Mathematics for Elementary Teachers with Activities (5th Edition)
5th Edition
ISBN: 9780134392790
Author: Beckmann, Sybilla
Publisher: PEARSON
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Textbook Question
Chapter 3.5, Problem 1P
- Write an Add To problem that fits naturally with the equation
- Write a Take From problem that fits naturally with the equation
Solve the problem, and explain why the solution makes sense.
Solve the problem, and explain why the solution makes sense.
(a)
Expert Solution
To determine
An ‘ADD TO’ problem for the given equation.
Solution to the framed problem.
Answer to Problem 1P
The temperature in Delhi was
Explanation of Solution
Given:
The given equation is:
Calculation:
An ADD TO problem can be framed as:
The temperature in Delhi was
The problem can be solved as
The diagram illustrating this can be drawn as
The temperature was 4 degrees below 0 degree. After the rise by 3 degrees, the temperature is -1 degree Celsius.
(b)
Expert Solution
To determine
An ‘TAKE FROM’ problem for the given equation.
Solution to the framed problem.
Answer to Problem 1P
The temperature in Delhi was
Explanation of Solution
Given:
The given equation is:
Calculation:
A TAKE FROM problem can be framed as:
The temperature in Delhi was
The problem can be solved as
The diagram illustrating this can be drawn as
The temperature was 4 degrees below 0 degree. After the fall by 3 degrees, the temperature is -7 degree Celsius.
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M = log
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Now consider equations of the form ×-a=v
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(f) Create an equation of this form that has 7 as a solution and
an extraneous solution. Give the extraneous solution.
(g)
What must be true about the value of bx + c to ensure that
there is a real number solution to the equation? Explain.
The equation ×+ 2 = √3x+10 is of the form ×+ a = √bx + c, where a, b, and
c are all positive integers and b > 1. Using this equation as a
model, create your own equation that has extraneous solutions.
(d) Using trial and error with numbers for a, b, and c, create an
equation of the form x + a = √bx + c, where a, b, and c are all
positive integers and b>1 such that 7 is a solution and there
is an extraneous solution. (Hint: Substitute 7 for x, and
choose a value for a. Then square both sides so you can
choose a, b, and c that will make the equation true.)
(e) Solve the equation you created in Part 2a.
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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