A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
12th Edition
ISBN: 9780321987297
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott
Publisher: PEARSON
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 7.2A, Problem 34A

ASSESSMENT

Estimate the sum or difference in each of the following by using (i) rounding and (ii) front-end estimation. Then perform the computations to see how close your estimates are to the actual answers.

a. 65.84 24.29 12.18 + 19.75 _ b. 89.47 − 32.16 _

c. 5.85 6.13 9.10 + 4.32 _ d. 223.75 − 87.60 _

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iid 1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution depend on the mean and variance of the underlying random variables (i.e., the population mean and variance). The approximation can be written to emphasize this, using the expec- tation and variance of one of the random variables in the sample instead of the parameters μ, 02: YNEY, · (1 (EY,, varyi n For the following population distributions f, write the approximate distribution of the sample mean. (a) Exponential with rate ẞ: f(y) = ß exp{−ßy} 1 (b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ } г( (c) Poisson with rate λ: P(Y = y) = exp(-\} > y! y²
2. Let Y₁,……., Y be a random sample with common mean μ and common variance σ². Use the CLT to write an expression approximating the CDF P(Ỹ ≤ x) in terms of µ, σ² and n, and the standard normal CDF Fz(·).
3. We'd like to know the first time when the population reaches 7000 people. First, graph the function from part (a) on your calculator or Desmos. In the same window, graph the line y = 7000. Notice that you will need to adjust your window so that you can see values as big as 7000! Investigate the intersection of the two graphs. (This video shows you how to find the intersection on your calculator, or in Desmos just hover the cursor over the point.) At what value t> 0 does the line intersect with your exponential function? Round your answer to two decimal places. (You don't need to show work for this part.) (2 points)

Chapter 7 Solutions

A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

Ch. 7.1 - Using Simon Stevins notation see Historical Note,...Ch. 7.1 - MATHEMATICAL CONNECTIONS If 1 mL is 0.001 L, how...Ch. 7.1 - MATHEMATICAL CONNECTIONS Explain whether day can...Ch. 7.1 - MATHEMATICAL CONNECTIONS Using the number line...Ch. 7.1 - Explain why you think a sign on a copy machine...Ch. 7.1 - MATHEMATICAL CONNECTIONS Explain how you could use...Ch. 7.1 - MATHEMATICAL CONNECTIONS Explain why, in Theorem...Ch. 7.1 - MATHEMATICAL CONNECTIONS Explain why appending any...Ch. 7.1 - MATHEMATICAL CONNECTIONS How can you tell each of...Ch. 7.1 - MATHEMATICAL CONNECTIONS Determine how decimal...
Ch. 7.1 - Using base-five blocks similar to base-ten blocks,...Ch. 7.1 - In small groups, research the history of decimals...Ch. 7.1 - MATHEMATICAL CONNECTIONS A student claims that is...Ch. 7.1 - Prob. 16MCCh. 7.1 - MATHEMATICAL CONNECTIONS A student claims that...Ch. 7.1 - Connecting Mathematics to the Classroom A student...Ch. 7.1 - Joe rode his bicycle from his house to his friends...Ch. 7.1 - 50-YARD RACE Girl Time seconds Christa 8.28 Kelly...Ch. 7.1 - The diameter of a red blood cell, in inches, is...Ch. 7.1A - Assessment 71A Write each of the following as a...Ch. 7.1A - Assessment 71A Rewrite each of the following as a...Ch. 7.1A - Assessment 71A Write each of the following as a...Ch. 7.1A - Write each of the following numerals in words. a....Ch. 7.1A - Write each of the following terminating decimals...Ch. 7.1A - Mentally determine which of the following can be...Ch. 7.1A - When possible, write each of the numbers in...Ch. 7.1A - Seven minutes is part of an hour. If 7 min were to...Ch. 7.1A - Given the U.S. monetary system, what reason can...Ch. 7.1A - In each of the following order the decimals from...Ch. 7.1A - Write the numbers in each of the following...Ch. 7.1A - Use a decimal grid with 100 squares and represent...Ch. 7.1A - If the decimals 0.804,0.84, and 0.8399 are...Ch. 7.1A - Write a decimal that has a ten-thousandths place...Ch. 7.1A - a. Show that between any two terminating decimals,...Ch. 7.1A - If decimals in other number bases work the same as...Ch. 7.1A - The five top swimmers in an event had the...Ch. 7.1A - Suppose a carpenters ruler was marked in...Ch. 7.1B - ASSESSMENT Write each of the following as a sum in...Ch. 7.1B - Prob. 2ACh. 7.1B - ASSESSMENT Write each of the following as a...Ch. 7.1B - ASSESSMENT Write each of the following numerals in...Ch. 7.1B - Write each of the following terminating decimals...Ch. 7.1B - ASSESSMENT Mentally determine which of the...Ch. 7.1B - ASSESSMENT Where possible, write each of the...Ch. 7.1B - ASSESSMENT What whole numbers of minutes less than...Ch. 7.1B - Prob. 9ACh. 7.1B - Prob. 10ACh. 7.1B - Write the numbers in each of the following...Ch. 7.1B - Use a grid with 100 squares and represent 0.23.Ch. 7.1B - Prob. 13ACh. 7.1B - Write a decimal that is between 8.345 and 8.3456.Ch. 7.1B - Prob. 15ACh. 7.1B - Prob. 16ACh. 7.1B - Assessment The five top swimmers in an event had...Ch. 7.1B - Prob. 18ACh. 7.2 - How much greater is 0.763 than 0.753? How can you...Ch. 7.2 - How is multiplication of decimals like...Ch. 7.2 - Prob. 3MCCh. 7.2 - Is a product of two positive decimals each less...Ch. 7.2 - What is the significance of the 1 above the 6 in...Ch. 7.2 - Prob. 8MCCh. 7.2 - Prob. 9MCCh. 7.2 - Prob. 10MCCh. 7.2 - Prob. 11MCCh. 7.2 - In multiplying 0.1250.08, Roger knew the rule that...Ch. 7.2 - Jamal wants to know why 0.3 and 0.30 are equal....Ch. 7.2 - Fred says that to multiply 32.72.6, he just...Ch. 7.2 - Prob. 16MCCh. 7.2 - Prob. 17MCCh. 7.2 - How would you respond to the following situations?...Ch. 7.2 - Write 14.0479 in expanded form.Ch. 7.2 - With out dividing, determine which of the...Ch. 7.2 - If the denominator of a fraction is 26, is it...Ch. 7.2 - 3556 can be written as a terminating decimal....Ch. 7.2 - How much greater is 0.763 than 0.753? How can you...Ch. 7.2 - Prob. 2NAEPCh. 7.2 - Prob. 3NAEPCh. 7.2 - Explain why subtraction of terminating decimals...Ch. 7.2A - Use base-ten blocks to model 3.2+2.32.Ch. 7.2A - Write the decimals as fractions and then add....Ch. 7.2A - ASSESSMENT Write the decimals as fractions and...Ch. 7.2A - Prob. 4ACh. 7.2A - Johns calculator calculates correctly but does not...Ch. 7.2A - ASSESSMENT Multiply each number below by 0.01...Ch. 7.2A - ASSESSMENT When you multiply a natural number by a...Ch. 7.2A - If Maura went to the store and bought a chair for...Ch. 7.2A - ASSESSMENT a. Complete the following magic square;...Ch. 7.2A - ASSESSMENT Karin bought lb of peaches at lb and lb...Ch. 7.2A - Automobile engines were once measured in cubic...Ch. 7.2A - ASSESSMENT A stock rose 0.24 in the market on...Ch. 7.2A - Prob. 13ACh. 7.2A - A kilowatt hour means 1000 watts of electricity...Ch. 7.2A - Prob. 15ACh. 7.2A - ASSESSMENT If each of the following sequences is...Ch. 7.2A - Prob. 17ACh. 7.2A - Prob. 18ACh. 7.2A - Estimate the placement of each of the following...Ch. 7.2A - Prob. 20ACh. 7.2A - Mikes class is building a model of the new World...Ch. 7.2A - Prob. 22ACh. 7.2A - Prob. 23ACh. 7.2A - Prob. 24ACh. 7.2A - Prob. 25ACh. 7.2A - ASSESSMENT Convert each of the following to...Ch. 7.2A - ASSESSMENT Write the numerals in each of the...Ch. 7.2A - Prob. 28ACh. 7.2A - ASSESSMENT Write the numerals in each of the...Ch. 7.2A - ASSESSMENT Write the results of each of the...Ch. 7.2A - Round each of the following numbers as specified....Ch. 7.2A - Prob. 32ACh. 7.2A - Audrey wants to buy some camera equipment to take...Ch. 7.2A - ASSESSMENT Estimate the sum or difference in each...Ch. 7.2A - ASSESSMENT Find the least and the greatest...Ch. 7.2A - Some digits in the following number are covered by...Ch. 7.2A - Iris worked a 40-hour week at 8.25/hr. Mentally...Ch. 7.2A - ASSESSMENT Mentally compute the number to fill in...Ch. 7.2A - ASSESSMENT Which of the following result in equal...Ch. 7.2A - Prob. 40ACh. 7.2B - Prob. 1ACh. 7.2B - Prob. 2ACh. 7.2B - Prob. 3ACh. 7.2B - Assume the multiplication shown below is correct...Ch. 7.2B - Prob. 5ACh. 7.2B - Prob. 6ACh. 7.2B - When you multiply a positive decimal less than 1...Ch. 7.2B - Prob. 8ACh. 7.2B - Prob. 9ACh. 7.2B - Prob. 10ACh. 7.2B - Prob. 11ACh. 7.2B - Prob. 12ACh. 7.2B - Prob. 13ACh. 7.2B - Prob. 14ACh. 7.2B - Prob. 15ACh. 7.2B - If the first term of a finite geometric sequence...Ch. 7.2B - Prob. 17ACh. 7.2B - Prob. 18ACh. 7.2B - Prob. 19ACh. 7.2B - Prob. 20ACh. 7.2B - Prob. 21ACh. 7.2B - Prob. 22ACh. 7.2B - Prob. 23ACh. 7.2B - Prob. 24ACh. 7.2B - Prob. 25ACh. 7.2B - Prob. 26ACh. 7.2B - Prob. 27ACh. 7.2B - Prob. 28ACh. 7.2B - Prob. 29ACh. 7.2B - Round each of the following numbers as specified...Ch. 7.2B - Prob. 31ACh. 7.2B - Prob. 32ACh. 7.2B - Find the least and the greatest possible products...Ch. 7.2B - Prob. 35ACh. 7.2B - Prob. 36ACh. 7.2B - Prob. 37ACh. 7.2B - Prob. 39ACh. 7.3 - a. If a grocery store advertised three lemons for...Ch. 7.3 - A friend claims that every finite decimal is equal...Ch. 7.3 - Some addition problems are easier to compute with...Ch. 7.3 - Prob. 4MCCh. 7.3 - Notice that...Ch. 7.3 - Prob. 6MCCh. 7.3 - a. Does your calculator allow you to enter...Ch. 7.3 - Prob. 8MCCh. 7.3 - A student argues that repeating decimals are of...Ch. 7.3 - A student asks if a sum of two repeating decimals...Ch. 7.3 - A student needs to find 0.333348 without using a...Ch. 7.3 - Joe says terminating decimals are those with...Ch. 7.3 - Prob. 14MCCh. 7.3 - Prob. 15MCCh. 7.3 - Prob. 16MCCh. 7.3 - Prob. 17MCCh. 7.3 - Prob. 18MCCh. 7.3 - Prob. 19MCCh. 7.3A - Prob. 1ACh. 7.3A - a. Do 0.45777,0.4577 and 0.457 represent different...Ch. 7.3A - Write the first 10 decimal places for each of the...Ch. 7.3A - Which of the following is greater: 0.3625or0.3625?Ch. 7.3A - Write the following using a bar to indicate the...Ch. 7.3A - Prob. 6ACh. 7.3A - ASSESSMENT Convert each of the following repeating...Ch. 7.3A - Express 1 min as a repeating decimal part of an...Ch. 7.3A - ASSESSMENT Order the following decimals from...Ch. 7.3A - Prob. 10ACh. 7.3A - Prob. 11ACh. 7.3A - Give an argument why 317 must be a repeating...Ch. 7.3A - Prob. 13ACh. 7.3A - Explain whether a terminating decimal could ever...Ch. 7.3A - Find three decimals between each of the following...Ch. 7.3A - Find the decimal halfway between the decimals 0.4...Ch. 7.3A - a. Find three rational numbers between 34 and...Ch. 7.3A - Prob. 18ACh. 7.3A - a. Write each of the following as a fraction in...Ch. 7.3A - Use the fact that 0.9=1 to find the terminating...Ch. 7.3A - Prob. 21ACh. 7.3A - Prob. 22ACh. 7.3A - Find the sum of the finite geometric sequence...Ch. 7.3A - Prob. 24ACh. 7.3A - Consider the repeating decimals 0.235 and 0.2356....Ch. 7.3A - Find values of x such that each of the following...Ch. 7.3A - If a, b and c are digits, write 0.abc as a...Ch. 7.3A - Prob. 28ACh. 7.3A - Prob. 29ACh. 7.3B - Assessment Will 31234567 be a terminating decimal?...Ch. 7.3B - Prob. 2ACh. 7.3B - Prob. 3ACh. 7.3B - Prob. 4ACh. 7.3B - Assessment Write the following using a bar to...Ch. 7.3B - Assessment Find the decimal representation for...Ch. 7.3B - Prob. 7ACh. 7.3B - Prob. 8ACh. 7.3B - Prob. 9ACh. 7.3B - Prob. 10ACh. 7.3B - Prob. 11ACh. 7.3B - Prob. 12ACh. 7.3B - Prob. 14ACh. 7.3B - Assessment Find three decimals between each of the...Ch. 7.3B - Prob. 16ACh. 7.3B - Prob. 17ACh. 7.3B - Prob. 18ACh. 7.3B - Prob. 19ACh. 7.3B - Prob. 20ACh. 7.3B - Prob. 21ACh. 7.3B - ASSESSMENT Use the fact that 0.01=199 and...Ch. 7.3B - Prob. 23ACh. 7.3B - Prob. 24ACh. 7.3B - Assessment 7-3B Consider the repeating decimals...Ch. 7.3B - Prob. 26ACh. 7.3B - Prob. 27ACh. 7.3B - Prob. 28ACh. 7.3B - Prob. 29ACh. 7.4 - Use mental math to find 11 of 850. Explain your...Ch. 7.4 - Does 0.4=0.4? Explain.Ch. 7.4 - What does it mean to reach 125 of your savings...Ch. 7.4 - Is 4 of 98 the same as 98 of 4? Explain.Ch. 7.4 - a. If 25 of a number is 55, is the number greater...Ch. 7.4 - Can 35 of one number can be greater than 55 of...Ch. 7.4 - Why does one picture have so much more shaded area...Ch. 7.4 - Why is it possible to have an increase of 150 in...Ch. 7.4 - Two equal amounts of money were invested in two...Ch. 7.4 - Because of a recession, the value of a new house...Ch. 7.4 - Prob. 11MCCh. 7.4 - Each year a cars value depreciated 20 from the...Ch. 7.4 - If 70 of the girls in a class wanted to have a...Ch. 7.4 - If 70 of the girls in a class wanted to have a...Ch. 7.4 - Abe and Barb were shopping at a department store....Ch. 7.4 - Prob. 16MCCh. 7.4 - MATHEMATICAL CONNECTIONS Look at newspapers and...Ch. 7.4 - Prob. 19MCCh. 7.4 - Prob. 20MCCh. 7.4 - Prob. 25MCCh. 7.4 - A student claims that if prices at a store can...Ch. 7.4 - Prob. 27MCCh. 7.4 - Prob. 28MCCh. 7.4 - Noel read that women used to make 75c for every...Ch. 7.4 - A student claims that if the value of an item...Ch. 7.4 - a. Human bones make up 0.18 of a persons body...Ch. 7.4 - Write each of the following decimals in the form...Ch. 7.4 - Write a repeating decimal equal to each of the...Ch. 7.4 - Write 0.00024 as a fraction in simplest form.Ch. 7.4 - Prob. 35MCCh. 7.4 - Write each of the following as a standard numeral....Ch. 7.4 - Prob. 1NAEPCh. 7.4 - NATIONAL ASSESSMENT OF EDUCATIONAL PROGRESS NAEP...Ch. 7.4 - NATIONAL ASSESSMENT OF EDUCATIONAL PROGRESS NAEP...Ch. 7.4A - Prob. 1ACh. 7.4A - Copy the number line and fill in the blanks so...Ch. 7.4A - Express each of the following as a percent. a....Ch. 7.4A - Convert each of the following percent to a...Ch. 7.4A - Fill in the following blanks to find other...Ch. 7.4A - Draw a percent bar to represent 125 of 60. Set up...Ch. 7.4A - Answer each of the following question. a. What is...Ch. 7.4A - Prob. 8ACh. 7.4A - Prob. 9ACh. 7.4A - Assessment Gail received a 7 raise last year. If...Ch. 7.4A - Prob. 11ACh. 7.4A - Assessment If a dress that normally sells for 35...Ch. 7.4A - Prob. 13ACh. 7.4A - Prob. 14ACh. 7.4A - An airline ticket costs 320 without the tax. If...Ch. 7.4A - Prob. 16ACh. 7.4A - If 6623 of 1800 employees favored a new insurance...Ch. 7.4A - Which represents the greater percent:325500 or...Ch. 7.4A - Assessment An advertisement reads that if you buy...Ch. 7.4A - Prob. 20ACh. 7.4A - Prob. 21ACh. 7.4A - A crew consists of one apprentice, one journeyman,...Ch. 7.4A - a. In an incoming freshman class of 500 students,...Ch. 7.4A - Assessment Ms. Price has received a 10 raise in...Ch. 7.4A - Prob. 25ACh. 7.4A - If you wanted to spend 25 of your monthly salary...Ch. 7.4A - Prob. 27ACh. 7.4A - A tip in a restaurant has been typically figured...Ch. 7.4A - Assessment Suppose the percent bar below shows the...Ch. 7.4A - Prob. 30ACh. 7.4A - Assessment Sunscreens block ultraviolet UV rays...Ch. 7.4A - Complete the following compound interest chart....Ch. 7.4A - Assessment Ms. Jackson borrowed 42,000 at 8.75...Ch. 7.4A - Prob. 34ACh. 7.4A - Prob. 35ACh. 7.4A - Prob. 36ACh. 7.4A - Prob. 37ACh. 7.4A - The New Age Savings Bank advertises 4 annual...Ch. 7.4A - Prob. 39ACh. 7.4B - Prob. 1ACh. 7.4B - Prob. 2ACh. 7.4B - Assessment Express each of the following as a...Ch. 7.4B - Assessment Convert each of the following percents...Ch. 7.4B - Assessment Fill in the following blanks to find...Ch. 7.4B - Draw a percent bar to represent 150 of 60. Set up...Ch. 7.4B - Prob. 7ACh. 7.4B - Prob. 8ACh. 7.4B - Prob. 9ACh. 7.4B - Assessment Brandy received a 10 raise last year....Ch. 7.4B - Prob. 11ACh. 7.4B - Assessment A used car originally cost 1700. One...Ch. 7.4B - Assessment On a certain day in Glacier Park, 728...Ch. 7.4B - Prob. 14ACh. 7.4B - Prob. 15ACh. 7.4B - Prob. 16ACh. 7.4B - Prob. 17ACh. 7.4B - Prob. 18ACh. 7.4B - Prob. 19ACh. 7.4B - Prob. 20ACh. 7.4B - Prob. 21ACh. 7.4B - Prob. 22ACh. 7.4B - Prob. 23ACh. 7.4B - Prob. 24ACh. 7.4B - Prob. 25ACh. 7.4B - Prob. 26ACh. 7.4B - Prob. 27ACh. 7.4B - Prob. 28ACh. 7.4B - Prob. 29ACh. 7.4B - Prob. 30ACh. 7.4B - Complete the following compound interest chart....Ch. 7.4B - Prob. 32ACh. 7.4B - Prob. 33ACh. 7.4B - Prob. 34ACh. 7.4B - Prob. 35ACh. 7.4B - Prob. 36ACh. 7.4B - If a publishing company signed an agreement to...Ch. 7.4B - Prob. 38ACh. 7.4B - Prob. 39ACh. 7.CR - a. On the number line, find the decimals that...Ch. 7.CR - Write each of the following as a rational number...Ch. 7.CR - Prob. 3CRCh. 7.CR - A board is 442.4 cm long. How many shelves can be...Ch. 7.CR - Write each of the following as a decimal. a. 47 b....Ch. 7.CR - Prob. 6CRCh. 7.CR - Round each of the following number as specified....Ch. 7.CR - Rewrite each of the following in scientific...Ch. 7.CR - Prob. 9CRCh. 7.CR - Prob. 10CRCh. 7.CR - a. Find five decimals between 0.1 and 0.11 and...Ch. 7.CR - Answer each of the following questions. a.6 is...Ch. 7.CR - Prob. 13CRCh. 7.CR - Change each of the following percents to a...Ch. 7.CR - Prob. 15CRCh. 7.CR - Five computers in a shipment of 150 were found to...Ch. 7.CR - On a mathematics examination, a student missed 8...Ch. 7.CR - A used car costs 3450 at present. This is 60 of...Ch. 7.CR - Prob. 19CRCh. 7.CR - Jane bought a bicycle and sold it for 30 more than...Ch. 7.CR - Prob. 21CRCh. 7.CR - Prob. 22CRCh. 7.CR - Prob. 23CRCh. 7.CR - Chapter 7 Review A company was offered a 30,000...Ch. 7.CR - Prob. 25CRCh. 7.CR - Chapter 7 Review The crust of a certain pumpkin...Ch. 7 - In a set of base-ten blocks, let 1 flat represents...Ch. 7 - Prob. 2NTCh. 7 - Prob. 3NTCh. 7 - Prob. 4NTCh. 7 - Prob. 5NTCh. 7 - Prob. 6NT
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