Mathematics For Elementary Teachers With Activities
5th Edition
ISBN: 9780134423401
Author: Sybilla Beckmann
Publisher: PEARSON
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Chapter 1.2, Problem 12P
Using-1, -2, and -1.68 as examples, describe in your own words where negative numbers are located on a number line, based on the locations of 0 and 1.
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Chapter 1 Solutions
Mathematics For Elementary Teachers With Activities
Ch. 1.1 - In your own words, discuss the connection between...Ch. 1.1 - If you give a child in kindergarten or first grade...Ch. 1.1 - For each of the following collections of small...Ch. 1.1 - In your own words, describe how you can use...Ch. 1.1 - In your own words, discuss the beginning ideas of...Ch. 1.1 - Children sometimes mistakenly read the number 1001...Ch. 1.1 - Explain why the bagged and loose toothpicks...Ch. 1.1 - Describe key features of the base-ten system....Ch. 1.1 - Draw number lines like the ones in Figure1.15 Plot...Ch. 1.1 - The students in Ms. Caven’s class have a large...
Ch. 1.2 - Suppose you want to show how the structure of the...Ch. 1.2 - Make math drawings of small bundled objects to...Ch. 1.2 - Describe and make drawings showing how to...Ch. 1.2 - Jerome says that the unlabeled tick mark on the...Ch. 1.2 - Students are sometimes uncertain about which zeros...Ch. 1.2 - Draw a number line on which the tick marks are...Ch. 1.2 - Draw a number line on which the long tick marks...Ch. 1.2 - Use a number line like the one in Figure 1.41 for...Ch. 1.2 - Cierral plots the decimal number 7.001 in the...Ch. 1.2 - Juan plots the decimal number 9.999 in the...Ch. 1.2 - For each number line in Figure 1.44 (a)-(d), draw...Ch. 1.2 - Using-1, -2, and -1.68 as examples, describe in...Ch. 1.2 - Students sometimes get confused about the...Ch. 1.2 - Draw a number line like the one in Figure 1.41 for...Ch. 1.2 - Explain why it is the case that whenever N is a...Ch. 1.3 - Explain in your own words why we compare numbers...Ch. 1.3 - Make a math drawing that shows bundled objects...Ch. 1.3 - Explain how to show which of 1.1 and 0.999 is...Ch. 1.3 - Some students have difficulty comparing decimals...Ch. 1.3 - Mary is labeling tick marks on a number line....Ch. 1.3 - Mark says that 0.178 is greater than 0.25. Why...Ch. 1.3 - Find a number between 3.24 and 3.241, if there is...Ch. 1.3 - Is there more than one decimal between 8.45 and...Ch. 1.3 - Find a number between 3.8 and 3.9, and plot all...Ch. 1.3 - For each of the following pairs of numbers, find a...Ch. 1.3 - Explain in two different ways why -8 < -5.Ch. 1.3 - Explain in two different ways why 3.251.4.Ch. 1.3 - Some students confuse decimals and negative...Ch. 1.3 - For each of the following pairs of numbers, find a...Ch. 1.3 - Describe an infinite list of decimals, all of...Ch. 1.3 - The smallest integer that is greater than 2 is 3....Ch. 1.3 - On the number line in Figure 1.55, assume that A...Ch. 1.3 - On the number line in Figure 1.55, assume that -A...Ch. 1.4 - Round 2.1349 to the nearest hundredth. Explain in...Ch. 1.4 - Round 27,003 to the nearest hundred. Explain in...Ch. 1.4 - Round 9995.2 to the nearest ten. Explain in your...Ch. 1.4 - Adam has made up his own method of rounding....Ch. 1.4 - The label on a snack food package says that one...Ch. 1.4 - The weight of an object is reported as 12,000...Ch. 1.4 - In a report, a population is given as 2700. Should...
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- Let {Yt} be an AR(2) process of the special form Yt = φ2Yt − 2 + et. Use first principles to find the range of values of φ2 for which the process is stationary.arrow_forwardDescribe the important characteristics of the autocorrelation function for the following models: (a) MA(1), (b) MA(2), (c) AR(1), (d) AR(2), and (e) ARMA(1,1).arrow_forwarda) prove that if (x) is increasing then (x~) is bounded below and prove if (is decrasing then (xn) is bounded above- 6) If Xn is bounded and monotone then (Xa) is Convergent. In particular. i) if (xn) is bounded above and incrasing then lim xn = sups xn: ne№3 n700 ii) if (X) is bounded below and decrasing then I'm Xn = inf\x₂,neN} 4500 143arrow_forward
- 5. Consider the following vectors 0.1 3.2 -0-0-0 = 5.4 6.0 = z= 3 0.1 For each of exercises a-e, either compute the desired quantity by hand with work shown or explain why the desired quantity is not defined. (a) 10x (b) 10-27 (c) J+Z (d) (x, y) (e) (x, z)arrow_forward1) let X: N R be a sequence and let Y: N+R be the squence obtained from x by di scarding the first meN terms of x in other words Y(n) = x(m+h) then X converges to L If and only is y converges to L- 11) let Xn = cos(n) where nyo prove D2-1 that lim xn = 0 by def. h→00 ii) prove that for any irrational numbers ther exsist asquence of rational numbers (xn) converg to S.arrow_forwardConsider the graph/network plotted below. 1 6 5 3 Explicitly give (i.e., write down all of the entries) the adjacency matrix A of the graph.arrow_forward
- . Given the function f: XY (with X and Y as above) defined as f(2) = 2, f(4) = 1, ƒ(6)=3, ƒ(8) = 2, answer the following questions. Justify your answers. (a) [4 points] Is f injective? (b) [4 points] Is f surjective? (c) [2 points] Is f bijective?arrow_forward1. Let 15 -14 A = -10 9 13-12 -8 7 11 15 -14 13 -12 -6 and B = -10 9 -8 7 -6 5 -4 3 -2 E 5 -4 3 -2 1 Explicitly give the values of A2,3, A1,5, and B1,4- Is A a 5 x 3 matrix? Explain your answer. Are A and B (mathematically) equal? Explain your answer.arrow_forwardGiven the following set X = {2, 4, 6, 8} and Y = {1, 2, 3}, explicitly give (e.g., write down the sets with numerical entries) of the outputs of the following requested set operations: (a) [2 points] XUY (Union) (b) [2 points] XY (Intersection) (c) [3 points] X\Y (Difference) (d) [3 points] XAY (Symmetric Difference)arrow_forward
- 4.2 Product and Quotient Rules 1. 9(x)=125+1 y14+2 Use the product and/or quotient rule to find the derivative of each function. a. g(x)= b. y (2x-3)(x-1) c. y== 3x-4 √xarrow_forward4.2 Product and Quotient Rules 1. Use the product and/or quotient rule to find the derivative of each function. 2.5 a. g(x)=+1 y14+2 √x-1) b. y=(2x-3)(x-:arrow_forwardFor what values of k will the equation (k + 1)x² + 6kx + 2k² - x = 0 have: a) one root equal zero b) one root the reciprocal of the other c) roots numerically equal but of opposite signarrow_forward
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