended by the far object on the line of position; the apparent shift in position of
an object with respect to its background due to a shift in the position of the observer.
Materials Needed (per group):
meter stick, metric ruler, tape, 2 thumbtacks, 2 drinking straws, 2 protractors with small central hole at
base
General Procedures:
1. The procedure is outlined on the student handout.
2. You may want to compile class data for section III, step 2 on the board. Hopefully, the students will
discover that the parallax angle gets smaller with increasing distance. This is a good place to discuss the
use of parallax to measure distances to stars. Since the angle decreases with distance, this method can
only be used for nearby stars.
3. One way to increase the use of parallax is to increase the line of position (section IV on the student
handout). Astronomers use the diameter of Earth's orbit (186 million miles) as a line of position. The use
of parallax is limited to stars that are closer to Earth than 300 light years.
General Information for Teachers:
1. Assembly of materials can be done ahead of time by a student aide. This not only saves time, but allows
you to check the placement of the protractors.
2. Though no worksheet is included, you may wish to make a class set of the procedure. Students can make
a data table on their own paper, similar to this:
Object Angle 1 Angle 2 Line of Position Meas. Dist. Calc. Dist.
1.
2.
3.
4.
5.
Scale drawings can go on the same paper.
3. Caution students to avoid rotating the measurer when they raise it to eye level during the outside portion
of this activity.
I. Assembly of Materials
1. Push one of the thumbtacks through the sticky side of a piece of tape. The tape should be long enough to
wrap around the meter stick.
2. Position the tape with the thumbtack over the 10 cm mark on the meter stick; secure it in place so that
the pointed end of the tack is sticking up.
3. Repeat the procedure with the second tack, positioning it over the 10 cm mark of the metric ruler.
4. Place a protractor over each tack. Position the protractor so its base is parallel to the edge of the meter
stick/ruler. Tape the protractor in place.
5. Place a straw on each tack. You will sight the object to be measured through the straw.
II. Using the Measuring Device
1. Place the meter stick and ruler end to end on a flat surface. You now have a line of position that is one
meter long.
2. Move the left straw so that it is at a right angle to the meter stick. Find a distant object in the classroom.
Without moving the meter stick or ruler, move the right straw until you can see the same object through
it.
3. Record the measurements of your 2 angles (one is 90 degrees) and your line of position (it should be 1
meter).
4. If possible, measure the distance to the object. You can then compare this distance to the distance
obtained by triangulation.
5. On a piece of paper, draw a scale model of your measurements. Use 10 cm to represent your 1 meter line
of position; draw this line near the bottom of your paper. Using a protractor, construct the 2 angles you
measured at the left and right ends of the line of position.
6. Extend the sides of the triangle until they meet. The angle formed at the top of the triangle is called the
parallax. What is its measurement? (Remember that the sum of the three angles of a triangle is 180
degrees.)
7. To find the distance to the object, measure the line between the right angle and the parallax angle. Use
your scale (10 cm = 1 m) to convert this to an actual distance.
8. How does your measured distance (from step 4) compare to the distance determined in step 7? What are
some sources of error?
III. Comparing Near to Far Objects
1. Move your distance measurer closer to the object Your were measuring. Repeat the steps in Part II.
2. As the distance to the object increases, what happens to the parallax? Compare your results with those of
others in your class to see if they are consistent.
IV. Increasing the Line of Position
1. To measure the distance to a much farther object, you will need a longer line of position. Your teacher
will direct you to a location outside in which to conduct your work.
2. Move the meter sticks and ruler farther apart measure the length of your new line of position. (Since the
protractors are already 1 meter apart, a space of nine meters between the meter stick and ruler will give
you a 10 m line of position.)
3. Since the meter sticks are at ground level, you need to lift them in order to sight through the straw. BE
CAREFUL TO AVOID ROTATING THE METER STICK AS YOU RAISE IT!
V. Using Trigonometry
1. So far, you have used scale drawings to find the distance to the measured object. There is another
method, using a branch of mathematics called trigonometry. Trigonometry enables us to find unknown
parts of triangles. The trig function you need for this exercise is called the tangent.
2. The tangent of an angle is the ratio of the side opposite the angle divided by the side adjacent to the
angle. In your measurements, you know the adjacent side (it is your line of position) and you want to
find the opposite side (the distance to the object). Using a trig table or calculator with a tangent function,
you can set up a ratio and solve for the distance to the object. An example follows:
Suppose you had a right triangle with a base of 10 m, and a side angle of 70 degrees, what is its height
(X) ?
Tan = opp / adj
Tan 70 = 2.7475 (from a trig. table or calculator)
2.7475 = X / 10.0 m
X = 27.5 m
Use the tangent function to calculate distances to the objects you measured. Compare the results with those
obtained from the scale drawings.
Measurement Rubric
Lesson Segment 1: Where are examples of angles found or used in the realworld?
Guessing game: Tell students you are thinking of a geometric idea and that you
will point to some examples of that idea in the room. When they think they might
know what the idea you are thinking of is, they may write the idea down. After
pointing to several examples that suggest where an angle might be formed, ask for
responses. Ask students to describe attributes for some of the angles you pointed to
such as where the vertex point might be, or where the line segments are which form
the angle. Show the math symbol for angle.
Lesson Segment 2: How can I describe attributes of angles?
Without giving information have students sort angles by cutting out the cards on
the Angle Sort paper. Partners cut and sort, writing the rule for their sort. Then have
the partners compare their sorting to another pair. Discuss with class the sort
bringing them to the idea that angles can be described by the wideness or openness of
the angle. This wideness is the measure of an angle. Remind them that they may
have heard words such as acute, right or obtuse when describing angles.
Have students use Two-color Circular manipulative to show attributes such as acute,
obtuse and right as you ask them to. (A two-color manipulative can easily be made to
allow the students to demonstrate angles. Make a cut in two different colored small
plastic plates from the circumference to the center of the plate. Slide the two plates
together at the cut.)
Have students re-sort the angles into acute, right and obtuse categories (if they did not
originally do so) and write the category on the back of the card.
Lesson Segment 3:
What is the measure for a given angle?
Use the “Measuring Angles” investigation worksheet and protractors to become more
familiar with the protractor and to measure angles.
Practice:
Make a three column foldable (as shown below). The back side of the foldable can be
labeled “Measuring and Classifying Angles”. Have students use their protractors to
measure each of the angles from the sort cards. Then have them use the protractor to
sketch the angles in the appropriate column on the Foldable and label the measure of
each angle.
Acute <’s
Obtuse <’s
Right <’s
Using the Two-Color Circular manipulative again, call out angle degrees and have the
students rotate the sections of their plate to show an estimation for the measure.
Angle Sorting
Cut the angle cards apart. Sort them into three categories and write the rule
for each category. Your categories can’t refer to angle positions such as upside-down, left or right.
1
2
3
4
5
6
7
8
9
10
11
12
Measuring Angles
Name_____________________
C
B
A
0˚
1) What is an angle? Use the circle drawing to help you understand and explain.
2) How can angles in circle A be the same size as angles in circle B and C when they
look wider?
3) When you turn around in a complete circle, you have traveled 360 degrees.
Degrees are used to label the distance of a turn. Use a colored pencil to trace the
line and label the degrees to show where each of the following turns would stop.
Begin at 0˚ each time. Each line represents a turn of 15 degrees. The degrees are
the measure of the angle.
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
A
A
A
A
A
A
A
A
A
A
15˚ turn
30˚ turn
45˚ turn
90˚ turn
120˚ turn
180˚ turn
210˚ turn
270˚ turn
315˚ turn
360˚ turn
4)
Look at a protractor. How is a protractor similar to the circle above? How is it
different?
5) Find the mark on your protractor that would represent the center of the circle.
Where is that mark? This is the vertex point mark.
6) Find the mark on your protractor that would represent 0˚. Where is the 0˚ mark?
7) Find the mark on your protractor that would represent 180˚. Where is the 180˚
mark?
8) Each angle sketched below represents a turn. Place your protractor so the center
mark is on the vertex of an angle. Line one of the segments up pointing to the 0˚
mark. Now find the mark where the other line segment is pointing. How many
degrees is the angle?
Name __________________
1.
2.
3.
4.
5.
Measuring Angles
Label 0° and 180° on this protractor.
Label “vertex” where the protractor will be placed on the angle vertex point.
Sketch and label where a ray forming a 120° angle might pass through.
Sketch a 45° angle in the space below the protractor.
Where in this room would you see:
An acute angle?
A right angle?
An obtuse angle?
Student Worksheet
Simple Test Multiple Choice questions on Trigonometry
The side of a square measures 6 cm. What is the exact length of the diagonal of the square?
cm.
cm.
cm.
cm.
A light post, shown at the right, is set in concrete and supported with a guy
wire while the concrete dries. The length of the guy wire is 10 feet and the
ground stake is 4 feet from the bottom of the light post. Which equation
could be used to find the height of the light post, x, from the ground to the
top of the light post?
In the diagram at the right, MH = 15, HT = 13, and AT = 5. Find
MA.
8
9
12
14
In the diagram shown at the right, what is the value of x to the nearest
whole number?
8
9
10
13
Mouse Mischief
PowerPoint
Student work –
Dynamic Excel on Star Chart
Student work –
Dynamic Excel on Triangulation
Pictures of the Classroom