© 21st Century Math Projects
Project Title: Dinosaur Encyclopedia Standard Focus: Geometry & Spatial Sense
Time Range: 3-5 Days Supplies: Scissors and Rulers
Topics of Focus: -
Scale
-
Measurement (and unit conversion)
-
Similarity and Proportions
Benchmarks: Ratios and Proportional Relationships
6.RP
1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
Ratios and Proportional Relationships
6.RP
3d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Ratios and Proportional Relationships
7.RP
2. Recognize and represent proportional relationships between quantities.
Ratios and Proportional Relationships
7.RP
2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Geometry
7.G
1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Quantities
N-Q
1. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
GCO
12. Make formal geometric constructions with a variety of tools and methods. Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Congruence
Procedures: A) Task 1: “Whose Leg is it Anyway” -- Students will use scale models to determine the actual dimensions of dinosaur bones. They range from simple scale model problems to using scale models to analyze. B) Task 2: “Bone Wars”—This could be done in a few ways. In any event, the dinosaur bones will need to be cut out in advance. You can laminate them for repeated use. I suggest to divide students into small groups of 4-5. You can either “hide” the bones and have the students go around the room to “excavate” them or you can simply give each student group 6 random bones. The goal is that a group will collect 6 bones of the same dinosaur. You can have students trade bones, steal bones, buy bones, whatever you feel comfortable with. There are 8 dinosaurs included, but you do not need to use each of them for the activity to work. When students collect the bones of their dinosaur they can verify © 21st Century Math Projects
with you that they have all six pieces. They are labeled with letters, numbers or symbols and a key is provided. All of the bones are perfectly to scale. C) Task 3: “Dinosaur Encyclopedia” – Students will use scale to construct their own illustrations for a dinosaur encyclopedia. There are six dinosaurs provided, but you do not necessarily need to use all of them. This can be done in small groups or individually. The task is complex because there are two different things that are scaled. Definitely read through the instructions on page 17!
Math it Up!
© 21st Century Math Projects
Archeological digs reveal mysteries of the earth’s history, and dinosaurs have been a central focus of our curiosity for over a century. When a fossil is discovered it goes through the painstaking process of identification. For this activity, this process has been scaled back (pun intended!) and simplified to practice the geometric concepts of similarity and proportions. Whether it is a sculpture, a drawing or a toy, scale models of dinosaurs are used because the humongous size of the actual creature is not practical. In each of these situations a scaled bone of a dinosaur has been measured and your job is to determine the approximate size of the actual bone, determine the scale or in some cases try to identify the species. Use the scale in each of the situations to estimate the actual size (watch the units!)
What is the approximate length (in feet) of an actual dorsal vertebrae of a spinosaurus?
If the approximate length of an allosaurus humerus is 5 ft 6 in, what is the scale of this piece?
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If a T-Rex skull is on average 4-6 feet in length, is this skull in the correct scale?
If the length of the skull ranges between 4-6 feet and a 1:4 scale was used, what would be a reasonable range of lengths for the model piece?
What is the approximate height and length (in feet) of a plate from a stegosaurus?
Stegosaurus plates closer to the head and tail have dimensions that are approximately 1 ft by 1 ft. Plates closer to the middle of the body have dimensions that are approximately 3 ft by 3 ft. Would you estimate that the plate is closer to the middle or closer to the end?
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After comparing the shape of the femur to other models in her science class, Hakim has decided that it belongs to one of these four dinosaurs. Use the scale and the table to determine what species you believe the femur most likely belongs to. Average Femur Length Which species do you believe this femur belongs to? Provide an explanation for your decision.
Apatosaurus
6 ft 8 in – 8 ft 4 in
Stegosaurus
2 ft 10 in – 3 ft 8 in
Triceratops
3 ft 2 in – 3 ft 10 in
Tyrannosaurus Rex
5 ft 4 in – 6 ft 10 in
After comparing the shape of the ribs to a dinosaur encyclopedia, Kasey has decided that it belongs to one of these four dinosaurs. Use the scale and the table to determine what species you believe the rib most likely belongs to. Average Rib Length Which species do you believe this rib belongs to? Provide an explanation for your decision.
Ankylosaurus
2 ft 5 in – 2 ft 7 in
Baryonyx
2 ft 11 in – 3 ft 5 in
Pachycephalosaurus
2 ft 1 in – 2 ft 6 in
Tarchia
2 ft 8 in – 3 ft 8 in
© 21st Century Math Projects
From 1877 to 1892 there was a stretch of U.S. history known as the “Great Dinosaur Rush”. After successful archaeological digs the search for new fossils reached a fevered pitch. At the center of the rush was a heated rivalry between two paleontologists, Edward Drinker Cope of the Academy of Natural Sciences in Philadelphia and Othniel Charles Marsh of the Peabody Museum of Natural History at Yale. These two paleontologists used dirty tactics to outdo each other including bribery and theft. Eventually, Cope and Marsh became bankrupt after repeated attempts to ruin each other, but their discoveries were the backbone to the study of dinosaurs and they named many of the species so familiar today. In this assignment, model bones of different dinosaurs were scattered and it’s your job to assemble a complete dinosaur with the correct parts. Each dinosaur will have 6 parts: a skull, two humeri, a rib and two femurs. All of the model bones are in 1:16 scale. Use the Average Measurement of Actual Dinosaur Bones table to help you determine which dinosaur bone you have found. Please note that all measurements are the longest lengths in the fossil. Put on your archaeologist hat, find bones, measure them, compute the actual length for the scale and determine which dinosaur it belongs to. How many complete dinosaurs can you make?
5ft 3in
2ft 8in
2ft 11in
3ft 0in
4ft 1in
3ft 0in
5ft 11in
3ft 9in
4ft 4in
5ft 4in
7ft 9in
5ft 1in
6ft 7in
4ft 5in
6ft 6in
4ft 9in
2ft 4in
2ft 0in
4ft 7in
3ft 7in
8ft 10in
2ft 10in
4ft 0in
2ft 5in
6ft 10in
4ft 7in
4ft 10in
4ft 1in
3ft 4in
1ft 7in
2ft 1in
2ft 0in
© 21st Century Math Projects
Sketch and label the bones of a single dinosaur. Compute the measurements of the actual bone length.
Model Length ________
Model Length ________
Model Length ________
Model Length ________
Actual Length _________
Actual Length _________
Actual Length _________
Actual Length _________
© 21st Century Math Projects
© 21st Century Math Projects
© 21st Century Math Projects
© 21st Century Math Projects
© 21st Century Math Projects
© 21st Century Math Projects
© 21st Century Math Projects
© 21st Century Math Projects
© 21st Century Math Projects
When dinosaurs roamed the earth they came in all shapes and sizes. However, unless someone has stood next to a skeleton they may have a hard time comprehending how big a dinosaur was compared to an average person. Educational publishers often use scale drawings of dinosaurs compared to humans to emphasize their size. In this project you will measure, use proportions and test your art skills to create scale images for your own dinosaur encyclopedia. Follow the four steps below to construct your own Dinosaur Encyclopedia Illustrations!
You will see coordinate grids that represent an illustration in the Dinosaur All of the men figures in this Encyclopedia. These pictures are on CM grid paper. (Note: These images are not assignment have dimensions drawn to scale.) The height of the man in this example illustration is 4 cm. 6 ft by 1 ½ ft Thus the scale of the man in this image would be: 6 ft : 4 cm and can be reduced to 3 ft : 2 cm
You will see a table that looks like this. Use the Scale (3 ft : 2 cm) to Calculate the Encyclopedia Height and Length of the Dinosaur.
Height Length
For each Dinosaur you will see a silhouette. You will need to measure the length and the width of the silhouette to determine the scale so you are Compute the Scale! able to redraw it. 6:67 cm to 2 cm AND 16.67 cm to 5 cm Scale: Model on the Right (cm) to Encyclopedia Ankylosaurus (cm)
Ankylosaurus Actual Encyclopedia 6.67 cm 10 ft 25 ft 16.67 cm Use will need to make multiple measurements and use the scale to draw an accurate picture!
3.33:1
© 21st Century Math Projects
Man Actual Height
6 ft
Length
1.5 ft
Encyclopedia
Scale: Actual (ft) to Encyclopedia (cm) Tyrannosaurus Rex Actual Height
18 ft
Length
23 ft
Encyclopedia
Scale: Model on the Right (cm) to Encyclopedia T-Rex (cm)
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Man Actual Height
6 ft
Length
1.5 ft
Encyclopedia
Scale: Actual (ft) to Encyclopedia (cm) Spinosaurus Actual Height
20 ft
Length
52 ft
Encyclopedia
Scale: Model on the Right (cm) to Encyclopedia Spinosaurus (cm)
© 21st Century Math Projects
Man Actual Height
6 ft
Length
1.5 ft
Encyclopedia
Scale: Actual (ft) to Encyclopedia (cm) Velociraptor Actual Height
3 ft
Length
6 ft
Encyclopedia
Scale: Model on the Right (cm) to Encyclopedia Velociraptor (cm)
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Man Actual Height
6 ft
Length
1.5 ft
Encyclopedia
Scale: Actual (ft) to Encyclopedia (cm) Triceratops Actual Height
10 ft
Length
17 ft
Encyclopedia
Scale: Model on the Right (cm) to Encyclopedia Triceratops (cm)
© 21st Century Math Projects
Man Actual Height
6 ft
Length
1.5 ft
Encyclopedia
Scale: Actual (ft) to Encyclopedia (cm) Stegosaurus Actual Height
11 ft
Length
21 ft
Encyclopedia
Scale: Model on the Right (cm) to Encyclopedia Stegosaurus (cm)
© 21st Century Math Projects
Man Actual Height
6 ft
Length
1.5 ft
Encyclopedia
Scale: Actual (ft) to Encyclopedia (cm) Apatosaurus Actual Height
26 ft
Length
35 ft
Encyclopedia
Scale: Model on the Right (cm) to Encyclopedia Apatosaurus (cm)
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Math it Up. Boomdiggy. © 21st Century Math Projects
Archeological digs reveal mysteries of the earth’s history, and dinosaurs have been a central focus of our curiosity for over a century. When a fossil is discovered it goes through the painstaking process of identification. For this activity, this process has been scaled back (pun intended!) and simplified to practice the geometric concepts of similarity and proportions. Whether it is a sculpture, a drawing or a toy scale models of dinosaurs are used because the humongous size of the actual creature is not practical. In each of these situations a scaled bone of a dinosaur has been measured and your job is to determine the approximate size of the actual bone, determine the scale or in some cases try to identify the species. Use the scale in each of the situations to estimate the actual size (watch the units!)
What is the approximate length (in feet) of an actual dorsal vertebrae of a spinosaurus? 64 in or 5ft 4in
If the approximate length of an allosaurus humerus is 5 ft 6 in, what is the scale of this piece? 66 inches. 1:33 scale
© 21st Century Math Projects
If a T-Rex skull is on average 4-6 feet in length, is this skull in the correct scale? 82 inches or 6ft 10in. This scale seems off because it doesn’t fit in the average range.
If the length of the skull ranges between 4-6 feet and a 1:4 scale was used, what would be a reasonable range of lengths for the model piece? 48 to 72 inches would be the actual inches so 12 to 18 inches would be reasonable for the model.
What is the approximate height and length (in feet) of a plate from a stegosaurus? 21 in by 35 in so 1ft 9in by 2ft 11in
Stegosaurus plates closer to the head and tail have dimensions that are approximately 1 ft by 1 ft. Plates closer to the middle of the body have dimensions that are approximately 3 ft by 3 ft. Would you estimate that the plate is closer to the middle or closer to the end? These would be closer to the middle of the body.
© 21st Century Math Projects
After comparing the shape of the femur to other models in her science class, Hakim has decided that it belongs to one of these four dinosaurs. Use the scale and the table to determine what species you believe the femur most likely belongs to. Average Femur Length Which species do you believe this femur belongs to? Provide an explanation for your decision. 44 inches is about 3ft 8in. I’d estimate it is most likely the triceratops because it is in the middle of the range. It could possibly be a stegosaurus, but it is on the extreme end of the range.
Apatosaurus
6 ft 8 in – 8 ft 4 in
Stegosaurus
2 ft 10 in – 3 ft 8 in
Triceratops
3 ft 2 in – 3 ft 10 in
Tyrannosaurus Rex
5 ft 4 in – 6 ft 10 in
After comparing the shape of the ribs to a dinosaur encyclopedia, Kasey has decided that it belongs to one of these four dinosaurs. Use the scale and the table to determine what species you believe the rib most likely belongs to. Average Rib Length Which species do you believe this rib belongs to? Provide an explanation for your decision. 30in or 2 ft 6in. This would most likely be an ankylosaurus, but it could also be a pachycephalosaurus.
Ankylosaurus
2 ft 5 in – 2 ft 7 in
Baryonyx
2 ft 11 in – 3 ft 5 in
Pachycephalosaurus
2 ft 1 in – 2 ft 6 in
Tarchia
2 ft 8 in – 3 ft 8 in
© 21st Century Math Projects
From 1877 to 1892 there was a stretch of U.S. history known as the “Great Dinosaur Rush”. After successful archaeological digs the search for new fossils reached a fevered pitch. At the center of the rush was a heated rivalry between two paleontologists, Edward Drinker Cope of the Academy of Natural Sciences in Philadelphia and Othniel Charles Marsh of the Peabody Museum of Natural History at Yale. These two paleontologists used dirty tactics to outdo each other including bribery and theft. Eventually, Cope and Marsh became bankrupt after repeated attempts to ruin each other, but their discoveries were the backbone to the study of dinosaurs and they named many of the species so familiar today. In this assignment, model bones of different dinosaurs were scattered and it’s your job to assemble a complete dinosaur with the correct parts. Each dinosaur will have 6 parts: a skull, two humeri, a rib and two femurs. All of the model bones are in 1:16 scale. Use the Average Measurement of Actual Dinosaur Bones table to help you determine which dinosaur bone you have found. Please note that all measurements are the longest lengths in the fossil. Put on your archaeologist hat, find bones, measure them, compute the actual length for the scale and determine which dinosaur it belongs to. How many complete dinosaurs can you make?
5ft 3in
2ft 8in
2ft 11in
3ft 0in
4ft 1in
3ft 0in
5ft 11in
3ft 9in
4ft 4in
5ft 4in
7ft 9in
5ft 1in
6ft 7in
4ft 5in
6ft 6in
4ft 9in
2ft 4in
2ft 0in
4ft 7in
3ft 7in
8ft 10in
2ft 10in
4ft 0in
2ft 5in
6ft 10in
4ft 7in
4ft 10in
4ft 1in
3ft 4in
1ft 7in
2ft 1in
2ft 0in
© 21st Century Math Projects
Sketch and label the bones of a single dinosaur. Compute the measurements of the actual bone length.
Model Length ________
Model Length ________
Model Length ________
Model Length ________
Actual Length _________
Actual Length _________
Actual Length _________
Actual Length _________
© 21st Century Math Projects
When dinosaurs roamed the earth they came in all shapes and sizes. However, unless someone has stood next to a skeleton they may have a hard time comprehending how big a dinosaur was compared to an average person. Educational publishers often use scale drawings of dinosaurs compared to humans to emphasize their size. In this project you will measure, use proportions and test your art skills to create scale images for your own dinosaur encyclopedia. Follow the four steps below to construct your own Dinosaur Encyclopedia Illustrations!
You will see coordinate grids that represent an illustration in the Dinosaur All of the men figures in this Encyclopedia. These pictures are on CM grid paper. (Note: These images are not assignment have dimensions drawn to scale.) The height of the man in this example illustration is 4 cm. 6 ft by 1 ½ ft Thus the scale of the man in this image would be: 6 ft : 4 cm and can be reduced to 3 ft : 2 cm
You will see a table that looks like this. Use the Scale (3 ft : 2 cm) to Calculate the Encyclopedia Height and Length of the Dinosaur.
Height Length
For each Dinosaur you will see a silhouette. You will need to measure the length and the width of the silhouette to determine the scale so you are Compute the Scale! able to redraw it. 6:67 cm to 2 cm AND 16.67 cm to 5 cm Scale: Model on the Right (cm) to Encyclopedia Ankylosaurus (cm)
Ankylosaurus Actual Encyclopedia 6.67 cm 10 ft 25 ft 16.67 cm Use will need to make multiple measurements and use the scale to draw an accurate picture!
3.33:1
© 21st Century Math Projects
Man Actual
Encyclopedia
Height
6 ft
4 cm
Length
1.5 ft
1 cm
Scale: Actual (ft) to Encyclopedia (cm)
6:4 or 3:2
Tyrannosaurus Rex Actual
Encyclopedia
Height
18 ft
12 cm
Length
23 ft
15.33 cm
Scale: Model on the Right (cm) to Encyclopedia T-Rex (cm)
6 : 12
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Man Actual
Encyclopedia
Height
6 ft
2.5
Length
1.5 ft
0.625 6:2.5 or 12:5
Scale: Actual (ft) to Encyclopedia (cm) Spinosaurus Actual
Encyclopedia
Height
20 ft
8.33 cm
Length
52 ft
21.66 cm
Scale: Model on the Right (cm) to Encyclopedia Spinosaurus (cm)
8.5:21.66
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Man Actual
Encyclopedia
Height
6 ft
13 cm
Length
1.5 ft
3.25
Scale: Actual (ft) to Encyclopedia (cm)
6 ft: 13 cm
Velociraptor Actual
Encyclopedia
Height
3 ft
6.5 cm
Length
6 ft
13 cm
Scale: Model on the Right (cm) to Encyclopedia Velociraptor (cm)
13:8
© 21st Century Math Projects
Man Actual
Encyclopedia
Height
6 ft
4 cm
Length
1.5 ft
1 cm
Scale: Actual (ft) to Encyclopedia (cm)
6:4 or 3:2
Triceratops Actual
Encyclopedia
Height
10 ft
6.67 cm
Length
17 ft
11.33 cm
Scale: Model on the Right (cm) to Encyclopedia Triceratops (cm)
8:11.33
© 21st Century Math Projects
Man Actual
Encyclopedia
Height
6 ft
5 cm
Length
1.5 ft
1.25 cm
Scale: Actual (ft) to Encyclopedia (cm)
6 ft: 5cm
Stegosaurus Actual
Encyclopedia
Height
11 ft
9.2 cm
Length
21 ft
17.5 cm
Scale: Model on the Right (cm) to Encyclopedia Stegosaurus (cm)
8.5:17.5
© 21st Century Math Projects
Man Actual
Encyclopedia
Height
6 ft
3 cm
Length
1.5 ft
.75 cm
Scale: Actual (ft) to Encyclopedia (cm)
2 ft : 1 cm
Apatosaurus Actual
Encyclopedia
Height
26 ft
13 cm
Length
35 ft
17.5 cm
Scale: Model on the Right (cm) to Encyclopedia Apatosaurus (cm)
5.33:13
© 21st Century Math Projects
