Mathematics
What is a Box Plot?
A box plot is a graph that displays both the frequencies and distributions of observations. It is useful for comparing two distributions. It is also called a "box and whisker" plot.
A movie begins at 5:45 p.m. It ends at 7:10 p.m. How long was the film? A. 85 minutes B. 95 minutes C. 125 minutes D. 165 minutes
A. 85 minutes The time between 5:45 p.m. and 7:10 p.m. is one hour and 25 minutes, which is 85 minutes. (Geometry and Measurement)
Juan received the following scores on his first four tests: 80, 84, 80, 92 He then receives a score of 94 on his sixth test. Select ALL the statements that are true. A. Juan's mean score increases by 2 points. B. The range increases by 2 points. C. The mode increases by 2 points. D. Juan's median score increases by 2 points.
A. Juan's mean score increases by 2 points. B. The range increases by 2 points. D. Juan's median score increases by 2 points. (Data, Statistics, and Probability)
The difference between a square and a cube is that A. a square is two-dimensional. B. a square is three-dimensional. C. a cube has fewer corners and edges. D. none of the above
A. a square is two-dimensional. A cube is a three-dimensional geometric solid. (Geometry and Spatial Sense)
A savvy early childhood teacher in the United States will practice counting items on a tabletop A. from left to right. B. from right to left. C. in random order. D. from top to bottom.
A. from left to right. In our language system, we read numbers and words from left to right and then scroll back to the left again. (Mathematical Thinking Skills)
When children first learn to regroup, they learn that two-digit numbers are composed of groups of tens and ones. Three-digit numbers would be composed of A. hundreds, tens, and ones. B. thousands, hundreds, and ones. C. neither A nor B D. both A and B
A. hundreds, tens, and ones. Three-digit sums to the problems would not include any number in the thousands place. (Numbers and Operations)
Children in second grade are given a basic set of paper tangrams to color, cut out, and paste into a new form. Some children make houses and animals. Others make vehicles, toys, or space creatures. This is a good way to A. manipulate geometric shapes. B. identify geometric shapes. C. name geometric shapes. D. practice fine-motor skills.
A. manipulate geometric shapes. The purpose of the activity is to move the shapes through space and reconfigure them to create something other than the original square. (Geometry and Spatial Sense)
On a table in the prekindergarten class sits a large bowl, a bin of flour, a container of salt, a pitcher of water, some vegetable oil, measuring cups, and measuring spoons. Mrs. Gardner tells her students that they will be making clay. She models how to use the kitchen tools and the ingredients and tells the children that they will be using their fingers to mix everything together. She is demonstrating A. measurement of volume. B. linear measurement. C. measurement of weight. D. measurement of time.
A. measurement of volume. (Measurement)
After interviewing her kindergarten class about the number and kind of pets they each have, a teacher asks each child to make a graph using stickers to show the number of each kind of pet. For instance, red stickers will represent the number of dogs in the class, green stickers will stand for the number of cats, blue stickers will show the number of birds, and yellow will show any other kind of pet. The teacher's purpose in doing this is to teach her students how to A. organize and record mathematical ideas. B. find answers to everyday math problems. C. show the concept of change. D. use symmetry.
A. organize and record mathematical ideas. (Mathematical Thinking Skills)
A second-grade teacher gives each child in the class a penny, paper, and a pencil. Each child is asked to divide the paper in half and record the number of times he or she gets "heads" or "tails" by flipping a penny. One tally mark represents each flip of the coin. What concept is practiced here? A. probability B. number sense C. geometry D. measurement
A. probability Children are studying the chance that heads or tails will occur as the result of a toss. (Measurement)
When children first learn to tell time using a clock face, they identify the numerals and hour and minute hands. Following that, the next thing they learn is A. to tell time on the hour. B. to tell time on the half hour. C. to tell time to the quarter hour. D. to tell time by the minute.
A. to tell time on the hour. The order of the answers is the order in which most early childhood instructors would teach the telling of time on an analog clock face. (Measurement)
The local public safety department comes to Englewood School every year to speak to the early childhood classes. They discuss the traffic signals and signs and explain the different meanings of each. Each sign is A. two-dimensional. B. three-dimensional. C. a geometric solid. D. none of the above
A. two-dimensional. Stop signs, yield signs, railroad crossing signs, and street signs are all two-dimensional, meaning that they are flat and have easily recognizable, predictable shapes (i.e., octagons, inverted triangles, circles, and rectangles). (Geometry and Spatial Sense)
Which decimal value is equivalent to 0.05%? A. 0.0005 B. 0.005 C. 0.05 D. 5
A. 0.0005 To convert from a percent to a decimal, you must move the decimal point two places to the left. (Numbers and Operations)
In the following number, how great is the value of the place value with the digit 9 compared to the value of the place value with the digit 3? 1,038,925 A. One-hundredth B. One-tenth C. One hundred D. One thousand
A. One-hundredth The digit 9 is in the hundreds place, and the 3 is in the ten-thousands place. Therefore, the smaller digit is one-hundredth the value of the larger digit. (Numbers and Operations)
Which inequality represents the solution to the inequality below? 3w + 3 < 12 A. w < 3 B. w > 3 C. w < 1 D. w < −3
A. w < 3 To solve this inequality, subtract both sides by 3, then divide both sides by 3 to isolate the variable. (Algebraic Thinking)
Which equation is an example of the associative property? A. (12 − 2) − 5 = 12 − (12 − 5) B. (5 × 4) × 9 = 5 × (4 × 9) C. (11 + 5) + 4 = 4 + (11 + 5) D. 3(6 + 9) = (3 × 6) + (3 × 9)
B. (5 × 4) × 9 = 5 × (4 × 9) The associative property of multiplication rearranges the placement of the parentheses but not the order of the number values. (Numbers and Operations)
At what age might children be expected to identify the numerals 1-10 and match them to corresponding sets of objects? A. by the end of first grade B. by the end of kindergarten C. by the end of pre-kindergarten D. before preschool
B. by the end of kindergarten Although children work above and below grade level, Head Start suggests that this skill ought to be achieved by the end of kindergarten. (Mathematical Thinking Skills)
Casey and Max are playing with wooden building blocks in their daycare classroom. Max wants all of the "square blocks," and he will give all the rest to Casey. Which blocks will Max give to Casey? A. rectangular solids and cubes B. cylinders and triangular solids C. both A and B D. neither A nor B
B. cylinders and triangular solids There may also be some round and half-round three-dimensional shapes. (Geometry and Spatial Sense)
Preschool children in Mr. Loehr's class like to toss craft sticks into a hula-hoop target placed on the floor about four feet away. For every stick they get into the hoop, they receive one point. Each child is on the honor system and keeps track of his or her own score. Adding up each successful toss in one's own head is a form of A. number sense. B. mental math. C. operations. D. measurement.
B. mental math. Because children will be adding up their own scores in their heads rather than on paper, this is the best answer. (Mathematical Thinking Skills)
In Mr. O'Reiley's preschool class, children count out items in a jar while the teacher draws four vertical lines with a diagonal across them as a way to show how many. We call this kind of visual representation A. counting with lines. B. tallies. C. slash marks. D. patterning.
B. tallies. It is true that the four vertical lines with a diagonal across from top-left to bottom-right could be a pattern if repeated over and over exactly, but the primary purpose for this exercise is as a reference—a method of keeping track of numbers. (Patterns)
Marcos flips a penny, a nickel, and a dime. What is the probability that all three coins will land on the same face (all heads or all tails)? A. 1/3 B. 1/4 C. 1/6 D. 1/8
B. 1/4 The probability of all three coins landing on heads is 1/2 × 1/2 × 1/2, which is 1/8. The probability of all three coins landing on tails is also 1/8. The probability of either is therefore the sum of the two fractions, which can be simplified to 1/4. (Data, Statistics, and Probability)
A record-breaking fish has a length of 674 millimeters. What is the length of the fish in meters? A. 0.674 B. 6.74 C. 67.4 D. 674,000
B. 6.74 To convert from millimeters to meters, you must divide by 1,000. (Geometry and Measurement)
Aubrey correctly solved five of the first six problems on a math quiz. If the entire quiz has a total of 42 problems and Aubrey answers the rest of the questions at the same proportion, how many questions will she answer incorrectly on the entire quiz? A. 6 B. 7 C. 9 D. 35
B. 7 You can set up a proportion where 5 to 6 is set equal to an unknown number to 42 (5/6 = x/42). The resulting value of the unknown number is 35, which represents the questions she got right. Subtract from 42 to get the answer. (Numbers and Operations)
Which is the value of the expression below if z = 9? 10z − z A. 10 B. 81 C. 90 D. 100
B. 81 You multiplied 10 by 9, then correctly subtracted 9 from the product. (Algebraic Thinking)
Alexandra spends $100 on clothing, food, jewelry, and a gift for her brother. Which graph would best display how much she spent on each item compared to the total amount of money she spent? A. Line graph B. Circle graph C. Scatterplot D. Box plot
B. Circle graph A circle graph is appropriate to show parts of a whole, such as how a person spends $100 on different items. (Data, Statistics, and Probability)
What is the value of the digit 9 in the number 807,192? A. Ten B. Ninety C. Ninety-two D. Nine hundred
B. Ninety The digit 9 is in the tens place, but its value is equivalent to 9 tens, or ninety. (Numbers and Operations)
Which of the following sets shows numbers in order from least to greatest? A. {101%,1.11,1.1,98} B. {101%,1.1,1.11,98} C. {1.1,1.11,98,101%} D. {98,101%,1.1,1.11}
B. {101%,1.1,1.11,98} The decimals, percent, and improper fraction are correctly ordered from least to greatest. (Numbers and Operations)
Which represents the value of 50 + (8 − 2)² − 3³? A.27 B.59 C. 69 D. 77
B.59 You correctly solved each operation following the order of operations (operations within parentheses first, then exponents). (Numbers and Operations)
Which is equal to 406,023? A. 400,000 + 60,000 + 20 + 3 B. 400,000 + 6,000 + 200 + 3 C. 400,000 + 6,000 + 20 + 3 D. 40,000 + 6,000 + 20 + 3
C. 400,000 + 6,000 + 20 + 3 (Numbers and Operations)
Children in Ms. Dinerstein's class are given graph paper that is marked in one-inch squares. They are directed to use their crayons and color one square in the first row, then two, then three, and so on. This kind of patterning is called A. a graph paper pattern. B. a color pattern. C. a growing pattern. D. a pattern of squares.
C. a growing pattern. Growing patterns expand by a number of units repeated over and over again. (Patterns)
Children learn that five plus something equals 11. This kind of thinking is an early form of A. connection-making skills. B. measurement. C. algebra. D. geometry.
C. algebra. Children are making connections and drawing conclusions, but this kind of reasoning is algebraic. (Numbers and Operations)
Early childhood teachers know that they can use wooden cubes (all the same size and weight) and a balance scale to teach A. weight in kilograms. B. weight by volume. C. greater than and less than. D. linear measurement.
C. greater than and less than. Children can stack the cubes and watch the scales tip, showing the side with the greater number of cubes. (Measurement)
In second grade, children learn that 5 + 4 = 9 and that 9 - 5 = 4. We call this process A. probability. B. number sense. C. reversibility. D. measurement.
C. reversibility. (Numbers and Operations)
The cost of a can of cat food is $0.79. A customer buys 52 cans. Which is the best estimation for the total cost for all the cans of cat food? A. $1.30 B. $25 C. $40 D. $50
C. $40 $0.79 rounds easily to $0.80, and the number of cans rounds down from 52 to 50 cans. The product of 50 and $0.80 is $40, which is the best estimate for the total cost. (Numbers and Operations)
Which is the value of 329,568 when rounded to the nearest hundred? A. 329,570 B. 329,500 C. 329,600 D. 330,000
C. 329,600 Because the digit in the hundreds place is a 5, the number is rounded up to the next highest hundred. (Numbers and Operations)
Which is a prime number? A. 27 B. 51 C. 67 D. 77
C. 67 The number 67 has only 1 and itself as factors, which means it is a prime number. (Numbers and Operations)
Which number is NOT a factor of 36? A. 1 B. 6 C. 8 D. 12
C. 8 The number 8 does not divide evenly into 36, so it is not a factor of it. (Numbers and Operations)
A probability is listed at 0.68. What is the likelihood of the event happening? A. Impossible B. Unlikely C. Likely D. Certain
C. Likely A probability of 0.68 represents a 68% chance of the event happening, which is likely. (Data, Statistics, and Probability)
Which equation can represent the cost, c, for s number of boxes of strawberries if each box costs $5? A. 5c = s B. c = 5 + s C. c = 5s D. 5 = cs
C. c = 5s The cost of $5 is multiplied by the number of boxes of strawberries, s, to equal the final cost, c. (Algebraic Thinking)
Which distance is equivalent to five miles? A. 5,000 feet B. 25,000 feet C. 25,400 feet D. 26,400 feet
D 26,400 feet To convert from miles to feet, you must multiply by 5,280. (Geometry and Measurement)
Ms. Ryanna distributes measuring tapes with inch markings on them. She directs the children in her class to find the perimeter of the following objects—math books, spelling journals, desktops, and pencil boxes—and to keep a record of their work. Which of the following is a part of the record-keeping process? A. accurately measuring each of the items according to a teacher's direction B. recording the results in a journal, on a slate, or piece of paper C. working in pairs where one student measures and another writes and reports the results D. all of the above
D. all of the above Accurately measuring each of the items according to a teacher's direction, recording the results in a journal, on a slate, or piece of paper, and working in pairs where one student measures and another writes and reports the results describe steps that test children's ability to make sense of information they collect. In addition, working in pairs where one student measures and another writes and reports the results is an example of division of responsibility that teaches each child on a team to be accountable to other group members. (Data)
Young children love to stand around the sand table and pour sand into sieves, measuring cups, and scoops. In this informal way, they are practicing A. estimation. B. weight. C. measurement. D. all of the above
D. all of the above As they pour the sand from cup to cup, they feel the weight of it; they guess the amount needed to fill a container, and they learn to fill containers to the top for accurate measurement. (Measurement)
In Mrs. Tejani's kindergarten class, a pocket chart is placed by the door. When children enter the class on any given day, they pick up a card with their name on it and place it in a pocket under a sign that is labeled "Present." Ten minutes into the school day, the rest of the cards are placed beneath another sign that is labeled "Absent." If children arrive later, they move their names from one side of the pocket chart to the others. This activity is designed to A. show children the number of students in attendance. B. teach children to read their friends' names. C. develop routine. D. all of the above
D. all of the above Children will, as a consequence of repeating this activity on a daily basis, consider it part of a school routine and learn to read some of the other children's names. (Data)
First graders in Mrs. Parker's class keep journals and note changes in the garden in front of the school. They note when leaves begin to fall off trees, when plants die back, when crocuses begin to push through the earth, and when butterflies return to the garden. They organize their journals according to the day and month of the school year. Why do they do this? A. to collect data B. to analyze data C. to make predictions D. all of the above
D. all of the above In this instance, children are collecting data and describing the changes over time. Because of prior knowledge, they will be able to make predictions or guesses about what will happen next. (Data)
Second graders at Elmwood Elementary keep track of the number of teeth they lose day by day on a large graph kept in the hallway. They place a round sticker with the date the tooth was lost next to their name. In this way, they can A. see how many teeth are lost all together. B. see how many teeth are lost by individuals. C. note in which month most teeth were lost. D. all of the above
D. all of the above Many early childhood teachers use this method of recording the loss of children's teeth as it is relevant to their experience and a very simple and yet effective way to show graphing and how results can change over time. (Data)
In Mr. Hamm's kindergarten class, one large table holds several sets of tongs, spatulas, ladles, blocks, pompoms, Unifix cubes, plastic eggs, and containers for each of these items. After modeling how to transfer items from one container to another, he allows children to enter into the process. What does Mr. Hamm know? A. These kinds of activities allow for curiosity and teach patience. B. Children begin to understand cause and effect. C. Children work toward a goal and gain confidence. D. all of the above
D. all of the above Opportunity to practice new skills at leisure and without pressure to perform promotes curiosity, cause-and-effect understanding, and confidence. (Mathematical Thinking Skills)
Second-grade students at Public School 55 keep math journals. Each night, they write and answer a story problem about something that happened at home. For instance, "I ate 16 green grapes for a snack. My brother Sal ate 21. How many did we eat all together?" Keeping this journal is one way of A. applying mathematics to other subject areas. B. drawing logical conclusions. C. experimentation. D. applying mathematics to daily life.
D. applying mathematics to daily life. Having the students recognize mathematical concepts in their daily lives helps reinforce learning. (Data)
Children can practice counting to 100 in all of the following ways EXCEPT A. counting by twos. B. counting by fives. C. counting by tens. D. counting by sevens.
D. counting by sevens. In counting by sevens, they will end at 98 or 105 but not exactly 100. (Patterns)
On a table in Ms. Pollock's kindergarten class are ten small plastic bowls. Each of the bowls has a numeral written on it from one to ten. Unifix cubes are arranged randomly around the bowls. Children are asked to place the correct number of cubes into each bowl. This task requires A. reasoning skills. B. operations. C. patterning. D. number sense.
D. number sense. Number sense implies understanding that a numeral represents a particular amount. (Numbers and Operations)
Children look forward to celebrating the 100th day of school. They keep track of the days by turning cards over from the blank side to the side printed with the number. These cards are placed in a pocket chart. If the pocket chart has 100 pockets and if the first number placed in the pocket chart is one, then all of the numbers running down the far left side of the chart will end with what number? A. zero B. two C. four D. one
D. one The numbers running down the left side of the pocket chart will be 11, 21, 31, 41, 51, 61, 71, 81, and 91. (Patterns)
Children in Mr. Fox's first-grade class love to play Snip, Snap, Clap. In this game, one child shows the others three simple movements to repeat over and over again. This is called A. physical education. B. operations. C. communication skills. D. patterning.
D. patterning. Repeating a series of anything (numbers, letters, movements, colors) over and over in order is called patterning. (Numbers and Operations)
When children count nickels, they count by fives. When they count dimes, they count by tens. We call this kind of counting A. borrowing. B. regrouping. C. estimating. D. skip counting.
D. skip counting. Whenever children think in terms of silent or voiced numbers in a line and following a distinct pattern, it is referred to as skip counting. Here is an example: __, __, 3, __, __, 6, __, __, 9. (Patterns)
Which expression has coefficients of 2, −3, and 1 and degrees of 4, 2, and 0? A. 4x² + 2x^−3 + x B. 2x^4 − 3x² + x C. 2x4 − 3x^−2 + 1 D. 2x^4 − 3x² + 1
D. 2x^4 − 3x² + 1 The coefficients of the expression are the numerical values in each term: 2, −3, and 1. The degrees are the exponent of the corresponding variable. Because the third term (1) has no variable, its degree is 0. (Algebraic Thinking)
What is the next number in this geometric sequence? 3, 12, 48, 192, 768... A. 772 B. 1,536 C. 3,042 D. 3,072
D. 3,072 The sequence follows a pattern where the previous number is multiplied by 4. The correct product of 768 and 4 is 3,072. (Algebraic Thinking)
If added to the data set below, which number would be considered an outlier? {12, 9, 7, 15, 12, 10, 12, 17, 11, 20, 12} A. 7 B. 12 C. 21 D. 33
D. 33 The number 33 is significantly larger than the largest value in the data set (20). Therefore, it is an outlier of the set. (Data, Statistics, and Probability)
The following set shows the numbers of pages for eight books on a shelf. 322, 240, 288, 240, 240, 308, 340, 244 If a book were added to the shelf, which length would affect the range of the pages of the books on the shelf? A. 240 pages B. 299 pages C. 333 pages D. 344 pages
D. 344 pages A book with a length of 344 pages would increase the range of the data set from 100 to 104. (Data, Statistics, and Probability)
At one point in its orbit, the moon is 400,000 km from the Earth. Which number shows this value, in km, using exponential notation? A. 400 × 10³ B. 4 × 10^6 C. 40 × 10^5 D. 4 × 10^5
D. 4 × 10^5 The value of 4 × 105 is equivalent to 400,000, so this is correct. (Numbers and Operations)
Which percent expresses the same value as 7/8? A. 0.78% B. 8.75% C. 78% D. 87.5%
D. 87.5% 7 divided by 8 is equal to 0.875. The percent equivalent is 87.5%. (Numbers and Operations)
The coordinate (3,−4) is in which quadrant of a coordinate plane? A. I B. II C. III D. IV
D. IV (3,−4) is in the fourth quadrant of the coordinate plane, which is below the x-axis and to the right of the y-axis. (Geometry and Measurement)
Each length of a cube is tripled to form a new cube. How much larger is the volume of the new cube compared to the original cube? A. It is 3 times larger. B. It is 6 times larger. C. It is 9 times larger. D. It is 27 times larger.
D. It is 27 times larger. When one side of a cube is increased, its volume increases by an exponent of 3. (Geometry and Measurement)
The following data set shows the snowfall (in inches) in a city for the past seven years. {5, 8, 11, 9, 36, 10, 5} Which value would best predict how much snowfall the city will get in the following year? A. Mode B. Range C. Mean D. Median
D. Median The median is the value in the middle of a data set when all the values are put in order from least to greatest. (Data, Statistics, and Probability)
Which three-dimensional figure has exactly four corners? A. Quadrilateral B. Square pyramid C. Rectangular prism D. Triangular pyramid
D. Triangular pyramid A triangular pyramid is the only solid figure with straight edges and exactly four corners. The base of the pyramid has three corners and the top has the fourth corner. (Geometry and Measurement)
What is the Volume Formula for a Rectangular Prism?
length x width x height
What is the formula for Surface Area?
length x width x number of faces
