Construct a triangle on the geoboard so that there is the largest number of pegs possible inside the triangle. How many pegs are inside?

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1 Problems of the Week Visual Construct a triangle on the geoboard so that there is the largest number of pegs possible inside the triangle. How many pegs are inside? 9 Feet on the Earth, Head in the Sky A six-foot tall person walks around the earth. How much farther does the person s head travel than the person s feet? From: Mathematical Challenges for the Middle Grades, NCCTM, 99, p. 24. Geometry/ Measurement By what factor does the volume increase if the radius and the height of a cylinder are doubled? Materials: stop watch Have students sit in rows of. Begin with row of students. At the timer s signal, the first student stands up, waves his or her arms overhead and sits down. Then each student repeats the wave. After the last student sits down, the timer records the time in seconds. Repeat for 0,, 20 and 2 students. Graph the ordered pairs on a coordinate plane (x-axis = # of students; y-axis = time) How long would it take students to complete the wave? 4 students? number of students in the 8th grade at your school? Problem-Solving Strategies How many ways are there in which Farmer Brown can place his animals (a donkey, a cow, a goat, a pig, a sheep and a horse) in two fields so that at least one animal is in each field? Explain how you would figure the surface area of a cylinder. Grade 8 Page

2 9 *See answer key. This section should not be duplicated for the students.. 8 ( ) 2. Change to an improper fraction: 9 0 Mental Math. Change 2 to a decimal. 4. Write as a fraction:.6. Find the mode for following set of scores: 9, 80, 77, 9, 69, Order from least to greatest: 8, 2, 7. Prime or composite? 6 8. List the factors of Write an expression that represents less than w. 0. Rewrite as an exponential expression. 4. Solve for m: m 2 = Write as a word phrase: x 8 4. Solve and check: x 2 = 0. Solve and check: g 0.7 = Estimate: Solve for c: (c + 4) = 8. If b = 4 and c = 7, give the value of b 2 c = 0. Find the least common multiple of 4, 6, and 0. Write answers here: Grade 8 Page 6

3 Visual Answer Key Mental Math Eight pegs are inside the triangle. Answer: 2π feet. If r = radius of earth, then C (head) = C(earth) + x 2π(r + 6) = 2πr + x x = 2π feet ,, composite 8.,, 9, w This section provides an oral drill for sharpening one's mental computation. Before each session give these directions, "Number your paper from to 0. Write your answer as the questions are called out. Each question will be repeated one time only." Geometry/Measurement Answer: 8 Answers may vary. Problem-Solving Strategies Field A Field B 6 ways 2 4 ways 20 ways 4 2 ways 6 ways 62 ways To determine the surface area of a cylinder you add the areas of the two circular bases and the lateral area of the cylinder. The lateral area is the area of the rectangular region that would correspond to a label on a can. 0.. m = ,200. a number decreased by 8 4. x = 0. g = c = Grade 8 Page 7

4 Problems of the Week Visual Mary planted three flower gardens. The area of the rose garden is half the area of the geranium garden; the begonia garden is twice the area of the geranium garden. The begonia garden is 8 square meters. What is the total area of the three gardens? Hint: Draw a picture. 20 A bag contains orange marbles, green marbles and 4 purple marbles. How many green marbles must be added so that the probability of drawing a green marble is 4?. Students collect graphs from newspapers, magazines, and the internet. 2. Place students in groups of four. The groups work to find misleading facts with each graph.. Groups will present their best graph with reasons to support their choice and the worst graph with reasons to support their choice. Geometry/ Measurement Find rectangles with integral centimeter dimensions through 0 using each value once so that you can put them together without overlapping and form a square. Problem-Solving Strategies Write an Equation The Mathematics Theater has twenty-five seats in the first row, twenty-seven seats in the second, twenty-nine in the third, and so on. How many seats are in the fifteen-row theater? A B When would you expect the median and mean to be close together? Explain your answer. Your math scores are 2, 00, 7, 72 and 78. Would you rather have your teacher use the mean or median? Explain your answer. Grade 8 Page 8

5 20 *See answer key. This section should not be duplicated for the students.. Use <, >, or = to complete: 2. Order from least to greatest: 4, 2,. Write using exponents: (0 + 2) Use <, >, or = to complete: Prime or composite? 6 Mental Math 8. 4 =? 6 9. Simplify: Find the range, median, and mode:, 0, 2, 20, 20, 20, 2. 8 ( 06) + 8 =. If x = 4 and y = 2, evaluate 4(x y). 4. Combine like terms: 9y + 6y y. Solve for a: 8 = a 6 6. List all the factors of Write in scientific notation: 6,42,000, Simplify: = 0. Write as an integer: 8 Write answers here: Grade 8 Page 9

6 Visual Answer: 4 m 2 Answer Key Mental Math. < , 4, 6 Answer: 24 green marbles added 27 6 = 4 Geometry/Measurement The dimensions of the rectangles are: 6 cm 0 cm, 7 cm 9 cm, cm 8 cm, 4 cm cm, and cm 2 cm. The dimensions of the square will be cm cm > 7. prime This section provides an oral drill for sharpening one's mental computation. Before each session give these directions, "Number your paper from to 0. Write your answer as the questions are called out. Each question will be repeated one time only." 0. 0 Answers will vary. Problem-Solving Strategies ( 2) + ( ) 8 seats Or make a table Row Seats A With a small range, you would expect the median and mean to be close together. B Median; median 7, mean 7.4 Grade 8 Page 60. range = median = 20 mode = y , 2,,, 6, 9, 0,, 8, 0, 4, x

7 Problems of the Week Visual The nine volumes of a mathematics encyclopedia are on the right. They are in this strange order because their owner, a lover of fractions, has noticed that the volume numbers can be read as a fraction which equivalent to one-half. Can you show how the 4 8 volumes can be arranged so that they make the fraction equivalent to one-fourth? Tina and Tess go shopping together and buy identical items. Each girl buys 4 pairs of shorts, shirts, and 2 pairs of shoes that can all be mixed and matched to wear. If each girl wears new clothes to school tomorrow, what is the probability that Tess shows up in exactly the same oufit as Tina? Geometry/ Measurement The polygon shown is a quilt pattern. The pattern measures 2 inches from A to B. The actual quilt block will be 8 inches from A to B. What will its area be? 2 A drawer contains black socks, brown socks, and blue sock. Jess is going to pull socks out of the drawer without replacing them. What is the probability that he gets a black sock first, a black sock second, and a blue sock third? Problem-Solving Strategies Make an Organized List Megan, Lindsay and Allison work out at the Fitness Center after school. Megan goes every days, Lindsay every 4 days and Allison plays soccer, so she can only go every 8 days. On what days in the next 6 weeks will Lindsay and Megan be at the Fitness Center on the same day? On what days will Lindsay and Allison be at the Fitness Center the same day? Adapted from The Problem Solver 8, 988 Creative Publications Describe the pattern in the third diagonal row A B Grade 8 Page 6

8 2 *See answer key. This section should not be duplicated for the students.. Estimate: ( 9). Which of the following is the largest: 0.48, 0., 0.004, 0.4? Mental Math 4. Find the reciprocal of Solve for b: b ( 2) = inches = feet Round 4.08 to the nearest hundredth.. Solve for k: = k 2. Solve for r: 26 = 2r. Solve for b: 22 7 = b 4. Arrange these numbers in order from least to greatest: 2, 4,,, 7, 2,. Simplify this expression: 4(m+ ) + 7(2m + 6). 6. Evaluate 42 ( b+ c) if a =, b =, and c = 4. 2c 7. Write as an inequality: y is less than Graph the set of numbers on a number line: {, 0, 2} 9. I = V R If I = 44 and R =, find V. 0. Write an inequality for the following: the amount, s, that Mrs. Phillips will spend is not more than $6. Write answers here: Grade 8 Page 62

9 Visual = 4 They have 4 2 of 40 outfit possibilities. Probability is /40. Answer Key Mental Math feet 2 This section provides an oral drill for sharpening one's mental computation. Before each session give these directions, "Number your paper from to 0. Write your answer as the questions are called out. Each question will be repeated one time only." Geometry/Measurement Answer: 44 square inches Answer: = 26 Problem-Solving Strategies Lindsay and Megan days 2, 24, 6 Lindsay and Allison days 8, 6, 24, 2, 40 Starting with the first number,, you add 2 to get the second number, ; then add to get the third number, 6; then add 4 to get the fourth number, 0; then add to get the fifth number, ; and then add 6 to get the sixth number, 2. Each time you add more than you did the previous time ,,, 2,, 2, 4. 4m m + 42 = 8m y < V = S 6 Grade 8 Page 6

10 Problems of the Week Visual Draw different arrangements of 6 cubes. 22 In the final four digits of a license plate, the sum of the first two equals the sum of the last two. Also, the sum of the first and last is twice the sum of the middle two, and the first two form a two digit number that is twice that formed by the last two. The number does not contain any 0 s. What are the final four digits in order? From Mathematics Teacher February 997 Geometry/ Measurement Collect a week's worth of newspapers. Stack, measure and find the volume of the newspapers. What would be the volume of a year s worth of newspaper? Mark off an area equivalent in volume in your classroom. Make a function table showing the accumulation of newspapers from to 20 years. Write an equation with two variables representing the function. Graph the function. Make your data count! Write an article to encourage recycling of newspapers. Support your position. Look through the almanac for data over time. See if you can find some data that fall along a straight line when graphed. Use the line to make predictions about the variables involved in the future. Problem-Solving Strategies Use a Formula: C = n ( + r) t A movie ticket costs $7 today. Inflation is expected to grow by 4 percent a year for the next several years. If n represents the current cost of the ticket, predict the cost (C) of the ticket if this inflation rate continues (a) for years (b) for 0 years. Explain how you would find the mean, median and mode of the following test scores: 00, 9, 9, 80, 92, 7, 99, 7, 76, 89 Grade 8 Page 64

11 22 *See answer key. This section should not be duplicated for the students.. Write the ratio 2:4 in 2 other ways. Mental Math 2. Write as an improper fraction: 7 8. Write 29 7 as a mixed number cm = m. Write lb. oz. in ounces. 6. Write 20% as a fraction. 7. Write as a decimal: 2% Solve for t: t = What percent of 8 is 6?. Write three fractions equivalent to. Write answers here:. 2. Find x: x = 4. Write % as a ratio = 6. 7% of.66 = 4 7. An angle greater than 90 is called. 8. Find the median and mode:, 2,,, 9, 7, = 0. 6 ( 9) = Grade 8 Page 6

12 Visual Answers will vary. It might be helpful to provide the students with isometric dot paper. Answer: 427 Geometry/Measurement Answers will vary. Answer Key Mental Math. 2 to 4, m. 49 ounces % This section provides an oral drill for sharpening one's mental computation. Before each session give these directions, "Number your paper from to 0. Write your answer as the questions are called out. Each question will be repeated one time only." Answers will vary. Problem-Solving Strategies (a) $8.2 ($ ) (b) $22.70 ($ ) Arrange the scores in ascending order. Average the middle two scores to determine the median. Divide the sum of the ten scores by ten to determine the mean. The mode is the most common score ,, : obtuse median =, mode = Grade 8 Page 66

13 Problems of the Week Visual Use two different colored number cubes. Identify one of the cubes as x -values and the other as the y -values. Roll the number cubes and create an ordered pair. Graph the point. Roll the cubes again and graph the point. What is the slope of the line determined by the two points? 2 Jack weighs 4 of his weight plus 40 pounds. What is Jack s weight? Geometry/ Measurement On a map, three towns lie in a straight line. Abbeyville is miles from Beantown. On the map this distance is 2 cm. The distance from Abbeyville to Clarkton is cm on the map. If Beantown is between Abbeyville and Clarkton, how far is it from Beantown to Clarkton in miles? What is the probability that when five people meet that at least two of them are born in the same month? How can you set up a simulation to discover this answer? Can you set it up with regular number cubes? A dodecahedron? A spinner? Marbles of different colors? Problem-Solving Strategies The number of chirps made by a cricket in one minute is a function of the temperature. The formula is t = 4 n + 40, where t is the temperature in degrees Fahrenheit and n is the number of chirps in one minute. A What is the temperature if a cricket makes 0 chirps per minute? B At 60 F, how many chirps a minute does a cricket make? C At what temperature does the cricket stop chirping? Explain how to change. to a fraction. Grade 8 Page 67

14 2 *See answer key. This section should not be duplicated for the students x Simplify 2 Mental Math. 4? = Find the perimeter of a garden that measures 2 feet by 4 feet. 6. How many minutes are in a day? 7. 2 = 8. Which is greater: 2 or 2? Write as a fraction: 8.. What is the theoretical probability of choosing a vowel from the word MATHEMATICS? 2. Cali bought a sweater priced at $60. If the sales tax is 9%, what is the total purchase price of the jacket?. Two angles whose measures have a sum of 80 are called = 4 2. Find the amount you save when you buy a $20 bicycle on sale for % off. 6. Find the interest to the nearest cent: $000, 8.%, year. 7. Write 2 % as a fraction. 8. Express as a unit rate million people in 400 square miles. 9. Solve the proportion: 4 = 9 N 0. On a scale drawing centimeter represents 2 meters. What length on the drawing should be used to represent.2 meters? Write answers here: Grade 8 Page 68

15 Visual Answers will vary. Answer: 200 pounds Geometry/Measurement Anwer: 92. miles Answer Key Answers may vary. The experiment would be hard to perform with number cubes, but students may find a way. With a dodecahedron, a spinner with 2 sections, or with marbles of 2 colors in a box, the students can assign a number or color to each of the 2 months. Then, the dice, docecahedron, or marbles will be used five times to select a month. When five have been selected, that represents a group of five people. If the experiment is done many times, the experimental probability can be calculated. Mental Math feet 6.,440 minutes $6.40. supplementary 2 This section provides an oral drill for sharpening one's mental computation. Before each session give these directions, "Number your paper from to 0. Write your answer as the questions are called out. Each question will be repeated one time only." Problem-Solving Strategies A 77. F B 80 chirps C 40 F Let n =. 0n =. ( n =. ) 9n = $.0 6. $ ,00 people in one square mile 9. N = centimeters n = 9 Grade 8 Page 69

16 Problems of the Week Visual Place the first six counting numbers in the circles so that the sum on each side of the triangle is nine. Is is possible to use the numbers four to nine to make the sum of each side the same? 24 Jenna has $6.00 to spend. She found a purse for $.9, a shirt for $8.00 and a pair of shoes for $28.0. She must pay 6% sales tax on her purchases. Which items should she buy if she wants to spend as much of the $6.00 as possible? (She might buy more than one of any item, if advantageous.) Explain your answer. Geometry/ Measurement On graph paper, draw one of your initials using block letters as shown. Now create a dilation of this letter using a scale factor of 2. How does the area of the dilation compare to the area of the original letter?. Have students attend or watch a basketball game and collect data on the number of shots attempted and the number of shots made (exclude foul shots). 2. Have students put data into a table.. Make a scatter plot using the data. 4. Does there appear to be a relationship between the number of shots attempted and the number of shots made? Problem-Solving Strategies Each of five friends has 20 baseball cards and they decide to trade cards as follows: Molly gives Jim one card, Kyle gives Bob one card, Molly gives Kyle two cards, Lisa gives Molly three cards, Lisa gives Bob five cards, Kyle gives Lisa one card, Molly gives Bob two cards, Bob gives Kyle one card, and Jim gives Bob three cards. Who has the greatest amount of cards? Who has the smallest amount of cards? Pam and Ellen are selling lemonade for a project at the local recreation center. They have calculated the cost of a cup of lemonade to be 22. They plan to make 0 cups of lemonade. If they sell each cup for 0, how much profit will they make? How many cups do they need to sell to make $2.00 profit? Explain how you got your answer. Grade 8 Page 70

17 24 *See answer key. This section should not be duplicated for the students.. cups = pints 2. 6 =. Write 20,000 in scientific notation. 4. Write in standard form.. If 27 = x, then x = 6. The point located at (, 7) is in which quadrant? 7. Find a solution for y = x Solve: What number increased by eight is? Mental Math 9. Write as a mixed number: =. ( 2 + ) = 2. Find the perimeter of a regular octagon with sides 2. meters.. Find the circumference of a circle with diameter of 6. cm. 4. If a= 2. Simplify: and x = 4, then (2a x)(2x 6) = Simplify: f + = 4 7. Solve for q: q ( 8) = Find the surface area of a cube with edges of cm ounces = pounds 0. An angle less than 90 is called. Write answers here: Grade 8 Page 7

18 Visual 4 Answer Key Mental Math. 7. pints x 0 This section provides an oral drill for sharpening 4. 0,700 one's mental computation. Before each session give these 6. II directions, "Number your paper from to Some possible answers: Answer: Two purses and a pair of shoes; $64.02 Write your answer as (4, 2)(2, 0)(, ) the questions are called out. Each question will be repeated one time Geometry/Measurement 9. 7 only." 4 The area of the dilation is four times the area of the original letter. 0. Answers will vary. Problem-Solving Strategies Bob has the most (0 cards) and Lisa has the least ( cards). $4.00 Actual cost $.00 Profit $2.00 They must sell cups to make $2 profit meters..8 cm f = q = cm pounds 0. acute Grade 8 Page 72

19 Problems of the Week Visual Eric drew two squares side by side. The perimeter of the resulting rectangle is 90 meters. What is the area of the rectangle? 2 When the line x + 4y = 48 crosses the first quadrant, a triangle is formed. Find the area of this triangle.. Students collect data from classmates on height in inches and foot length. 2. Make a scatter plot using the information.. Students determine relationship of data. Geometry/ Measurement Draw this design after it has been rotated clockwise around the origin 90. Problem-Solving Strategies Drawing a Picture or Making a Model A nonagon is a polygon with 9 sides. How many different diagonals can be drawn in a nonagon? Describe two ways an equation and inequality are different. Grade 8 Page 7

20 2 *See answer key. This section should not be duplicated for the students.. Write as a decimal: three hundred-fifty two and thirty-six thousandths. 2. Evaluate 2m if m =.. 00 = Mental Math 4. Write 2 as an improper fraction.. Express as a unit rate: 20 miles in 4 hours 6. Write the ratio as a percent: :00 7. Simplify: 6x + x + 2y 8. Name the first five whole numbers. 9. True or false: 0.6 = 0. Give the coordinate of the point that is 6 units to the right of the y-axis and 4 units below the x-axis.. Find the area of a rectangle whose length is yards and whose width is 9 yards. 2. Solve for r: 2r 78.. Find the median: Write the expression and evaluate: seven cubed divided by seven squared.. Find the GCF for 6y and 40y Give four positive multiples of 0. Write answers here: Write the fraction in simplest form: 9. Which is greater: 4 or? 0. Factor Grade 8 Page 74

21 Visual Answer: 40 m 2 The triangle has vertices at (0,0), (0,2) and (6,0). The area is 96 square units. Geometry/Measurement Answer Key Mental Math miles/hour 6. % 7. 9x + 2y 8. 0,, 2,, 4 9. True 0. (6, 4) 2 This section provides an oral drill for sharpening one's mental computation. Before each session give these directions, "Number your paper from to 0. Write your answer as the questions are called out. Each question will be repeated one time only.". square yards 2. r 8. 0 Answers will vary. Problem-Solving Strategies Answer: 27 ) An equation has one answer and an inequality has more than one. 2) The signs used in writing an equation and an inequality are different y = , 60, 90, Grade 8 Page 7

22 Problems of the Week Visual Distinct numbers are assigned to regions A, B, and C in the given rectangle. The numbers shown in the circles represent the sums of the numbers assigned to the regions that border each circle. What number is assigned to region B? A The sum of the ages of the Smith s four children is 2. Maria s oldest brother is six times as old as she is. Her next-to-theoldest brother is years older than she is, and the youngest of her brothers is twice Maria s age. How old is each of the Smith s children? Geometry/ Measurement You have a circular swimming pool with a radius 6 meters and volume of about.8 cubic meters. Your neighbor has a circular pool with a diameter that is the same as the radius of your pool. The depth of the pools are the same. Explain how to find the volume of your neighbor s pool. Find the volume. Compare the volumes. You and your neighbor decide to drain the pools and paint the inside surfaces. If your neighbor needs three cans of paint for his pool, how many cans of paint will you need to paint your pool? Explain your solution. 29 C B Ages of 24 Night Class Students A B C D E Find mean, median and mode of the data set. Which of the measures from part A best represents the data set? Explain your thinking. Construct a box-and-whiskers plot for the data. Give the range, lower extreme, upper extreme, lower quartile and upper quartile. What percent of the data is represented by the box in the box-and-whiskers plot? Problem-Solving Strategies A cylinder has a radius of inch. How tall 2 must it be if the volume should be at least cubic inches? Explain why this statement can be misleading: A negative and a negative is a positive. Grade 8 Page 76

23 26 *See answer key. This section should not be duplicated for the students.. Simplify (x 2 ) 2. Solve for x: x 7 0 = 9 0 Mental Math. Do the following ratios form a proportion? 4, 7 4. Simplify: (2x 2 )(x ) 20. State the quadrant in which the x-coordinate is negative and the y-coordinate is positive. 6. How many hours are in a week? 7. Is the ordered pair (, 0) a solution to 6x + y = 0? Identify the variable in the expression: 2x lb 2 oz + 4 lb 8 oz. 2. Round to the nearest tenth:.82,.9, 4.694, What is the top number of a fraction called? What is the measure of a right angle? 4. Write the next terms: 2, 9, 26,. Is the bottom figure a rotation, translation, or reflection of the top figure? 6. Solve for b : b 2 8 = 2 Write answers here: Express as a fraction Solve for m: = m 0. Evaluate (x + y) 2 if x and y = Grade 8 Page 77

24 Visual Answer: B = 8 Answer: 2, 4, 7, 2 Geometry/Measurement You can find the height of your pool by using V = πr 2 h..8 = π(6 2 )h; h is approximately 4.7 meters. The neighbor's pool would have volume: π( 2 )(4.7) = about cubic meters. (You could also reason that the neighbor's pool has to have 4 the volume of yours.) The surface that the neighbor paints is π(9) + π(6)(4.7) = 6.9 square meters. The surface area you will paint is π(6) + π(2)(4.7) = 290. square meters. Now set up a ratio: x = x = about 7. so 8 cans should be bought. A Mean 4.8, median 4., mode 4 B C Answer Key No, statistically there is not enough difference. Mental Math. 6x 2.. yes 4. numerator. Quadrant II hours 7. yes x 0. lb 4oz. numerator 2..2,.9, 4.7, , 47, 4. translation 26 This section provides an oral drill for sharpening one's mental computation. Before each session give these directions, "Number your paper from to 0. Write your answer as the questions are called out. Each question will be repeated one time only." D range = 2, lower extreme = 2, E 0% upper extreme = 48, lower quartile =., upper quartile = 8. Problem-Solving Strategies Answer: at least 9. inches = 7 8 It needs to say the product of two negative numbers is a negative number. Grade 8 Page 78

25 Problems of the Week Visual The diagram consists of four congruent squares made with twelve 2-inch toothpicks. By moving exactly three toothpicks, form three congruent squares so that each toothpick forms a side of a square. What is the percent of increase in the perimeter of the figure? 27 One zip weighs as much as four zaps. Six zaps weigh as much as three zowwies. Five zowwies weigh as much as two swooshes. If one swoosh weighs one hundred pounds, how many pounds does one zip weigh? At one point early this season Chipper Jones was batting.00. After getting hits in 0 atbats in his next 2 games, his average dropped to.. How many hits and at-bats must he have altogether? Geometry/ Measurement The Big Brown Teddy Bear Factory uses two geometrically similiar patterns to produce 0"-tall bears and 0"-tall bears. If one bag of stuffing is needed to fill the entire volume of a 0"-tall bear, how many bags of stuffing will be needed to fill the volume of a similar 0"-tall bear? From Mathcounts School Handbook Problem-Solving Strategies Mr. Money has nickels, dimes, and quarters. In how many ways can he make change for 0? When you change from a smaller unit of measure to a larger unit of measure, you get a smaller number for an answer. Explain why? Grade 8 Page 79

26 27 *See answer key. This section should not be duplicated for the students.. The sum of the measures of two angles of a triangle is 8. What is the measure of the third angle? 2. If one acute angle of a right triangle measures 2, what is the measure of the other acute angle?. True or False: = :8 = 6: Simplify: x 2 + 2x 2 + x + 4x = 9. If a = 20, find the value of 4a Write as a simplified algebraic expression: the product of 2x and 0r. Mental Math Find the volume of a cylinder with a radius of feet and a height of 7 feet.. What are the prime factors of 72? =. Solve for k: k = 6. 0% of what number = Write the reciprocal of Simplify: gal 2 qt + gal 6 qt 0. Write as a word phrase: 9n Write answers here: Grade 8 Page 80

27 Visual perimeter = 8 units Answer: 80 pounds Geometry/Measurement Answer: 27 bags perimeter = 2 units 0% increase Answer Key Mental Math False x 2 + 7x 7. ray rx 27 This section provides an oral drill for sharpening one's mental computation. Before each session give these directions, "Number your paper from to 0. Write your answer as the questions are called out. Each question will be repeated one time only." 4 hits 2 at - bats =. Problem-Solving Strategies Make a systematic list The chart shows 9 ways ft. 2, 2, 2,, k = gal 8 qt or 6 gal 0. the product of 9 and a number n When measuring an object, it takes fewer of a larger unit of measure than it takes of a smaller unit of measure. Examples: 6 inches = feet, 4 quarts = gallon, feet = yard, 00 cm = m, 000m = km Grade 8 Page 8