Math Methods test 2

What is the value for x in the equation 3x - 5 = 7x + 7?

-3

Which of the following is the largest number? 0.26, 1/8, 0.078, 3/16

0.26

A garden store buys clay pots from a distributor for $15 each and then sells them for $40 each in the store. What is the profit of each pot as a percentage of the cost price paid to the distributor?

166.7%

What are two equivalent fractions for the fraction 1/4?

2/8, 5/20

Crystal needs to buy bread for her party. She knows that one loaf will feed 8 people, and there are 371 people coming to her party. How many loaves of bread does she need to buy?

47

What fraction is equivalent to the decimal 0.625?

5/8

Which of the following concepts do students need to have mastered before learning how to add fraction?

Least common denominator

Which of the following is not a way to illustrate equivalent fractions?

Multiply the numerator and denominator by the same number.

Which of the following is shown through research to be a common error or misconception when students are comparing or ordering decimals?

The decimal that is the shortest is the largest.

The benefits of using a rectangular area to represent multiplication of fractions include all of the following except which?

They are easy for students to draw.

The school bus drives at a constant rate of 35 miles per hour. Based on this rate, which of the following distances are correctly attributed to their time?

b. 45 minutes = 26.25 miles C. 1 hour, 15 minutes = 43.75 miles cross mulitply

Mathematical models are useful in both real life and mathematics because:

models such as equations, graphs, and tables can be used to analyze empirical situations, to understand them better, and to make predictions.

Which of the following is a good explanation for how to add fractions?

Add equal-sized parts—finding a common denominator can help to solve the problem.

Which of the following statements is not true?

Variables are not appropriate for elementary-age students; a box is a more concrete representation.

A good teaching option for developing a full understanding of computation with decimals is to focus on:

concrete models, drawings, place value knowledge, and estimation.

A student is practicing the addition of fractions by drawing fraction models to represent the problems. The student is currently solving the problem 1/4+1/3. Which fraction model should the student draw in order to represent the correct answer?

d. (it has 12 squares)

question 26 on quiz 8

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question 33 on quiz 8

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question 36 on quiz 8

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question 37 on quiz 8

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question 39 on quiz 8

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The decimal 0.125 is equal to what fraction?

1/8

Simplify the following: 2y + 9 + 8y + 7

10y + 16

Which of the following is important to do before students learn the formal algorithms?

Address misconceptions.

What is the correct expansion of (a+b)3 ?

a3 + 3a2b + 3ab2 + b3

Mr. Winter's fifth grade class is conducting a survey at their elementary school about favorite meals served in the cafeteria. When they finish collecting their data, Mr. Winter's class discovers the following facts. 10% of respondents like beef tacos best. 25% of respondents like chicken sandwiches best. 30% of respondents like enchiladas best. 35% of respondents like pizza best. If 18 respondents like enchiladas best, how many people did Mr. Winter's class interview in all?

60 use proportion on each one

Stacy went to the store to purchase a loaf of bread. She originally thought she had only $9.55 in nickels in her purse. She then discovered she had 10 extra nickels in her pocket. How many nickels did she originally have in her purse?

191 This problem provides unnecessary information to solve the problem. The fact that Stacy discovers 10 extra nickels in her pocket is inconsequential to the solution of the problem. Since a nickel is $0.05 and she had $9.55 in nickels in her purse, divide $9.55 by $0.05 to obtain the number of nickels she had in her purse.

Joe can place a maximum of 5 apples in a sack. If he needs to put 32 apples in sacks, how many sacks will he need?

7 To find out how many sacks are required, we can divide the amount of apples that Joe has by the number that fit in a sack. The result of the division is 6.4. So, it could be assumed that "5" and "8" are not correct from this. However, "6.4" is also incorrect because it is not physically possible to obtain 0.4 of a bag. Therefore, one should round up to 7.

Which of the following best describes how to teach multiplication involving a whole number and a fraction?

A "fraction times a whole number" and a "whole number times a fraction" are conceptually different, so they should be taught separately.

Which of the following strategies would you like students to decide to use when determining which of these fractions is greater than the other? 7/8 and 5/6

Compare how far from 1

The teachers in the following answer choices have identified three manipulatives to use when teaching fraction concepts. Each teacher intended to select one manipulative for each type of model. Which teacher succeeded in selecting one manipulative of each type?

Denise selected tangrams, color tiles, and number lines. Tangrams are an area model, color tiles are a set model (though they can also be used as an area model if they are used to cover a surface), and number lines are a length model.

Which of the following is not a common misconception or limited conception related to fractional parts?

Leaving answers as fractions rather than writing them as mixed numbers

Which of the following reasons best describes why arithmetic and algebra should be closely connected?

Place value and operations are generalized rules; a focus on algebraic thinking can help students make connections across problems and strengthen understanding.

If a/b = c/d, which of the following statements is true?

Substitute numbers to solve each answer choice, for example, a = 2, b = 3, c = 4, and d = 6, so, 2/3 = 4/6. Check each answer choice with these values to confirm that each is true.

All of the following are important considerations for teaching proportions except which?

Teach key words that can support students in effectively setting up proportions correctly.

Mrs. Paul is a fifth grade math teacher. While reviewing a student's work, she finds this mistake Using this mistake as a guideline for reteaching, on which skill should Mrs. Paul focus with this particular student?

Placing the decimal appropriately in the product.

According to your textbook, which of the following trios of real-world situations represent common uses for estimating percentages?

Tips, taxes, and discounts

In a two-week period (including weekends and holidays), Max spent $71. 47 on lunch. About how much money did Max spend on this daily lunch?

$5.00 There are many ways to approach this problem. One way is to realize that there are 14 days in a two-week period. Then, take the amount of money Max spent on lunch ($71.47) and divide this by 14. However, this may result in a messy solution when all we need is an approximation. Instead, try to find a number that, when multiplied by 14, gets you pretty close to the total Max spent. In this case, if $5 is selected, this will approximate an expense of $70 over the two-week period.

"Emily's softball team is celebrating the end of a winning season at a pizza restaurant. The restaurant charges $8.25 per pizza, and each topping costs $1.75." Emily's team decides to order 7 pizzas and a total of 15 toppings. How much will the team need to pay?

$84 The expression that shows how much money the team will need to pay for their party is 8.25p + 1.75t, where p=the number of pizzas Emily's team orders and t=the number of toppings Emily's team orders. Therefore, (8.25 × 7) + (1.75 × 15) = 84.

check question 5 on week 8 quiz

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question 16 from quiz 8

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question 23 on quiz 8

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question 24 on quiz 8

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question 25 on quiz 8

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question 9 quiz 8

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Annie earned $7.89 last week for doing chores. She has decided to split her money into 3 equal groups: one for spending, one for saving, and one for charitable giving. Annie calculates that each group will get $26.30. What mistake did Annie probably make in her calculation?

. Annie misplaced the decimal.

Mrs. Cameron plans to buy carpeting for her living room floor. The room is a rectangle measuring 14 feet by 20 feet. She wants no carpet seams on her floor even if that means that some carpeting will go to waste. The carpeting she wants comes in 16-foot-wide rolls. What is the minimum amount of carpeting that will have to be wasted if Mrs. Cameron insists upon her no-seams requirement?

40 ft^2 Since Mrs. Cameron does not want any seams in her carpet, the carpet must be 20 ft long (at least) to cover the entire space. Since the room is only 14 ft wide and the carpet is 16 ft wide, there will be 2 ft of wasted carpet for the entire length of the room (20 ft). Therefore, the amount of carpet that is wasted is 20 × 2 = 40 ft2 of carpet.

Mr. Robinson is organizing paint brushes for groups of art students. Mr. Robinson has a total of 618 paint brushes that he would like to share evenly among 14 student groups. How many paint brushes will each student group receive?

44 paint brushes Divide the total number of paint brushes by the number of student groups: 618 / 14 = 44.14. Since it is impossible to give each group 0.14 of a paint brush, each group will receive 44 paint brushes.

Ms. Watson wants to find the total number of calories contained in the recipe. What is the total number of calories in 2¾ cups of whole-kernel corn?

495 calories This question asks you to use mathematics skills in everyday living. Since there are 4 half cups in 2 cups (4 × 1/2 = 2), multiply 90 times 4 to get 360 calories. To find the number of calories in ¾ cup (¾ = ½ + ¼), add 90 (the calories in ½ cup) to 45 (the calories in ¼ cup) to get 135 calories. Adding 360 to 135 results in 495, the number of calories in 2¾ cups.

One of the following explanations is flawed because the name of the strategy and the description of the strategy do not match. Which one is flawed?

A double number line is created on a coordinate axis; points on the graph can be used to solve problems.

Last week, a grocery store sold eggs for $4.25 per dozen. This week, the same store is running a sale on eggs, now charging $5.00 for 2 dozen. David buys 5 dozen eggs this week. What is a reasonable amount David paid for the eggs?

Between $10 and $15 We can break 5 dozen down into 2 dozen + 2 dozen + 1 dozen, and since we know that 2 dozen equals $5.00, we can quickly see that the total price will be just over $5 + $5, or $10.

Of the following statements, which is the most central to effectively teaching ratios and proportions?

Engage students in a variety of strategies for solving proportions, including ratio tables, tape diagrams and graphs.

What is the value of the 4 in the number 36,179.405?

Four tenths

Base-ten models, the rational number wheel with 100 markings around the edge, and a 10- by-10 grid are all models for linking which three concepts together?

Fractions, decimals, and percents

Which of the following best describes the relationship between iterating and partitioning?

Partitioning is finding the parts of a whole, whereas iterating is counting the fractional parts.

Which of the following would be an appropriate manipulative with which to introduce fractions to a class of fourth graders?

Pattern Blocks

Which of the following is not important when teaching properties?

Providing opportunities for students to name and match properties to examples

Which of the following statements is true?

Ratios can be interpreted as composed units or as rates.

The manipulatives shown below can be used to demonstrate equivalency in fractions by completing which activity?

Use manipulatives A and B to show how individual, smaller parts can combine to make a whole, larger shape

Algebraic thinking includes several characteristics. Which of the following statements is not a part of algebraic thinking?

Using manipulatives to reason about situations

Functions:

describe a relationship between two variables and may be linear or not.

The role of the decimal point in a number is to:

designate the units position.

"Janice is using a recipe that calls for 3 cups of flour and 1.5 teaspoons of baking soda for every 1 batch of cookies." Janice would like to use 6 cups of flour for her next batch of cookies. What proportion will correctly solve for x, the number of teaspoons of baking soda she needs? (Choose two answers)

look at question 31 answer on week 8

check quiz 8 Question 1

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Solve the following problem. Express the answer as a mixed number. 1.6 - 3/8

1 9/40 This problem can be solved by converting the decimal to a fraction, or the fraction to a decimal and then subtracting. If the decimal is converted to a fraction, 1.6 becomes 1 6/10. In order to subtract, we should now get a common denominator. The lowest common denominator between 8 and 10 is 40. Therefore, the problem becomes 124/40 - 15/40 = 19/40.

If a can weights 14 oz., how many cans would you need to have a ton? (Round your answer to the nearest ones place and pick the best answer.)

2,286 An easy way to solve this problem is to use basic algebra. Knowing that there are 16 oz. in a pound and that there are 2,000 lbs. in a ton helps ease the difficulty of the problem. We want to find out the number of cans x it will take to obtain a ton. Therefore, we have Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '. . If both sides of the equation are multiplied by 16 and then we divide both sides by 14, we will obtain the approximate number of cans it will take to obtain one ton. Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '. . We see that many of the answers are close to this value. When we round this number, we will obtain 2,286.

Erica is working on her math homework. She has completed 12 problems, which represent 60% of her homework. How many total problems are on Erica's homework?

20

There are 16 more apples than orange in a basket of 62 apples and oranges. How many oranges are in a basket?

23 This problem is easily solved by using some basic algebraic reasoning. Since we are interested in determining the number of oranges that are in the basket, we will set this as a variable called b. The number of apples, a, and the number of oranges, b, sum to a total of 62. We also know that there are 16 more apples than oranges (a = b + 16). This gives b + (b + 16) = 2b + 16 = 62. Solving for b yields 23 oranges in the basket.

Which of the following teaching ideas for teaching partitioning is not consistent with the research findings?

Give students area models that are already partitioned and ask them to record the fractional amount shaded.

A taxi driver records the following trip details in one day of working: What was the taxi driver's total distance travelled in that one day?

252.5 miles First, convert each time given to hours. Then, calculate the distance traveled for each trip by creating proportions: Trip 1: 30 min = 1/2, or 0.5 hour; Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '. , x = 7.5 miles Trip 2: 75 min = 5/4, or 1.25 hour; Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '. , y = 50 miles Trip 3: 180 min = 3 hours; Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '. , z = 195 miles Now, add all distances traveled for each trip: 7.5 + 50 + 195 = 252.5 miles

"Janice is using a recipe that calls for 3 cups of flour and 1.5 teaspoons of baking soda for every 1 batch of cookies." Janice is baking a new batch of cookies and is planning to use 4 teaspoons of baking soda. How many cups of flour will she need to use?

8 Use cross products to solve: 1.5x = 3(4). x = 8

"Emily's softball team is celebrating the end of a winning season at a pizza restaurant. The restaurant charges $8.25 per pizza, and each topping costs $1.75." If p = the number of pizzas Emily's team orders and t = the number of toppings Emily's team orders, write an expression that shows how much money the team will need to pay for their party.

8.25p + 1.75t To find the total amount to pay, multiply both the number of pizzas ordered by the price of one pizza and the number of toppings ordered by the price of one topping. Add these two calculations together to find the total amount.

A student says, "My answer must be wrong—my answer got bigger." Which of the following responses will best help the student understand why the answer got bigger?

Ask the to explain the meaning of 8 ÷ 2, using cutting ribbon as a context, and then ask her to re-explain to you using 8 ÷ 1/2 , still using cutting ribbon as a context.

You and your family go out to dinner one night. At the end of the meal you receive a bill for the meal. The total bill, before tax, is $78.60. Assuming tax for the meal is 5%, what would you need to do first in order to find out the amount of tax you need to pay?

Multiply the total by 0.05 Since a percentage represents a part of 100, a tax of 5% is equal to a decimal value of 5/100 = 0.05. To find out how much tax is added to a bill of $78.60, we must multiply this total by the percentage of tax.

Which of the following options is not a recommendation for supporting student understanding of fractions?

Tell students that fractions are different from whole numbers, so the procedures are also different.

Which number property is demonstrated in the equation below? 15(4 + 3) = 15 × 4 + 15 × 3

The distributive property of multiplication over addition

Which of the following is an expression that represents the following statement: three times one-half of a number less eighty percent?

The statement "three times one-half of a number less eighty percent" implies that we do not know the actual number. Therefore, it must be represented by a variable. This fact eliminates "3×4/2 - 0.8". Knowing that 80% is equivalent to 80/100 or 0.8 eliminates "3×x/2 - 8/100" and "3×x/2 - 80". Therefore, the only choice that is left happens to be "3×x/2 - 0.8".

Mixed numbers:

can be changed into fractions or "improper" fractions and added