Dr. Sun Yat Sen Classica l Chinese Garden: Math Walk

Intended for Grades 5 and 6

Created by Eloginy Tharmendran, PDP, SFU, August 2013

Complete this first part in the computer lab before going on the math walk.

Skill-building videos to watch before the trip:

Pretend that you need to cover the floor of the room you are in with new tiles. You get to pick what shapes the floor gets covered with, but you can only pick two different shapes at the most and they have to fit together without any gaps.

Visit the website below and watch one or both of these videos, and think about what shapes you want to use.

Draw the shapes beside the links.

Website “Understanding Tessellation”: http://www.csun.edu/~lmp99402/Math_Art/Tesselations/tesselations.html

Here are two videos about “tessellation”:http://www.youtube.com/watch?v=ej1GIS3J_lU http://www.youtube.com/watch?v=DHKijB_L5II

Working with photos on an iPad or iPhone

You will be taking photos on your iPads, phones or cameras and then drawing shapes on top of the photos. “You Doodle” is a free app that you can download on an iPad or iPhone. Here is a video showing how to draw on photos using You Doodle: http://www.youtube.com/watch?v=wXIrAqphyds

Here’s another video showing how to crop and draw on photos using You Doodle on an iPad/iPhone http://www.youtube.com/watch?v=S48GrEoU0Vs

Working with photos on cameras and word

If you are using other phones or cameras, then you can upload your photos to a Word document at the computer lab or at home and draw on the photos in Word.

How to transfer photos from a digital camera to your computer: http://www.youtube.com/watch?v=4T37lrL_4a8

How to insert and crop photos in Word: http://www.youtube.com/watch?v=T87Iwh3TYFc

How to insert and draw on photos in word:

To draw on photos in Word: Use insert-photo and choose the photos you want to insert from your files. The benefit of doing it this way, instead of copy-pasting, is that the photo will fit nicely onto your page. Then go into the insert tab again and click on shapes. You will find a scribble option. You can draw on your photos using this tool. You can also change the colour of the lines, similarly to how you can change the colour of text.

Welcome to the Dr. Sun Yet Sing Classical Chinese Garden.

Complete this part during your Math Walk at the garden.

Work in groups of up to four people.

Each person must hand in their own work.

Show all of your work for full marks.

Stations can be completed in any order.

If you have any questions, ask members of your group or another group before asking instructors.

Bonus questions are mostly optional but you need to answer at least 4 of the 15 bonus questions to get full marks. (30 questions total)

(bonus questions start with a B)

Join in on one of the guided tours to find some of the answers and other interesting information.

Maps are available via the Virtual Tour Museum http://www.museevirtuel-virtualmuseum.ca/sgc-cms/expositions-exhibitions/erudit-scholar/tour/index.php?usr=n5|null|true|eng, or paper copies are available at the entrance.

ENJOY!!

Station 1: Entrance Costs

1) How much would it cost for your family to enter the garden for one day?

(Your family can be who you live with, who takes care of you, or who you call family)

Show all of your work. Here are some questions to guide you.

How many people are in your family?

How much does it cost for each person to enter the garden?

What is the family rate and how many people does it include?

Would it be cheaper to get the family rate?

2) How much would it cost for the same family members to come here three different times?

Bonus

B1) Would your family save money if they bought an annual memberships? If yes, then how much money would they save over the three visits?

Station 2: Exploring for patterns. Take photos, crop if needed and insert into the spaces provided. If not working with an iPad then this sheet will be made available electronically so that you can paste your photos using Word.

Everything in the garden was intentionally designed. Walk around the garden and look for patterns all around you. Ask the tour guide what the principles of yin and yang are and how they relate to shapes and the design of the garden.

3) Place a photo of a shape or symbol that you can see repeated throughout the garden.

4) Take a photo that depicts both yin and yang principles in the same frame and place the photo below.

5) Are yin and yang shapes distributed randomly across the garden, or is one side of the garden more yin and the other more yang? Place two photos below to support your answer.

6) Find evidence of a plant that is Canadian and a plant that is Chinese in close proximity. Place your photo below.

Station 3: Maple Hall and Multiplications

The beams over our heads in the China Maple Hall each have 15 coats of lacquer on them to protect them from weather damage. When the craftsmen were putting the coats of lacquer on the beams, each coat took a week to dry.

7) How many weeks would it have taken the craftsmen to put all 15 coats of lacquer on the beams? How many days is that?

8) What if it only took 6 days to dry and they were in a hurry to get it done. How many days would it have taken the craftsmen to put all 15 coats of lacquer on in this case?

9) What if they only had 100 days to get as many coats of lacquer on as possible, and it took 9 days to dry between coats – how many coats could they apply on the beams during that time?

Station 4: Tessellation

Informative website:http://www.csun.edu/~lmp99402/Math_Art/Tesselations/tesselations.html

Video showing how to crop and draw on photos with You Doodle on an iPad/iPhone: http://www.youtube.com/watch?v=S48GrEoU0Vs

10) Photograph two different “leak windows” that have only one repeating shape in each window – the two windows don’t have to have the same shape, just one shape each. Crop and re-size each photo to include only the leak window and post the two photos below.

11) Photograph two leak windows that each have two different shapes that are repeating throughout the window. Crop and re-size each photo to include only the leak window and post the two photos below.

12) We have been learning about the actions of translation, reflection and rotation. In the windows you photographed in #11, identify where any two of these actions can be seen in the shapes in the leak windows. Identify the shapes by filling them in with different colours. Clearly label which shape corresponds to which action.

Station 5: Playing with images on the ground.

Find the floor that is shown in the photo.

This floor is between the Scholar’s Room and the Pond (not the Scholar’s Courtyard).

Look for shapes in the floor. Also look for ways to combine shapes to make bigger shapes. Look for polygons with four sides, and polygons with more than four sides.

13) Photograph two polygons on the floor with more than four edges. Paste the photos below. Give a brief description identifying each polygon, and name the polygons. (You can draw a sketch in the area below if not working with an iPad to help you remember the shapes.)

14) Imagine sketching your initials by using only the lines between shapes on the floor. Your first name and last name are fine but you can include all of your initials if you like. Take a photo from the same region, but include a larger area in your photo. Draw on the photo to show how your initials can be drawn using the lines between shapes. (Diagonal lines can be used if necessary.) Paste the photo below along with your initials drawn. Count and describe how many vertices, edges, and faces you used in drawing your initials.

Example

Bonus

B2) Count how many right angles, acute angles and obtuse angles were used to write your initials.

Station 6: The Building of the Dr. Sun Yat Sen Classical Chinese Garden.

Data collection:

How many craftsmen were involved in building this garden? _________________________

Where did the craftsmen travel from? ______________________________

What date did construction begin on the garden and what date did the garden open? _________________________

15) How many months did it take to build the garden?

16) Approximately many weeks did it take to build the garden?

17) If the craftsmen worked 12 hours per days and 6 days per week for the whole time the garden was being built, how many hours did each of them work in total?

Bonus:

B3) How many hours were worked in total by all workers if they each worked for 12 hours per day and 6 days per week during the construction period? (also referred to as person-hours)

B4) What if the craftsmen worked only from 9am to 5pm for 5 days per week. How many hours in total would they each have worked during the construction period in this case? How many person-hours would the construction crew have worked all together in this case?

Station 7: Area of the Hall of Hundred Rivers

18) Measure and calculate the total area of the inside of the Hundred Rivers Hall. State the area below along with your calculations.What metric unit of measurement would be most appropriate for describing the area of the hall?

19) What unit of measurement makes sense to describe the area of one of the tiles on the floor? Give one metric unit and one imperial unit. What is the area of each tile on the floor? How many tiles are there in the hall (you can add the half tiles together)

20) How many people do you think would comfortably fit into this room on folding chairs? Explain how you arrived at this answer. After you have guessed, ask a volunteer or tour guide for the room’s maximum capacity for people. (i.e. how many people can legally fit into the room according to the fire department regulation.)

Station 8: Looking at the Public Garden and Paid Garden in Different Ways

The paid part of the garden takes up about 2/3rd of an acre. The public part takes up a about 1/3rd of an acre.

21) What is the ratio of the area of the paid part to the unpaid part?

22) What percent of the garden is public?

23) If 1 acre = 4,046.9 m², approximately what is the area of the paid part of the garden in square meters?

Bonus

B5) If this whole garden is 15 times smaller than a typical garden in the Chinese Ming Dynasty, then approximately how much bigger would a typical garden be in square meters?

Station 9: “Leak Window” to the Outside World – Probability and Ratios. (Only for those classes that have learned about probability)

Find the leak window pictured here at the garden:

Colour Black and white

24) How many different kinds of shapes can you see in this leak window? Name each shape.

25) Which shape(s) are the most common in this window?

26) If you stood far away and shot 100 arrows through this window, approximately how many arrows do you estimate would pass through each of the different kinds of shapes?

Bonus:

B15) Is it more likely that a particular arrow would go through the bigger shape or the smaller shape? Of the 100 arrows, do you estimate that more would go through the bigger shapes or the smaller shapes?

Addition bonus questions:

B6) What mammal is represented throughout the garden that represents good luck in Chinese cultures, but that most westerns are a little afraid of?

B7) Give two reasons why the garden contains a “double corridor”?

B8) What was left out in the construction of the garden that most builders today use a lot of?

B9) What is a penjing?

B10) What is a ting and why is it situated so high?

B11) What four things do “leak windows” leak?

B12) Why do you think the pond is cloudy?

B13) Why is the new area called the Hall of One Hundred Rivers?

B14) What shape would the traditional entrance be in a Chinese classical garden?

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