Mathematics For Elementary Teachers With Activities
5th Edition
ISBN: 9780134423401
Author: Sybilla Beckmann
Publisher: PEARSON
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Textbook Question
Chapter 1.2, Problem 3P
Describe and make drawings showing how to represent 1.438 and 0.804 as lengths by using strips of paper in a way that fits with and shows the structure of the base-ten system.
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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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- 8. Perform Singular Value Decomposition (SVD) on a Matrix The SVD problem can be found on page 66. Decompose the given matrix into its singular values, left singular vectors, and right singular vectors. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2ql5dbpVLCS/view? usp=sharing] Show the complete process and verify the decomposition.arrow_forward6. Diagonalize the Matrix and Verify the Result Check page 64 of the document for the matrix diagonalization problem. Find the eigenvalues and eigenvectors to diagonalize the matrix, then verify the result. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Present all calculations systematically.arrow_forward9. Analyze the Fourier Transform of a Discontinuous Function Refer to page 67 for the Fourier transform problem. Compute the Fourier transform of the given piecewise function and discuss its properties. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Present all steps in detail.arrow_forward
- 4. Determine the Taylor Series Expansion About a Point Refer to page 62 for the Taylor series problem. Find the Taylor series expansion of the function about the specified point and include the radius of convergence. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Explain the methodology and verify the series.arrow_forward10. Prove the Orthogonality of Eigenfunctions Go to page 68 of the document for the eigenfunction problem. Prove the orthogonality of the eigenfunctions of a given Sturm-Liouville problem. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Provide a rigorous proof, including necessary integrals and conditions.arrow_forwardShow what to do on the graph visually please!arrow_forward
- 1. Perform a Change of Variables for the Given Integral Refer to page 59 in the shared document for the integral problem. Apply a specified change of variables to simplify the integral and evaluate it. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Clearly outline each step in the transformation and solution.arrow_forward9. Solve the System of Ordinary Differential Equations Using Matrix Methods Turn to page 57 for the system of ODES. Solve the system using matrix methods, such as eigenvalue decomposition or diagonalization. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxp RyejKEMg1t2q15dbpVLCS/view? usp=sharing] Show a clear, step-by-step solution.arrow_forwardA study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho PP2 H₁: P1 P2 OC. Ho H₁₂ H₁: P₁arrow_forward3. Solve the Differential Equation Using the Method of Characteristics Go to page 51 for a partial differential equation problem. Use the method of characteristics to solve the given equation. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxp RyejKEMg1t2ql5dbpVLCS/view? usp=sharing] Include all detailed steps in your solution.arrow_forward8. Determine the Fourier Series Expansion of the Function Refer to page 56 of the document for the Fourier series problem. Compute the Fourier series expansion of the given periodic function. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxp RyejKEMg1t2q15dbpVLCS/view? usp=sharing] Include all steps involved in the calculation.arrow_forwardFind the regression equation, letting the first variable be the predictor (x) variable. Using the listed lemon/crash data, where lemon imports are in metric tons and the fatality rates are per 100,000 people, find the best predicted crash fatality rate for a year in which there are 475 metric tons of lemon imports. Is the prediction worthwhile? Use a significance level of 0.05. Lemon Imports 235 264 356 Crash Fatality Rate 16 15.9 15.6 476 518 15.3 D 15.1 Find the equation of the regression line. + (Round the y-intercept to three decimal places as needed. Round the slope to four decimal places as needed.) The best predicted crash fatality rate for a year in which there are 475 metric tons of lemon imports is fatalities per 100,000 population. (Round to one decimal place as needed.) Is the prediction worthwhile? OA. Since there appears to be an outlier, the prediction is not appropriate. OB. Since all of the requirements for finding the equation of the regression line are met, the…arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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