Grade 6 Practice Problems: Measurement
Examples from Standards Revision and GLEs
6M-18) Answer: 120 meters
A rectangular yard is 14 meters by 21 meters. The lawn (green) is bordered by a concrete walk 3 meters wide as shown. How many square feet are in the lawn? Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-17) Answer: 60 inches
The small boxes in figures A and B at the right are congruent squares. If the perimeter of figure A is 48 inches, what is the perimeter of figure B? (The perimeter of a figure is the distance around it.) Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-16) Answer:
Each square represents a table. A rental company charges $10 per table. You’ve ordered 8 tables. How can you arrange the tables so that they seat the most people? Write the number of people that can be seated beside your drawing. What arrangement would seat the fewest number of people? Write the number of people that can be seated beside your drawing. Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-15) Answer: 150 feet
Six lords came to live in the city. The first lord built himself a tower. The second lord built a tower that was 6 feet higher than the first lord's tower. The third lord built a tower 6 feet taller than the second lord's tower. Each lord built a tower 6 feet taller than the tower built by the lord before him. The sixth lord's tower was 40 feet high. If the six towers were piled on top of each other, how high would they reach? Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-14) Answer: $8 change
Andy went to the local supermarket to shop for his mom. He bought 3 loaves of bread at $1.59 a loaf, 5 pounds of bananas at 59 cents a pound, and 2 boxes of cereal at $2.59 a box. He had a 45 cent coupon for 1 box of the cereal, which the store doubled. How much change did he receive from a $20 bill? Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-13) Answer: no - only 18 students per day
During registration, Mrs. Drucker must advise her 20 students. She needs 20 minutes for each student. She schedules her appointments from 9:00 A.M. to 4:00 P.M., with one hour out for lunch. Can she see all her students in one day? Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-12) Answer: 8 Popsicle sticks
If three pieces of chalk are the same length as 2 Popsicle sticks, how many Popsicle sticks would be the same length as 12 pieces of chalk? Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-11) Answer: 4 AM, L.A. time
Jennifer's mother is in Paris; Jennifer lives in Los Angeles. When it is 11:00 A.M. in New York, it is 5:00 P.M. in Paris. Jennifer wants to call her mother from Los Angeles at 1:00 P.M., Paris time. At what time in Los Angeles should she place her call? (Note: New York and Los Angeles are three time zones, or three hours, apart.) Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-10) Answer: 1 dime + 6 nickels; 2 dimes + 4 nickels; 3 dimes + 2 nickels
Lucy had a cold drink at the local ice cream parlor. She paid for the drink with a $1.00 bill and received 40 cents in change, all in nickels and dimes. How many nickels and how many dimes did she get? Give all possible solutions. Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-9) Answer: five coins
Rudolph bought a video for $18.62. He gave the clerk a $20 bill and received his change with the fewest number of bills and coins. How many coins did he receive? Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-8) Answer: 28.8 gallons
Six percent of the gasoline used by automobiles in the U.S. is burned while the cars are sitting in traffic jams. If the average car uses 480 gallons of gasoline a year, how many gallons does it burn in traffic jams? Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-7) Answer: 8 feet
The perimeter of a rectangle is 28 feet. The width of the rectangle is 6 feet. What is its length? Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-6) Answer: 1:35 PM
The Saturday movie starts at exactly 2:00 P.M. Laurie and her mom take 15 minutes to walk to the movie theatre. They want to get there 10 minutes early to get a good seat. At what time should they leave for the theater? Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-5) A lady went to the bank, gave the teller $1 and asked for 50 coins in exchange. What coins did the cashier give her? Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-4) Allison is ordering copy machine paper for the office. She can purchase a 10-pack box with 200 sheets in a pack for $18, or she can get a 5-pack with 500 sheets in a pack for $20. The third option is to buy a box containing 10 packs of 600 sheets each for $55. Which is the better buy? Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-3) Give the dimensions of four different rectangles that have an area of 24 square inches. Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-2) June is conducting an experiment that involves measuring the growth of a plant over five days. On the first day the plant was .5 cm tall. On the fifth day it was 1.75 cm tall. If the rate of growth was constant, how big was the plant on days 2, 3, and 4? Draw a line graph to show how you reached your conclusion. Explain in detail how you found your answer using words, numbers, and/or pictures.
6M-1) Place 20 pennies in a row on the table. Replace every fourth coin with a nickel. Now replace every third coin with a dime. Now replace every sixth coin with a quarter. What is the value of the 20 coins now on the table? Explain in detail how you found your answer using words, numbers, and/or pictures.
Expectations and Examples of Measurement from the 2008 Math Standards Revision (draft) – Grade 6
Identify the ratio of the circumference to the diameter of a circle as the constant p, and recognize 22/7 and 3.14 as common approximations of p. Find the perimeter and area of triangles, rectangles, and parallelograms. Find the circumference and area of circles. Find the perimeter and area of composite figures that can be divided into shapes, such as triangles, rectangles, and parts of circles. Students select relevant information and use appropriate strategies. Use the relationships among radius, diameter, circumference, and area of circles to solve problems. Measure angles; identify pairs of angles as complementary, supplementary, adjacent, or vertical; and use these relationships to find missing angle measures. |
Examples of Measurement from the 2006 GLEs – Grade 6
Represent the volume for given rectangular prisms using pictures or models. Describe and provide examples of surface area and volume. Explain and give examples of how area and surface area are related. Describe the relationship between surface area and volume of a rectangular prism. Label measurements of rectangular prisms to show understanding of the relationships among linear dimensions, surface area, and volume of rectangular prisms. Select appropriate units for area and volume in given situations. Explain why volume is measured in cubic units. Explain how the selected unit of length affects the size of cubic units. Explain why area is measured in square units and volume is measured in cubic units. Suggested Procedure:
Select and describe the appropriate units and/or tools for measuring length, area, and/or volume. Measure the volume of rectangular prisms using manipulatives or pictures and counts the number of units as part of the measurement procedure. Determine whether measurement has been done correctly. Describe situations in which estimated measures are sufficient. Estimate and label volume or capacity. Use estimation to determine reasonableness of a volume of a rectangular prism. Describe a procedure to find a reasonable estimate of volume or capacity. Explain why estimation would be used rather than a direct measurement. |