Problem Solving Approach to Mathematics for Elementary School Teachers
Problem Solving Approach to Mathematics for Elementary School Teachers
13th Edition
ISBN: 9780135184097
Author: BILLSTEIN
Publisher: PEARSON CO
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Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba…
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Chapter 6.3A, Problem 10A

Without actually doing the computation, choose the phrase in parentheses that correctly describe each.

a. 13 14 ⋅ 17 19       ( greater than 1, less than 1 )

b. 3 2 7 ÷ 5 1 9           ( greater than 1, less than 1 )

c. 4 1 3 ÷ 2 3 100           ( greater than 2, less than 2 )

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Chapter 6 Solutions

Problem Solving Approach to Mathematics for Elementary School Teachers

Ch. 6.1 - Mathematical Connections Explain why 25 cents is...Ch. 6.1 - Mathematical Connections In each of two different...Ch. 6.1 - Prob. 3MCCh. 6.1 - Prob. 4MCCh. 6.1 - Mathematical Connections Explain why in...Ch. 6.1 - Prob. 6MCCh. 6.1 - MATHEMATICAL CONNECTIONS Explain how you could use...Ch. 6.1 - Prob. 8MCCh. 6.1 - How would you show 14 of the combined area of the...Ch. 6.1 - Prob. 10MC
Ch. 6.1 - Prob. 11MCCh. 6.1 - MATHEMATICAL CONNECTIONS A students claims that...Ch. 6.1 - Prob. 13MCCh. 6.1 - MATHEMATICAL CONNECTIONS Ann claims that she...Ch. 6.1 - Prob. 15MCCh. 6.1 - Prob. 16MCCh. 6.1 - Prob. 17MCCh. 6.1 - Prob. 18MCCh. 6.1 - Prob. 19MCCh. 6.1 - MATHEMATICAL CONNECTIONS Michelle wants to know if...Ch. 6.1 - MATHEMATICAL CONNECTIONS Claire claims that 13 is...Ch. 6.1 - Prob. 22MCCh. 6.1 - Prob. 1NAEPCh. 6.1 - Prob. 2NAEPCh. 6.1 - NATIONAL ASSESSMENT OF EDUCATIONAL PROGRESS NAEP...Ch. 6.1 - Prob. 4NAEPCh. 6.1A - Write a sentence that illustrates the use of 78 in...Ch. 6.1A - For each of the following, write a fraction to...Ch. 6.1A - If the entire rectangle is a whole, what fraction...Ch. 6.1A - Prob. 4ACh. 6.1A - Based on your visual observations, could the...Ch. 6.1A - In each case, subdivide the figure shown on the...Ch. 6.1A - Referring to the figure, represent each of the...Ch. 6.1A - Prob. 8ACh. 6.1A - For each of the following fractions, write three...Ch. 6.1A - Find the simplest form for each of the following...Ch. 6.1A - For each of the following fractions, choose the...Ch. 6.1A - Find the simplest form for each of the following...Ch. 6.1A - Determine whether the following pairs are equal....Ch. 6.1A - Determine whether the following pairs are equal by...Ch. 6.1A - Draw an area model to show that 34=68.Ch. 6.1A - If a fraction equals 34 and the sum of the...Ch. 6.1A - Mr. Gomez filled his cars 16 gal gas tank. He took...Ch. 6.1A - Solve for x in each of the following. a. 23=x16 b....Ch. 6.1A - For each of the following pair of fractions,...Ch. 6.1A - For each of the following, find two rational...Ch. 6.1A - a. 6 oz is what part of a pound? A ton? b. A dime...Ch. 6.1A - Based on your visual observation write a fraction...Ch. 6.1A - Arrange each of the following in descending...Ch. 6.1A - Determine whether the following is true: If a, b,...Ch. 6.1A - Fill in missing numbers for x, y, z, and w to...Ch. 6.1A - Prove that any integer n can be written as a...Ch. 6.1A - Prob. 27ACh. 6.1A - Ten bulbs were in a chandelier. One-fifth of the...Ch. 6.1A - At a party, there were 35 guests. Two-fifths of...Ch. 6.1B - Write a sentence that illustrate the use of 710 in...Ch. 6.1B - For each of the following write the fraction to...Ch. 6.1B - If the entire rectangle is a whole, what fraction...Ch. 6.1B - Complete each of the following figures so that it...Ch. 6.1B - Based on your visual observation, could the shaded...Ch. 6.1B - Each model below represents the given fraction....Ch. 6.1B - Referring the figure represent the each of the...Ch. 6.1B - Prob. 8ACh. 6.1B - For each of the following write three equal...Ch. 6.1B - Find the simplest form for each of the following...Ch. 6.1B - Prob. 11ACh. 6.1B - Find the simplest form for each of the following...Ch. 6.1B - Determine whether the following pairs are equal....Ch. 6.1B - Determine whether the following pairs are equal by...Ch. 6.1B - Prob. 15ACh. 6.1B - Prob. 16ACh. 6.1B - The following two parking meters are next to each...Ch. 6.1B - Solve for x in each of the following. a.23=x18...Ch. 6.1B - For each of the following pairs of fractions,...Ch. 6.1B - Prob. 20ACh. 6.1B - a. 12oz is what part of a pound. b A nickel is...Ch. 6.1B - Prob. 22ACh. 6.1B - Fill in missing numbers for x, y, z, and w to...Ch. 6.1B - Use the Fundamental Law of Fractions Theorem 6-1...Ch. 6.1B - Prob. 25ACh. 6.1B - Prob. 26ACh. 6.1B - Ten light bulbs were in a chandelier. Three-fifths...Ch. 6.1B - At a party, there were 40 guests. One-fifth of the...Ch. 6.1B - Sketch four different windows having different...Ch. 6.2 - Suppose a large pizza is divided into 3 equal...Ch. 6.2 - Prob. 2MCCh. 6.2 - When we add two fractions with unlike denominators...Ch. 6.2 - Prob. 4MCCh. 6.2 - Kara spent 12 of her allowance on Saturday and 13...Ch. 6.2 - Compute 334+513 in two different ways and leave...Ch. 6.2 - Prob. 7MCCh. 6.2 - Write a story problem for 2314.Ch. 6.2 - a. With the exception of 23, the Egyptians used...Ch. 6.2 - Kendra showed that 13+34=47 by using the following...Ch. 6.2 - Prob. 11MCCh. 6.2 - Prob. 12MCCh. 6.2 - Explain the error pattern on Jons test. a....Ch. 6.2 - Prob. 14MCCh. 6.2 - Prob. 15MCCh. 6.2 - Prob. 16MCCh. 6.2 - Answer the ConvinceMe question on the School Book...Ch. 6.2 - Prob. 18MCCh. 6.2 - Prob. 19MCCh. 6.2 - Prob. 20MCCh. 6.2 - Prob. 21MCCh. 6.2 - Melinda ate 35 of the cookies and left the rest...Ch. 6.2 - Prob. 23MCCh. 6.2 - Prob. 1NAEPCh. 6.2 - Prob. 2NAEPCh. 6.2A - Perform the following additions or subtractions....Ch. 6.2A - Change each of the following fractions to a mixed...Ch. 6.2A - Change each of the following mixed numbers to a...Ch. 6.2A - Approximate each of the following situations with...Ch. 6.2A - Use the information in the table to answer each of...Ch. 6.2A - Sort the following fraction cards into the ovals...Ch. 6.2A - Approximate each of the following fractions by...Ch. 6.2A - Prob. 8ACh. 6.2A - Compute each of the following mentally. a. 234 b....Ch. 6.2A - The following ruler has region marked M, A, T, H....Ch. 6.2A - Use clustering to estimate the following sum....Ch. 6.2A - A class consists of 25 freshmen, 14 sophomores,...Ch. 6.2A - A clerk sold three pieces of one type ribbon of...Ch. 6.2A - Martine bought 834yd of fabric. She wants to make...Ch. 6.2A - Give an example illustrating each of the following...Ch. 6.2A - Prob. 16ACh. 6.2A - Prob. 17ACh. 6.2A - Alyssa runs 58mi in 10 min. Bryan runs 78mi in 10...Ch. 6.2A - One recipe calls for 134 cups of milk and a second...Ch. 6.2A - The table below shows census date for a particular...Ch. 6.2A - Two fractions have a sum of 1. If one of the...Ch. 6.2A - Prob. 22ACh. 6.2B - Perform the following additions or subtractions....Ch. 6.2B - Change each of the following fractions to a mixed...Ch. 6.2B - Prob. 3ACh. 6.2B - Place the numbers 2,5,6, and 8 in the following...Ch. 6.2B - Use the information in the table to answer each of...Ch. 6.2B - Sort the following fraction cards into the ovals...Ch. 6.2B - Prob. 7ACh. 6.2B - Prob. 8ACh. 6.2B - Compute each of the following mentally. a. 678 b....Ch. 6.2B - Prob. 10ACh. 6.2B - A class consists of 14 freshmen, 15 sophomores,...Ch. 6.2B - The Acme Company sells its products in many...Ch. 6.2B - A recipe requires 312 cups of milk. Ran put in 134...Ch. 6.2B - A 1534in. board is cut in a single cut from a...Ch. 6.2B - Students from Rattlesnake School formed four teams...Ch. 6.2B - Insert four fractions between the numbers 1 and 3...Ch. 6.2B - Solve for x in each of the following. a. x56=23 b....Ch. 6.2B - Joe has 34 cup of paint in a container. He uses 13...Ch. 6.2B - a. Find 12+14. b. Find 12+14+18. c. Find...Ch. 6.2B - Prob. 21ACh. 6.3 - Suppose you divide a natural number n by a...Ch. 6.3 - If the fractions represented by points C and D on...Ch. 6.3 - If the product of two numbers is 1 and one of the...Ch. 6.3 - Bente says to do the problem 1214334 you just find...Ch. 6.3 - Amy says that dividing a number by 12 is the same...Ch. 6.3 - Dani says that if we have 3425, we could just...Ch. 6.3 - Noah says that dividing a number by 2 is the same...Ch. 6.3 - Jim is not sure when to use multiplication by a...Ch. 6.3 - A student claims that division always makes things...Ch. 6.3 - A student simplified the fraction m+np+n to mp....Ch. 6.3 - Jillian says she learned that 17 divided by 5 can...Ch. 6.3 - Joanie said that if you multiply a fraction less...Ch. 6.3 - Julius claims that when you use invert and...Ch. 6.3 - Bob says that when you divide a positive whole...Ch. 6.3 - Ann is calculating 34(1225) by finding 34 of 12=9...Ch. 6.3 - Shelly says that 234(415)=24+3415=8+320=8320. Is...Ch. 6.3 - Noah is calculating (56)2. He draws the figures...Ch. 6.3 - Prob. 18MCCh. 6.3 - Work the two Try It problem on the School Book...Ch. 6.3 - Perform each of the following computations. Leave...Ch. 6.3 - Each student at Sussex Elementary School takes one...Ch. 6.3 - Find each sum or difference; simplify if possible....Ch. 6.3 - Determine which of the following is always...Ch. 6.3 - Both figures below show the same scale. The marks...Ch. 6.3 - Jim has 34 of a yard of string which he wishes to...Ch. 6.3 - Nick has a whole pizza. Nick says he will eat 12...Ch. 6.3A - In the following figures, a unit rectangle is used...Ch. 6.3A - Use a rectangular region to illustrate each of the...Ch. 6.3A - Find each of the following products of rational...Ch. 6.3A - Prob. 4ACh. 6.3A - Find the multiplicative inverse of each of the...Ch. 6.3A - Solve for x. a. 23x=76 b. 34x=12 c. 56+23x=34 d....Ch. 6.3A - Show that the following properties do not hold for...Ch. 6.3A - Compute the following mentally. Find the exact...Ch. 6.3A - Choose from among the numbers in parentheses the...Ch. 6.3A - Without actually doing the computation, choose the...Ch. 6.3A - A sewing project requires 618yd of material that...Ch. 6.3A - Five-eighths of the students at Salem State...Ch. 6.3A - Alberto owns 59 of the stock in the N.W. Tofu...Ch. 6.3A - A suit is on sale for 180. What was the original...Ch. 6.3A - John took all his money out of his savings...Ch. 6.3A - Al gives 12 of his marbles to Bev. Bev gives 12 of...Ch. 6.3A - Write each of the following in simplest form using...Ch. 6.3A - Write each of the following in simplest form using...Ch. 6.3A - Solve for the integer n in each of the following....Ch. 6.3A - Solve each of the following inequality for x,...Ch. 6.3A - Determine which fraction in each of the following...Ch. 6.3A - Show that the arithmetic mean of two rational...Ch. 6.3A - In the School of Design, 1725 of the students were...Ch. 6.3A - Prob. 25ACh. 6.3A - Some friends went to a movie and bought 2 bags of...Ch. 6.3A - If 133 of all deer in the United States are in...Ch. 6.3A - If 14 of an estate is to be distributed equally to...Ch. 6.3B - In the following figures, a unit rectangle is used...Ch. 6.3B - Use a rectangular region to illustrate each of the...Ch. 6.3B - Assessment Find each of the following products of...Ch. 6.3B - Assessment Use the distributive property to find...Ch. 6.3B - Assessment Find the multiplicative inverse of each...Ch. 6.3B - Prob. 6ACh. 6.3B - Assessment Find a fraction such that if you add...Ch. 6.3B - Assessment Compute the following mentally, find...Ch. 6.3B - Assessment Choose from among the numbers in the...Ch. 6.3B - Assessment Without actually doing the...Ch. 6.3B - When you multiply a certain number by 3 and then...Ch. 6.3B - Di Paloma University had a faculty reduction and...Ch. 6.3B - A person has 2912yd of material available to make...Ch. 6.3B - Every employees salary at the sunrise software...Ch. 6.3B - Jasmine is reading a book. She has finished 34 of...Ch. 6.3B - Prob. 16ACh. 6.3B - Write each of the following in the simplest form...Ch. 6.3B - Prob. 18ACh. 6.3B - Prob. 19ACh. 6.3B - Prob. 20ACh. 6.3B - Solve each of the following inequalities for x,...Ch. 6.3B - Prob. 22ACh. 6.3B - Prob. 23ACh. 6.3B - Joan attended school for 2 weeks longer than 34 of...Ch. 6.3B - In the school of Design, 825 of the students were...Ch. 6.3B - Prob. 26ACh. 6.3B - Prob. 27ACh. 6.3B - Prob. 28ACh. 6.4 - Prob. 1MCCh. 6.4 - Prob. 2MCCh. 6.4 - Prob. 3MCCh. 6.4 - Prob. 4MCCh. 6.4 - Prob. 5MCCh. 6.4 - Prob. 6MCCh. 6.4 - Prob. 7MCCh. 6.4 - Prob. 8MCCh. 6.4 - Prob. 9MCCh. 6.4 - Prob. 10MCCh. 6.4 - MATHEMATICAL CONNECTIONS Al is 5ft tall and has a...Ch. 6.4 - Prob. 12MCCh. 6.4 - George and Mike are mixing paints for an art...Ch. 6.4 - If the numerator of a rational number is 6 times...Ch. 6.4 - Prob. 15MCCh. 6.4 - Explain why any integer is a rational number?Ch. 6.4 - Prob. 17MCCh. 6.4 - Prob. 18MCCh. 6.4 - Prob. 19MCCh. 6.4 - Prove that 9998 is less than 9796.Ch. 6.4 - a. Amal can finish a job in 12 of a day working by...Ch. 6.4 - Prob. 1NAEPCh. 6.4 - NATIONAL ASSESSMENT OF EDUCATION PROGRESS NAEP The...Ch. 6.4 - Prob. 3NAEPCh. 6.4 - Prob. 4NAEPCh. 6.4 - A map shows the location of town A and town B. On...Ch. 6.4A - Answer the following regarding the English...Ch. 6.4A - Solve for x each of the following proportions. a....Ch. 6.4A - a. If the ratio of boys to girls in a class is...Ch. 6.4A - There are approximately 2lb of muscle for every...Ch. 6.4A - Prob. 5ACh. 6.4A - Prob. 6ACh. 6.4A - Prob. 7ACh. 6.4A - Two numbers are in the ratio 3:4. Find the numbers...Ch. 6.4A - Gary, Bill, and Carmella invested in a corporation...Ch. 6.4A - Sheila and Dora worked 312hr and 412hr...Ch. 6.4A - Vonna scored 75 goals in her soccer kicking...Ch. 6.4A - Express each of the following ratios in the form...Ch. 6.4A - Write three other proportions from the following...Ch. 6.4A - The rise and span for a house roof are identified...Ch. 6.4A - Gear ratios are used in industry. A gear ratio is...Ch. 6.4A - A Boeing 747 jet is approximately 230 ft long and...Ch. 6.4A - A recipe calls for 1tsp of mustard seeds, 3c of...Ch. 6.4A - The electrical resistance of a wire, measured in...Ch. 6.4A - In a photograph of a father and his daughter, the...Ch. 6.4A - The amount of gold in jewelry and other products...Ch. 6.4A - If Amber is paid 8 per hour for typing, the table...Ch. 6.4A - a. In Room A, there are 1 man and 2 women; in Room...Ch. 6.4A - A car travels about 26 miles on 1 gallon of gas,...Ch. 6.4A - Susan bikes 20 miles in 2 hours, while Nick bikes...Ch. 6.4A - There are 40 students in a classroom, and the...Ch. 6.4A - The ratio of oblong tables to round tables at a...Ch. 6.4A - A recipe uses 112 c flour to make 2 dozen cookies....Ch. 6.4A - Use a bar model to solve each of the following. a....Ch. 6.4A - Use the bar model to solve the following exercise....Ch. 6.4B - Answer the following regarding the letters in the...Ch. 6.4B - Solve for x in each of the following proportions....Ch. 6.4B - There are 5 adult drivers to each teenage driver...Ch. 6.4B - A candle is 30 in. long. After burning for 12 min,...Ch. 6.4B - A rectangular yard has a width-to-length ratio of...Ch. 6.4B - A grasshopper can jump 20 times its length. If...Ch. 6.4B - Juan found out that after working for 9 months he...Ch. 6.4B - At Rattlesnake School, the teacher-student ratio...Ch. 6.4B - At a particular time, the ratio of the height of...Ch. 6.4B - The following table shows several possible widths...Ch. 6.4B - Find three sets of x- and y-values for the...Ch. 6.4B - If rent is 850 for each 2 weeks, how much is the...Ch. 6.4B - Leonardo da Vinci in his drawing Vitruvian man...Ch. 6.4B - On a city map, a rectangular park has a length of...Ch. 6.4B - Lees car will travel 240 mi on 15 gal of gas. How...Ch. 6.4B - Some model railroads use an 0 scale in replicas of...Ch. 6.4B - a. On an American flag, what is the ratio of stars...Ch. 6.4B - On an American flag, the ratio of the length of...Ch. 6.4B - If xy=ab,a0,x0 is true, what other proportion do...Ch. 6.4B - If a certain recipe takes 112c flour and 4 c milk,...Ch. 6.4B - To estimate the number of fish in a lake,...Ch. 6.4B - Prob. 22ACh. 6.4B - Prob. 23ACh. 6.4B - Prob. 24ACh. 6.4B - The ratio of oblong tables to round tables at a...Ch. 6.4B - Prob. 26ACh. 6.4B - Prob. 27ACh. 6.4B - Use bar model to solve each of the following. a....Ch. 6.4B - The ratio of Marks books to Nans Book is 11:3....Ch. 6.CR - CHAPTER 6 REVIEW For each of the following, draw a...Ch. 6.CR - Write three rational numbers equal to 56.Ch. 6.CR - Write each of the following rational numbers in...Ch. 6.CR - Prob. 4CRCh. 6.CR - CHAPTER 6 REVIEW Find the additive and...Ch. 6.CR - Prob. 6CRCh. 6.CR - Prob. 7CRCh. 6.CR - Prob. 8CRCh. 6.CR - CHAPTER 6 REVIEW John has 5414 yd of material. a....Ch. 6.CR - Prob. 10CRCh. 6.CR - Prob. 11CRCh. 6.CR - CHAPTER 6 REVIEW. Find two rational numbers...Ch. 6.CR - Prob. 13CRCh. 6.CR - Prob. 14CRCh. 6.CR - Prob. 15CRCh. 6.CR - Prob. 16CRCh. 6.CR - Prob. 17CRCh. 6.CR - The carvings of the faces at Mount Rushmore in...Ch. 6.CR - A student argues that the following fraction is...Ch. 6.CR - Prob. 20CRCh. 6.CR - If 23 of all students in the academy are female...Ch. 6.CR - Explain which is greater: 119 or 1210.Ch. 6.CR - Prob. 23CRCh. 6.CR - Prob. 24CRCh. 6.CR - Prob. 25CRCh. 6.CR - Mike drew the following picture to find out how...Ch. 6.CR - Tom tossed a coin 30 times and got 17 heads. a....Ch. 6.CR - Which bottle of juice is a better buy cost per...Ch. 6.CR - Eighteen-karat gold contains 18 parts grams gold...Ch. 6.CR - A recipe for fruit salad serves 4 people. It calls...Ch. 6.CR - If the scale on a drawing of a house is 1cm to...Ch. 6.CR - Prob. 32CRCh. 6.CR - Prob. 33CRCh. 6.CR - Prob. 34CRCh. 6.CR - Prob. 35CRCh. 6.CR - Prob. 36CRCh. 6.CR - Prob. 37CRCh. 6.CR - Prob. 38CRCh. 6.CR - Use Xs below to illustrate each of the following....Ch. 6.CR - Prob. 40CRCh. 6.CR - Prob. 41CRCh. 6.CR - Prob. 42CRCh. 6.CR - Prob. 43CRCh. 6.CR - The ratio of boys to girls in a class is 4:3. a....Ch. 6.CR - Prob. 45CRCh. 6.CR - Prob. 46CRCh. 6.CR - Prob. 47CRCh. 6.CR - Prob. 48CRCh. 6.CR - Prob. 49CRCh. 6 - Prob. 1NTCh. 6 - Prob. 2NTCh. 6 - Prob. 3NTCh. 6 - Prob. 4NTCh. 6 - Prob. 5NTCh. 6 - Prob. 6NTCh. 6 - Prob. 7NT
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