Math Methods

What fraction is equivalent to the decimal 0.625?

5/8

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.

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.

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

a^3 +3a^2b +3ab^2 +b^3

An area model that demonstrates how figures can have the same area composed of different shapes is:

tangrams.

he 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? a. All of them B. 45 minutes = 26.25 miles C. 1 hour, 15 minutes = 43.75 miles d. 15 minutes = 7.75 miles e. B & C

B & C

George built a rectangular fence in his backyard. The length of the fence measures 20 feet and the perimeter of the fence measures 50 feet. What is the width measurement of George's fence?

5 ft

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.

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

Multiply the numerator and denominator by the same number.

Carlos has a square garden in his backyard that has a length of 8 feet. His neighbor, Elizabeth, also has a garden, but her garden's perimeter is half the size of Carlos's.

The area of Carolos's garden is four times the area of Elizabeth's garden.

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.

A good task to use with students to assess their understanding of the use of a standard ruler is:

measuring with a "broken ruler."

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

-3

Which of the following is the largest number?

0.26

Dan and Stacy live on a farm where they are no longer allowed to let their cattle roam free. They need to add a fence around their land which has a shape like the figure below. How many feet of fence do they need to buy in order to fence in all of their land?

1,380 ft

Use this scenario to answer the following question: "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)

1.5/5 = x/6

Simplify the following: 2y + 9 + 8y + 7 a. 10y + 16 b. 26 c. 10y + 9 + 7 d. 26y

10y + 16

Find the value of the missing side in the following right triangle: 5| \13 _?

12

Students in Mr. Lewis's class took a survey to determine what their favorite school subjects were. The students showed their preferences by writhing their initial in a portion of the Venn diagram below: "According to the diagram, what is the total number of students who like both math and science?"

2

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

23

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.

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.

An input-output table shown: Which of the following statements regarding values in this chart is true? a. All of them b. A=B X2 + B c. B = A \ 3 d. A= B x #

All of them

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

All of them

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.

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.

Figure I below was cut along the dotted line and reassembled as shown in Figure II. Which statement about the area and perimeters of the figures is true?

The area of Figure I is equal to the area of Figure II, but the perimeter of Figure II is greater than the perimeter of Figure I

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

Tips, taxes, and discounts

Which of the following is a nonlinear function?

f(X) = x/5 -,/x

Students are shown this Input-Output table: This function is written as:

x + 5 = y

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? a. 60 b. 12 c. 18 d. 20

20

A square has a perimeter of 24 inches. What is the area of the square?

36 inches ^2

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

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

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? a. 48 b. 46 c. 47 d. 33

47

Use this scenario to answer the following question: "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 this scenario to answer the follow question: "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

Mr. Menendez has displayed the following coordinate plane in his sixth grade classroom: Which of the following describe the transformations needed in order to move from Triangle JKL to Triangle J'K'L'? a. A translation 1 unit down, followed by a translation 8 units to the right. b. A translation 1 unit up, followed by a translation 8 units to the left. c. A reflection across the y-axis, followed by a translation 1 units up. d. A reflection across the x-axis, followed by a translation 1 unit up.

A translation 1 unit up, followed by a translation 8 units to the left.

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

Least common denominator

Henry works in a bank approving loans. Four bank customers have applied for a loan today, and Henry has just researched their credit scores: Henry has his choice of offering an interest rate of 0.75% or 2.50% on loans. Using only their credit scores as guidance, which two customers should receive the 0.75% loan? a. Mr. Allen and Ms. Kash b. Mr. Weaver and Mrs. Butler c. Mr. Allen and Mrs. Butler d. Mr. Weaver and Ms. Kash

Mr. Weaver and Mrs. Butler

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.

Coordinate grids are often used in geometry to explore:

transformations.

Use this table of coordinate points to answer the question that follows. x | y -4 | -2 -2 | -1 2| 1 Which equation represents the values seen in the chart?

y = 1/2 x

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

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 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

An isosceles triangle is a polygon with two equal sides. What else does this imply?

It has two equal angles.

Mrs. Paul is a fifth grade math teacher. While reviewing a student's work, she finds this mistake: 3.19 x16.4 ________ 1276 19140 +31900 __________ 5231.6

Placing the decimal appropriately in the product.

Algebraic thinking includes several characteristics. Which of the following statements is not a part of algebraic thinking? a. The study of patterns, relations, and functions b. Generalized arithmetic, such as the properties for the operations c. Using manipulatives to reason about situations d. A way to use mathematics to solve real problems

Using manipulatives to reason about situations

Which of the following statements is not true? a. Variables mean many things and students need more opportunities to think about situations in which variable varies (versus the variable representing an unknown). b. The equal sign is difficult for students to understand partly because students often see it used as an indication to find the answer. c. Inequalities might be less difficult for students if they were more common in the curriculum and if connections to graphing were included more often. d. Variables are not appropriate for elementary-age students; a box is a more concrete representation.

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

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? a. 166.7% b. 25% c. 100.5% d. 187.6%

a. 166.7%

A function is shown on the graph below. a. y = x + 6 b. y = 6x - 6 c. y = x -6 d. y = -6x + 6

a. y = x + 6

Which is the following is a linear equation?

all of them

Angles are measured by:

using a smaller angle to fill or cover the spread of the rays.

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? a. $4.50 b. $5.50 c. $5.00 d. $4.75

$5.00

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.) a.2,285 b.2,300 c.2,286 d.2,287

2,286

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

2/8 , 5/20

The following four peoples are waiting in line at the post office: Marcie made a graph showing the relationship between the age and the height of the four people.

point b

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?

++++ ++++

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

1 9/40

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? 242.5 miles 248.5 miles 258.5 miles 252.5 miles

252.5 miles

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

3 X x/2 -0.8

Students are designing a class quilt using squares of fabric. Each day new squares are added to the design. The diagram below shows how the students are arranging the squares of fabric: If the pattern continues, what is the number of fabric squares needed for Friday's quilt?

32

A right triangle has a hypotenuse with a length of 53 inches. One leg of the triangle measures 28 inches. What is the length of the second leg of the triangle?

45 inches

Ms. Watson is preparing a recipe that requires 2¾ cups of whole-kernel corn. The nutrition label from the can of corn she will use is shown below. 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

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? a. 100 b. 36 c. 85 d. 60

60

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? a. 8 b. 7 c. 6.4 d. 5

7

Bill went to sleep at 9:57 P.M. and awoke the next morning at 6:28 A.M. How many hours and minutes did Bill sleep?

8 hours and 31 minutes

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

Address misconceptions.

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? a. Between $20 and $25 b. Between $5 and $10 c. Between $15 and $20 d. Between $10 and $15

Between $10 and $15

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 is not a common misconception or limited conception related to fractional parts?

Leaving answers as fractions rather than writing them as mixed numbers

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? a. Divide by 5 b. Multiply the total by 0.05 c. Multiply the total by 5 d. Divide by 0.05

Multiply the total by 0.05

Colleen's teacher has asked her to draw a quadrilateral with all sides congruent. Which of the following shapes could Colleen have drawn that would follow her teacher's directions?

Rhombus & Square

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 a. The distributive property of multiplication over addition b. The associative property of multiplication c. The commutative property of multiplication d. The identity property of multiplication

The distributive property of multiplication over addition

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 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

functions: a. are the same as equations. b. are patterns that represent a growing situation. c. describe a relationship between two variables and may be linear or not. d. are linear situations in which the independent and dependent variable have a one-to-one correspondence.

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.

Mixed numbers:

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

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.

What will come next in the following sequence:

d

Use this scenario to answer the follow question: "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 decimal 0.125 is equal to what fraction?

1/8

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 reasons best describes why arithmetic and algebra should be closely connected? a. Algebra can help students learn their basic facts because it helps students see groups of related facts. b. The earlier algebra is introduced, the less difficult it will be for students; thus, algebra examples for number, place value, and operations should be included. c. Place value and operations are generalized rules; a focus on algebraic thinking can help students make connections across problems and strengthen understanding. d. Place value uses the properties of the operations, which are based in algebra.

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

Which of the following is not important when teaching properties? a. Engaging students in justifying that two expressions are equivalent, based on applying the properties b. Illustrating how the properties can be used to solve problems efficiently c. Providing opportunities for students to name and match properties to examples d. Connecting the properties to generalizations in number, using concrete examples

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.

Mathematical models are useful in both real life and mathematics because: a. models such as equations, graphs, and tables can be used to analyze empirical situations, to understand them better, and to make predictions. b. examples are important in helping students generalize to more abstract concepts. The more problems they encounter, the more they understand the power of mathematics. c. visuals make mathematics more easily understood by a range of learners, particularly visual learners. d. creating a real-life model is more engaging and so builds stronger understanding.

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