7.G.1
GOAL: Students will solve problems involving scale drawing of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Questions to consider:
- How does the ratio between the perimeters change as the scale factor changes?
- How does the ratio between the areas change as the scale factor changes?
Materials Needed:
3x5 note card
8 ½” X 11” sheet of paper (or graph paper)
paper larger than the desk top
scissors
tape
model examples: (Matchbox car), globe, atlas
ruler (cm)
Resources:
The Once Upon a Time Map Book; B.G. Hennessy(Author)
Vocabulary:
· Scale: The ratio between two sets of measurements. Scales can use the same units or different units.
· Scale factor: The ratio dimensions related to the dimensions of the actual object.
· Scale drawing: The proportional (enlarged or reduced) drawing of an object.
· Scale model: is a proportional model of a 3-D object. Both scale drawings and scale models can be enlarged or reduced representation of the original object.
· Enlarge: using a scale factor to increase the size of the original.
· Reduce: using a scale factor to decrease the size of the original.
· Proportion: the relationship between two variables that are constant.
· Ratio: the relation between two similar magnitudes with respect to the number of times the first contains the second.
· Area: Length x Width
Develop Understanding
Goal: Students will create multiple scale drawings from the original model or drawing, using different scales.
Anticipation of Problems:
The students will make the whole piece of paper their model.
“Won’t that work?”
Some will actually measure and cut the paper to scale.
Some will guess.
They will try to double the size.
Different scale factors
Make mistake with their sheet of paper.
Students measuring at the curve, where should the desk be measured?
Precision and measurement may vary.
Table will lead in to scale factors. Use the cm ruler.
Length / Width / Area: L x W8 ½” X 11” paper
3” X 5” note card
Enlarged paper
Make the corrections for understanding of proportions or scaled from the 1st piece of paper.
Individual:
Activity 1: Measure the length and width of the desktop.
Find the area of your desktop.
Group:
Proportions of the group need to be the same.
With 3X5 note card, determine a scale factor using proportions.
Solidify Understanding
In your groups:
Place 2 objects on your desktop and draw them to scale.
Create a graph from the table above.
· Straight line will show scale is proportionate. If the line isn’t straight, the scale will not be proportionate.
Practice Understanding
Practice Worksheets: See below
PROJECT:
Make a scaled drawing of the floor-plan of your bedroom and a scaled
drawing of either the wall with a door or a wall with a window.
· Determine the area of a wall that needs to be painted. Be sure to use the wall with a window or a door.
· The floor needs new carpet. How much carpet is needed? You will be using carpet squares. (1 sq. = 1 ft.)
· Make scale models of two pieces of furniture in your room.
Practice Activity:
NAME ______
Choose a map and a write down the route you would travel from the two cities.
You are planning a trip from ______to ______on Highway ______.
You want to determine the distance between these cities by using the map using the scale.
1. How many miles are represented by 1 inch on the map?
2. How inches would equal 150 miles?
3. How did you get your answer?
4. How many inches are there between the two cities you choose to travel from your map?
5. Set up a proportion to find the miles between these two cities?
______
6. You are making a scale drawing with a scale of 2 in. = 21 ft. Explain how you decide how long you should draw an object that has an actual length of 64 ft.
7. The actual length of a boxcar is 602 in. What is the scale of the model?
The length of the boxcar is 6 in.
8. Use the centimeter ruler to measure the length of the following images. Determine the size of the size of the images.
(1 cm = 3 inches)
The Seahorse is 4 cm. What is the size of the actual size of the seahorse? ____
(2 cm = 1 meter)
The Orca is 3.5 cm. What is the actual size of the average male Orca? ______
9. Jane had a diamond that she was looking at through a loop (a type of magnifying glass) one of the diamond’s edges was actually 3 mm and through the loop it appeared to be 9 mm. How much did the loop magnify the diamond?
10. Yolanda created an electrical circuit that needed to amplify a radio signal by 20%. On the Oscilloscope the original signal was 10.0 mV and the amplified signal was 12.0 mV. Did Yolanda’s circuit amplify the original circuit by 20%? Explain.
11. scale: 0.25 in. = 20 mi. 12. Scale: 0.5 in. = 6 ft. 13. Scale: 4 cm= 5 km
drawing: n= ______drawing: n=______drawing: n=______
actual: 480 mi. actual: 36 ft. actual: n= ______
14. Scale: 0.5in= 35mi. If the drawing shows 5 in., the actual length is ______miles.
15. Scale: 2.5cm= 6km. If the drawing shows ___ cm, the actual length is 24 km.
16. Scale: 2in.= 22mi. If the drawing shows ___ in., the actual length is 55 miles.
17. Scale: 3cm= 19km. If the drawing shows 12cm, the actual length is ___ km.