Around and About the San Juans
Assessments:
1. Due to local flooding a small lake has been formed. Three brothers decide to
measure its perimeter over time to compare it to other periods of flooding. They
have three possible measuring devices that they could use by flipping them endover-end and counting the number of lengths around the lake. Alvin has a one-foot
ruler; Brian has a 3-foot yardstick; and Charles has a 6-foot rod. Which of these
measuring devices will give the most accurate measurement of the lake’s perimeter?
A. Alvin’s one-foot ruler
B. Brian’s 3-foot yardstick
C. Charles’ 6-foot rod
D. All three will be equally accurate.
2. Concrete is to be poured into a form the shape of a rectangle that is 20 feet by 25
feet. The form is to have an average depth of 6 inches. Approximately how much
concrete is needed to fill the form?
A. 90 cubic feet
B. 250 cubic feet
C. 500 cubic feet
D. 3000 cubic feet
3. Concrete is to be poured into a form the shape of a rectangle that is 20 feet by 25
feet. The form is to have an average depth of 6 inches. The total number of feet of
6 inch high form material needed for the form is approximately
A. 45 feet
B. 90 feet
C. 250 feet
D. 500 feet
Around and About the San Juans
Assessment Materials Page 1 of 14
4. Concrete is to be poured into a form the shape of a rectangle that is 20 feet by 25
feet. The builder estimates that the time needed to finish ten square feet of concrete
surface is approximately one minute. Once the concrete is poured, approximately
how long will it take to finish the surface?
A. 9 minutes
B. 45 minutes
C. 50 minutes
D. 90 minutes
5. Concrete is to be poured into a form the shape of a rectangle that is 20 feet by 25
feet. The form is to have an average depth of 6 inches. Concrete is usually sold by
the cubic yard. One foot = 12 inches. One yard = 3 feet. Approximately how many
cubic yards of yards of concrete is needed to fill the form?
A. 10 cubic yards
B. 25 cubic yards
C. 50 cubic yeards
D. 300 cubic yards
Around and About the San Juans
Assessment Materials Page 2 of 14
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2
5
10
6. Determine the area of the region outlined in the grid above.
A. 30 square units
B. 32 square units
C. 40 square units
D. 50 square units
7. Determine the perimeter of the region outlined in the grid above.
A. 30 units
B. 32 units
C. 34 units
D. 40 units
Around and About the San Juans
Assessment Materials Page 3 of 14
8. Mrs. Berg is planning to re-seed a region of her property that is elliptical in shape.
She needs to put a fence around it while the new grass is growing.
50 feet
Estimate the length of the fence and the area being reseeded. Each side of the
small squares is 5 feet in length.
Show your work in words, numbers and/or diagrams.
The estimated length of the fence is __________ feet.
The estimated area being reseeded is __________ square feet.
Around and About the San Juans
Assessment Materials Page 4 of 14
9. Boromir is estimating the perimeter and area of the ellipse below using the darkened
lines. The length of the one side of a square in the grid is one-half a foot.
Estimate the length and area of the ellipse in feet and square feet.
Show your work in words, numbers and/or diagrams.
The estimated length of the ellipse is __________ feet.
The estimated area being reseeded is __________ square feet.
Around and About the San Juans
Assessment Materials Page 5 of 14
10. This is a map of Waldron Island. The side length of each square in the grid is 0.4
miles.
Use this grid to estimate the perimeter and the area of the island.
Show your work in words, numbers and/or diagrams.
The estimated perimeter of the island is __________ miles.
The estimated area of the island is __________ square miles.
Around and About the San Juans
Assessment Materials Page 6 of 14
11. Each side of a square in the grid represents 3 cm. Thomas used this to estimate
that the perimeter of the ellipse was 96 cm and to estimate that the area was 468
cm2.
Confirm that Thomas’s estimates are reasonable by showing that
• His estimates are greater than the perimeter and area of a rectangle that fits
inside the ellipse and by showing that
• His estimates are less than the perimeter and area of a rectangle that fits
around the ellipse.
Show support for your work in words, numbers and/or diagrams.
Around and About the San Juans
Assessment Materials Page 7 of 14
Around and About the San Juans
Assessments Solutions
1. Due to local flooding a small lake has been formed. Three brothers decide to
measure its perimeter over time to compare it to other periods of flooding. They
have three possible measuring devices that they could use by flipping them endover-end and counting the number of lengths around the lake. Alvin has a one-foot
ruler; Brian has a 3-foot yardstick; and Charles has a 6-foot rod. Which of these
measuring devices will give the most accurate measurement of the lake’s perimeter?
A. Alvin’s one-foot ruler
B. Brian’s 3-foot yardstick
C. Charles’ 6-foot rod
D. All three will be equally accurate.
2. Concrete is to be poured into a form the shape of a rectangle that is 20 feet by 25
feet. The form is to have an average depth of 6 inches. Approximately how much
concrete is needed to fill the form?
A. 90 cubic feet
20 + 25 + 20 + 25
B. 250 cubic feet
0.5 x 20 x 25
C. 500 cubic feet
20 x 25
D. 3000 cubic feet
6 x 20 x 25
3. Concrete is to be poured into a form the shape of a rectangle that is 20 feet by 25
feet. The form is to have an average depth of 6 inches. Approximately how many
feet of 6 inch high material are needed to make the form ?
A. 45 feet
20 + 25
B. 90 feet
20 + 25 + 20 + 25
C. 250 feet
0.5 x 20 x 25
D. 500 feet
20 x 25
Around and About the San Juans
Assessment Materials Page 8 of 14
4. Concrete is to be poured into a form the shape of a rectangle that is 20 feet by 25
feet. The builder estimates that the time needed to finish ten square feet of concrete
surface is approximately one minute. Once the concrete is poured, approximately
how long will it take to finish the surface?
A. 9 minutes
(20 + 25 + 20 + 25) / 10
B. 45 minutes
20 + 25
C. 50 minutes
20 x 25 ÷ 10
D. 90 minutes
20 + 25 + 20 + 25
5. Concrete is to be poured into a form the shape of a rectangle that is 20 feet by 25
feet. The form is to have an average depth of 6 inches. Concrete is usually sold by
the cubic yard. One foot = 12 inches. One yard = 3 feet. Approximatelyhow many
cubic yards of concrete are needed to fill the form?
A. 10 cubic yards
≈ 0.5 x 20 x 25 ÷ 33
B. 25 cubic yards
≈ 0.5 x 20 x 25 ÷ 32
C. 50 cubic yards
≈ 20 x 25 ÷ 32
D. 300 cubic yards
≈ 6 x 20 x 25 ÷ 32
Around and About the San Juans
Assessment Materials Page 9 of 14
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2
5
10
6. Determine the area of the region outlined in the grid above.
A. 30 square units
B. 32 square units
C. 40 square units
D. 50 square units
7. Determine the perimeter of the region outlined in the grid above.
A. 30 units
B. 32 units
C. 34 units
D. 40 units
Around and About the San Juans
Assessment Materials Page 10 of 14
8. Mrs. Berg is planning to re-seed a region of her property that is elliptical in shape.
She needs to put a fence around it while the new grass is growing.
50 feet
Estimate the length of the fence and the area being reseeded. Each side of the small
squares is 5 feet in length.
Show your work in words, numbers and/or diagrams.
Approx. 48 squares within the boundary • 25 sq. ft. per square = 1200 sq. ft. for the
area
Approx. 32 sides around the shape • 5 ft. per side = 160 feet for the perimeter
The estimated length of the fence is __________ feet.
The estimated area being reseeded is __________ square feet.
2 points response – does both of the following
• gives an area estimate in the interval of 1200 to 1400 square feet and
• gives a perimeter estimate of 160 feet
1 point response – does one of the following
• correctly estimates and labels both the number of squares within the boundary,
48-56 & the distance around, 32 sides
• gives an area estimate in the interval of 1200 to 1400 square feet
• gives a perimeter estimate of 160 feet
0 point response – shows little understanding of the problem situation
Around and About the San Juans
Assessment Materials Page 11 of 14
9. Boromir is estimating the perimeter and area of the ellipse below using the darkened
lines. The length of the one side of a square in the grid is one-half a foot.
Estimate the length and area of the ellipse in feet and square feet.
Show your work in words, numbers and/or diagrams.
52 squares within the boundary • 1/4 sq. ft. per square = 13 sq. ft. for the area
32 sides around the shape • 0.5 ft. per side = 16 feet for the perimeter
The estimated length of the ellipse is __________ feet.
The estimated area being reseeded is __________ square feet.
2 points response – does both of the following
• gives an area of 13 square feet and
• gives a perimeter of 16 feet
1 point response – does one of the following
• correctly estimates and labels both the number of squares within the boundary, 52
squares and the distance around, 32 sides
• gives an area of 13 square feet
• gives a perimeter of 16 feet
0 point response – shows little understanding of the problem situation
Around and About the San Juans
Assessment Materials Page 12 of 14
10. This is a map of Waldron Island. The side length of each square in the grid is 0.4
miles.
Use this grid to estimate the perimeter and the area of the island.
Show your work in words, numbers and/or diagrams.
Approx. 30-32 squares within the boundary • 0.16 sq. mi. per square = 4.8 to 5.2 sq. mi.
for the area
Approx. 28 sides around the shape • 0.4 mi. per side = 11.2 miles for the perimeter
The estimated perimeter of the island is __________ miles.
The estimated area of the island is __________ square miles.
2 points response – does both of the following
• gives an area estimate in the interval of 4.8 to 5.2 square miles and
• gives a perimeter estimate of 11.2 feet
1 point response – does one of the following
• correctly estimates and labels both the number of squares within the boundary,
30-32 squares and the distance around, 28 sides
• gives an area estimate in the interval of 4.8 to 5.2 square miles
• gives a perimeter estimate of 11.2
0 point response – shows little understanding of the problem situation
Around and About the San Juans
Assessment Materials Page 13 of 14
11. Each side of a square in the grid represents 3 cm. Thomas used this to estimate
that the perimeter of the ellipse was 96 cm and to estimate that the area was 468
cm2.
Show that Thomas’s estimates are reasonable by showing that they are more than
the perimeter and area of a rectangle that fits inside the ellipse and by showing that
they are less than the perimeter and area of a rectangle that fits around the ellipse.
Show your work in words, numbers and/or diagrams.
4 point response: The student does all four of the following:
• The rectangle inside has dimensions 12 cm by 24 cm.
• The rectangle outside has dimensions 24 cm by 30 or 36 cm.
• For the perimeter, 2(12 + 24) < 96 < 2(24 + 30) cm
• For the area, 12•24 < 468 < 24•30 sq. cm
3 point response: The student does three of the following:
• The rectangle inside has dimensions 12 cm by 24 cm.
• The rectangle outside has dimensions 24 cm by 30 or 36 cm.
• For the perimeter, 2(12 + 24) < 96 < 2(24 + 30) cm
• For the area, 12•24 < 468 < 24•30 sq. cm
2 point response: The student does two of the following:
• The rectangle inside has dimensions 12 cm by 24 cm.
• The rectangle outside has dimensions 24 cm by 30 or 36 cm.
• For the perimeter, 2(12 + 24) < 96 < 2(24 + 30) cm
• For the area, 12•24 < 468 < 24•30 sq. cm
1 point response: The student does one of the following:
• The rectangle inside has dimensions 12 cm by 24 cm.
• The rectangle outside has dimensions 24 cm by 30 or 36 cm.
• For the perimeter, 2(12 + 24) < 96 < 2(24 + 30) cm
• For the area, 12•24 < 468 < 24•30 sq. cm
0 point response: Student shows little or no undrstanding.
Around and About the San Juans
Assessment Materials Page 14 of 14