Grade 8 Practice Problems: Measurement
Examples from Standards Revision and GLEs
8M-25) Answer: 4200 cubic centimeters
If one liter is 1000 cubic centimeters, how many cubic centimeters are in 4.2 liters?
Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-24) Answer: 13 1/2 or 13.5 sq. in. or in.2
If the lengths of all the sides of the trapezoid in the figure below are tripled, what is the area of the resulting trapezoid? (Note that the dots are spaced 1 inch apart vertically and horizontally? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-23) Answer: 16 to 1
If the triangle shown below was enlarged so that each side was 4 times as long as its original length, what would be the ratio of the area of the enlarged triangle to the area of the original triangle? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-22) Answer: 63 hours
If 4 construction workers take 9 hours to build a brick wall 14 m long and 12 m high, how long will it take 6 workers to build a brick wall 98 m long and 18 m high? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-21) Answer: 11 square units
In each small square in the grid below is 1 square unit in area and has a side 1 unit length, what is the estimated perimeter of the quadrilateral shown? (In other words, do not give your answer in the form of a decimal number. (round to the nearest whole number). Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-20) Answer: 20 rectangles or 20 sets (Other arrangements lead to greater waste.)
Jessica is making cardboard stands for the science fair. Each stand is made from two right triangles, 12 cm ´ 16 cm. How many stands can Jessica make out of a piece of cardboard 80 cm ´ 50 cm with the least amount of waste? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-19) Answer: 25 hours and 27 minutes (Answer depends on use ofuse of 3.14 forpi.)
A cylindrical corn silo has a radius of 3 meters and a height of 18 meters. If a blower can load 1 cubic meter of corn in 3 minutes, how many hours and minutes (to the nearest minute) will it take to fill this silo with corn? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-18) Answer: varied answers, should show coordinate graph (ex. as length increases your width decreases; Yes, you should connect points)
Recall that the perimeter of a rectangle is the sum of its side lengths. Make a table of all the possible whole-number values for the length and width of a rectangle with a perimeter of 24 meters. Make a coordinate graph of your data. Put length on the x-axis and width on the y-axis. Describe what happens to the width as the length increases. Would it make sense to connect the points in this graph? Explain your reasoning. Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-17) Answer: varied answers, should show coordinate graph and table (ex. as length increases your width decreases- As your width and length measurements are close together your perimeter gets smaller.)
Recall that the area of a rectangle is its length times its width. Make a table of the different whole-number values for the length and width of a rectangle with an area of 24 square meters. Make a coordinate graph of your data. Put length on the x-axis and width on the y-axis. Describe what happens to the width as the length increases. Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-16) Answer: 2 hours
How many hours will a car traveling at 45 miles per hour take to catch up with a car traveling at 30 miles per hour if the slower car starts one hour before the faster car? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-15) Answer: About 3 cups
Treet’s favorite recipe for macadamia nut cookies makes 48 cookies and calls for 1 1/3 cups of macadamia nuts. Treet wants to make a larger batch of cookie dough that will make exactly 108 cookies. How many macadamia nuts will he need to use in this larger batch? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-14) Answer: 960
The eighth-grade class is preparing the food for the all-school Halloween party, and Gary is making the ice cream. Garlic ice cream. He flips the cookbook open to the recipe, but finds a chocolate stain covering the number that tells how many cloves of garlic he is supposed to use. There's a note at the end of the recipe that says 1/8 teaspoon of garlic powder may be substituted for 1 clove of garlic. If 9/15 of the number of teaspoons of garlic powder, added to 48, equals the total number of teaspoons needed, how many cloves of garlic must Gary use? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-13) Answer: 9 hours: 2--bike9, skate 18, walk 15; 1--bike 18, skate 6, walk 18
Three friends decided to make a trip to a state park 42 miles away. None of them walked very fast, so they decided to take a bike and a skateboard to share. They knew that each one walked 3 miles per hour, biked 9 miles per hour, and skateboarded 6 miles per hour. They worked out a plan to exchange the skateboard and bike on the hour, but only so that nobody had to wait for anyone else. They could also leave the skateboard or the bike for someone coming along who could pick it up on the hour. The bike could also be locked to a tree and left for the trip home, if necessary. Draw a diagram to show how they made their exchanges, in order to all arrive at the park at the same time. How long did it take them and how far did each one bike, skateboard, and walk? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-12) Answer: Aug 11, 11:26 pm
Twisted Tuba is a heavy metal rock group, featuring tuba players. The group's only recording, "Material Tuba," was #99 on the charts. The Twisted Tuba's manager, Harry Hornblower; is concerned because the group's concerts have been largely unattended. To raise money, Harry has decided to have a marathon tuba-tooting session, for which sponsors agree to pay 9 cents for each minute the group can continually play their tubas. In order to make up the money they lost on their concerts, they need to make $288,977.40. Harry scheduled the marathon to begin on January 1 at noon. If the group gets 10 sponsors for each minute and reaches their goal, when will they finish tooting their tubas? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-11) Answer: 14
As Ginger and her friends were leaving Yulip at 10:00 this morning, they spotted some river rafters who were just arriving. The rafters said they had started out from Rogue Rapids 6 hours before. Ginger and her friends were just beginning their 7-hour hike along the South Fork of the Tubonia River to Rogue Rapids. They saw many rafters along the way, because a new group left Rogue Rapids every hour on the hour, from 4 o'clock in the morning to 8 o'clock at night. How many groups of rafters did Ginger and her friends see along their way? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-10) Answer: 19 2-gallon tanks; 18 5-gallon tanks; 17 10-gallon tanks; 16 15-gallon tanks; 15 26-gallon tanks; 14 43-gallon tanks
"Dad, look! What a beauty!" Veronica exclaims as she pulls a plastic bag out of the box marked LIVE FISH: HANDLE WITH CARE. Her father's new tropical fish store will open in another two weeks and her whole family has been working to get it ready. Veronica has just opened a box containing Bette Splenden, the Siamese fighting fish. She floats the bag carefully on top of the water in a 2-gallon tank. Veronica looks at all the brand-new, glistening tanks, some of which already have fish in them. There are 99 tanks, and they hold varying amounts of water. Some, like the tank into which Veronica put the fighting fish, hold only 2 gallons. Others hold 5, 10, 15, 26, or 43 gallons. It took Veronica's father 5 hours and 6 minutes, at a water flow rate of 5 gallons per minute, to fill all the tanks to capacity. How many of each size tank are there in the store? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-9) Answer: 53
Aida was buying decorations for the Halloween Haunt. When she realized that she only had $1.15 in her pocket, she headed for the sale table. She found large rubber tarantulas for 60 cents, small rubber black widows for 25 cents, paper bats for 10cents, cardboard monsters for 80 cents, and tiny black cats for 5 cents. What are all the possible combinations of decorations from the sale table that she could buy? Explain in detail how you found your answer using words, number, and/or pictures.
8M-8) Answer: 46
Otto B. Wright is responsible for feeding the otters at Sea Circus. He has to feed them one pound of fish each day. He can feed them smelt, perch, sardines, and squid. The smelt weigh 3 ounces each, the perch weigh 4 ounces each, the sardines weigh 1 ounce each, and the baby squid weigh 1 1/2 ounces each. How many different combinations of fish can Otto use to feed the otters? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-7) Answer: $517.50
The government is sending a fly up on the next space shuttle, to study the effects of weightlessness on flies. Sherman Shadfly wants to be the first fly in space, but as everyone knows, the life span of the adult shadfly is only 3 hours, and Sherman is afraid he won't last until the launch. His friend Sharkey knows a fly who makes a secret potion that is guaranteed to extend the life span for 3 minutes for each ounce of potion consumed. Sherman suspects that this is a fly- by-night operation, but he is willing to try anything to make the launch. The potion is expensive: $5.75 for a 4-ounce bottle and $11.00 for the 8-ounce economy size. Sherman believes in being frugal, so he has purchased the potion in 8-ounce bottles. He takes his first sip at 11:00 PM., Tuesday the 4th. The shuttle is scheduled for launch on Saturday the 22nd at 5:00 A.M. How much money did Sherman save by buying the economy-size bottles? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-6) Answer: 4th layer from the bottom
Finally, after days of planning their wedding, they saw all their plans come together. The ultimate challenge of their plans was the wedding cake, but the workers were ready for it. "Go for it!" shouted their leader Colonel Andrew Ant. The couple looked up, on their wedding day, in awe at the layered wedding cake. Their goal was the white rose on the very top layer. The bottom layer of the cake was 20 inches by 40 inches, and each of the other layers was 2 inches shorter and 2 inches narrower than the layer on which it rested. The couple scaled the side of each layer then devoured every square inch of frosting on the top of it to prepare them for the climb up the next layer. When they had consumed 78% of the frosting from the tops of the layers, they were too stuffed to go forward! On what layer did they stop? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-5) Answer: 200 gallons
It is the maiden voyage of SpacExpress I, the first interstellar commute shuttle. The shuttle will leave planet Earth, make five stops to refuel at satellites along the way, land on planet Zeron, and then return to Earth. After taking off with a full tank of fuel, SpacExpress I burns 1/2 of its fuel before arriving at Satellite I. The shuttle takes on 50 gallons of fuel. The shuttle burns 1/3 of its fuel before arriving at Satellite II, where it takes on 100 gallons. The shuttle burns 1/4 of its fuel on the way to Satellite Ill, where it takes on only 10 gallons. Before arriving at Satellite IV the shuttle uses up 1/2 its fuel, and then takes on 100 gallons. On the way to Satellite V, 1/4 of the fuel supply is consumed, and 15 gallons are taken on when the shuttle stops. On the last leg of the journey to Zeron the shuttle burns 7/8 of its fuel supply, landing on Zeron with 18.75 gallons left. What is the capacity of the SpacExpress I fuel tank? Explain in detail how you found your answer using words, numbers and/or pictures.
8M-4) Answer: $12,934.35
William Tremblesword was a tall poet who had been trying unsuccessfully to get his poems published. He was puzzled by all the rejection slips he received, because he knew he had written some lovely poems, like "Ode on a Forklift," and "Rime of the Ancient Metal Detector." One day William met a publisher who offered to pay 14 of 1 cent for each word. The longer the poem is the better it is for William. He took the phone off the hook and put a DO NOT DISTURB sign on the door. He figured he could crank out 26 words per minute. Armed with a thesaurus of very short words, he sat down at his typewriter and looked at his watch. It was 7:30 P.M. on October 14. He took a deep breath, repeating softly "I before E except after C," and began typing. He went nonstop right through Halloween, Thanksgiving, Christmas, New Year's (which would be a leap year), and the Presidents' birthdays. At midnight on the last day of February, he typed the words THE END, and slumped across his keyboard, exhausted. He called his poem "My Love is Like a Red, Red Convertible," and he knew it was his finest work. It was a long poem, but then, he was a long fellow. How much money were William's words worth? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-3) Answer: 4 times
If the radius of a circle is increased 100%, how much is the area increased? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-2) Answer: 1.6 centimeters
Using a telephoto lens, a photographer can make a 21 centimeter picture of a 6 centimeter flower. If a bee on the flower looks 5.6 centimeters long through the telephoto lens, what is the actual length of the bee? Explain in detail how you found your answer using words, numbers, and/or pictures.
8M-1) Answer: 15 cats
If seven cats catch seven mice in seven minutes, how many cats would it take to catch 100 mice in 50 minutes? Explain in detail how you found your answer using words, numbers, and/or pictures.
Expectations & Examples of Measurement from the 2008 Math Standards Revision (draft) - Grade 8
Model and use the Pythagorean theorem and its converse to solve problems. Use the Pythagorean theorem to find the distance between two points on the coordinate plane.
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Examples of Measurement from the 2006 GLEs – Grade 8
Determine and/or describe the impact that a change in one dimension has on volume and surface area in right cylinders and rectangular prisms. Determine and/or describe a change in a linear dimension given a change in volume and/or surface area of rectangular prisms and cylinders. Determine and/or describe the impact on perimeter and/or area of a rectangle caused by a change in two dimensions. Explain the concept of a rate or slope in a given situation. Explain how division of measurements produces a derived unit of measurement. Calculate a rate of change or slope in a situation. Use unit analysis to find equivalent rates. Use rate to determine a measured outcome and labels units. Describe or explain why different situations require different levels of precision. Compare situations that require different levels of precision. Select and describe an appropriate unit of measure for the precision needed in a given situation. Convert between units in a measurement system to demonstrate understanding of the precision required. Explain how to use a formula to calculate and label the surface area and volume of a prism or cylinder. Use the Pythagorean Theorem to determine and label a missing dimension of a right triangle or prism. Determine and label surface areas of right cylinders and right prisms. Determine and label dimensions of a triangle, prism, or cylinder based on a given perimeter, circumference, area, and/or volume. Describe situations in which estimated measures are sufficient. Use estimation to determine and label volume and surface area for right cylinders and right prisms and explain why an approximation is appropriate. Use estimation strategies to determine and label the approximate length of the third side of a right triangle given the lengths of two sides. Use estimation strategies to determine and labels the approximate distance or height in a situation using similar triangles or the Pythagorean Theorem. Describe a procedure that would obtain an estimated measurement. Explain why estimation would be used rather than a direct measurement. |