Praxis 5006- Math & Science

Ms. Marley is working with her students on fraction addition. She wants to highlight how the commutative property of addition can be used to make landmark numbers when adding fractions. Which of the following expressions best highlights the use of the commutative property of addition for this purpose? a. 1/3+1/4+1/3 b. 1/3+1/4+2/3 c. 2/3+2/3+2/3 d. 3/5+2/5+2/3

b. 1/3+1/4+2/3

Consider the following incomplete statement about rounding a decimal number. When 390.396 is correctly rounded to the nearest BLANK________________________, the result is 390. Which of the following words make the preceding statement true when inserted into the blank in the statement? Select ALL that apply. a. hundredth b. tenth c. unit d. ten e. hundred

c. unit

value of x for 8x=136

x=17

An athlete runs 3 laps around an oval track. The distance the athlete runs in one lap is 400 meters. What is the total distance in kilometers?

1.2 kilometers. 1 kilometer - 1000 meters. 1200 x 1/1000=1.2

A chef uses 1/8 pound of shredded potatoes to make a serving of hashed brown potatoes. How many servings of hashed brown potatoes can the chef make with 5 pounds of shredded potatoes?

40 servings

A worker made stacks of either 6 chairs or 4 chairs with the chairs used during a band practice session. The worker put 3/4 of the chairs in stacks of 6 and the rest of the chairs in stacks of 4. The worker stacked 48 chairs in all. What was the total number of stacks of chairs that the worker made?

9 stacks

Students completed a simulation examining the erosion of soil by water and made several conclusions. Which of the following conclusions presents a misconception? Answer the question by selecting the correct response. A. "Erosion is always harmful to the environment." B. "Erosion involves the movement of material from one place to another." C. "The slope of the land affects erosion." D. "The amount of vegetation affects erosion."

A. "Erosion is always harmful to the environment."

Ms. Aguilar's class is learning about word problems involving division. Ms. Aguilar's goal is to assess whether her students recognize when the remainder forces the answer to the next-highest whole number when solving a word problem. Which of the following word problems is aligned with Ms. Aguilar's goal? Answer the question by selecting the correct response. A. 15 quarts of orange juice will be poured into a certain number of 2-quart containers. What is the least number of containers needed for the orange juice? B. 16 markers will be put into a certain number of bags. There will be 5 markers in each full bag. How many full bags of markers can be made? C. 3 children will share a chocolate bar equally. How much of the chocolate bar will each child get? D. 10 yards of fabric will be cut into 3 equal pieces. What is the length, in yards, of each piece?

A. 15 quarts of orange juice will be poured into a certain number of 2-quart containers. What is the least number of containers needed for the orange juice?

Ms. Egbuniwe wants her students to analyze information and provide evidence that individuals inherit traits from their parents but with variation between the individuals and their parents. She would like to provide them with resources that contain appropriate evidence for an upper-elementary student. Of the following, which TWO would provide the best evidence? Answer the question by selecting the correct responses. A. A picture of a female cocker spaniel with her litter of eight puppies, some black, some golden, some brown B. An illustration that shows the evolution of the modern horse over geologic time, including representations of older, extinct species in the horse family C. A picture of a large tree, surrounded by shoots sprouting from its roots D. A diagram that shows a corn plant with red kernels and a corn plant with yellow kernels that have produced offspring containing both red and yellow kernels

A. A picture of a female cocker spaniel with her litter of eight puppies, some black, some golden, some brown D. A diagram that shows a corn plant with red kernels and a corn plant with yellow kernels that have produced offspring containing both red and yellow kernels

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? Answer the question by selecting the correct responses. 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.

A. A square is a rectangle that has 4 sides of equal length. D. A square is a rhombus that is also a rectangle.

In an activity, Mr. Shope's students mix one cup of warm water, one tablespoon of borax powder, and one‑fourth cup of glue. After a period of thorough mixing, the students are left with a puttylike substance commonly referred to as slime. The students determine the properties of their substance and record their observations. Mr. Shope then asks the students to state whether they created a mixture or a new substance and to support their claim with evidence. Which of the following students made the best use of evidence to support his or her claim? Answer the question by selecting the correct response. A. Alyssa, who wrote that they had created a new substance because the slime has properties that are different from the properties of the three ingredients B. Max, who wrote that they had created a mixture because all three ingredients were mixed together C. DeShawn, who wrote that they had created both a mixture and a new substance because they mixed the ingredients together and that by mixing them in water, they could not get the ingredients back again D. Alessandro, who wrote that they had created a mixture because they could use filtration to separate the slime into the original ingredients

A. Alyssa, who wrote that they had created a new substance because the slime has properties that are different from the properties of the three ingredients

A teacher presents the students in a class with the characteristics of a certain animal. The teacher describes the animal as having a backbone and soft, moist skin covered by a slippery layer of mucus. The teacher also says that the animal goes through complete metamorphosis in its life cycle and that it lives part of its life in water and part of its life on land. The teacher then asks the students to classify the animal on the basis of its characteristics. Based on the information provided, the animal is best classified as a member of which of the following groups? Answer the question by selecting the correct response. A. Amphibians B. Insects C. Mammals D. Reptiles

A. Amphibians

Which of the following describes a student-created model that best represents the movement of matter through an ecosystem? Answer the question by selecting the correct response. A. An interconnected web showing the movement of matter between plants, animals, decomposers, and the environment B. A pyramid model showing the relative biomass at each trophic level C. A linear model showing the movement of matter from plants to animals to decomposers to the environment D. A concept map diagramming how a plant uses water, soil, and decomposed materials to grow and reproduce

A. An interconnected web showing the movement of matter between plants, animals, decomposers, and the environment

Which THREE of the following actions will result in reduced energy consumption? Answer the question by selecting the correct responses. A. Commuting to work using public transportation instead of driving alone in a gasoline-powered car B. Setting the thermostat for a home cooling system to a higher temperature in warm weather C. Leaving the engine of a gasoline-powered car running when the car will be parked for more than five minutes D. Preventing electrical appliances from drawing power in standby mode by unplugging them when they are not in use

A. Commuting to work using public transportation instead of driving alone in a gasoline-powered car B. Setting the thermostat for a home cooling system to a higher temperature in warm weather D. Preventing electrical appliances from drawing power in standby mode by unplugging them when they are not in use

In a classroom activity using images of the night sky, a teacher helps the students observe that the positions of stars seen in the summer at 11 P.M. are different than those seen in the winter at the same time. Which of the following statements best helps explain the observation? Answer the question by selecting the correct response. A. Earth revolves around the Sun. B. The Moon revolves around Earth. C. Constellations are moving away from Earth. D. Constellations revolve around Earth.

A. Earth Revolves around the Sun.

Students in a classroom worked with a partner to solve the following problem. One-fourth of Anne's hot chocolate is made of milk. What is the amount of milk in 8 cups of Anne's hot chocolate? Devon explained how he found the answer to the problem, saying, "If one fourth14 is milk, it's like the hot chocolate is 4 cups and 1 of them is the milk. Then if you double the hot chocolate, you have to double the milk, so in 8 cups there are 2 cups of milk." Devon's partner, Milena, represented Devon's strategy using cubes as represented in the following figure. Which of the following statements best characterizes how Milena's work represents Devon's strategy? Answer the question by selecting the correct response. A. Milena's work accurately represents Devon's strategy because it shows 1/4 of 4 and how that result was doubled. B. Milena's work accurately represents Devon's strategy, but an area model for multiplication would better represent the different units of measure involved in the problem. C. Milena's work does not accurately represent Devon's strategy because unit cubes cannot be used to represent parts of a whole. D. Milena's work does not accurately represent Devon's strategy because Devon's strategy used a different whole than the whole Milena used in her work.

A. Milena's work accurately represents Devon's strategy because it shows 1/4 of 4 and how that result was doubled.

During a lesson on physical and chemical changes, a teacher asks the students to come up with examples of changes in matter that can be observed in everyday life. Which of the following is an example of a chemical change? Answer the question by selecting the correct response. A. The cooking of an egg B. The mixing of salt and pepper C. The breaking in half of a pencil D. The freezing of water in a plastic tray

A. The cooking of an egg

Ms. Stewart asked her students to find the quotient 5/9÷5/7. One student's answer is represented in the following work. 5/9÷5/7=35/63÷45/63=35/45 Which of the following statements is true of the student's method? Answer the question by selecting the correct response. A. The method is valid for dividing any two fractions. B. The method is valid for dividing fractions only when the quotient is less than one. C. The method is valid for dividing fractions only when the fractions in the original problem have the same numerator. D. The method is not valid for dividing fractions because division of fractions requires multiplying the first fraction by the reciprocal of the second fraction.

A. The method is valid for dividing any two fractions.

A student is asked to compare three pairs of decimal numbers. The student correctly states that 0.59 is less than 0.721. The student correctly states that 0.96 is greater than 0.008. The student incorrectly states that 0.7 is less than 0.021. Which of the following misconceptions most likely explains the student's answers? Answer the question by selecting the correct response. A. The student is comparing decimals as if they are whole numbers. B. The student is assuming the longer decimal will always be the greater decimal. C. The student thinks that the decimal with more zeros will always be the greater decimal. D. The student thinks that the decimal with the larger digit in the rightmost place will always be the greater decimal.

A. The student is comparing decimals as if they are whole numbers.

Students are studying various aspects of magnetism. Which of the following questions should upper-elementary students be able to answer experimentally with classroom resources? Answer the question by selecting the correct response. A. What would cause a compass to not point to the north? B. Why do all magnets have a north and south pole? C. Is navigation using a compass more accurate than using the Sun and stars? D. Why are magnets made of particular materials?

A. What would cause a compass to not point to the north?

Ms. Vargas asked her students to write an expression equivalent to 4(x−y)4(x−y). A student named Andrew tried two substitutions of values for the ordered pair (x,y) in the expression, then incorrectly wrote that 4x−y is equivalent 4(x−y), based on the substitutions he tried. Which TWO of the following substitutions of values for the ordered pair (x,y) could be ones that Andrew tried? Answer the question by selecting the correct responses. A. x=0 and y=0 B. x=0 and y=1 C. x=1 and y=0 D. x=1 and y=1 E. x=1 and y=−1

A. x=0 and y=0 C. x=1 and y=0

On a class field trip, students look at a profile of a local canyon wall. Sandy says, "I didn't realize this area was once an ocean." The teacher asks the other students to explain why they think Sandy may have come to this conclusion. Which student response indicates a lack of understanding about the evidence and geologic history? Answer the question by selecting the correct response. A. "I can see a layer of rock with all kinds of shells in it." B. "The layers of rock are in different colors in the shape of an ocean wave." C. "Two of the layers are sand, with a layer of shells between them." D. "The fossils we can see are from species that lived in the ocean."

B. "The layers of rock are in different colors in the shape of an ocean wave."

Ms. Stine is doing an activity with her students in which she says a decimal number out loud and her students respond by writing the numeral. When Ms. Stine says, "one hundred eight and eight‑hundredths," a student named Roy writes the numeral "108.800." The students are then asked to write the numeral corresponding to "three hundred twenty‑four and seven‑thousandths." Which of the following responses shows an error that is most similar to the error Roy made? Answer the question by selecting the correct response. A. 324.0007 B. 324.7000 C. 30024.0007 D. 30024.7000

B. 324.7000

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? Answer the question by selecting the correct response. A. A counting strategy B. A benchmarking strategy C. An estimation strategy D. A place-value strategy

B. A benchmarking strategy

A teacher poses the following problem to the class. Helena has 20 red beads for making bracelets. She has 12 more red beads than yellow beads. How many yellow beads does she have? Which of the following problems has the same mathematical structure as the problem the teacher poses? Answer the question by selecting the correct response. A. Alex has 25 toy cars and 12 more stuffed animals than toy cars. How many stuffed animals does he have? B. Chanelle has 13 crayons. Chanelle has 7 more crayons than Chuck has. How many crayons does Chuck have? C. Britney has 7 more packs of snacks than Bella has. Bella has 5 packs of snacks. How many packs of snacks does Britney have? D. Daryl has some white shirts. After buying 3 new white shirts, he has 8 white shirts. How many shirts did Daryl have before buying the 3 new white shirts?

B. Chanelle has 13 crayons. Chanelle has 7 more crayons than Chuck has. How many crayons does Chuck have?

Which THREE of the following phenomena are related to the relative positions of the Sun, the Moon, and Earth? Answer the question by selecting the correct responses. A. Solar flares B. Eclipses C. Phases of the Moon D. Tides

B. Eclipses C. Phases of the Moon D. Tides

A student presents a project to the class describing the relationship between flowering plants and bees. The student concludes the presentation by stating, "Flowers have bright colors so they can trick bees into helping them reproduce." Which of the following responses by the teacher would best help the student develop a more accurate view of the relationship between bees and flowers? Answer the question by selecting the correct response. A. Have you considered the role of other animals in helping plants reproduce? B. Have you considered a benefit for bees when they help flowers reproduce? C. What benefits do humans receive from this bee-flowering plant relationship? D. Do flowering plants produce more pollen when bees are present?

B. Have you considered a benefit for bees when they help flowers reproduce?

Ms. Lee is teaching her first graders addition and subtraction within 20 by counting. She has her students work individually on finding the answer to 7 plus 57+57+5. During the whole-class discussion of the answer to the problem, James says, "I think 7 plus 5 equals 11, because I counted 7, 8, 9, 10, 11." James puts up a finger each time he says a number in the sequence. Which of the following statements most likely explains the reason behind James's error? Answer the question by selecting the correct response. A. James does not know the count sequence. B. James did not start his count on the correct number. C. James does not understand that the last count word indicates the amount of the set. D. James does not know how to decompose numbers greater than 10 into tens and ones.

B. James did not start his count on the correct number.

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? Answer the question by selecting the correct response. A. There are 4 shelves in Joaquin's bookcase, and there are 28 books on each shelf. How many books are in Joaquin's bookcase? B. 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? C. 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? D. 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?

B. 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?

Students in an upper elementary classroom are studying fossils. Which resource would best support the idea that fossils provide evidence that ecosystems can change over time? Answer the question by selecting the correct response. A. Actual samples of fern fossils found in a swamp B. Pictures of seashell fossils found in a desert C. A map showing locations in a forest where scientists have discovered woolly mammoth fossils D. A chart listing the number of extinct shark teeth found at different shorelines around the world

B. Pictures of seashell fossils found in a desert

When Sean, a third-grade student, solved the following problem, he gave an incorrect answer. Adele is baking cakes. Each cake needs 3 eggs. How many cakes can she make with 22 eggs? Sean said the answer was "7 remainder 1 cakes." Which of the following statements describes the error Sean made to arrive at his incorrect answer? A. Sean divided incorrectly. B. Sean interpreted the remainder incorrectly. C. Sean did not use the correct units in his answer. D. Sean used a strategy that works only with certain numbers.

B. Sean interpreted the remainder incorrectly.

Which of the following activities would best introduce students to a method of erosion control? Answer the question by selecting the correct response. A. Students form mounds of soil that vary in height. After pouring water on the mounds, they compare the amount of erosion in each sample. B. Students blow through a straw on a tray of sand. They blow with varying force and compare the amount of sand that is blown away after each test. C. Students pour a different amount of water onto each of three identical trays of soil set at various slope angles, graphing the relationship between the amount of runoff and the slope angle. D. Students are presented with two trays of soil set at a slight angle, one containing growing grass. The students pour water on both samples and compare the amounts of soil lost.

B. Students blow through a straw on a tray of sand. They blow with varying force and compare the amount of sand that is blown away after each test.

Mr. Wilson wrote the numbers 657, 756, and 576 on the board and asked the students to state which number is the greatest and explain why. One student, Lily, answered, "756 is the greatest. The first number has 6 hundreds, the second number has 7 hundreds, and the third number has 5 hundreds, so 756 is the greatest." Which of the following statements best describes the evidence of understanding place value that Lily's explanation provides? Answer the question by selecting the correct response. A. The value of the digit in each place of a three-digit number is a multiple of a power of 10. B. The leftmost digit in a three-digit number represents the number of hundreds in the number. C. A digit in a certain place has ten times the value the digit would have in the next place to the right. D. The greatest three-digit number that can be made with three different digits is the number that has the digits in order from greatest to least.

B. The leftmost digit in a three-digit number represents the number of hundreds in the number.

A student investigated whether matter is conserved during a change of state. The student weighed an empty glass beaker and then filled it with water before weighing it again to determine the weight of the water. The student then poured the water from the beaker into an ice-cube tray and placed it in a freezer. The student later removed the ice cubes from the tray and weighed them. After repeating the procedure five times, the student found that the weight of the ice cubes was slightly less than the initial weight of the water. The student concluded that freezing the water reduced its mass. Which of the following modifications to the procedure would best remove the error that affected the student's data? Answer the question by selecting the correct response. A. Removing the water from the beaker and the ice cubes from the tray using a spatula B. Weighing the water after it is placed in the tray and the ice cubes before they are removed from the tray C. Repeating the experiment three times instead of five times D. Drying the beaker and ice-cube tray with a paper towel before water is added

B. Weighing the water after it is placed in the tray and the ice cubes before they are removed from the tray

A third-grade teacher wants to assess students' mastery of providing explanations. The teacher asks the class to select a species that lives in groups and to write an explanation of how certain interactions within a group will help increase the likelihood of an individual's survival, growth, and reproduction. Which of the following explanations best meets the objective? Answer the question by selecting the correct response. A. "Whales live in pods. Whales migrate to warmer waters to survive." B. "Bees live in colonies. Each bee has a specific duty to maintain the colony." C. "Fish live in schools. By being one of a large number of fish, each individual has less chance of being eaten." D. "Elephants travel in herds. The calves run slower and are surrounded by the older elephants."

C. "Fish live in schools. By being one of a large number of fish, each individual has less chance of being eaten."

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? Answer the question by selecting the correct responses. 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

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

Which two of the following word problems can be answered by dividing 4 by 1/5? A. A quilt requires 1/5 square meter of purple cloth. How many square meters of purple cloth are needed for 4 of these quilts? B. A machine working at a constant rate takes an hour to sort 4 bins of mail. How many bins of mail does the machine sort in 1/5 hour? C. Each person at a dinner was served 1/5 of a fish fillet. A total of 4 fish fillets were served. How many people were served at the dinner? D. A roll of copper wire that was 4 meters long was cut into sections that were each 1/5 meter long. How many sections were made from the roll of copper wire? E. Each of 4 people in a study group read 1/5 of the total chapters in a book. No student read the same chapter as any other student. What fraction of the total chapters in the book did the study group read?

C. Each person at a dinner was served 1/5 of a fish fillet. A total of 4 fish fillets were served. How many people were served at the dinner? D. A roll of copper wire that was 4 meters long was cut into sections that were each 1/5 meter long. How many sections were made from the roll of copper wire?

Students are conducting an investigation on dissolving solids in a liquid. After mixing a spoonful of salt into a large container of water, a student says, "I can no longer see the salt in the water because the salt is gone." What can the teacher do to clarify this misconception? Answer the question by selecting the correct response. A. Add another teaspoon of salt to the water and stir B. Show the students that other substances also can dissolve by mixing sugar and water together C. Evaporate the water and show that the salt still remains D. Give the students a magnifying glass and allow them to inspect the sample

C. Evaporate the water and show that the salt still remains

Mr. Bennett's class was discussing strategies for adding whole numbers. One student, Katie, said, "When I add two numbers, I get the same answer as when the numbers switch places." Mr. Bennett asked his students to explain why Katie's claim is true when adding any two whole numbers. After giving the class time to work, he asked another student, Joel, to present his explanation. Joel said, "If the answer is a little number like 4, then 2 plus 2 is the same either way. And if the answer is a big number like 400, then 200 plus 200 is the same either way." Which of the following statements best characterizes Joel's explanation? Answer the question by selecting the correct response. A. It clearly explains why Katie's claim is true when adding any two whole numbers. B. It assumes that Katie's claim is true, but it does not establish in general why her claim is true. C. It neither gives useful examples for showing that Katie's claim is true, nor does it establish in general why her claim is true. D. It gives only two examples that show that Katie's claim is true, but more examples are needed to establish in general why her claim is true.

C. It neither gives useful examples for showing that Katie's claim is true, nor does it establish in general why her claim is true.

Marina explained how she found the difference 35 minus 18, saying, "I knew that 18 plus 2 is 20, and 35 plus 2 is 37, so 35 minus 18 is the same as 37 minus 20, which is 17. So 35 minus 18 is 17." Marina's partner, Jeremy, represented Marina's strategy using a number line, as shown in the following figure. Which of the following statements best characterizes how Jeremy's work represents Marina's strategy? Answer the question by selecting the correct response. A. Jeremy's work accurately represents Marina's strategy because it shows that she correctly found the difference between 35 and 18. B. Jeremy's work accurately represents the part of Marina's strategy in which she considered 20 instead of 18 as the subtrahend, but it does not accurately represent how she took 20 away from 37. C. Jeremy's work does not accurately represent Marina's strategy because Marina's strategy involved shifting the problem, but Jeremy's work shows a counting-up strategy. D. Jeremy's work does not accurately represent Marina's strategy because Marina used a comparison interpretation of subtraction, but Jeremy's work shows a takeaway interpretation of subtraction.

C. Jeremy's work does not accurately represent Marina's strategy because Marina's strategy involved shifting the problem, but Jeremy's work shows a counting-up strategy.

Mr. Aslanian's class watched a video about a species of mosquito that is found only at relatively high altitudes on a particular mountain in Africa. Mr. Aslanian then asked the students to use the information presented in the video to propose an explanation for the mosquitoes' limited geographical range. Which of the following responses indicates the most accurate understanding of the factors that influence the natural range of a species? Answer the question by selecting the correct response. A. Farran wrote that the mosquitoes probably migrate up and down the mountain every day, but that scientists study the mosquitoes only when the mosquitoes are high up on the mountain. B. Nash wrote that the mosquitoes live at high altitudes on the mountain because they need air, sunlight, water, and a source of food to live. C. LaShawn wrote that the mosquitoes are better adapted to the cooler, damper climate at higher altitudes on the mountain than to the hotter, dryer climate at lower altitudes. D. Cole wrote that mosquitoes that like warmer climates probably want to live where there is clear sunlight, and clear sunlight is often found at the top of a mountain.

C. LaShawn wrote that the mosquitoes are better adapted to the cooler, damper climate at higher altitudes on the mountain than to the hotter, dryer climate at lower altitudes.

While Mr. Lynch's students were working on finding the answer to the problem 5/6÷1/3, one student, Maggie, said the following. "I think that fraction division works just like fraction multiplication. You can divide the numerators and the denominators to find the answer. Like in this problem, 5 divided by 1 is 5, and 6 divided by 3 is 2, so the answer is 5 over 2." Which of the following is true of Maggie's conjecture about fraction division? Answer the question by selecting the correct response. A. Maggie's conjecture is not true, because her method did not produce the correct answer to the problem. B. Maggie's conjecture is not true, because division of fractions requires multiplying by the reciprocal of the second fraction. C. Maggie's conjecture is true for all fraction division problems, but in some problems, the resulting quotients from the numerators and denominators will not be whole numbers. D. Maggie's conjecture is partially true. Her method gave the correct answer in this problem because the denominators and numerators divided evenly, but the method will not give the correct answer in other problems.

C. Maggie's conjecture is true for all fraction division problems, but in some problems, the resulting quotients from the numerators and denominators will not be whole numbers.

Ms. Lussier asked one of her students, Matthew, to explain how he found the answer to the subtraction problem 54−37. Matthew explained his answer as follows. "I didn't want to have to trade, so I added 3 to 54 so I would have 7 like in 37. Then I added 3 to 37 to keep the problem the same, but now I have 57 minus 40 so I just do 7 minus 0 and 5 minus 4." Which of the following statements best characterizes Matthew's strategy for finding the answer to two-digit subtraction problems? Answer the question by selecting the correct response. A. Matthew's strategy is not valid because he solved a different subtraction problem than the one given. B. Matthew's strategy is not valid because it can only be used when the ones digit of the number to be subtracted is greater than the ones digit of the number from which to subtract. C. Matthew's strategy is valid, but it will not always provide an equivalent subtraction problem where the ones digit of the number to be subtracted is less than the ones digit of the number from which to subtract. D. Matthew's strategy is valid, and it will always provide an equivalent subtraction problem where the ones digit of the number to be subtracted is less than the ones digit of the number from which to subtract.

C. Matthew's strategy is valid, but it will not always provide an equivalent subtraction problem where the ones digit of the number to be subtracted is less than the ones digit of the number from which to subtract.

Ms. Hammonds asked one of her students, John, to write the number five hundred. John wrote "500" in his workbook. Next, Ms. Hammonds asked John to write the number that is ten more than five hundred. John immediately said, "Five hundred ten," and wrote "50010" in his workbook. Which of the following mathematical skills is most evident in John's response? Answer the question by selecting the correct response. A. Reading any three-digit number B. Writing any three-digit number C. Mentally adding ten to a three-digit number D. Understanding the value of the digits in a three-digit number

C. Mentally adding ten to a three-digit number

Mr. Wilson's upper elementary class is researching the positive and negative effects of pesticide and herbicide use in local agriculture. The class has already spent many hours searching on the Internet but has collected very little information. He would like to provide two additional opportunities for the students to collect information that would be the most useful. Which TWO activities would provide the best opportunities to collect useful information? Answer the question by selecting the correct responses. A. Mr. Wilson can schedule a trip to a local soybean farm. The students will tour the farm and interview the farmer for information on his farming practices. B. Mr. Wilson can schedule a trip to a pesticide production plant. The students will have a chance to interview the scientists employed by the company and receive materials that may not be present on the Internet. C. Mr. Wilson can meet with the school librarian, outlining his objectives and requirements. He can then bring his class to the library for several research periods after the librarian has had a chance to collect and lay out relevant journals, newspapers, and books. D. Mr. Wilson can schedule a panel discussion with representatives from the Environmental Protection Agency, United States Department of Agriculture, and the local extension service. They can provide materials that may not be available on the Internet, provide suggestions for additional resources, and answer student questions.

C. Mr. Wilson can meet with the school librarian, outlining his objectives and requirements. He can then bring his class to the library for several research periods after the librarian has had a chance to collect and lay out relevant journals, newspapers, and books. D. Mr. Wilson can schedule a panel discussion with representatives from the Environmental Protection Agency, United States Department of Agriculture, and the local extension service. They can provide materials that may not be available on the Internet, provide suggestions for additional resources, and answer student questions.

A teacher shows students a short video of a ball being thrown vertically upward, momentarily coming to rest, and falling back down toward the ground. When asked about the force of gravity on the ball throughout its motion, a student says that gravity pulls down on the ball at all times except for when the ball stops briefly before reversing direction. Which of the following responses by the teacher will best help the student overcome the misconception about gravity? Answer the question by selecting the correct response. A. Showing the video again but in slow motion B. Posing a follow-up question: How does a parachute change the motion of a skydiver in free fall? C. Posing a follow-up question: If gravity is not pulling on the ball when it stops, why does it start to fall back down? D. Showing a video highlighting variations in gravity between Earth and the Moon and at different altitudes on Earth

C. Posing a follow-up question: If gravity is not pulling on the ball when it stops, why does it start to fall back down?

A teacher helps the students in a class create a poster showing a food web in a prairie ecosystem. The teacher asks the students to label the organisms in the food web according to each organism's role in the ecosystem. Which of the following terms should the students use to label an animal that grazes on grass as its primary source of food? Answer the question by selecting the correct response. A. Producer B. Carnivore C. Primary consumer D. Secondary consumer

C. Primary Consumer

Ms. Karp gives each of her students 24 counters. She asks the students to count the number of counters each of them has and to write the number on their worksheets. All the students write "24" on their worksheets. Next, she asks the students to explain the meaning of the 2 and the 4 in "24." Which of the following student explanations provides the most evidence of place-value understanding? Answer the question by selecting the correct response. A. The 2 is in the tens place and the 4 is in the ones place. B. The 2 is twenty counters and the 4 is four single counters. C. The 2 is two groups of ten counters and the 4 is four counters. D. The 2 is two counters and the 4 is four counters, and so it's twenty-four.

C. The 2 is two groups of ten counters and the 4 is four counters.

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? Answer the question by selecting the correct response. 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 from1 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.

C. The teacher gives each student a shuffled deck of 10 cards, each with a single number from1 to 10. When the students draw a number card, they must count to 20, starting from the number on the card they drew.

M. Keller presents the following equations to his class and asks his students to decide whether each equation is true or false. 2+3=4+1 2+4=6-1 5=8-3 7=7 5=6 Which of the following is most clearly highlighted by the activity? A. Fluently adding and subtracting within 10 B. Determining the value of unknown numbers C. Understanding the meaning of the equal sign D. Using properties of operations to add and subtract

C. Understanding the meaning of the equal sign

During a class demonstration, a teacher floats a small toy boat in the center of a long, narrow rectangular tank filled with water. Initially, the water is still and the boat is not moving. The teacher asks students to predict what will happen if they use their hand to create a wave crest that travels toward the other end of the tank. A student predicts that the boat will be carried by the wave to the other end of the tank. Which of the following statements indicates a misconception that the student most likely has about water waves? Answer the question by selecting the correct response. A. Water waves get smaller as they get further away. B. Water waves transfer energy from one location to another. C. Water particles at the surface move along the surface with the wave. D. Water waves slow down when they encounter an obstacle.

C. Water particles at the surface move along the surface with the wave.

One of Mr. Terry's students, Yvonne, found the answer to the problem 3/8×2/9 as represented in the following work. The figure shows a student's work. The work is as follows. 3/8*2/9=2/8*3/9=1/4*1/3=1/12 When Mr. Terry asked Yvonne to explain her work, she said, "It's easier to just switch the numerators to make simpler fractions." Which of the following statements is true of Yvonne's strategy? Answer the question by selecting the correct response. A. Yvonne's strategy can only be used to rewrite products of fractions where the difference between the numerators is 1 and the difference between the denominators is 1. B. Yvonne's strategy can only be used to rewrite products of fractions where both fractions are less than 1. C. Yvonne's strategy can be used to rewrite any product of two fractions, but it will not always result in fractions that can be simplified. D. Yvonne's strategy can be used to rewrite any product of two fractions, and it will always result in fractions that can be simplified.

C. Yvonne's strategy can be used to rewrite any product of two fractions, but it will not always result in fractions that can be simplified.

An elementary school class has been learning about how animals can change the environment to meet their needs. After viewing a video of a beaver building a dam, the students are asked to explain how changing its environment helps the beaver to support its needs. Their explanation needs to be supported by evidence. Which explanation responds to the teacher's direction and is most likely to be supported by evidence from a video about beavers? Answer the question by selecting the correct response. A. "When the dam is built, the flow of water in the river changes, and a lake is formed." B. "Dams are good for beavers, and beavers that build dams are better off than beavers without dams." C. "Beavers are very good swimmers and can stay underwater for long periods of time." D. "Because the beaver lives in a lodge in the lake formed by the dam, it is protected from predators."

D. "Because the beaver lives in a lodge in the lake formed by the dam, it is protected from predators."

In an investigation, students kicked soccer balls along thick grass, short grass, and smooth pavement. The students' teacher then asked the students to use ideas about forces to explain the observed changes in the movement of the soccer balls. One student responded by saying, "The ball rolled after I kicked it. The force of my leg made the ball move. When that force was gone, the ball stopped rolling." Based on the student's response, the teacher should focus on which of the following concepts to correct the student's misunderstanding? Answer the question by selecting the correct response. A. A force can change the direction in which an object is moving. B. A push or pull can cause an object to start moving. C. A heavier object can require a larger force to start it moving. D. An object will continue moving at a constant velocity unless a force is exerted on it.

D. An object will continue moving at a constant velocity unless a force is exerted on it.

A teacher leads a discussion about the impact of environmental change on an ecosystem. The teacher asks the students in the class to explain how the death of a tree can be beneficial. To help the students, the teacher suggests that they consider how a fallen tree can affect the species diversity of the surrounding forest. In which of the following ways can a tree-fall gap result in increased species diversity in a mature forest community? Answer the question by selecting the correct response. A. By reducing the amount of carbon dioxide gas in the atmosphere B. By increasing competition between birds for limited resources C. By creating a barrier to the dispersal of seeds produced by mature trees D. By providing a habitat in which shade-intolerant plants can grow

D. By providing a habitat in which shade-intolerant plants can grow

Mr. Marquez and his students are working on naming fractions with denominators of 10 or 100 using decimal notation. Mr. Marquez finds an activity online that involves having students shade some parts of a tenths grid and some parts of a hundredths grid, name the fractions that have been shaded, and write the fractions in decimal notation. The following figure shows an example from the activity. Which of the following is the most significant limitation of using the grids in this way? Answer the question by selecting the correct response. A. It does not make the equivalency of a fractional part of a whole and a fractional part of a set clear. B. It does not make the equivalency between decimal notation and fraction notation clear. C. It makes it difficult to determine what constitutes the unit fraction in each representation. D. It does not make the relative value of the wholes in the two representations clear.

D. It does not make the relative value of the wholes in the two representations clear.

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? Answer the question by selecting the correct response. 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

D. Knowing that each previous number name refers to a quantity which is one less

Mr. Marzotto asks his students the following question. "If you have a 2 and a 5, what is the greatest two-digit number you can make using the 2 and the 5 ?" One student, Addy, responds, "With those two digits, I can make 25 and 52. The greatest number of the two is 52 because it has 5 tens, and 25 only has 2 tens, and 5 is greater than 2." Addy has demonstrated evidence of understanding which of the following mathematical ideas or skills? Answer the question by selecting the correct response. A. Using numerals to describe quantities B. Recognizing that 1 ten is made of 10 ones C. Mentally calculating 10 more than a given number D. Knowing the value of each place in a two-digit number

D. Knowing the value of each place in a two-digit number

Ms. Pellegrino divides her class into four groups and gives each group a dozen bean seedlings to monitor for the semester. She asks each group to use the seedlings to investigate whether plants need sunlight to grow. Although she wants each group to develop its own procedure, she wants to prevent errors that will result in the collection of unusable data. Which of the following is a procedural error that Ms. Pellegrino should correct to prevent the collection of unusable data? Answer the question by selecting the correct response. A. Measuring plant height in inches instead of centimeters B. Not having a backup plan if all the students in the group are absent for one day C. Recording data on loose-leaf paper instead of in a bound laboratory notebook D. Measuring the final heights of the plants but not the initial heights

D. Measuring the final heights of the plants but not the initial heights

Ms. Keane had her students plant seeds in pots of soil. The students then placed some of the pots on a sunny windowsill and some on a table that was out of direct sunlight. As the seeds began to sprout, the students cared for them and observed their growth. After a weeklong break, the students found that some of their plants were wilted and some were dead. Ms. Keane asked the students to suggest a way to investigate why some of the plants had died and others had not. Which of the following plans will best allow the students to collect data that can be used to determine why some of the plants died? Answer the question by selecting the correct response. A. Move all of the dead plants to the windowsill and water them the same amount each day. B. Move all of the wilted plants to the dark and water half of them daily and half of them weekly. C. Examine the pots with the wilted plants to determine whether the soil is dry and water each plant when the soil feels dry. D. Place new groups of plants in the original locations and water half of the plants in each group daily and water the other half weekly.

D. Place new groups of plants in the original locations and water half of the plants in each group daily and water the other half weekly.

Ms. White's students investigate why some stars appear to be brighter than others in the night sky. They take observational notes about the apparent brightness of two different-sized flashlights that they shine from various distances onto the same wall. After the investigation, the students conclude that brighter stars must be larger than dimmer stars. Which of the following activities will provide the best data for directing the students toward a more accurate conclusion? Answer the question by selecting the correct response. A. Repeating the investigation, aiming the flashlights at black construction paper taped to the wall B. Combining the observations with those made by the students in another class C. Repeating the investigation, measuring the diameter of the circles of light produced at various distances D. Repeating the investigation, using two flashlights of the same size

D. Repeating the investigation, using two flashlights of the same size

Which of the following activities provides fourth-grade students with the best opportunity to make and test predictions about the transfer of kinetic energy between objects? Answer the question by selecting the correct response. A. Dropping a soccer ball from the roof of a building and measuring the height of the rebound B. Placing two soccer balls touching each other on the floor with both balls at rest C. Measuring the distance traveled by a soccer ball when it is allowed to roll down a ramp and onto a smooth, flat surface D. Rolling one soccer ball along the floor into another that is not moving

D. Rolling one soccer ball along the floor into another that is not moving

A teacher provides students with several rectangular samples of flexible materials, with the same length and width but with varying thickness. The students are asked what causes the difference in stiffness among the materials. A student picks up a thin sample that is very flexible and a thick sample that is much stiffer. The student concludes that the thick sample must be made of a stiffer material since it is harder to bend. Which of the following sets of samples should the teacher provide to allow the student to determine that both the type of material and the thickness of the material can affect stiffness? Answer the question by selecting the correct response. A. Two samples of the same material of equal thickness B. Samples of the same material but of varying thickness C. Thick samples of one material that can be peeled in layers D. Samples of two different materials with two thicknesses each

D. Samples of two different materials with two thicknesses each

In Ms. Werner's classroom, students are measuring the length of objects around the room. Shaun measures the length of the rug using a ruler and gets 108 inches. Tim measures the length of the same rug using a yardstick and gets 3 yards. Ms. Werner overhears them discuss their results. Shaun says that inches are bigger than yards because there are more inches in the length of the rug, but Tim says that yards are bigger than inches because there are fewer yards. Which of the following statements best expresses Shaun's misconception about measurement? Answer the question by selecting the correct response. A. The final measurement does not depend on the length of the unit. B. The size of the unit of measure is dependent on the distance it covers. C. The same measurement cannot be obtained when using different measurement tools. D. The number of units of measure increases as the size of the unit of measure increases.

D. The number of units of measure increases as the size of the unit of measure increases.

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? Answer the question by selecting the correct response. A. The strategy is not valid because the same unit must be used to measure each side of the desk. B. The strategy is valid only if the note cards are squares. C. The strategy is valid and the unit of measurement is square units. D. The strategy is valid and the unit of measurement is note cards.

D. The strategy is valid and the unit of measurement is note cards.

Ms. Chambers writes the following equation on the board. 5*19-40=40-5*19 Ms. Chambers asks her students to determine if the equation is true. One student says, "The equation is true because on both sides of the equation, you subtract after you multiply 5 times 19." Which of the following statements most likely gives the reason underlying the student's error? Answer the question by selecting the correct response. A. The student disregarded the order of operations. B. The student incorrectly applied the associative property. C. The student does not understand the meaning of the equal sign. D. The student has overgeneralized by applying the commutative property to subtraction.

D. The student has overgeneralized by applying the commutative property to subtraction.

Ms. Aggarwal tells her students that the x in the equation x+4=7 is called a variable. She then asks her students to write down what they think the word "variable" means in this context. One student wrote, "The variable is a letter that stands for something we don't know." Which of the following revisions to the student's definition most improves the precision of the definition as it relates to this use of the word "variable"? Answer the question by selecting the correct response. A. The variable is a letter that stands for any number that is unknown. B. The variable is a letter that stands for a number that is unknown in the equation. C. The variable is a letter that stands for an unknown number that can take on different values. D. The variable is a letter that stands for the unknown number that will make the equation true.

D. The variable is a letter that stands for the unknown number that will make the equation true.

In an activity using an illustration of a plant, a teacher guides students through a lesson about the different parts of a plant. When discussing the structure and function of the roots, the teacher points to small projections that are shown on the plant's roots. The teacher tells the students that the projections are called root hairs and asks the students to predict what would happen if all the root hairs were suddenly gone. Which of the following is likely to be the most direct effect on the plant of the sudden loss of all its root hairs? Answer the question by selecting the correct response. A. Excess water will build up in the stem. B. Transport of sugars throughout the plant will stop. C. Carbon dioxide will not be able to reach the leaves. D. Water and minerals will not be absorbed from the soil.

D. Water and minerals will not be absorbed from the soil.

Ms. Sengupta is working with her students to name fractions represented by area models. In particular, she wants her students to focus on the importance of equal parts. She asks her students to write their answers to the following problem. The figure shows a problem, which consists of a question and a figure. The question reads: What fraction of the big square is shaded? The figure is a big square. A vertical line is drawn through the center of the square, which first divides the square into two parts. The left part of the big square is further divided by a horizontal line that extends from the midpoint of the left side of the square to the center of the square. The big square is divided into two small squares and one small rectangle. One of the small squares is shaded. End figure description. Ms. Sengupta notices that students wrote several different incorrect answers. She wants to choose an incorrect answer to discuss as a class that will highlight the importance of attending to equal parts when naming a fraction. Which of the following incorrect answers best supports Ms. Sengupta's mathematical goal? a. 1/3 b. 1/2 c. 3/4 d. 1 1/2

a. 1/3

A student found an incorrect answer to the problem 19.9 plus 1.3 The student's answer is represented in the following work. The figure shows a student's work. The work is as follows. 19.9 plus 1.3, equals 20.12. The numbers are arranged vertically, such that the decimal points are aligned. End figure description. Which of the following incorrect answers to the problem 12.94+1.08 is the result of an error that is most similar to the error made in the preceding work? a. 13.102 b. 13.92 c. 14.74 d. 23.74

a. 13.102

Ms. O'Neil asked her students to find the sum five sixths plus seven tenths, plus two fifteenths56+710+21556+710+215. One student found the sum as represented in the following work. The figure shows a student's work. The work is as follows. Five sixths plus seven tenths, plus two fifteenths, equals the fraction with numerator 25 plus 21, plus 4, and denominator 30, which equals the fraction 50 over 30. End figure description. Which THREE of the following mathematical strategies were used in the student's process? a. finding equivalent fractions b. finding a common denominator c. finding the simplest forms of fractions d. finding the least common multiple of the denominators e. finding the greatest common factor of the denominators

a. finding equivalent fractions b. finding a common denominator d. finding the least common multiple of the denominators

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. a. 15 b. 16 c. 20 d. 24 e. 27 f. 30

b. 16 c. 20

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? a. asking students to read the numbers 20-29 b. asking students to represent the number 35-53 using base-10 blocks c. asking students how many tens and how many ones are in the number 33 d. showing students 23 and 32 cubes and asking them which quantity is greater

b. asking students to represent the numbers 35 and 53 using base-10 blocks

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? a. having students line up according to the number of the day of the month in which they were born. b. showing students 10 pencils and asking them to get enough erasers for all the pencils. c. showing students a row of 12 buttons and asking them to make a pile of 8 buttons. d. asking students to count the number of triangles printed on the classroom rug

b. showing students 10 pencils and asking them to get enough erasers for all the pencils

Ms. Robinson is working with her students on mixed-number subtraction, and she wonders how well her students understand that each whole in a mixed number is equivalent to the fraction n/n equal parts. She wants to construct a subtraction problem for her students that will assess their understanding of the concept. Which of the following problems will give Ms. Robinson the most information about her students' understanding that each whole in a mixed number is equivalent to the fraction n/n equal parts? a. 5 3/4-3 1/2 b. 6 4/5-2 2/7 c. 4 1/3-1 5/6 5 2/5-4 2/5

c. 4 1/3-1 5/6

1, 9, 17, 25, 33, 41, 49, 57 Which of the following statements best describes the numbers in the preceding list? a. all whole numbers are not divisible by 4 and are less than 60 b. all whole numbers are not divisible by 8 and are less than 60 c. all whole numbers that are less than 60 and have a remainder of 1 when divided by 4 d. all whole numbers that are less than t60 and have a remainder of 1 when divided by 8

d. all whole numbers that are less than 60 and have a remainder of 1 when divided by 8

Ms. Lawson asks one of her students, Jen, to explain how to use base-10 blocks to add 67 and 40. Jen lays out some base-10 blocks as shown in the following figure. The figure shows two groups of base-10 blocks. The first group consists of 6 ten-unit blocks and 7 one-unit blocks. The second group consists of 4 ten-unit blocks. End figure description. Jen says, "I used 6 rods for the 6 tens in 67 and 7 cubes for the ones. Then I used 4 rods for 4 tens because I have to add 40. I counted all the rods and cubes and got 10 rods and 7 cubes, so it makes 10 tens and 7 ones altogether." Jen has demonstrated evidence of understanding which of the following mathematical ideas or skills? A. understanding that 100 is equivalent to 10 tens b. using base-10 written numerals to describe quantities c. mentally calculating ten more or ten less than a number without counting. d. understanding that the digits of a two-digit number represent amounts of tens and ones.

d. understanding that the digits of a two-digit number represent amounts of tens and ones.