IM 7.4.1 Lesson: Lots of Flags
Which of the geometric objects are scaled versions of each other?
Pick two of the objects that are scaled copies and find the scale factor.
One standard size for the United States flag is 19 feet by 10 feet. On a flag of this size, the union (the blue rectangle in the top-left corner) [br]is [math]7\frac{5}{8}[/math] feet by [math]5\frac{3}{8}[/math] feet.[br][br]There are many places that display flags of different sizes.[br][list][*]Many classrooms display a U.S. flag.[/*][*]Flags are often displayed on stamps.[/*][*]There was a flag on the space shuttle.[/*][*]Astronauts on the Apollo missions had a flag on a shoulder patch.[/*][/list][img]data:image/png;base64,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[/img][br][br]Choose [b][i]one [/i][/b]of the four options and decide on a size that would be appropriate for this flag. Find the size of the union.
Share your answer with another group that used a different option. What do your dimensions have in common?
[size=150]On a U.S. flag that is 19 feet by 10 feet, the union is [math]7\frac{5}{8}[/math] feet by [math]5\frac{3}{8}[/math] feet. For each question, first estimate the answer and then compute the actual percentage.[/size][br][br]What [b]percentage[/b] of the flag is taken up by the union?
What percentage of the flag is red? Be prepared to share your reasoning.[br]
The largest U.S. flag in the world is 225 feet by 505 feet.
Is the ratio of the length to the width equivalent to [math]1:1.9[/math], the ratio for official government flags?
If a square yard of the flag weighs about 3.8 ounces, how much does the entire flag weigh in pounds?
IM 7.4.1 Practice: Lots of Flags
A rectangle has a height to width ratio of [math]3:4.5[/math]. Give two examples of dimensions for rectangles that could be scaled versions of this rectangle.
One rectangle measures 2 units by 7 units. A second rectangle measures 11 units by 37 units. Are these two figures scaled versions of each other? If so, find the scale factor. If not, briefly explain why.
Ants have 6 legs. Elena and Andre write equations showing the proportional relationship between the number of ants, [math]a[/math], to the number of legs [math]l[/math]. Elena writes [math]a=6\cdot l[/math]. Andre writes [math]l=\frac{1}{6}\cdot a[/math]. Do you agree with either of the equations? Explain your reasoning.
On the grid, draw a scaled copy of quadrilateral ABCD with a scale factor ⅔.
Solve the equation mentally.
[math]\frac{5}{2}\cdot x=1[/math]
[math]x\cdot\frac{7}{3}=1[/math]
[math]1\div\frac{11}{2}=x[/math]
Lin has a scale model of a modern train. The model is created at a scale of 1 to 48.
The height of the model train is 102 millimeters. What is the actual height of the train in meters? [i]Explain [/i]your reasoning.
On the scale model, the distance between the wheels on the left and the wheels on the right is [math]1\frac{1}{4}[/math] inches. The state of Wyoming has old railroad tracks that are 4.5 feet apart. Can the modern train travel on those tracks? [i]Explain [/i]your reasoning.