Grade 7 Practice Problems: Measurement
Examples from Standards Revision and GLEs
7M-23) Answer: 16 minutes
Lotano and Lucia were making banners for the Pumpkin Festival. The cloth was 45 yards long, and they were going to cut it into 5-yard pieces for the banners. It took Lotano two minutes to make each cut, because he had to cut very carefully. How many minutes did it take him to cut the fabric into 5-yard pieces? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-22) Answer: Thursday, Oct.12, 4:20 am (1 day, 17 hours, 40 minutes)
Rob Hoop and his Merry Hoods were playing a marathon concert. They began with great enthusiasm, but finally collapsed at 10:00 P.M, Friday, October 13 after playing for 150,000 seconds. When did the concert begin? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-21) Answer: 32 ounces
A jar filled with jellybeans weighs exactly 48 ounces. When exactly half of the jellybeans are eaten, the jar and the remaining jellybeans weigh 32 ounces. How many ounces of jellybeans were originally in the jar? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-20) Answer: 18 inches from each side
Carla is hanging a picture that is 40 inches tall and 28 1/2 inches wide on a panel that measures 36 inches wide. How far from one edge of the panel should she put the picture hook so that the picture will be centered on the panel? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-19) Answer: 56 feet
Jones High School is constructing a circular ice skating rink. They want to design the rink so that 15 trips around the outside rail will equal exactly one mile. To the nearest foot, what should the radius be? (circumference = 2 times pi times the radius) Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-18) Answer: 4 quarters and 4 half dollars
Maxine paid her restaurant check of $3.00 by using the same number of half-dollars and quarters. How many of each did she use? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-17) Answers: 7 hot dogs + 6 soft drinks; 6 hot dogs + 8 soft drinks; 5 hot dogs + 10 soft drinks
Raymond and Boris went to the ball game last evening. They spent exactly $20.00 on hot dogs and soft drinks. They bought at least 5 hot dogs at $2.00 each and at least 5 soft drinks at $1.00 each. What exactly did they buy? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-16) Answer: Ruth $27; Jeanette $27; Harriett $18
Ruth and Jeanette are taking Gladys to lunch for her birthday. At the last minute, Harriett decides to come along. Ruth and Jeanette are paying Gladys's share of the bill, but Harriett is paying only for her own share. If the total bill came to $72, how much does each girl pay? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-15) Answer: 330 feet
The senior class is sponsoring a fair at the school. In the potato race, 10 "potatoes" are placed in a straight line, each three feet apart. The first "potato" is three feet from the basket. A contestant runs to the first potato and returns it to the basket. The contestant then runs to the second potato and returns it to the basket. The same thing is done with each potato in succession, until all 10 potatoes are in the basket. How far does a contestant run to complete this race? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-14) Answer: 3 AM Thursday
When it is 9:00 P.M. in Paris, it is 3:00 P.M. in New York City and 12:00 noon in San Diego. Joan and her family are on vacation in Paris, and wish to call home to San Diego. If they want their call to reach San Diego at 6:00 P.M. on Wednesday, at what time in Paris should they make the call? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-13) Answer: yes
You want to pass some electrical cable through a hole. The cable is 5/16 in. thick at its thickest point. Will a drill with a 3/8 in. bit do the job? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-12) Answer: 19 13/16 inches
You work for a place that installs window glass. A window frame measures exactly 19 7/8 inches across. You want to cut a pane of glass 1/16 inch shorter so it will fit the window frame. How wide do you cut it? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-11) Answer: 23 7/16 inches
You work for a store that makes window shades. You are about to cut a shade roller to be 23 3/8 inches long. Your boss says, "Better make it 1/16 inch longer." How long does she want it to be? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-10) Answer: 1/2 inch
You are working with a piece of sheet metal that is 6 11/16 inches wide. You want to cut it to be 6 3/16 inches wide. How much do you cut off? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-9) Answer: 7 1/4 inches
You operate a paper cutter in a printing plant. You have to trim 3/16 inch off a stack of paper that is 7 7/16 inches wide. How wide will the stack be after you trim it? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-8) Answer: 4 1/4 inches
You are making a chart for your boss. You want to draw a line down the center of a piece of paper to divide it in half. The paper is 8 1/2 inches wide. How far from each edge is the dividing line? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-7) Answer: 15/16 inch
You are gluing a 3/16 inch thick piece of plywood to a board that is 3/4 inch thick. How thick will the two be together? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-6) Answer: yes
You are trying to fit a pipe that is 5/8 inch wide into a space 3/4 inch wide. Will it fit? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-5) Answer: 227 1/2 lb
7 rolls of paper weigh 32 1/2 lb. each. What is the total weight? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-4) Answer: a marble weighs 3 grams, the can weighs 15 grams
A can with 40 marbles in it weighed 135 grams. The same can with 20 marbles weighed 75 grams. How much does each marble weigh? What is the weight of the can? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-3) Answer: $1.80
Bananas are on sale at 5 pounds for $1. How much should you pay for 9 pounds? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-2) Answer: $ 100.00
Sam is helping his brother Jason do carpentry and general repair jobs. Jason gave Sam some money for supplies. Sam bought some tools for $20.80, then spent one half of what was left for wood. He spent one third of what was left after that on paint and one third on buckets and brushes, and he returned with $13.20. How much money did Jason give Sam? Explain in detail how you found your answer using words, numbers, and/or pictures.
7M-1) Answer: 16 pi (or about 50) square feet
The Cooking Club is planning to build a single pizza for the entire student body. If the radius of the pizza will be 4 feet, what will be the area of the top? Explain in detail how you found your answer using words, numbers, and/or pictures.
Expectations & Examples of Measurement from the 2008 Math Standrds Revision (draft) - Grade 7
Use models, pictures, or verbal reasoning to determine formulas for surface area and volume of prisms and cylinders. The net of a cylinder is composed of two circles and a rectangle; this net can be used to determine the surface area of a cylinder. Use formulas to find the surface area and volume of prisms and cylinders. Example:
Explore the relationship between the volumes of pyramids and their related prisms and the volumes of cones and their related cylinders, describe why the related volume formulas make sense, and find the volume of pyramids and cones. The relationships between the pyramid and the related prism, or between the cone and the related cylinder, could be explored by filling models with water, sand, etc. Solve contextual problems involving the surface area or volume of prisms and cylinders and the volume of pyramids and cones, and justify the reasonableness of the solutions. Example:
Select, convert (within the same system), and use appropriate units of measurement. Examples:
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Examples of Measurement from the 2006 GLEs – Grade 7
Determine and/or describe the impact on the perimeter, circumference, and/or area of a rectangle, triangle, and/or circle caused by a change in one dimension. Determine and/or describe the impact on one dimension caused by a change in perimeter, circumference and/or area of a rectangle, triangle, and/or circle. Identify, describe, or explain how the unit selected for a situation can affect the precision of the measurement. Explain why measurement systems have different size units and how that allows for different levels of precision. Convert between units within a system to demonstrate understanding of the precision required. Suggested Procedure:
Measure angles in assorted shapes and figures using the suggested procedure. Select and describe the appropriate units and/or tools for measuring angles. Use a protractor to draw angles accurate to within 3°. Determine whether measurement has been done correctly. Use formulas to determine and label missing measurements for circles, including radius, diameter, circumference, and area, in given situations. Use formulas to determine and label missing measurements for rectangular prisms, including length, width, height, volume, and surface area, in given situations. Use formulas to determine and label missing measurements for triangles, including base, height, perimeter, and area, in given situations. Demonstrate or explain how to use a formula for finding the area and circumference of a circle. Calculate and label dimensions of rectangular prisms with given volumes and/or surface areas. Determine the surface area of a rectangular prism. Describe situations in which estimated measures are sufficient. Estimate and label circle, right triangle, and rectangular prism measurements. Use common approximations of pi to estimate and label the circumference and the area of circles. Use or describe a process to find a reasonable estimate of measurements. Explain why estimation or precise measurement is appropriate in a given situation. |