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Totem Pole Carving & Scale Factor

Totem Pole Carving & Scale Factor.

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Totem Pole Carving & Scale Factor

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  1. Totem Pole Carving & Scale Factor The totem pole pictured left stands proudly on the Tla’Amin First Nations Reserve located on the Sunshine Coast in Powell River, BC. The 30-foot pole was carved by Tla’Amin artist Jackie Timothy. It was commissioned by the band to commemorate the recent deaths of many elders and community members and is the first carving erected in the area in recent years.(Powell River Peak, Nov 10, 2009) . The full news story of the Totem Pole can be found online at : http://prpeak.com/articles/2009/11/10/news/doc4af8cca624e1d573388542.txt

  2. Diagram Brad & Ely’s Carving Brad and Ely are cousins from the Tla’Amin (a.k.a.Sli’ammon) band on the Sunshine Coast of BC. Years ago their great grandfather, who was a shaman, carved an illustrious totem pole. The carving symbolized deep cultural and spiritual meaning for family and community. Unfortunately, this artwork was destroyed by peoples who did not understand the value of Indigenous art. Fortunately, Brad and Ely have a diagram of the carving. Also depicted in this diagram is a well known building that is known to have stood 15 feet to the west of the long lost totem pole. Brad and Ely would like to honour their grandfather by replicating the carving. They both know that this project will take hours of labor, patience and masterful skill. But the cousins are up to the challenge because they know the carving’s re-creation will honor family and community. Note: Fictional Story. The main characters are inspired by the author’s friends Brad and Ely who are both from Tla’Amin First Nations families. However, in real life, they are friends rather than cousins.

  3. Help the young carvers out: Before starting, Brad and Ely need to figure out how much wood to procure. This is difficult because they cannot measure the original carving. But, they know that the totem pole once stood 15 feet west of the building. • In the diagram, the totem pole symbol is 1.25 inches to the left of the building symbol. • The diagram width of the totem pole is 0.3125 inches ( 5/16 of an inch). • The diagram height of the totem pole is 2.25 inches. Using the diagram above, find the approximate volume of wood needed to make the carving. (Hint: start by creating a scale factor to determine the real life dimensions of the totem pole.) State your answer in cubic feet. • Note: Assume the totem pole is the same width all the way around. The totem pole in the diagram is just a symbol. The real totem pole does not have eagle wings.

  4. Solution:Step 1: Determine Scale Factor Remember that the real life distance between the totem pole and the building is 15 feet. We can compare this real distance to the diagrammed distance of 1.25 inches to create a scale factor. To do this , we must first express real distance and diagram distance in terms of the same units. We will use inches. Conversion of real life distance to inches: ( Answering the question: “How many inches is 15 feet?”) 12 inches = X inches 1 foot 15 feet Cross multiply to solve for X: (12 inches) 15 feet = ( 1 foot) X (12)(15)= X 180 = X X = 180 inches. This means that the real life distance of 15 feet can also be expressed as 180 inches. Now that we have all units in inches we can determine the scale factor: Scale Factor (SF) = Real Size (inches)____= 180inches____ = 144 (SF has no units) Diagram Size (inches) 1.25 inches This means that the real life distance between the two objects is 144 times longer than the pictured distance! Remember the picture is drawn to scale. Therefore, the real life totem pole is 144X larger than the diagrammed totem pole.

  5. Step 2: Use SF to find the real life height & width of the totem pole. Height: A general scale factor formula is: (SF)= Real Size____ . So our scale factor formula will be: SF= Real Totem Height Diagram Size Diagram Totem Height Rearranging for Real Size, we get: Real Size = (SF) (Diagram Size) So then: Real Totem Height = (SF) (Diagram Totem Height) We already know that our SF is 144 . We also know the diagram height of the totem poleis 2.25 inches. So Real Totem Height = (144) (2.25inches) = 324 inches We want this in feet: 324inches X 1 foot____ = 27 feet 12 inches We now know that the real totem pole height was 27 feet!

  6. Step 2: Use SF to find the real life height & width of the totem pole. Width: We will use the same principle as before to find the real life totem pole width: As before: (SF)= Real Size__ Our scale factor formula for width will be: SF= Real Totem Width Diagram Size Diagram Totem Width Rearranging to solve for width: Real Totem Width= (SF) (Diagram Totem Width) Known: SF is 144 . Diagram width is 0.3125 inches. So Real Totem Width= (144) (0.3125inches) = 45 inches We want this in feet: 45 inchesX 1 foot____ = 3.75 feet 12 inches We now know that the real totem pole widths were 3.75 feet!

  7. Step 3: Use real life totem pole dimensions to find its real life volume. The totem pole is the same width all the way around. So the dimensions of the totem pole are 27feet X 3.75feet X 3.75feet. Volume = height X width X depth (For this totem pole width = depth) Therefore, totem pole volume = (27’)(3.75’)(3.75’) = 379.6875 cubic feet We want to make sure that Brad & Ely have more than enough wood so we will round the volume measurement up to the nearest one. Therefore, they will need 380 cubic feet of wood to make the carving.

  8. Alternate Solution: Finding scale factor by converting diagrammed distance into feet: Conversion of diagrammed distance to feet: 12 inches = 1.25 inches 1 foot X feet Cross multiply to solve for X: (12 inches) X feet = (1.25 inches) 1 foot 12X = 1.25 X = 1.25 / 12 X = 0.1042 feet So we know that the diagrammed distance between the totem pole and the building is 0.1042 feet. We can compare the diagramed distance to the real distance to find a scale factor. Scale Factor (SF) = Real Size (in feet) = 15 ft____ = 143.953935 (SF has no units & is not exact because we rounded diagram distance to 4 decimal places) Diagram Size (ft) 0.1042ft This means that the real life distance between the two object is 143.95 times longer than the pictured size! Our goal is to ensure that Ely has enough material to make the carving. So, we can round the scale factor up to the nearest one. This way we will have an easier number to work with and he will have more than enough material. Let’s round the scale factor up to 144. The rest of the solution can be done as described in slides 6 and 7.

  9. For teachers: PLO’s Referred To: Foundations of Mathematics 11 A2. Solve problems that involve scale diagrams, using proportional reasoning. A3. Demonstrate an understanding of the relationships among scale factors, areas, surface areas and volumes of similar 2-D shapes and 3-D objects. Prior Knowledge PLO’s: Foundations of Mathematics and Pre-Calculus 10 A2. Apply proportional reasoning to problems that involve conversions between SI and imperial units of measure. Sources Used: Newspaper Article: Totem Pole Honors Families and Friends, Powell River Peak, Nov 10, 2009. http://prpeak.com/articles/2009/11/10/news/doc4af8cca624e1d573388542.txt YouTube Video: Scale Factor, viewed Oct 15, 2013, http://www.youtube.com/watch?v=XtkU4VkWh8I Ministry of Education BC Website, Mathematics Curriculum Documents, viewed Oct 26, 2013 http://www.bced.gov.bc.ca/irp/subject.php?lang=en&subject=Mathematics

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