E-06 Math
Which of the following terms best describes a polygon with 4 sides with only 2 angles of equal measure?
Quadrilateral A quadrilateral is a shape with 4 sides and 4 vertices. It can have any combination of equal angle measures.
A two-dimensional net of a three-dimensional figure has 5 faces, 8 edges, and 5 vertices. What figure is represented by the net?
Rectangular Pyramid A rectangular pyramid has a rectangular base with triangular sides that meet at a vertex.
Mr. Harris assigns his students to create a factor tree of the products of a number. One student turns in the product factor tree of 32 shown here. Which of the following best describes the error in this factor tree?
The factor tree identifies the sums and not the product factors of many of numbers. The third level of factors is the sum of the second level numbers (4 + 4 = 8). The correct factors of eight would be either (4 and 2) or (1 and 8).
Caitlin knows that all birds have a beak. Adam is a bird. Therefore, Caitlin concludes that Adam has a beak. What type of reasoning is Caitlin using?
deductive reasoning Deductive reasoning involves statements such as: every dog is happy; Sally is a dog; therefore Sally is happy. Caitlin is using exactly this type of reasoning.
Which three dimensional figure has 6 vertices, 9 edges, and 5 faces?
triangular prism A triangular prism has 6 vertices, 9 edges, and 5 faces.
The state sales tax is 7.5%. Which number could also represent 7.5%?
3/40 There is always the option of arriving at the answer by eliminating incorrect answer choices, but it is always a good idea to double-check the final choice. In the case of this question, 3/40 = 3 ÷ 40 = 0.075 = 75/1000 = 7.5/100 = 7.5%.
Jessica is working on adding 8 to 25. She starts counting at 25, using her fingers to count 8 more numbers out loud. Which counting technique is she using?
Counting on When counting on, a student starts at one number and counts until a second number is reached
Which of the following comparisons between equations and inequalities is NOT true?
Equations are solved using inverse operations while inequalities cannot be solved with inverse operations. This is false; both equations and inequalities can be solved using inverse operations to isolate the variable.
Mr. O'Malley is teaching his students about pyramids and prisms. Which is the most appropriate learning goal for the unit?
Students will be able to differentiate between various pyramids and prisms. This encompasses the other learning outcomes
Mr. Barrios is teaching a unit on multiplication to his fifth-grade class. On the very first day he gives an exit slip with the following problem on it: 123.456 \times 789 =123.456×789= _______ Every single student gets the question correct. How should he adjust his teaching?
Teach more advanced multiplication content to challenge his students. This is the best answer. While every student getting the answer to the exit correct could indicate stellar teaching, it could also indicate that students had previously mastered the material. He should consider adding more advanced content to his lessons to keep his students challenged and engaged.
Mrs. McCoy writes two equations on the board for her class. +5 - 5 = 0+5−5=0 -20 + 20 = 0−20+20=0 Which of the following properties of integers is Mrs. McCoy most likely trying to illustrate?
The additive inverse property The additive inverse property is that each number has an inverse that, when added to the number, equals 0: -a + a = 0−a+a=0 and a - a = 0a−a=0. Combining a number with its additive inverse yields the answer "0".
A student tosses a six-sided die, with each side numbered 1 through 6, and flips a coin. What is the probability that the die will land on the face numbered 1 and the coin will land showing tails?
The probability of getting any number on a six-sided die is one out of six (1/6), because there are six equally possible sides. The probability of a coin landing on tails is one in two (1/2) because there are two equally possible outcomes. To find the probability of a 1/6 instance happening at the same time as a 1/2 instance, simply multiply the probabilities together. This yields (1/6) * (1/2) = (1/12).
Which of the following is the best way for elementary students to learn inverse operations?
Use a number line to illustrate adding and subtracting the numbers in a fact family. This allows students to visualize the concept and understand opposite operations.
Of the following higher-order thinking questions, which would be the most appropriate in a fourth-grade classroom?
Using the information you have collected, create a bar graph to display the data. A fourth-grader is capable of using data to create a bar graph
Which of the following is not considered a higher-order thinking question?
What is the product of 6 and 3? This question could be solved by recall and may not require any analysis by the studen
Which of the following would be an appropriate time for a classroom teacher to use a formative assessment?
as a closing activity at the end of a class period B when students are involved in a cooperative group project C as the teacher is introducing a new concept
Students are asked to solve the word problem below. The school carnival is coming up and Jenny and Sarah plan to sell cupcakes. Since the school carnival is a fundraiser, Jenny and Sarah's parents make a donation to their cupcake booth to get them started. Jenny starts with a $5 donation and sells her cupcakes for $3 each. Sarah starts with a $10 donation and sells her cupcakes for $2 each. How many cupcakes do Jenny and Sarah have to sell for their profits to be equal? One student's response is "Zero, because if Jenny sells her cupcakes for more money, then she will always have more profit." Which of the following activities could help the student realize his misconception?
graphing the scenarios Graphing the two scenarios will help the student see where the graphs intersect and therefore are equal in profit.
The teacher provides a word problem for her students: Sandra is making sandwiches for her family's camping trip. She has 72 slices of turkey, 48 slices of cheese, and 96 pieces of lettuce. What is the greatest number of sandwiches she can make if each sandwich has the same filling of turkey, cheese, and lettuce? Which of the following mathematical concepts is she most likely teaching in this lesson?
greatest common factor The greatest common factor is the largest number that can be evenly divided into a set of numbers. Finding the greatest common factor is the first step to solving this problem.
Which of the names below is not a proper classification for \frac{48}{3}348 ?
irrational Irrational numbers can not be written as a fraction. Therefore, this number is not irrational.
Which of the following cannot form a regular tessellation?
pentagon A regular tessellation must be able to tile a plane with no overlaps or gaps by repeating a regular polygon. The only regular polygons that can form a regular tessellation are the triangle, square, and hexagon. A regular pentagon does not form a regular tessellation.
A first-grade student is asked to find the total value of the following coins: 3 dimes, 1 nickel, and 4 pennies. The student's response is that the coins are worth $0.12. Based on this response, what concept does this student likely need help with?
recognizing different coins and their respective values Based on their answer, the student most likely recognized the nickel as 5 cents but thought that the dime and pennies were all the same type of coin and worth 1 cent each. The teacher should plan on working with the student on recognizing the difference between dimes and pennies and recalling the values of each.
Students in Mr. Miller's class are given a worksheet with the different combinations that can be reached when flipping a coin and rolling a standard die. Students then work in pairs to flip and roll all of the combinations. What topic is Mr. Miller teaching?
sample space The sample space is the list of all possible outcomes.
Which three dimensional figure has 5 vertices, 8 edges, and 5 faces?
square pyramid A square pyramid has a square as a base and four triangular faces. It has 5 vertices and 8 edges.
The equation 5 \left( 7+1 \right) =5 \left( 1+7 \right)5(7+1)=5(1+7) illustrates which of the following properties of real numbers?
the commutative property of addition The commutative property of addition states that the sum of 2 values remains the same when you switch the order of the values.
Which of the following is not a rational number?
π The value of pi (π) never ends and does not repeat, making it irrational.
Which of the following demonstrates the identity property of addition?
−8+0=−8 In the identity property for addition, adding any number and 0 does not change the value of the number
Jessica is having 42 friends over for her party. She baked 7 extra-large pizzas with 12 slices each. If everyone shares equally, how much of one pizza will each friend eat?
1/6 To find how much each person eats, we need to split 7 pizzas into 42 portions, so \frac{7}{42}=\frac{1}{6}427=61, so each person will eat \frac{1}{6}61 of a pizza.
Tosha has 8 coins in her pocket. She has a mixture of pennies, nickels, dimes and quarters, but she has no more than 3 of any coin. What is the largest amount of money she could possibly have?
$1.11 To satisfy the prompt given, there must be at least one of each coin. She will need to have the most number of the coins with the greatest value: quarters and dimes. So, that would be 3 quarters, 3 dimes, 1 nickel, and 1 penny. This totals $1.11.
Which of the following is an example of the associative property of addition?
(3x+7y)+8=3x+(7y+8) The associative property of addition allows the grouping of addends to change without changing the sum
Which of the following numbers is neither prime nor composite?
1 One is neither a prime number nor a composite number.
Mr. White displayed 3 sequences on his whiteboard during math class: 20, 10, 5, 0, -2.5, ...20,10,5,0,−2.5,... 324, 108, 36, 12, 4, ...324,108,36,12,4,... -6, 1, 8, 15, 22, ...−6,1,8,15,22,... He asked his students to pick one of the sequences, determine if it was arithmetic or geometric, and explain their reasoning for their answer. Which student answer correctly identifies the sequence and has a sufficient explanation?
"-6, 1, 8, 15, 22, ...−6,1,8,15,22,... is an arithmetic sequence because if you add 77 to each term, you get the value of the next term in the sequence. When you have a common difference, the sequence is arithmetic." An arithmetic sequence has a common difference. In -6, 1, 8, 15, 22, ...−6,1,8,15,22,..., 77 is added to each term to continue the sequence. This statement is correct.
A first-grade teacher has created three different ramps by stacking large blocks and laying pieces of cardboard from the tops of the block towers to the floor. One ramp is built with two large blocks, one with three, and one with four. After students have had a chance to roll a ball down each of the ramps, the teacher decides to ask students a question. Which of the following questions is most appropriate to ask at this point in the experiment?
"What have you noticed about how the ball rolls differently with the different ramps?" This question encourages students to make observations, an important step at this point in the experiment.
Mrs. Janie asked her class to write their own geometric sequence. As she walked around the room, she noticed Brad had 3, 6, 2, 4, \frac{4}{3}, \frac{8}{3}, ...3,6,2,4,34,38,...written on his paper. When Mrs. Janie asked Brad to explain his sequence, he replied, "My sequence is a geometric sequence because you multiply by 22, then multiply by \frac{1}{3}31, then you multiply by 22 again, then multiply by \frac{1}{3}31 again and so on." What is the best teacher response to Brad's statement?
"Your reasoning has an error. In order for a sequence to be a geometric sequence, you must multiply by the same common ratio each time. You can not use two different ratios." This is correct, you must multiply by the same common ratio each time to calculate the next term in the sequence. Brad created a complex sequence.
If the number 180 is written as the product of its prime factors in the form a²b²c, what is the numerical value of a + b + c, where c = 5 and a and b do not equal 1?
10 The prime factors are the numbers that, when multiplied together, equal a number. In this problem there are three prime factors, where two are squared. We know that c = 5 so the equation (a²)(b²)(c) can be written (a²)(b²)(5) = 180. We can then divide by 5 and simplify this to (a²)(b²) = 36. Take the square root from each side simplifies the equation further to (a)(b) = 6. We know that a and b do not equal 1, so they must equal 2 and 3. So (2²)(3²)(5) = 180 and a + b + c is 2 + 3 +5 = 10.
Tim rolls a pair of dice 25 times and records the sum of the two numbers. How many different sums are possible?
11 To work these sorts of problems, draw a sample space. In this case, you would list the possible sums when adding 1-6 on one die and 1-6 on the other die. This would give you a list of "2, 3, 4, 5, 6, 7, 8, 9 10, 11, 12" which is 11 possible unique sums
ut the following fractions in order from least to greatest: \frac{1}{2}, \frac{3}{4}, \frac{5}{7}, \frac{3}{16}21, 43, 75, 163
163, 21, 75, 43 The easiest way to order these is to convert them to decimals and round to the hundredths place: 1/2 = 0.5 3/4 = 0.75 5/7 = 0.71 3/16 = 0.19 Then order the decimals and pair with their fraction equivalent
Students are plotting improper fractions on a number line. Quincy places a fraction between the 5 and the 6 on the line. If the denominator is 3, which of the following could be the numerator?
17 The fraction must be greater than 5, which is equal to 15/3, and less than 6, which is equal to 18/3. 17 is the only number that meets the requirements.
Sheila has a large collection of stickers. She gives ½ of her collection to Sue, ½ of what is remaining to Sandra, and then gave ⅓ of what was left over to Sarah. If she has 30 stickers remaining, how many stickers did she begin with?
180 stickers
Hy is interviewing new candidates for a position at his company. If he schedules \frac{1}{3}31 of an hour for each interview, how long will it take him to interview 66 applicants?
2 hours Hy wants to find the total amount of time given the number of equal parts for each interview, hence multiplication will be used. To find the total time Hy will spend interviewing, multiply the time for one interview with the total number of interviews: \frac{1}{3}\times 6=\frac{1}{3}\times \frac{6}{1}=\frac{6}{3}=2 \text{ hours}31×6=31×16=36=2 hours
If a number ends in zero, what number(s) can it be divided by?
2 nd 5
If a number is divisible by 6 and 8, what other number(s) can also divide into it?
2-3-4
Which of the numbers below represents 23 tenths?
2.3 Since 23 \times \frac{1}{10}=23 \times 0.1=2.323×101=23×0.1=2.3, this is the correct representation for '23 tenths.'
Approximately what fraction of the population is within one standard deviation of the mean in a dataset with a normal distribution?
2/3 68.2% of the population will be within one standard deviation of the mean. The closest benchmark fraction to this percentage is ⅔.
The numbers 2, 3, and 5 are the only prime factors of which of the following products?
27×40 The product of 27\times 40 = (3\times 3\times 3)(2\times 2\times 2\times 5)27×40=(3×3×3)(2×2×2×5). The numbers 22, 33, and 55 are the only prime factors of this product.
Jessie draws a marble from the bag shown and then, without replacing the first marble, he draws a second one. Which expression shows the probability that he drew a red marble both times?
3/10 • 2/9 This is an example of dependent events. P(red) = 3/10 for the first draw. However, the first marble is not returned to the bag, changing our sample to 9 marbles. If the first marble drawn was red, that leaves only 2 red marbles, so on the second draw, P(red) = 2/9. The probability of both events happening is the product: 3/10 • 2/9.
Out of the options below, which number has a digit in the thousands place that is exactly three times the value of the digit in the tens place?
346, 129 In this number, 6 is the digit in the thousands place and 2 is the digit in the tens place. 6 is three times the value of 2.
What is the greatest odd factor of 1120?
35 The prime factorization of 1120 is 2^5\times 5\times 725×5×7. The greatest odd factor is given by the product of the two greatest odd prime factors: 5\times 7=355×7=35.
What is the greatest odd factor of 2,496?
39 The prime factorization of 2,496 is 26 × 3 × 13. When multiplying the odd numbers (3 and 13), the greatest odd factor is 39
If the number 888 is written as a product of its prime factors in the form a3bc, what is the numerical value of a + b + c?
42 The prime factorization of 888 is 23 \times× 3 \times× 37. 42 is the correct answer because 2 + 3 + 37 is 42.
How many unique even factors and how many unique odd factors does 24 have?
6 even factors and 2 odd factors The number 24 has 8 factors, all listed below. 24=1\times 24=2\times 12=3\times 8=4\times 624=1×24=2×12=3×8=4×6 Six of the factors are even (24, 2, 12, 8, 4, 6) and two of the factors are odd (1, 3
A second-grade teacher is planning a lesson to review three-dimensional shapes. Students have already learned the attributes of three-dimensional shapes and the necessary vocabulary, such as faces, edges, and vertices. Which of the following questions could the teacher include in her lesson that would be most likely to encourage higher-order thinking?
A 3D shape has at least one face that is a rectangle. What are some of the 3D shapes that it could be? This question encourages students to think about 3D shapes in a different way. Students are using higher-order thinking skills to visualize the rectangular face and evaluate the possible 3D shapes that it could be.
A student asks the teacher, "Why is the area of a triangle formula ½bh?" Which of the following would be the most appropriate answer for the teacher to provide?
A parallelogram is the combination of two congruent triangles. Since the area of a parallelogram is bh, one half of the area of a parallelogram equals the area of a triangle. Every parallelogram is made up of two congruent triangles. The area for a parallelogram is base × height (bh), so the area of each of the two congruent triangles is one half of the parallelogram, or (1/2bh).
How many faces does a rectangular prism have?
A rectangular prism has 6 faces.
Which of the following statements about number systems is true?
All integers are natural numbers.
Amy is making croissants. She has 11 pounds of dough. If each croissant uses \frac{1}{6}61 of a pound of dough, how many croissants can she make?
Amy is taking the total amount of dough and dividing it into equal parts, hence division will be used. To find the number of croissants Amy can make, divide the total amount of dough by the weight of each croissant:6111=11÷61=11×16=66 croissants
Mrs. Spiser is teaching students about populations and samples. At the start of their lunch period, they are going to the cafeteria to take a randomized survey of how many students bought lunch. They will then compare that to the whole school to determine how many kids buy lunch each day. What should she include in her lesson plan that morning to reinforce the concept?
As students enter her room, they randomly draw a red or black card. She teaches the concept by explaining that the class is the population and students who drew a red card are the sample group. This demonstrates random sampling by showing that a random amount of students in the class (the population) will be surveyed (the sample group). When they go to the cafeteria, they will randomly sample some students (the sample group) to evaluate the entire school (the population).
Mr. James plans to assess his students' knowledge during a unit on linear functions and would like feedback from the students on how well they feel they are learning the concepts. Which of the following assessment would be the most appropriate for Mr. James to use during the unit?
Daily open-ended formative assessment in which the students complete a problem, with justification and any questions they still have about the material from that day. These assessments would best allow Mr. James to assess student learning and gain insight on where they are struggling.
Mrs. Gore is teaching about simple and compound events in probability. As she walks around the room, she has students draw a marble from a bag and answer the probability of drawing certain colors. What is the main motivation for teaching it this way?
Giving students an interactive way to learn The interaction increases participation and therefore learning
What details should a teacher consider when choosing appropriate higher-order thinking questions for math?
Grade level and subject matter standards It is pertinent to tailor questions to the skill level and material being taugh
Mrs. Wheelan is teaching geometric shapes and wants to use informal reasoning questions for discussion. What question is best to start with?
How do geometric shapes play a role in daily life? This is an open-ended question and it allows for real-world connections.
Which of the following statements is false?
Inductive reasoning never leads to a correct conclusion. Inductive reasoning, or reasoning from specific examples to end with a more general conclusion, may or may not lead to a correct conclusion. It is incorrect to say that inductive reasoning never leads to a correct conclusion.
Which of the following sentences is true?
Irrational numbers often include a symbol, such as square root or pi. Irrational numbers can not be expressed as a ratio of two integers and are thus often written with a symbol or radical. D Integers include all natural numbers, whole numbers, and their opposites. Integers are positive and negative counting numbers and zero.
Suppose Mike's actual weight is 165 lbs. His scale says his weight is 164 lbs. What can be said about his scale? A It is accurate.
It is accurate. This scale is accurate because it gives a weight close to his actual weight.
Which of the following is true of a statistical experiment?
Its outcome is determined by chance. The outcome of a statistical experiment is determined at random. Only one outcome will occur for each statistical experiment and all possible outcomes are known beforehand, but which outcome will occur is not predetermined.
Which situation could best be represented by the equation: 12x = 5412x=54?
Marty made car payments on her car for 54 months until it was paid off. What is x, the number of years it took Marty to pay off her car? To get the total months, 54, multiply the number of years, x, by the number of months in a year, 12; 12x = 5412x=54.
Which statement about a rectangular prism and a rectangular pyramid is true?
Only the pyramid has triangular faces. Prisms have rectangular faces while pyramids have triangular faces. A pyramid has one base and a prism has two bases that are parallel to each other. A prism and a pyramid are named by their bases.
Anytown School District wants all elementary students to be able to use computational strategies fluently and estimate appropriately. Which of the following learning objects best reflects this goal?
Students evaluate the reasonableness of their answers. If a student is able to use computational strategies, strategies for computing an answer, as well as estimate properly, then the student should be able to evaluate the reasonableness of his final answer. A student who is fluent in computational strategies and is good at estimating will know if his answer is about what he expected the answer to be, or if he should review his answer because it does not match what he expected.
In the pair of dice that Tim rolled 25 times, he recorded a sum of 4 on three of those rolls. What is the difference between the theoretical probability and the experimental probability of rolling a pair of dice and getting a sum of 4 based on Tim's experiment?
The experimental probability is about 4% greater than the theoretical probability. Theoretical probability is determined by analyzing the situation, in this case the rolling of a pair of dice, and determining the number of successful outcomes divided by the number of possible outcomes. The experimental probability is the probability that occurred in this specific experiment. The theoretical probability of rolling a sum of 4 is PT(4) = 3/36 = 1/12, about 8.3%. When Tim rolled his dice 25 times, he got a 4 on three of those rolls. While the theoretical probability of rolling a pair of dice and getting a sum of 4 is always about 8.3%, the probability that occurred in Tim's experiment, the experimental probability, is PE(4) = 3/25 = 0.12 = 12%. This means his experimental probability was about 4% greater than the theoretical probability (12% - 8.3% = 3.7%, about 4%).
Mrs. Kellie teaches her students about the theoretical probability of rolling a 6-sided die and it landing on any one side. Then her students break into groups and take turns rolling a die to collect experimental data. After 100 trials, one group has the following results: Number on Die Frequency 1 16 2 12 3 18 4 17 5 17 6 20 Based on the data, which of the following student conclusions is correct?
The experimental probability of rolling a 6, 20%, is higher than expected based on the theoretical probability. The theoretical probability of rolling a 6 is 100 \div 6=16.7\%100÷6=16.7%, so an experimental probability of 20% is higher than expected.
The numbers 2, 5, and 11 are the only prime factors of which of the following products?
The product of 44\times 50 = (2\times 2\times 11)(2\times 5\times 5)44×50=(2×2×11)(2×5×5). The numbers 22, 55, and 1111 are the only prime factors of this product.
Students are asked to identify the answer to a problem without actually solving it. She asks them: What answer is best when given the expression: 1/10 × 7/60 ?
When 2 fractions are multiplied, the product is smaller than either original fraction When 2 fractions are multiplied, their product will always be smaller than the original number.
A teacher prompted his class to write their own examples of arithmetic sequences on their papers. As the teacher is circulating, he sees the following written on one Tasha's paper: 2, 3, 5, 8, 12, 17, 23... When asked to explain her work, Tasha explains, " The sequence is arithmetic because to get the next number in the sequence, you +1, +2, +3, +4, +5, see? So you always add one more to get the next number." Which of the following is the best teacher response to Tasha's reasoning?
Your reasoning is incorrect; you must add by the same number every time for the sequence to be arithmetic. This is correct; arithmetic sequences require you to add by the same number every time to get the next number in the sequence (ex: adding +1 to get the next number every time, or adding +5 every time to get the next number).
A fifth-grade student was asked to multiply 15 and 35. His work is provided below. As his teacher, what remediation would you plan on providing?
a remedial lesson on place value The errors come from a lack of understanding of place value. When the student multiplied 5 and 5, they should have decomposed the 25 into 20 and 5. The 20 would have carried as a 2 above the 3 and added to the product of 5 and 3. The student should have added an additional zero at the end of the result when he multiplied the 1 in the number 15 because its actual value is 10, not merely 1.
A second-grade teacher encourages her students to add two-digit to one-digit numbers by "grabbing the larger number in their mind" and using their fingers to count up to find the total. What counting technique are students using when they do this?
counting on By starting with the larger number in their head and counting up with their fingers, students are using a strategy of counting on
A survey is taken of students in a math class to determine what pets the students have. 7 students have birds; 15 students have cats; 18 students have dogs. Some students have more than 1 animal. For example, 3 students have cats and dogs and 4 students have cats, dogs, and birds. All students have at least one of these three types of pets. Which of the following would be the best strategy to use to answer a question about how many total students are in the class?
draw a Venn diagram A Venn diagram is a visual strategy.
Michelle is assigned homework to flip a coin 10 times, then 100 times, then 1000 times. She decides to use her computer to generate a 1 for heads or a 2 for tails. She has the following results: Number Of Trials Number of Heads (1s) Number of Tails (2s) 10 7 3 100 45 55 1000 507 493 The students are then asked to calculate the percentage of flips that are heads versus tails. What topic is the teacher wanting students to explore?
empirical probability Empirical probability looks at the exact percentage of outcomes that occurs in a real situation.
Colin is a child learning about animals. He notices that dogs have four legs and a tail. When he sees a cat he incorrectly calls it a dog. What type of reasoning is Colin using?
inductive reasoning Inductive reasoning or generalizing knowledge from one area to another is used to make predictions. This is what Colin is doing when he predicts that a cat is a dog.
A mathematics teacher gives her class a two-question clicker quiz at the end of each class period and tabulates their answers according to their mathematical understanding, misconceptions, and error patterns. If her goal is improvement in her students' mathematical proficiency, her best use of the data would be to use it to:
inform upcoming instructional strategies. Data on student understanding, misconceptions, and error patterns is best used to inform instructional strategies on the same or subsequent topics.
Mr. Swan wants to ensure that his students truly understand the material he is teaching. When students get questions incorrect on a test, he presents them the opportunity to correct their answers for half credit. He asks students questions such as "what if I changed this number?" and "why did you do this?" What process is Mr. Swan trying to get his students to engage in?
metacognition Metacognition is reflecting on one's thought process to deepen understanding. This is what Mr. Swan is attempting to do.
A first-grade student is finding the value of a set of six nickels. What counting skill will this student most likely need in order to complete this task?
skip counting In order to efficiently count the value of six nickels, the student will need to already be familiar with skip counting by fives.