Praxis Practice Test Math 7803-Elementary Education
Match each fraction with its equivalent decimal number. 20/100 2/10 20/10 200/100 2/100 Categories: 0.02 0.2 2
2/100 = 0.02 20/100 and 2/10 = 0.2 20/10 and 200/100 = 2
Mr. Kirk asked his students to compare 0.196 and 0.15. Four of his students correctly answered that 0.196 is greater than 0.15, but they gave different explanations when asked to describe their strategies to the class. Indicate whether each of the following student explanations provides evidence of a mathematically valid strategy for comparing decimal numbers. A. 0.196 is larger because there is one in the tenths, and then nine hundredths is more than five hundredths. And then I'm done. B. 0.196 is greater because in the thousandths place six is greater than five, and in the hundredths place nine is greater than one. C. 0.196 is bigger than 0.15 because if it is three numbers long, it will always be bigger than if it is two numbers long. D. 0.196 is more than 0.15 because nineteen hundredths is bigger than fifteen hundredths.
A. Provides Evidence B. Does NOT Provide Evidence C. Does NOT Provide Evidence D. Provides Evidence
Ayana's banana bread recipe uses 3 bananas to make 2 loaves of banana bread. Natalie's banana bread recipe uses 4 bananas to make 3 loaves of banana bread. Whose recipe results in a greater amount of banana in each loaf of banana bread? Mr. Ma asked his class to solve the word problem shown. Three students correctly answered that Ayana's recipe results in a greater amount of banana in each loaf, but they gave different explanations when describing their strategies to the class. Indicate whether each of the following student explanations provides evidence of a mathematically valid strategy for determining whose recipe results in a greater amount of banana in each loaf. A. In Ayana's recipe there are 3 bananas for 2 loaves, so there is a whole banana for each loaf and you split the last banana in half. In Natalie's recipe there is one banana for each loaf and the fourth banana is split in 3. So in Ayana's loaf there are 1 and a half bananas, and in Natalie's there are 1 and a third, and a half is more than a third. B. In Ayana's recipe the bananas are split between only 2 loaves, while in Natalie's recipe the bananas are split between 3 loaves. If I have to split a cookie, I would rather split it in two because I get more, so Ayana's loaves contain more bananas. C. Ayana makes only 2 loaves and Natalie makes 3 loaves. If they made the same number of loaves, like 6, then Ayana would use 9 bananas and Natalie would use 8. So Ayana's loaves have more because 9 is more than 8.
A. Provides Evidence B. Does NOT Provide Evidence C. Provides Evidence
Which of the following word problems can be represented by the equation 4×n+8=16? A) A set of 5 baskets holds a total of 16 apples. The first basket has 8 apples and the other baskets each hold an equal number of apples. How many apples are in each of the other baskets? B) There are 12 baskets, 8 of which are empty. There are 16 apples, with an equal number of apples in each of the other 4 baskets. How many apples are in each of the 4 baskets? C) There are 16 baskets, 8 of which are empty. Each of the other baskets contains 4 apples. How many apples are there in all? D) There are 8 baskets with 4 apples in each basket and 16 apples that are not in a basket. How many apples are there in all?
Option (A) is correct. If there are 5 baskets and one basket holds 8 apples, the rest of the apples are split evenly among the other 4 baskets. Therefore, to find the number of apples in each of the 4 baskets, the equation 4×n+8=16 can be set up, where n is the number of apples in each of the 4 baskets.
A rectangular message board in Aleyah's dormitory room has a length of 30 inches and a perimeter of 108 inches. A rectangular bulletin board in the hallway outside Aleyah's room is twice as long and twice as wide as the message board. Which of the following statements about the bulletin board is true? The bulletin board has a width of 48 inches. The bulletin board has a length of 96 inches. The area of the bulletin board is twice the area of the message board. The perimeter of the bulletin board is four times the perimeter of the message board.
Option (A) is correct. Since the message board has a length of 30 inches and a perimeter of 108 inches, the width of the message board can be found by solving the equation 2(30)+2w=108 for w. To solve the equation for w, subtract 60 from both sides of the equation and then divide both sides of the equation by 2 to find that w=24. This means that the length and width of the bulletin board are 60 inches and 48 inches, respectively, and it can be concluded that the area of the message board is 720 square inches, the perimeter of the bulletin board is 216 inches, and the area of the bulletin board is 2,880 square inches. Thus, the only true statement is that the bulletin board has a width of 48 inches.
Ms. Garrett has been working on verbal counting with her students. She wants them to be more aware of patterns in the way number names are typically constructed. Which of the following number names LEAST reflects the typical pattern in the way number names are constructed in the base ten system? Eleven Sixteen Twenty-five Ninety
Option (A) is correct. The number name "eleven" does not follow any pattern of number-name construction with reference to the tens and ones. Option (C) is not correct because "twenty-five" follows the most typical structure of how number names are constructed for whole numbers, since the number of tens in the number is referred to first, followed by the number of ones. Although the numbers in options (B) and (D) do not follow the most typical structure like "twenty-five" does, where the tens are called out specifically, the numbers in these options do follow a structure of the number of ones being named, followed by "teen," which refers to the ten in the number. Therefore, these numbers follow a pattern, unlike "eleven."
Mr. Walters asked his students to order 89, 708, 37, and 93 from least to greatest, and to be ready to explain the process they used to order the numbers. One student, Brianna, ordered the numbers correctly, and when Mr. Walters asked her to explain her process, she said, "The numbers 89, 37, and 93 are less than 100, so they are all less than 708, since that is greater than 100. Also, 37 is the least because it comes before 50 and the other two numbers are close to 100. Then 89 is less than 90, but 93 is greater than 90." Which of the following best describes the strategy on which Brianna's explanation is based? A counting strategy A benchmarking strategy An estimation strategy A place-value strategy
Option (B) is correct. Brianna first indicates that 708 is the greatest number because it is greater than 100, while 37, 89, and 93 are all less than 100. Next, Brianna indicates that 37 is the least number because it is less than 50, while 89 and 93 are greater than 50. Finally, Brianna recognizes that 89 is less than 93 because 89 is less than 90, while 93 is greater than 90. Thus, over the course of her explanation, Brianna used 100, then 50, and then 90 as points of reference for comparisons, which is exactly what benchmark numbers are—points of reference for comparison. Brianna did not count between any of the numbers, estimate the numbers, or use the place values in any of the numbers to make her comparisons, so the other options do not describe the strategy on which Brianna's explanation is based.
Ms. Roderick asked her lunch helper in her kindergarten class to get one paper plate for each student in the class. Which of the following counting tasks assesses the same mathematical counting work as this task? Having students line up according to the number of the day of the month in which they were born Showing students 10 pencils and asking them to get enough erasers for all the pencils Showing students a row of 12 buttons and asking them to make a pile of 8 buttons Asking students to count the number of triangles printed on the classroom rug
Option (B) is correct. Getting one paper plate for each student in the class assesses whether students can determine when the number of objects in one set is equal to the number of objects in another set, and the task described in option (B) involves a similar determination. The task in option (A) assesses whether students can compare and order numbers. The task in option (C) assesses whether students can count a subset of objects from a larger set. The task in option (D) assesses whether students can count the number of objects in a set.
Ms. Simeone is working with her first-grade students on writing two-digit numerals. She wants to use an activity to assess whether her students are attending to the left-to-right directionality of the number system. Which of the following activities is best aligned with Ms. Simeone's purpose? Asking students to read the numbers 20 through 29 Asking students to represent the numbers 35 and 53 using base-ten blocks Asking students how many tens and how many ones are in the number 33 Showing students 23 cubes and 32 cubes and asking them which quantity is greater
Option (B) is correct. Having the students represent 35 and 53 using base-ten blocks will help Ms. Simeone assess whether students know which place is the tens place and which place is the ones place or whether students have reversed the ones place and the tens place, thinking the ones place is on the left and the tens place is on the right. Representing the numbers provides more information about students' understanding of place value than just reading numbers.
In word problems that have a multiplicative comparison problem structure, two different sets are compared, and one of the sets consists of multiple copies of the other set. Which of the following best illustrates a word problem that has a multiplicative comparison problem structure? There are 4 shelves in Joaquin's bookcase, and there are 28 books on each shelf. How many books are in Joaquin's bookcase? Marcus drives 3 times as many miles to get to work as Hannah does. Hannah drives 16 miles to get to work. How many miles does Marcus drive to get to work? A football field is 360 feet long and 160 feet wide. A soccer field is 300 feet long and 150 feet wide. The area of the football field is how many square feet greater than the area of the soccer field? An ice cream parlor sells 29 different flavors of ice cream and 4 different types of cones. How many different combinations consisting of an ice cream flavor and a type of cone are available at the ice cream parlor?
Option (B) is correct. In the problem in option (B), the two values being compared are the number of miles that Marcus drives to get to work and the number of miles that Hannah drives to get to work, and the number of miles that Marcus drives is 3 times the number of miles that Hannah drives. The problem in option (A) has an equal-groups problem structure, the problem in option (C) has a product-of-measures problem structure (since the product is a different type of unit from the factors in the problem), and the problem in option (D) has a combinations problem structure.
Answer the question below by clicking on the correct response. Question: The figure presents two congruent squares. Each square is divided into 4 equal sections. During a lesson in her second-grade class, Ms. Costa draws two squares of the same size, each representing the same whole. She then divides and shades the squares as represented in the figure. Her students consistently identify the area of each shaded region as one-fourth, but when they are asked if the areas are equal, some students say no. Which of the following statements most likely explains why the students see the areas as not being equal? The students think that the areas are not equal because the wholes are different sizes. The students think that the areas are not equal because the shaded regions are different shapes. The students have difficulty determining the size of geometric figures that include diagonal lines. The students have difficulty determining the part-to-whole relationship when working with visual models of fractions.
Option (B) is correct. One misconception that students often have when first beginning to work with area models of fractions is that the parts of the whole must be congruent for the areas of the parts to be equal, and this misconception explains the responses described in the question. The statement in option (A) is not correct because students at this level do not normally attend to the size of the whole when working with visual models of fractions, and the question states that Ms. Costa draws two squares of the same size. The statement in option (C) is not correct because students will make a similar error even when figures do not include diagonal lines. The statement in option (D) is not correct because it does not explain the situation presented, since the students consistently identify the area of each shaded region as one-fourth.
The scenario in a word problem states that an office supply store sells pens in packages of 12 and pencils in packages of 20. Which of the following questions about the scenario involves finding a common multiple of 12 and 20 ? A) In one package each of pens and pencils, what is the ratio of pens to pencils? B) How many packages of pens and how many packages of pencils are needed to have the same number of pens as pencils? C) If the store sells 4 packages each of pens and pencils, what is the total number of pens and pencils sold in the packages altogether? D) How many gift sets can be made from one package each of pens and pencils if there are the same number of pens in each set, the same number of pencils in each set, and all the pens and pencils are used?
Option (B) is correct. The least common multiple of 12 and 20 is 60, and 5 packages of pens and 3 packages of pencils are needed to have 60 of each writing utensil
Answer the question below by clicking on the correct response. Question: 1/3=3/9=6/18 1/4=4/16=3/12 Ms. White's students are working on generating equivalent fractions like the ones shown. She asks her students to write a set of instructions for how to generate equivalent fractions. One student writes, "You have to multiply the bottom and the top of the fraction by a number." Which of the following revisions most improves the student statement in terms of validity and generalizability? You have to multiply both denominator and numerator by the same number. You have to multiply both denominator and numerator by the same nonzero number. You have to multiply both denominator and numerator by the same whole number. You have to multiply both denominator and numerator by the same positive whole number.
Option (B) is correct. To generate an equivalent fraction, it is not necessary to multiply the numerator and denominator of the original fraction by a whole number, but it is necessary to multiply the numerator and the denominator by the same number and for that number to be a number other than zero. The revision in option (B) is the only sentence that restates the student conjecture, makes it valid, and generalizes it by including all fractions.
Which of the following fractions has a value between the values of the fractions 7/9 and 8/11? 1/2 2/3 3/4 4/5
Option (C) is correct.
Ms. Rodriguez is working with her kindergarten students to develop the skill of counting on. Which of the following tasks is best aligned with the goal of having students count on? A) The teacher gives each student a number book with a different number on each page. The students must count out and glue the same number of pictures to match the given number on each page. B) The teacher gives each student a 10-piece puzzle, disassembled with a single number written on each piece. The students must put the puzzle together with the numbers in order. C) The teacher gives each student a shuffled deck of 10 cards, each with a single number from 1 to 10. When the students draw a number card, they must count to 20, starting from the number on the card they drew. D)The teacher gives each student 8 blocks and a number cube, with the sides of the number cube numbered from 3 to 8. When the students roll the number cube, they must count out the same number of blocks as the number rolled and create a tower with that number of blocks.
Option (C) is correct. A student would begin with the number drawn and count on from that number until 20 is reached. For example, if the student draws a card with 15 on it, the student would count on from 15, saying, "15, 16, 17, 18, 19, 20." The other tasks described do not require students to count on.
One of Mr. Spilker's students, Vanessa, incorrectly answered the addition problem 457+138 as represented in the work shown. The figure presents the work the student did to add the numbers. The problem is written vertically. The work shows 457 + 138= 585. Mr. Spilker wants to give Vanessa another problem to check whether she misunderstands the standard addition algorithm or whether she simply made a careless error. Which of the following problems will be most useful for Mr. Spilker's purpose? 784+214 555+134 394+182 871+225
Option (C) is correct. In the work shown, after adding the ones and recording the 5 in the ones place, Vanessa did not record that the additional 10 ones were 1 ten, nor did she add the regrouped ten in the tens place. The problem in option (C) will be most useful for Mr. Spilker's purpose because it requires regrouping from the tens place to the hundreds place. The problems in options (A) and (B) do not require any regrouping, and Vanessa may just record 10 hundreds without thinking about regrouping when answering the problem in option (D).
Ms. Cook's class was discussing strategies to compare two fractions. One student, Levi, said, "When the top numbers are the same, you know that the one with the smaller number on bottom is bigger." Ms. Cook asked her students to explain why Levi's claim is true. After giving the class time to work, she asked another student, Maria, to present her explanation. Maria said, "It's just like Levi said. For 1/4 and 1/2, they both have ones on top, and 4 is greater than 2, so 1/4 is less, just like 1/4 of a pizza is less than 1/2 of a pizza." Which of the following statements best characterizes Maria's explanation? It clearly explains why Levi's claim is true. It clearly explains why the converse of Levi's claim is true, but it does not explain why his actual claim is true. It shows that Levi's claim is true for one example, but it does not establish why his claim is true in general. It assumes that Levi's claim is true, but it does not establish why his claim is true in general.
Option (C) is correct. Maria explains why 1/4 is less than 1/2, which provides one example for which Levi's claim is true, but it does not explain why whenever two fractions have the same numerator, the fraction with the smaller denominator will always be the greater fraction. A general explanation would point out that when a whole is broken into a greater number of pieces of equal size, then each of those pieces will be smaller than the pieces when the whole is broken into fewer pieces of equal size.
Ms. Duchamp asked her students to write explanations of how they found the answer to the problem 24×15 One student, Sergio, wrote, "I did 24 times 10 and got 240, then I did 24 times 5 and that's the same as 12 times 10 or 120, and then I put together 240 and 120 and got 360." Ms. Duchamp noticed that four other students found the same answer to the problem but explained their strategies differently. Which of the following student explanations uses reasoning that is most mathematically similar to Sergio's reasoning? A. Since 24 is the same as 12 times 2 and 15 is the same as 5 times 3, I did 12 times 5 and got 60, then I did 2 times 3 and got 6, and 60 times 6 is 360. B. To get 24 times 5, I did 20 times 5 and 4 times 5, which is 120 altogether, and then I needed 3 of that, and 120 times 3 is 360. C. 15 times 20 is the same as 30 times 10, and that gave me 300, and then I did 15 times 4 to get 60, and 300 plus 60 is 360. D. 24 divided by 2 is 12, and 15 times 2 is 30, so 24 times 15 is the same as 12 times 30, and so my answer is 360.
Option (C) is correct. Sergio first uses the distributive property to think of 24×15 as 24×(10+5), or 24×10+24×5. After Sergio multiplies 24 and 10 to get 240, he multiplies 24 and 5 using a doubling and halving strategy. Since 24=12×2, 24×5=(12×2)×5=12×(2×5)=12×10, so the product of 24 and 5 is equal to the product of 12 and 10, which is 120. The explanation in option (C) also uses the distributive property but in a different way. This student thinks of 24×15 as (20+4)×15, or 20×15+4×15. After the student multiplies 20 and 15, the student uses the doubling and halving strategy to find the product of 4 and 15. Therefore, this explanation uses reasoning that is most mathematically similar to Sergio's reasoning. The explanations in options (A) and (B) do not use the doubling and halving strategy, and the explanation in option (D) does not use the distributive property.
Answer the question below by clicking on the correct response. Question: Ms. Shaughnessy is working with her class on measuring area using nonstandard units. While the students are finding the area of the surface of their desks using rectangular note cards, one student says, "I can just measure the long side of the desk with the long side of the card, then measure the short side of the desk with the short side of the card, and multiply them." Which of the following best describes the validity of the student's strategy? The strategy is not valid because the same unit must be used to measure each side of the desk. The strategy is valid only if the note cards are squares. The strategy is valid and the unit of measurement is square units. The strategy is valid and the unit of measurement is note cards.
Option (D) is correct. Area can be measured using any two-dimensional unit that covers a surface, but the label of the area must reflect that unit. In this case the student has used note cards as the unit to measure the area of the desk. When using square units, one counts how many times the side of the square unit fits on each side of the rectangle whose area is to be measured. When using a unit that is not a square, like a note card, it is important to keep the orientation of the unit constant to cover the area without overlapping. This method results in one dimension of the rectangle being measured with the long side of the note card and the other dimension of the rectangle being measured with the short side of the note card.
Ms. Howe's students are learning how to use models to help them answer word problems. The models use bars to represent the relationships between the given quantities and the unknown quantity. In each model, the unknown quantity is represented with a question mark. The quantities given in the word problem occupy the other boxes. Ms. Howe shows the following model to her students. Which of the following word problems best corresponds to the model shown? A. Max had $24. He gave $18 to Olivia and the rest to Sarah. How much money did Max give to Sarah? B. Max had $24. He gave 1/3 of his money to Sarah and the rest to Olivia. How much money did Max give to Olivia? C. Max gave $24 to his friend Sarah and $18 to his friend Olivia. What is the total amount of money Max gave to his two friends? D. Max has $24 in his piggy bank, which is 2/3 of the amount of money that Max has altogether. How much money does Max have altogether?
Option (D) is correct. In the model shown, the total amount is the unknown quantity, and the quantity of $24 given in the problem is 2/3 of the total quantity. Since the problem in (D) asks for the total amount of money that Max has and states that $24 is 2/3 of the total, it is the problem that best corresponds to the model.
Ms. Carter shows one of her students, Brandon, a set of cubes. She tells Brandon that there are 13 cubes in the set and asks him to take 1 cube away from the set. Ms. Carter then asks Brandon, "How many cubes do you think are in the set now?" Brandon quickly answers, "Twelve." Brandon has demonstrated evidence of understanding which of the following mathematical ideas or skills? A. Using numerals to describe quantities B. Counting with one-to-one correspondence C. Recognizing a small quantity without counting D. Knowing that each previous number name refers to a quantity which is one less
Option (D) is correct. In the scenario, Ms. Carter shows Brandon a set of cubes, explicitly tells him how many cubes are in the set, and asks him to take one cube away from the set. This process allows Ms. Carter to ensure that Brandon knows that there is now one less cube in the set. When Ms. Carter asks how many cubes are in the set after one cube is removed, Brandon readily states, without counting the cubes, that there are 12 cubes. This provides evidence that Brandon knows that 12 is the number name that precedes 13 and that 12 refers to a quantity that is one less than 13; it can also be assumed that Brandon has the same understanding for other whole numbers. Brandon did not use written numerals in the scenario, so option (A) is not correct. Also, Brandon is told how many cubes are in the set, so there is no evidence that he can count with one-to-one correspondence or recognize a small quantity without counting, so options (B) and (C) are not correct.
A student incorrectly answered the problem 305.74×100 . The student's answer is represented in the work shown. 305.74 X 100 = 305.7400 Which of the following student work samples shows incorrect work that is most similar to the preceding work? 246.7 X 100= 2,467 13.05 X 100= 13,500 46.13 X 10 = 460.130 94.03 X 10 = 94.030
Option (D) is correct. In the work shown, when the student multiplied 305.74 by 100, the student rewrote 305.74 and added two zeros at the end. The work sample that is most similar to this is the sample in option (D), since this sample shows that when the student multiplied 94.03 by 10, the student rewrote 94.03 and added one zero at the end.
Answer the question below by clicking on the correct response. Question: Last Tuesday, a group of 5 researchers in a laboratory recorded observations during a 24-hour period. The day was broken into 5 nonoverlapping shifts of equal length, and each researcher recorded observations during one of the shifts. Which of the following best represents the amount of time each researcher spent recording observations last Tuesday? A.) Between 4 and 4 1/4 hours B.) Between 4 1/4 and 4 1/2 hours C.) Between 4 1/2 and 4 3/4 hours D.) Between 4 3/4 and 5 hours
Option (D) is correct. Since the 24-hour period is broken into 5 overlapping shifts of equal length, the problem is solved by finding 24/5
Ms. Fisher's students are working on identifying like terms in algebraic expressions. When Ms. Fisher asks them how they know when terms are like terms, one student, Coleman, says, "Like terms have to have the same variable in them." Ms. Fisher wants to use a pair of terms to show Coleman that his description of like terms is incomplete and needs to be refined. Which of the following pairs of terms is best for Ms. Fisher to use for this purpose? 9d and 5 8xy and xy 5a^4 and 2a^4 4h^2 and 7h^3
Option (D) is correct. The best pair of terms for Ms. Fisher's purpose should contain the same variable but should not be like terms. The only option that shows such a pair is option (D), in which the variables are the same but the terms are not like terms because they have different exponents.
A grocery store sells both green grapes and red grapes for a regular price of $2.89 per pound. Nelson buys 1.5 pounds of green grapes and 2.25 pounds of red grapes at the store on a day when the regular price is reduced by $0.75 per pound. Which of the following expressions represents the amount, in dollars, that Nelson will pay for the grapes? 1.5+2.25×2.89−0.75 (1.5+2.25)×2.89−0.75 1.5+2.25×(2.89−0.75) (1.5+2.25)×(2.89−0.75)
Option (D) is correct. To find the amount, in dollars, that Nelson will pay for the grapes, the total weight of the grapes, in pounds, needs to be multiplied by the reduced price of the grapes, in dollars. The total weight of the grapes, in pounds, is 1.5+2.25, and the reduced price of the grapes, in dollars, is 2.89−0.75, so the amount, in dollars, that Nelson will pay for the grapes is (1.5+2.25)×(2.89−0.75). The parentheses must be included in the expression as shown so that the total weight of the grapes will be multiplied by the reduced price of the grapes.
Mr. Varela asked his students to define a square in terms of other two-dimensional geometric figures. Which two of the following student definitions precisely define a square? A) A square is a rectangle that has 4 sides of equal length. B) A square is a parallelogram that has 4 angles of equal measure. C) A square is a parallelogram that has 4 sides of equal length. D) A square is a rhombus that is also a rectangle. E) A square is a rectangle that is not a rhombus.
Options (A) and (D) are correct. A square is a quadrilateral with 4 sides of equal length and 4 angles of equal measure, whereas a rectangle is a quadrilateral with 4 angles of equal measure, a rhombus is a quadrilateral with 4 sides of equal length, and a parallelogram is a quadrilateral where opposite sides are parallel. Therefore, a rectangle that has 4 sides of equal length is a square, and a rhombus that is also a rectangle is a square, so options (A) and (D) are both precise definitions of a square. Option (B) describes a rectangle that is not necessarily a square, option (C) describes a rhombus that is not necessarily a square, and option (E) describes a rectangle that is not a square.
Which three of the following word problems can be represented by a division equation that has an unknown quotient? A.) Ms. Bronson works the same number of hours each day. After 8 days of work, she had worked 32 hours. How many hours does Ms. Bronson work each day? B.) Mr. Kanagaki put tape around 6 windows before painting a room. He used 7 feet of tape for each window. How many feet of tape did he use? C.) Micah used the same number of sheets of paper in each of 5 notebooks. He used 45 sheets of paper in all. How many sheets of paper did Micah use in each notebook? D.) Each shelf in a school supply store has 8 packs of markers on it. Each pack has 12 markers in it. How many markers are on each shelf in the store? E.) Trina gave each of 7 friends an equal number of beads to use to make a bracelet. She gave the friends a total of 63 beads. How many beads did she give to each friend?
Options (A), (C), and (E) are correct.
Click on your choices. Question: Mr. French's students are working on finding numbers less than 100 that are multiples of given one-digit numbers. When Mr. French asks them how they know when a number is a multiple of 6, one student, Crystal, says, "Even numbers are multiples of 6!" Mr. French wants to use two numbers to show Crystal that her description of multiples of 6 is incomplete and needs to be refined. Which of the following numbers are best for Mr. French to use for this purpose? Select two numbers. 15 16 20 24 27 30
Options (B) and (C) are correct. The best numbers for Mr. French's purpose are even numbers that are not multiples of 6, and 16 and 20 are both even numbers, but they are not multiples of 6. Options (A) and (E) are incorrect because 15 and 27 are not even numbers, and options (D) and (F) are incorrect because 24 and 30 are both multiples of 6.
Mr. Benner places a row of 5 cubes on a student's desk and asks the student, Chanel, how many cubes are on the desk. As Chanel points at the cubes one by one from left to right, she counts, saying, "One, two, three, four, five." Then she says, "There are five cubes!" Mr. Benner then asks Chanel to pick up the third cube in the row. As Chanel points at three cubes one by one from left to right, she counts, saying, "One, two, three." She stops, then picks up the three cubes, and gives them to Mr. Benner. Chanel has demonstrated evidence of understanding which two of the following mathematical ideas or skills? A. Using numerals to describe quantities B. Recognizing a small quantity by sight C. Counting out a particular quantity from a larger set D. Understanding that the last word count indicates the amount of objects in the set E. Understanding that ordinal numbers refer to the position of an object in an ordered set
Options (C) and (D) are correct. Chanel first counts the cubes one by one and then she states that there are 5 cubes.
Which two of the following inequalities are true? A) 0.56>0.605 B) 0.065>0.56 C) 0.56>0.506 D) 0.605<0.056 E) 0.506<0.65 F) 0.65<0.605
Options (C) and (E) are correct. To compare these decimal numbers, first compare the digits in the tenths place—the decimal number with the greater digit in the tenths place will be the greater number. If the digits in the tenths place are the same, compare the digits in the hundredths place to determine which decimal number is greater. This process can be continued as needed.
A chef at a restaurant uses 1/5 liter of lemon juice and 3/10 liter of teriyaki sauce to make a marinade for 2 kilograms of salmon. How many liters of marinade does the chef use per kilogram of salmon? Give your answer as a fraction.
The correct answer is 1/4. This means that the chef uses 1/2÷2=1/4 liter of marinade per kilogram of salmon.
Joshua walks the length of each of three trails on a hike. The first trail is 3.6 kilometers long. The second trail is 3.7 kilometers long. The third trail is 600 meters shorter than the sum of the lengths of the first two trails. Joshua walks at an average speed of 3 kilometers per hour over the course of the entire hike. How many minutes does it take Joshua to complete his hike?
The correct answer is 280 minutes. Since 600 meters is equivalent to 0.6 kilometers, the third trail is 3.6+3.7−0.6=6.7 kilometers long. Therefore, Joshua walked a total distance of 3.6+3.7+6.7=14 kilometers on his hike. Since Joshua walks at an average speed of 3 kilometers per hour and there are 60 minutes in an hour, the proportion 3 kilometers/60 minutes=14 kilometers/x minutes can be used to find how many minutes it takes Joshua to complete his hike. Based on the proportion, 3x=(14)(60), and since (14)(60)=840, x=8403=280, which means that it takes Joshua 280 minutes to complete his hike.
