Elementary Education: Mathematics and Science (5008)
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?
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?
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.
16 20
What value of x makes the equation 8x = 136 true
17
A student uses cubes to build a rectangular solid. Each of the cubes has a side length of 1/2 inch. The rectangular solid has a length of 4 inches, a width of 3 inches and height of 2 1/2 inches. How many cubes does the student use the build the rectangular solid?
240
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?
324.70000
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
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 benchmarking strategy
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?
A picture of a female cocker spaniel with her litter of eight puppies, some black, some golden, some brown 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?
A square is a rectangle that has 4 sides of equal length. A square is a rhombus that is also a rectangle.
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?
Chanelle has 13 crayons. Chanelle has 7 more crayons than Chuck has. How many crayons does Chuck have?
Which THREE of the following actions will result in reduced energy consumption?
Commuting to work using public transportation instead of driving alone in a gasoline-powered car Setting the thermostat for a home cooling system to a higher temperature in warm weather 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?
Earth revolves around the Sun
Which THREE of the following phenomena are related to the relative positions of the Sun, the Moon, and Earth?
Eclipses Phases of the moon Tides
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?
Evaporate the water and show that the salt still remains
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?
Have you considered a benefit for bees when they help flowers reproduce?
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?
Counting out a particular quantity from a larger set Understanding that the last word count indicates the amount of objects in the set
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?
"Because the beaver lives in a lodge in the lake formed by the dam, it is protected from predators"
Students completed a simulation examining the erosion of soil by water and made several conclusions. Which of the following conclusions presents a misconception?
"Erosion is always harmful to the environment"
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?
"Fish live in schools. By being one of a large number of fish, each individual has less chance of being eaten"
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?
"The layers of rock are in different colors in the shape of an ocean wave"
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, that the athlete runs?
1.2 1 meter = 0.001 kilometers
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?
1/3 + 1/4 + 1/3
A student found an incorrect answer to the problem 19.9 + 1.3. The student's answer is represented in the following work. 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?
13.102
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?
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. 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?
Measuring the final heights of the plants but not the initial heights
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?
Mentally adding ten to a three-digit number
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?
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?
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?
Samples of two different materials with two thicknesses each
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?
Sean interpreted the remainder incorrectly
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?
Showing students 10 pencils and asking them to get enough erasers for all the pencils
Which of the following activities would best introduce students to a method of erosion control?
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
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?
The student is comparing decimals as if they are whole numbers
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?
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
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"?
The variable is a letter that stands for the unknown number that will make the equation true
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
1, 9, 17, 25, 33, 41, 49, 57 Which of the following statements best describes the numbers in the preceding list?
All whole numbers that are less than 60 and have a remainder of 1 when divided by 8
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?
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?
Amphibians
Which of the following describes a student-created model that best represents the movement of matter through an ecosystem?
An interconnected web showing the movement of matter between plants, animals, decomposers, and the environment
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?
An object will continue moving at a constant velocity unless a force is exerted on it
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 represent the numbers 35 and 53 using base-10 blocks
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?
By providing a habitat in which shade-intolerant plants can grow
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?
It neither gives useful examples for showing that Katie's claim is true, nor does it establish in general why her claim is true
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 + 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?
James did not start his count on the correct number
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?
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?
Knowing the value of each place in a two-digit number
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?
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
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?
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?
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?
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 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
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?
Pictures of seashell fossils found in a desert
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?
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
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?
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?
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?
The 2 is two groups of ten counters and the 4 is four counters
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?
The cooking of an egg
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?
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?
The strategy is valid and the unit of measurement is note cards
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. 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?
Understand that the digits of a two-digit number represent amounts of tens and ones
Consider the following incomplete statement about rounding a decimal number. When 390.396 is correctly rounded to the nearest _____ 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.
Unit Ten
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?
Water and minerals will not be absorbed from the soil
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?
Water particles at the surface move along the surface with the wave
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?
Weighing the water after it is placed in the tray and the ice cubes before they are removed from the tray
Students are studying various aspects of magnetism. Which of the following questions should upper-elementary students be able to answer experimentally with classroom resources?
What would cause a compass to not point to the north?
