Mathematics for Elementary Teachers with Activities (5th Edition)
5th Edition
ISBN: 9780134392790
Author: Beckmann, Sybilla
Publisher: PEARSON
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Chapter 3.2, Problem 2P
Discuss the difference between the commutative property of addition and the associative property of addition.
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3. Construct a triangle in the Poincare plane with all sides equal to ln(2). (Hint: Use the fact that, the circle with center (0,a) and radius ln(r), r>1 in the Poincaré plane is equal to the point set { (x,y) : x^2+(y-1/2(r+1/r)a)^2=1/4(r-1/r)^2a^2 }
n. g. = neutral geometry
<ABC = angle ABC
\leq = less or equal than
sqrt{x} = square root of x
cLr = the line in the Poincaré plane defined by the equation (x-c)^2+y^2=r^2
1. Find the bisector of the angle <ABC in the Poincaré plane, where A=(0,5), B=(0,3) and C=(2,\sqrt{21})
Task:
2 Multivariable Calculus: Divergence Theorem
Refer to Question 42 in the provided document.
Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing
Chapter 3 Solutions
Mathematics for Elementary Teachers with Activities (5th Edition)
Ch. 3.1 - Write an Add To problem that fits naturally with...Ch. 3.1 - Write a Put Together/Take Apart, Both Addends...Ch. 3.1 - Write two versions of a Compare, Difference...Ch. 3.1 - Write two versions of a Compare, Bigger Unknown...Ch. 3.1 - Identify the type and subtype of each of the...Ch. 3.1 - Write an Add To, a Put Together/Take Apart, and a...Ch. 3.1 - Write a Take From, a Put Together/Take Apart, and...Ch. 3.1 - Write an Add To problem that can be solved by...Ch. 3.2 - Many teachers have a collection of small cubes...Ch. 3.2 - Discuss the difference between the commutative...
Ch. 3.2 - Figure 3.13 indicates a make-a-ten method for...Ch. 3.2 - Tomaslav has learned the following facts well: All...Ch. 3.2 - Give an example of an arithmetic problem that can...Ch. 3.2 - Give an example of an arithmetic problem that can...Ch. 3.2 - Describe a way to calculate 304-81 mentally, by...Ch. 3.2 - To calculate 15973, a student writes the following...Ch. 3.2 - To calculate 20188, a student writes the following...Ch. 3.2 - David and Ashley want to calculate 8.272.98 by...Ch. 3.2 - Tylishia says that she can calculate 324197 by...Ch. 3.2 - *Is there an associative property of subtracting?...Ch. 3.2 - *Is there a commutative property of subtraction?...Ch. 3.3 - Refer to Class Activity 3l, Adding and Subtracting...Ch. 3.3 - Describe how to use bundled things to explain...Ch. 3.3 - Describe how to use bundled things to explain...Ch. 3.3 - Allie solves the subtraction problem 3049 as...Ch. 3.3 - Zachary added 3.4+2.7 and got the answer 5.11. How...Ch. 3.3 - To solve 512146, a student writes the following:...Ch. 3.3 - Problem: Matteo is 4 feet 3 inches tall. Nico is 3...Ch. 3.3 - Problem: A container holds 2 quarts and 4 fluid...Ch. 3.3 - On a space shuttle mission, a certain experiment...Ch. 3.3 - We can write dates and times in a sort of expanded...Ch. 3.3 - Erin wants to figure out how much time elapsed...Ch. 3.3 - The standard subtraction algorithm described in...Ch. 3.3 - The standard subtraction algorithm described in...Ch. 3.3 - Here’s how Mo solved the subtraction problem...Ch. 3.3 - *After you solve part (b) of this problem, think...Ch. 3.4 - Using the example 27+37, explain why we add...Ch. 3.4 - Using the example 23+34, explain why we add...Ch. 3.4 - Using the example 356, describe the procedure for...Ch. 3.4 - Use two number lines, one labeled with (fractions...Ch. 3.4 - For each of the following decimals, show how to...Ch. 3.4 - Show how to calculate the sum 25+0.25 and show how...Ch. 3.4 - Show how to calculate 538+123 in two different...Ch. 3.4 - Show how to calculate 423+134 in two different...Ch. 3.4 - Find two different positive fractions whose sum is...Ch. 3.4 - John says 23+33=46 and uses the drawing in Figure...Ch. 3.4 - Denise says that 2312=13 and gives the reasoning...Ch. 3.4 - Arnold says that 223=45, and he uses the drawing...Ch. 3.4 - Can the following problems about voters be solved...Ch. 3.4 - Can the following problems about a bird feeder be...Ch. 3.4 - Can the following problems about Sarah’s bead...Ch. 3.4 - Can the following problem about Jim’s medicine be...Ch. 3.4 - a. Write and solve a word problem for 34+23. b....Ch. 3.4 - a. Write and solve a word problem for 212+113. b....Ch. 3.4 - a. Write and solve a Compare problem that can be...Ch. 3.4 - a. Write and solve a Put Together/Take Apart...Ch. 3.4 - For each square in Figure 3.33, determine the...Ch. 3.4 - For each square in Figure 3.34, determine the...Ch. 3.4 - Broad Street divides Popperville into an east side...Ch. 3.4 - Anklescratch County and Kneebend County are two...Ch. 3.4 - There are two elementary schools in the town of...Ch. 3.4 - Suppose you start with a fraction and you add 1 to...Ch. 3.4 - *In the first part of the season, the Bluejays...Ch. 3.5 - Write an Add To problem that fits naturally with...Ch. 3.5 - Write a Compare problem that fits with the...Ch. 3.5 - a. Show how to use a number line to calculate...Ch. 3.5 - For each of these four expressions,...
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- 2. Let l=2L\sqrt{5} and P=(1,2) in the Poincaré plane. Find the uniqe line l' through P such that l' is orthogonal to l.arrow_forward38 Topology: Brouwer Fixed-Point Theorem Task: Refer to Question 38 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharingarrow_forwardTask: o Functional Analysis: Spectral Theorem Refer to Question 40 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharingarrow_forward
- Task: Linear Algebra: Jordan Canonical Form Refer to Question 31 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharingarrow_forward35 Ordinary Differential Equations: Nonlinear Systems Task: Refer to Question 35 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharingarrow_forwardTask: 4 Abstract Algebra: Galois Theory Refer to Question 34 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharingarrow_forward
- 33 Vector Calculus: Green's Theorem Task: Refer to Question 33 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharingarrow_forward36 Probability: Central Limit Theorem Task: Refer to Question 36 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharingarrow_forwardLet ABCD be a Saccheri quadrilateral in a neutral geometry. Show that m(<ABC) \leq 90, and m(<ABC)=90 if and ony if the geometry is Euclediaarrow_forward
- Let A, B and C be three points in neutral geometry, lying on a circle with center D. If D is in the interior of the triangle ABC, then show that m(<ABC) \leq 1/2m(<ADC).arrow_forward6. Show that 1{AU B} = max{1{A}, I{B}} = I{A} + I{B} - I{A} I{B}; I{AB} = min{I{A}, I{B}} = I{A} I{B}; I{A A B} = I{A} + I{B}-21{A} I {B} = (I{A} - I{B})².arrow_forwardTheorem 3.5 Suppose that P and Q are probability measures defined on the same probability space (2, F), and that F is generated by a л-system A. If P(A) = Q(A) for all A = A, then P = Q, i.e., P(A) = Q(A) for all A = F.arrow_forward
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