Math Trail in Beacon Hill Park Victoria, BC

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1 Math Trail in Beacon Hill Park Victoria, BC Malgorzata Dubiel, Department of Mathematics and Statistics, SFU, Modified by Jill Kissick, Matthew Heim, Bradley Carlson

2 Math Trail: An Outdoor Math Experience What is the goal of a math trail? Taking mathematics outside the classroom allows students to experience it, to see that it is all around us and not only in textbooks. And to have fun with it! What can we do on a math trail? We can look for patterns, shapes and numbers. We can count or estimate quantities, distances, areas and volumes. We can compare objects and their properties. We can write stories or word problems about the objects we discover. We can discuss how the objects were constructed. We can design a better playground or a garden, or draw a map of the neighbourhood. Of course, many of these activities should be actually done afterwards, as a follow-up project, and the trail could be part of a research for the project. We can learn to ask questions about objects around us, and see everything as a potential source of mathematics problems. We can learn that looking for questions can be even more exciting than looking for answers! Where can we go on a math trail? We can go on a first math trail around the school grounds. Part of, or even the whole of, the trail can be inside the school. A nearby park or any interesting location in the neighbourhood would be a great destination for a follow-up trail. If appropriate for the age group, you can ask students to design their own math trails: around their houses, neighbourhoods or other favourite locations. If you can go to a park, you can combine mathematics activities with other topics, for example science or environment, or even history. You can learn a lot about the history of Victoria if you go through Beacon Hill Park. Or, with older students, you can have a great math trail through the Parliament Buildings, for example. Which age groups are math trails appropriate for? Students of all ages will enjoy a math trail experience, as will their parents. But of course you will have to choose activities appropriate to the age levels of the participants. In our handout, we include a wide range of activities without clearly indicating for which age levels they are appropriate. Many of these activities are appropriate for all age levels, though of course not all students will conduct them in the same way. Measurement is one such example. The youngest students will be able to look for objects smaller or bigger than their shoe size. Those a bit older will enjoy looking for objects 1 centimetre in length. With fifth and sixth graders, you may attempt estimating diameters of trees, measuring their circumferences, estimating heights of objects, and discussing units of measurement. You, as their teacher, will know best what they are capable of, and enjoy doing. We hope that you will find something appropriate for your class. But, most of all, we hope that our trail will inspire you to create your own questions and activities.

3 General Activities 1. Estimating Students will need to do some guess work, using their own judgement and techniques. Example: Hug a tree! Everyone s hug (arm span) is a different length. 2. Counting Students will need to count different objects during their math trail exercise. Number of benches, sides, corners, rocks, tiles, etc. (Hint: Students can use multiplying and volume formulas to make this process quicker.) 3. Patterns and shapes Look for shapes: buildings, windows, fences, benches, manhole covers, garbage cans, trees, leaves, flowers etc. Discuss types of geometrical shapes used and the reasons for the particular shape. Notice the various patterns found on fences, gardens, flowerbeds and other objects. Notice the tilings on the sidewalks and in the playground, the pinecones, and leaves. Let students collect small objects and use them later in class to create their own patterns. 4. Math stories (a follow-up activity) Let students create math stories (addition stories, subtraction stories, etc.) based on events or objects experienced on the trail. 5. Measurement For younger children: small groups of students can look for objects smaller than, the same size as, or bigger than their shoe, and record the name or a picture of the object on a chart. For children who can use a ruler: using paper rulers, students can search for as many objects as they can find which are one centimetre long. Collect or make a list of the objects. Share the most unusual objects found. Ask them to find a way to discover how much is 1 metre. Discuss the fact that, if you stretch out your arms at your sides, the distance between the fingertips on your left and right hands will be very close to your height. Show the famous drawing Vetruvian Man by Leonardo da Vinci. 6. Measuring heights of objects Students can estimate heights of objects (trees, buildings, basketball backboards, etc.) and then verify their estimates as follows: Fold a rectangular piece of paper at one corner, so the sides line up to get a 45 angle. Put this folded corner of the paper near your eye with the paper vertical and one edge parallel to the ground. Sight along the other edge. Move until you can see the top of the object. (Keep the bottom edge level.) The height of the object is obtained by adding your height (to eye level) to the distance from you to the object. There are other ways of finding an approximate height of an object, like comparing it to the height of another object, the size of which you know, for example the height of a person.

4 Beacon Hill Park Trail Classes will be starting their math trail at the children s farm parking lot. There are many interesting objects in the park, and to investigate all of them would take several hours. So, choose the ones that appeal to you most. Perform the activities suggested, and think of other questions one might ask about the various objects encountered along the way. Note that the map on the back page shows an approximate location of some of the objects featured. Others, like benches or garbage containers, you can find all around the park. Children's Farm (Petting Zoo) How many different types of animals are there? How many chickens? How many goats? How many small buildings? Large buildings? What are the shapes of the buildings? Draw them. Here is a version of my favourite problem about chickens and goats: Jill and Joe were standing near one of the corners of the farm, watching chickens and goats. Jill decided to count all the heads she saw, and Joe decided to count the legs. Jill counted 50 heads, and Joe counted 140 legs. How many chickens and how many goats were there?

5 . Big Redwood There is a very large redwood across the street from the children s farm. Try to estimate the diameter of this tree at the base, in hugs. Calculate the diameter. How good were your estimates? Look at the other trees around the lake. Totem Pole How tall is the totem pole? How many faces do you count on the totem pole? How many times taller is the pole than you? (Ans: 127 ft 7 in)

6 Queen s Lake This is the small lake just before Goodacre Lake. How much smaller is this lake than Goodacre Lake? Is it smaller or larger than the island in Goodacre Lake? Monkey Puzzle Tree There is a small monkey puzzle tree near the redwoods. These trees have very interesting patterns of branches and scalelike leaves. Guess how many branches this tree has. Check your guess by counting them. Investigate the pattern of growth for its branches. Notice how regular and symmetric this growth is! Why do you think it is called a Monkey Tree? (Ans: Monkeys cannot climb it due to the prickly leaves.)

7 Sundial Garden Try to draw a plan of the garden. How many different flowerbeds are there? What are their shapes? How large is the garden? Can you find the radius of the entire garden? (Hint: Starting at one edge count your steps as you walk towards the sundial this will give you the radius of the circle in feet) What time is it according to the sundial? How many bricks per pathway? Playground This is a gold mine of shapes, sizes, and ideas for math stories. You can create a whole math trail around this playground! What shape is the Gazebo? Count the posts. How do they relate to the corners of the Gazebo? (Hint: How many corners in an octagon?) What shapes do you see in the park? (Name and draw as many as you can!) How many swings? How many spirals? What are the shapes of the mirrors? How many circles on the car? What are the shapes of the different roofs on the play castles?

8 Cameron Pavilion Built in 1948, the theatre is used for outdoor concerts during the summer. How many flags can you see hanging from the pavilion? What shapes make up the flags? There are two staircases going up to the stage. How many stairs all together? Birdcage Not very far from the lake you can find a Gazebo a construction like those used to cage exotic birds. Describe the shape of the building. How many sides does it have? Can you estimate the area of the floor? How many doors are in the birdcage and how many rectangles can you see per door? How many rectangles in total? (Hint: Multiply) Look for patterns and shapes you see on the sides of the building and on the fence.

9 Goodacre Lake and the Stone Bridge The stone bridge was constructed in How old it? The lake covers 2.43 acres. Can you tell how many football fields this is? How many basketball courts? Walk across the bridge. How wide is the lake at this point? Estimate the length of the lake. If you have time, walk around the lake and measure the perimeter by counting how many steps you take. Can you guess the area of the island in the lake? Look at the pattern of stones on the sides of the bridge. Estimate how many stones were used to make the bridge. Estimate the height of the bridge deck above the water. Rose Corridor How many posts are there? How many triangles do you see per post? What is the total amount of triangles in the entire corridor?

10 Emily Carr Bridge Estimate the number of stones that make up the walls of the bridge. (Hint: Think! volume = length x width x height) Remember, there are two walls. Giant Watering Can What is the height of the can? If this notch is 3 ft then how high is it? How old is it? (Ans: It was built in 2005.) Sketch the can including any shapes that you see.

11 Throughout your walk, look for: Benches How many types of benches can you find? Which shapes and patterns can you find on them? Garbage cans How many types of garbage can are to be found? What are their shapes? Which do you think can hold more: the blue metal ones or the concrete ones? Manhole covers Look for them inside the park and on the sidewalks around the park. How many types of covers can you find? What are the patterns on them? One of the covers looks like this: The grooves on the cover form six circles. Look at the circles in order of size. The diameter of the second circle is twice as large as that of the first one. The diameter of the third one is three times as large as the first, and so on. Guess how much larger the area of the second circle is than that of the first? How much larger is the area of the third? Bonus question: Why are manhole covers round? (Ans: A circle is the only shape that cannot fall into itself!) And most of all look for patterns, because math is the study of patterns!

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