course: grade 9 applied mathematics (mfm1p) unit 1: …€¦ · gemma wants to tile her bathroom...

Course: Grade 9 Applied Mathematics (MFM1P)

Unit 1: Measurement (2D & 3D)

MFM 1P - Grade 9 Applied Mathematics – Unit 1: Measurement 2D & 3D (DPCDSB Dec 2008) 1-2

Unit 1 Measurement (2D & 3D)

Section Activity Page 1.1.1 Investigation - Comparing Volumes 3 1.1.2 Pair Share – Volume 4 1.2.1 Melting Ice Cream 6 1.2.J Journal Activity 7 1.2.2 Applications of Volume 8 1.2.P Practice 11 1.3.2 Scale Drawing Details 13 1.3.P Practice 16 1.4.2 Composite Figures Notes 17 1.4.3 Exploring Composite Shapes 19 1.4.P Practice 20 1.4.4 Use What You Know 23 1.4.5 Frayer Model 24 1.5.1 The Rope Stretchers 25 1.5.3 Right or Not? 26 1.5.5 The Pythagorean Theorem Notes 28 1.5.P Practice 30 1.5.6 Pythagorean Theorem Puzzle 31 1.6.1 Coach or Be Coached 32 1.6.2 The Container! 34 1.6.P Practice 36 1.6.J Journal Activity 38 1.W Definition Page 39 1.S Unit Summary Page 41 1.R Reflecting on My Learning (3, 2, 1) 42 1.RLS Reflecting on Learning Skills 43

1.1.1: Investigation – Comparing Volumes Purpose Compare volumes of shapes that have the same base and height. Hypothesis I think that...

1.

× _________ =

2. × _________ =

3. × _________ =

Investigate How many times will the volume of the shape on the left fill the shape on the right? 1. Vcone × ___ = Vcylinder 2. Vsquare pyramid × _____ = Vsquare prism 3. Vtriangular pyramid × _____ = Vtriangular prism Conclusion


1.1.2: Pair Share – Volume A – Prisms Circle the shapes that are prisms.

Volume of a prism = area of __________ × __________. B – Pyramids Circle the shapes that are pyramids.

Volume of a pyramid = volume of a prism ÷__________.


1.1.2: Pair Share – Volume (continued) Calculate the volume of the following figures. Show your work. A

Calculate the volume of the following figures. Show your work. A B

5 cm

12 cm 8 mm 15 mm


1.2.1: Melting Ice Cream


• Heather purchased an ice cream cone. • The scoop of ice cream was a sphere. • The height of the cone equals the diameter of both the

cone and the sphere.

• If the ice cream melts, how much will overflow the cone?

In Pairs A. What do we already know?

1.

=

÷ _______

Volumecone = Volume ______ ÷ _______

2. Volumecylinder = (Area of Base) × ( )

3. Volumecone = (Area of Base) × ( ) ÷ _____ B. Using the two 3-D relational solids of the cone and sphere, compare. 1. Heightcone and Heightsphere Comparison:

2. Radiuscone and Radiussphere Comparison:

3. Volumecone and Volumesphere Comparison:

C. Conclusion

_______ ×

=

D. How much ice cream will overflow? Write a relationship statement.


1.2.J: Journal Activity 1. Using words, pictures, numbers, and symbols, describe the relationships you

discovered today. 2. Use the 3-D relational sets and record as many paired relationships as you can.

For example, the small triangular prism is half the volume of the small square-based prism.


5 cm 5 cm

15 cm 3 cm

8 cm

1.2.3: Applications of Volume 1. Calculate the volume of the perfume bottle. 2. How much soup can this container hold? 3. Calculate the volume of the rectangular prism.

10 cm

7 cm

6 cm. 4 cm.

5 cm.

1.2.3: Applications of Volume (continued) 4. Which popcorn container will hold more?

15 cm 16 cm

16 cm

15 cm

8 cm 5. How many times bigger is the second sphere?

5 m 15 m


1.2.3: Applications of Volume (continued) 6. How much more expensive should the large aquarium be than the small aquarium if the cost

is based on the volume?

32 cm.

16 cm.

24 cm.8 cm.

12 cm.16 cm.

3 m

2 m

6 m

6 m

7. Determine the volume of the cabin. Show your work.


1.2.P: Practice 1. Using the relationships you have discovered, calculate the volume of each of the

following 3-D figures. (a)

14 mm

4 mm

6 mm 5mm

(b) 3 m

8 m

3 m

8 m

(c)


4 m

2 m

1.2.P: Practice (continued) 2. A movie theatre wants to compare the volumes of popcorn in two containers, a

cube with edge length 8.1 cm and a cylinder with radius 4.5 cm and height 8.0 cm.

Which container holds more popcorn? Draw diagrams to support your solution.

3. An entertainment room is 10.5 m long by 7.5 m wide by 3.5 m high. If of air is needed for each person, how many people can use the room at one time?

35 m


1.3.2: Scale Drawing Details 1. Consider the two composite figures. (a) Identify the geometric shapes in each. Write the names on the diagrams.

Figure 1 Figure 2

(b) Area

For determining the area of the shaded regions, describe the features and calculations that are: i) the same ii) different

(c) Which of the two figures is larger? By how much? Justify your answer using pictures, symbols, and words. (d) Perimeter

Use a coloured pencil to outline the perimeters of the two figures. How do these two perimeters compare?


1.3.2: Scale Drawing Details (continued) 2. Use the diagram above a) What dimensions are needed to determine the perimeter? b) What dimensions are needed to determine the area? c) Calculate:

Area Perimeter 3. Provide an example in daily life of a figure that involves more than one geometric shape.


1.3.2: Scale Drawing Details (continued)

5 cm

40 cm

2. Use the diagram above a) What dimensions are needed to determine the area of the square? b) What dimensions are needed to determine the area of the circle? c) Calculate:

Area of square Area of circle

Area of shaded area

3. Provide an example in daily life of a figure that involves more than one geometric shape.

Example: a church window


1.3.P: Practice 1. (a) Design a logo of your first and last initial, made of two or more simple geometric

shapes.

Make the appropriate measurements and calculate the total area and perimeter of your logo.


1.4.2: Composite Figures Notes


1.4.2: Composite Figures Notes (continued)



3 cm 3 cm 1.4.3: Exploring Composite Shapes

Perimeter Calculation

8 cm

14 cm

4 cm

4 cm

7 cm

7 cm

Shape Divisions Area Calculations

Option A

?

Option B

Option C

1.4.P: Practice

21. Carpeting costs $12.50/m . How much would it cost to carpet the room below including GST and PST?

10 m

5 m

6 m

7 m


1.4.P: Practice (continued) 2. Calculate the area and perimeter of each figure.

8 cm

12 cm (a)

5 cm

4.6 cm

4 cm

(b)

4m

6 m

7 m

6.7 m

(c)


1.4.P: Practice (continued) 3. Find the area of the shaded regions only. a)

30 cm

200 cm

150 cm

b)


1.4.4: Use What You Know

Knowledge and Skills


Reasoning and Proving Calculate the area of the given circle. Westview School has a track. Show your work.

r = 2.5 cm

Hint: A = πr2

You want to run 2 km every day. Determine how many times you have to go around the track. Show your work.

Communicating Connecting Gemma wants to tile her bathroom counter with mini tiles. She needs to determine the area of her counter space. Explain with words, diagrams, and symbols how she should determine the area.

This figure has a radius of r units.

r

Which of the following formulas could be used to determine the perimeter?

π − + + π

π + + π −

21a) 2 b) 0.754

3 1c) (2 ) d) 24 4

r r r

r r r r

r

Give reasons for your answer.

1.4.5: Frayer Model

Composite Figures

Definition Facts/Characteristics

Examples Non-Examples


1.5.1: The Rope Stretchers In ancient Egypt, mathematicians developed many useful ideas for everyday living. One

example was used by Egyptian farmers. Each year the Nile River flooded, leaving behind a

stretch of fertile land where the Egyptians grew t

when the river flooded, the boundaries of the fields

were lost and had to be accurately “redrawn.”

Egyptian surveyors or “rope stretchers” used

lengths of ropes with equally spaced knots tied

them to measure land boundaries. When two fie

bordered one another, the rope stretchers ha

measure a right angle to form the corners of the

fields. The establishment of boundaries was also important because the area of the land

determined the amount of taxes, and the scribes kept the accounts for taxation.

Excerpted from http://www.edhelper.com/RJuly 26, 2005

heir crops of barley and emmer wheat. But,

in

lds

d to

eadingComprehension_35_193.html

y Connections need to redraw the boundaries every year.

______________ ______________

_______________________________________ _______________________________________

_________________________________ ________________________________

______________________ ______________________

Literac 1. Why do the rope stretchers __________________________________________________________ __________________________________________________________ 2. Why is it important to have boundaries? _________________________________ _________________________________ 3. Why is it important that the boundaries are 90˚? _______________________________________ ________________________________________ ________________________________________________________________________ 4. Provide examples where you could use this technique today. __________________________________________________ __________________________________________________ ________________________________________________________________________ ________________________________________________________________________


1.5.3: Right or Not? Part A: Group Work 1) Record the three side lengths:

Card A _____________________ Card B ___________________ 2) Follow the instructions on the overhead to construct your two triangles.

Draw a labelled diagram of the triangle created by the three squares. Show side lengths.

Card A Card B

3) Complete the table:

Square with Square with Largest Square Type of TriangleCard


4) Share your data with another group. What observations can you make about the data?

side a side b with side c Right or Not


1.5.3: Right or Not? (continued) Part B: Class Work 5) Complete the data table:

Group Area of Square with side a

Area of Square with side b

Area of Largest Square with side c

Type of Triangle Right or Not

6) What other observations can you make about the class data set?

Verbal Model: Visual Model: Algebraic Model:

1.5.5: The Pythagorean Theorem Notes


1.5.5: The Pythagorean Theorem Notes (Continued)


1.5.P: Practice 1. Imagine you are a rope stretcher. Find two different combinations, not in the

class list, which would create right-angled triangles. Explain how you know that the triangles are right-angled.

Hint: Class Triangle 1: 3, 4, 5 Class Triangle 2: 6, 8, 10 What do you notice about these two triangles?


1.5.6: Pythagorean Theorem Puzzle

Instructions:

1. Colour the 5 pieces of the puzzle above and the 5 pieces you received from your teacher.

2. Cut out pieces 1-5 only from copy your teacher provided. 3. Fit the 5 pieces of the puzzle into the large square above. Be sure that the pieces fit

exactly into the square (There should be no paper overlapping, and no blank spaces)


1.6.1: Coach and Be Coached

A coaches B B coaches A

5 mm

x

12 mm


14 cm

z

9 m 12 m x

2 cm

2 cm

p

3 m

8 m12 m 8 m

m

10 cm

y

1.6.1: Coach and Be Coached (continued)

A coaches B B coaches A


A hydro pole casts a shadow that is 10 m long. A technician measures the wire that runs from the top of the pole to the end of the shadow and finds it to be 26 m. How tall is the pole?

Don is building a loft in his garage. The ladder he is using extends to 10 metres. The loft is 8 m from the floor. How far away from the wall should he anchor the ladder?

w

130 cm 55 cm

h44 cm

60 cm

1.6.2: The Container! The Geobellies company wishes to make a new type of container for their product. The designer has created two containers: one the shape of a square-based pyramid, and the other a cone. Your job is to determine which container holds more. 1) Label the dimensions from your group card. Pyramid Cone


slant height ______ base length ______

slant height _____ diameter ________

2) Discuss with your partner how you could find the height of each container. 3) Record your ideas using words, pictures, and symbols. 4) Determine the height of each container. Show all of your work. Pyramid Cone

1.6.2: The Container! (Continued) 5) How much can each container hold? Show your work. Pyramid Cone 6) If the geobellies cost $0.005/cm3, how much will it cost to fill each container? 7) Identify the shape with the greater volume. 8) Make a recommendation for the preferred design shape. Provide at least two reasons for

your choice.


1.6.P : Practice 1. Calculate the length of the missing side in each triangle. (a)

13 cm

c 10 cm

(b) 9 cm

b

15 cm

(c)

12 m

5 m

y



1.6.P : Practice (continued) 2. A 5-m ladder is leaning against a house. Draw a diagram and add in any

given measurements. The foot of the ladder is 3 m from the base of the wall. How high up the wall does the ladder reach? 3. Adam has made a picture frame. Draw a diagram and add in any given

measurements. The frame is 60 cm long and 25 cm wide. To check that the frame has square corners, Adam measures the diagonal.

How long should the diagonal be? Sketch a diagram to support your answer.


1.6.J: Journal Activity Your friend was away for today’s lesson. Write an email describing how to find the height of a pyramid or cone when given the base length and slant height or diameter and slant height. Provide your own example.


1.W: Definition Page Term Picture / Sketch Definition Perimeter

Length

Width

Radius

Diameter

Circumference

Circle

Area

Rectangle

Square

Rhombus

Parallelogram


1.W: Definition Page (Continued) Term Picture / Sketch Definition Triangle

Right-Angled Triangle

Hypotenuse

Composite Figure

Volume

Prism

Rectangular Prism

Cylinder

Sphere

Hemisphere

Cone

Pyramid


1.S: Unit Summary Page Complete the following table to summarize the formulas you used in this unit. 2D Shape Sketch / Description Area Formula Example Rectangle / Square

Triangle

Circle

Parallelogram

Trapezoid

3D Solid Sketch / Description Volume Formula Example Rectangular Prism

Cylinder

Sphere

Cone

Pyramid

1.R Reflecting on My Learning (3, 2, 1) 3 Things I know well from this unit 2 Things I need explained more 1 Question I still have



1.RLS: Reflecting on Learning Skills

Students should be aware of the importance that these skills have on your performance. After receiving your marked assessment, answer the following questions. Be honest with yourself. Good Learning Skills will help you now, in other courses and in the future.

E – Always G – Sometimes S – Need Improvement N – Never

Organization E G S N I came prepared for class with all materials E G S N My work is submitted on time E G S N I keep my notebook organized.

Work Habits E G S N I attempt all of my homework E G S N I use my class time efficiently E G S N I limit my talking to the math topic on hand E G S N I am on time E G S N If I am away, I ask someone what I missed, E G S N I complete the work from the day that I missed.

Team Work E G S N I am an active participant in pairs/group work E G S N I co-operate with others within my group E G S N I respect the opinions of others

Initiative E G S N I participate in class discussion/lessons E G S N When I have difficulty I seek extra help E G S N After I resolve my difficulties, I reattempt the problem E G S N I review the daily lesson/ideas/concepts

Works Independently E G S N I attempt the work on my own E G S N I try before seeking help E G S N If I have difficulties I ask others but I stay on task E G S N I am committed to tasks at hand

Yes No I know all the different ways available in my school, where I can seek extra help. Yes No I tried my best. What will I do differently in the next unit to improve? ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________

course: grade 9 applied mathematics (mfm1p) unit 1: …€¦ · gemma wants to tile her bathroom...

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