Which of the following summative assessment prompts on fractions will best reveal whether a student understands fraction applications in the real world?

What is the place value of the "5" in the number 15,436,129?

Sabrina finds a coat on sale for 18% off the original price of $85. She computes her potential savings in the following way:

\$85 \times 0.18

$85×0.18

Which of the following methods could Sabrina also use to correctly determine the potential savings?

What is the place value of the "9" in the number 6,587.9213?

The expression 3^-3×3² is equivalent to:

Which of the following cannot be expressed as a real or an imaginary number?

Which of the following is the additive inverse element of 3+ 2i?

What is the digit in the hundreds place in the product of 63 × 31?

Mr. Chappel hangs posters in each corner of the room with different names of number categories. One corner has a sign that says integers, another has a sign that says rational numbers, another says irrational numbers, and the last says whole numbers. Students are assigned a corner to start and on the first rotation they must add a definition to the sign. On the second rotation, they must add numbers that are examples to the sign. What should be the third rotation task?

What is the exponential notation of 1656 and its prime factors?

If x is between 10 and 20, and y is between 100 and 200, ​ x/ y must be

In a school with 900 students, 15 percent of the students are in 7th grade. If there are 5 evenly sized 7th grade classes, how many students are in each class?

Angela has a stack of construction paper on her desk. Each day she takes one piece of paper, cuts it into 3 pieces to make 3 greeting cards for friends. If Angela has been making greeting cards for 12 days, how many greeting cards has she made?

Which of the following equations could a student use to solve this problem?

If the value of A equals 1/5 and the value of B equals 1/2, which of the following equals C?

Which of the following is the correct order from least to greatest?

3^–3, 1/(3²), 3⁰, (3^–2)³, 3^–250

What is the value of the "3" in the number 17,436,825?

Which of the following statements is correct?

Michal is riding his bike at a constant 12 miles per hour. At noon he sees a road sign stating that Longtown is 14 miles away and Lyons is 16 miles away. How far will he be from Lyons at 12:45 p.m.?

What is the prime factorization of 36?

What is the difference between rounding 57,213 to the thousands place and the ten thousands place?

Which symbol most accurately reflects the relationship between the two numbers below? 0.7 ☐ 4/5

What is the scientific notation of 674.9723?

In Anytown ISD, 13 out of every 20 students ride the bus. Which ratio compares the number of students who ride the bus to those who do not?

When Joshua moved into a new apartment, his monthly rent decreased from 35% of his budget to 30%. If he budgets $3,200 monthly, how much will he save annually?

Which symbol most accurately reflects the relationship between the two numbers below?

0.6 ☐ 3/5

What is the difference between -5² and (-5)²?

Use the table shown to answer the following question.

Of the three subjects tested, a student correctly answered the number of questions shown in the table. What percentage of the questions on the entire test did the student get wrong?

The Johnson boys are splitting the last of a cake their mom made yesterday. When they start, ⅔ of the cake has already been eaten. Sam eats ⅙ and Scott eats ⅜ of the remaining cake. Jack eats what is left after Sam and Scott take their slices away. Who ate the most cake?

Use the table shown to answer the following question. Of the three subjects tested, a student correctly answered the number of questions shown in the table. What percentage of the questions on the entire test did the student get wrong?

The Johnson boys are splitting the last of a cake their mom made yesterday. When they start, ⅔ of the cake has already been eaten. Sam eats ⅙ and Scott eats ⅜ of the remaining cake. Jack eats what is left after Sam and Scott take their slices away. Who ate the most cake?

Put the following fractions in order from least to greatest:

$$\frac{1}{2},\ \frac{3}{4},\ \frac{5}{7},\frac{3}{16}$$  

For homework, Mr. Waters asked students to bring in 3 receipts from home. In class, they practiced rounding the prices of items and then totalling them to compare to the final price paid. What is the best reason this is good teaching method?

Which of the following describes the most helpful first step(s) in determining whether a given number is prime or composite?

On the number line, what value is exactly halfway between –⅞ and 1½?

Shep has the numbers 1 through 8 to arrange in the largest possible number with each numeral only being used once. The 8 must be in the ten-thousands place. What number did he create?

Which of the following points on a number line is the greatest distance from .5?

Order these least to greatest:

$$\left(\frac{1}{4}\right)^2,3^{-4},\ 4^3$$  

She instructs her students to write down the smallest number possible with the 8 in the thousands place and the 1 in the tens place. Which of the following would be the correct answer?

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?

What is the prime factorization of 18?

If each square in the decimal square has a value of 0.1, then which of the following is the decimal numeric representation of the shaded area?

Bobby is buying gumballs for 7 of his friends. There are 51 gumballs before Bobby makes his purchase at the store. Bobby wants to give each of his friends the same amount of gumballs and not have any gumballs left. Which of the following approaches can Bobby use to find the greatest number of gumballs he can purchase to give his friends?

Which of the following is the product of -2 + 4i and 1+ 3i in simplest form?

At Memorial High School, 60 of the 240 freshmen students are on an athletic team sponsored by the school. If the ratio is the same for the sophomore class, how many of the 220 sophomores are NOT athletes?

A class is learning about ratios and percentages. The teacher tells the class that at last Friday night's football game there were between 800 and 1000 people. Of those at the football game, about 13-17 percent of the people had blonde hair. Which of the following is the most reasonable estimate of the number of people at the football game with blonde hair?

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?

Team 1 scored 31.25% of the points. Team 2 scored 0.375 of the points. Team 3 scored 3/16 of the points, and Team 4 scored 1/8 of the points.

What percentage of the points were scored by even-numbered teams?

Which of the following sentences is true?

Select all answers that apply.

A sweater is on sale for $43.75. It is 30% off the original price. What is the original price?

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?

Which of the following fractions has the smallest value?

Which of the following numbers is between 4,681,700 and 4,872,300?

John's coach wants him to reduce his mile time by at least 2%. Currently he can run a mile in 4 minutes and 45 seconds. About how many seconds shorter must his new mile be to satisfy his coach?

Two friends painted a barn. The friends painted at a consistent rate. If the barn took 20 hours total to paint, how long did it take them to complete 35 percent of the painting?

If the value of c is between 0.00082 and 0.0026, which of the following could be c?

A shoe store is offering a 10% discount on a pair of new basketball shoes that normally cost $63.22. What is the price of the shoes, before tax, after the discount is applied?

The state sales tax is 7.5%. Which number could also represent 7.5%?

The numbers below are listed from least to greatest.

$$\frac{1}{5},\frac{5}{4},m,\frac{23}{12},\frac{22}{7}$$  

Which of the following answer choices could NOT be the value of m?

A school board is proposing a 5% decrease in the length of the school day. Currently the school day is 7 hours (420 minutes) long. How many minutes shorter would the school day be with the proposed decrease?

Which symbol most accurately reflects the relationship between the two numbers below?

1.2 ☐ $$\frac{9}{10}$$  

​

Which of the following sets of numbers and number representations is in the correct order from least to greatest?

Students were asked to name point B. Zoe wrote that B equals -2.4, Julio responded that it equals -2 ¼, Sage said that it equaled -3 ¾ and Kaitlyn said that Zoe and Julio were both correct because the numbers were equivalent. Which student was correct in their response?

In an omelet made of only cheese and eggs, the ratio of ounces of cheese to omelette is 2 to 7. How many ounces of egg are needed to make the jumbo 21-ounce omelet?

Angela and Patrick will divide a profit of $350 in the ratio 4:3. If Patrick receives the larger amount, which proportion could be used to find his share of the profit?

Which of the following is not a rational number?

which numner is not natural

What is the value of the "8" in the number 17,436,825?

The term "imaginary" is perhaps an unfortunate, but historical, word choice because it often leads to student confusion when imaginary numbers are introduced. Which of the following could Mr. Brown do to reduce this confusion among his students?

In order to compare fractions, students must first find the least common denominator first. A student has been given the fractions ¼, ⅜, 7/12, and ⅚. He determined the least common denominator is 24. What error has this student made in preparing to compare these fractions?

¼ = 1/24 ⅜ = 3/24 7/12 = 7/24 ⅚ = 5/24

An electronics store is offering a 20% discount on a pair of noise-cancelling headphones that normally cost $169.79. What is the price of the headphones, before tax, after the discount is applied?

Students are working on measurement principles.

Kali measures a countertop in the classroom that is 5,743 mm long.

Lauren finds that the distance on a map between New York City and Washington D.C. is drawn as 364.1 mm.

How does the 3 in Kali's number compare to the 3 in Lauren's number?

Which of the following is the greatest common divisor of 3300 and 1050?

The high school gym holds 1430 spectators per event. At the last basketball game, the attendance was 1152 spectators. What percent of the seats were empty?

Which of the following numbers would fall between 1/3 and 2/3 on a number line?

Select all answers that apply.

$$\frac{6}{9}<_{\ -}<\frac{10}{12}$$  

​

Which of the following values can fill the empty box and satisfy the statement above?

What is 19,968 rounded to the hundreds place?

Order the following numbers from greatest to least: -2, ½, 0.76, 5, √2, π.

What is the value of the "7" in the number 432.0769?

Which of the following numbers is neither prime nor composite?

The senior class in a local school district has 2430 students. Approximately 4 out of 10 students will take a physics class while in high school. Which of the following best approximates the number of seniors in the district who will have taken a physics class by the time they graduate from high school?

In which of the following are the numbers ordered from greatest to least?

The table shown gives the number of cookies sold by each person at a bake sale. Who has not sold ⅓ of their cookies?

When considering the addition problem 1/3 + 3/8, which of the following statements is true?

Select all answers that apply.

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?

Use the number line below to answer the question:

Which of the following decimals can be represented on a number line between the points A and B?

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?

Put these fractions, decimals and percentages in order from greatest to least:

15%, 0.34, 245%, 2 ¾, 1.5, 1/15

When Mr. Troutner introduces scientific notation to his math class, Jerome asks why they are learning about science during math class. What is the best answer to his question?

If A is equal to -4², then what is the value of C?

Which of the names below is not a proper classification for $$\frac{48}{3}$$  ?

The sizes of four microscopic organisms are measured for comparison in a research project. Of the four recordings below, which is the shortest in length?

Which symbol most accurately reflects the relationship between the two numbers below?

0.8 ☐ 4/3

What is the greatest odd factor of 2,496?

Mr. Kolbein wants his students to practice sorting numbers by order of magnitude. He thinks a game would be most engaging, and writes various numbers on index cards, one per card. He then designs a game in which pairs of students compete against other pairs of students to see which pair can sort number cards the fastest. Which of the following additional activities would increase the engagement and learning value of the game?

Which symbol most accurately reflects the relationship between the two numbers below?

0.4 ☐ 2/5

Which of the following is the product of 2 odd numbers and 1 even number, each of which is greater than 1?

Sally walked to her friend's house and then they went for a walk together. According to the graph, how much time of Sally's walk was spent a mile or less from home?

Mr. Wheeler has taught prime factorization to his class this week. In an effort to differentiate instruction, he decides to block off time to provide remediation for students with learning disabilities. What is the main problem with this approach?

What value does 8 represent in the number 2.86 x 10^4?

Mr. Jones is hosting a career day for his sixth-grade class. Jeremy tells him that his father cannot come present because his job has nothing to do with math because he did not attend college. Mr. Jones asks Jeremy what his dad does for a living. Jeremy says his dad is a carpenter. What should Mr. Jones tell Jeremy?

The formula for permutations is: nPr = $$\frac{n!}{\left(n-r\right)!}$$  

​

while the formula for combinations is: nCr= $$\frac{n!}{r!\left(n-r\right)!}$$  

.

As a warm-up, Ms. Caulkins asks her students to compare these two formulas and identify the differences and similarities before she has taught what the formulas are used for. What is her goal in this exercise?

which of the following corresponds to the progression of stages of learning about a new mathematical concept from most basic to most advanced?

A teacher engages her class in a discussion of the coordinate plane. The students are asked to identify the quadrants, the coordinate axes, and the mathematical notation for various points in the plane. Students are asked to develop a way to quickly identify the quadrant in which various points lie. Which of the following objectives is the teacher most likely trying to address with this lesson?

Mr. Kopko's class is learning about long division. He asks students to use the calculator to check their results. On the following division problem several students are confused by their results.

22/7 = 3R1 = 3.142857

How should Mr. Kopko instruct students to deal with remainders?

Maria has recently moved from Mexico City to the U.S. She is a secondary student who speaks little English, but who came from her school in Mexico City with excellent grades. Which of the following would be the most appropriate accommodation for Maria's math teacher to use with Maria?

At the end of a lesson on factoring, Ms. Wilson gave her class an exit ticket. After she reviewed the responses on the exit ticket, Ms. Wilson realized that many of her students were still struggling with the concept of factoring. Which of the following strategies would be best for Ms. Wilson to use in her next lesson on factoring to help the students solidify their conceptual understanding of factoring?

Mrs. Jones is teaching a lesson on slope-intercept form. She requires each student to find the slope and y-intercept of a set of graphs, then put them into a formula that describes the graph. The students work one problem at a time and Mrs. Jones circulates to check their work. If a student has the correct answer, Mrs. Jones gives them a checkmark and they move on to the next question. If the student has the wrong answer, Mrs. Jones directs them to the incorrect portion of their work and they revise their answer. Mrs. Jones continues to circulate the room until all students have finished the assignment. Which of the following learning theories best matches the activity Mrs. Jones uses with her students?

Students are separating costs of running a concession stand into expenses that depend on sales volume and those that do not. What concept does the teacher want students to understand through this activity?

Which activity can emphasize the interdisciplinary connections that math has to other subjects?

Anytown School District provides a 50 multiple-choice question mathematics assessment to all students. The students complete the assessment, the tests are scored, and the scores are compared throughout the school district. Which of the following mathematics component is most likely the goal of this type of assessment?

Students are using a curve-fitting computer simulation program. Which of the following is the best activity for the teacher to ask students to do using the software?

In a unit on personal finance, a sixth-grade teacher wants students to be able to identify the difference between fixed and variable costs. Which of the following examples would best highlight this difference?

A seventh-grade teacher has been teaching her students about areas of regular polygons. She has already introduced them to the topic at the concrete level by having students interact with magnet tiles. In which way should the teacher continue teaching the topic?

Mr. Fischer, a bilingual teacher, teaches a mathematics class composed of native English speakers and English language learners (ELLs). He has introduced a new topic with new vocabulary words in which he presented the vocabulary words with several examples. Which of the following strategies should Mr. Fischer use next to check each student's understanding of the vocabulary words?

Mr. Erikson has his friend Ted, who is an architect, come present to the class about how he uses math in his job. What is Ted likely to talk about?

A seventh-grade teacher is teaching her students to determine the area of circles. She gives them the formula area = πr2 and several word problems to complete. She notices many students are getting quadruple the area that they should. What went wrong?

A math teacher plans her instructional delivery method on resolving the difficulty students have distinguishing between mode and median. She plans to have students first work alone calculating the mode and median of sets of performance results from the school track team. Next, her students will work in groups of 2 or 3 to discuss and interpret their results, and record a summary of the significance of the results on whiteboards. Finally, the groups will present their summaries to the class, along with a teacher-led discussion of the findings.

By planning such an activity, the teacher demonstrates that she understands:

Which representation is best for demonstrating probabilities?

A seventh-grade teacher is teaching his students to determine area of circles. He wants to use manipulatives to help students truly understand the material. He brings coins of various sizes so students can measure and calculate area. He then has students count the number of drops of water that fit on each coin to see how closely the two are related. Select all of the following activities that would improve this activity.

Select all answers that apply.

Mr. Ginger is teaching his students about solving single variable equations. He decides to host a team competition where students are placed in groups of four and earn points for the team if they solve the equation the fastest. Only the fastest team can receive any points. Team A receives 160 points, Team B receives 40 points, Team C and Team D both receive 0 points. How can he improve this activity?

Use the multiplication problem below to answer the question that follows.

$$13\times12=\left(10\times12\right)+\left(3\times12\right)=120+36=156$$  

A student in a mathematics class wants to know whether the method above for multiplying integers is correct. Of the following, which is the best teacher response to the student?

Ms. Davis teaches a fifth-grade math class primarily composed of English language learners (ELL). Which of the following can support her ELL students?

Select all answers that apply.

A consumer takes out a loan for $500 that charges 10% annual interest. What is the total cost of the loan if the consumer pays it back one year from the date of origination?

A teacher is teaching students to graph linear equations. He wants students to use the graphing calculator to check their answers. He gives students graphing calculators and begins teaching how to graph linear equations. He finds that many students are unable to graph equations without the calculator. How can he improve his instruction?

Mr. Sherlock is teaching his students to convert units such as miles per hour to other units such as meters per second. Which is the best first activity for his students to master this concept?

A teacher wants to use concrete manipulatives to help her students learn about areas of regular polygons. Which of the following is the most suitable manipulative?

Which of the following would be the least appropriate use for handheld calculators in the classroom?

Students in Mrs. Rogers algebra class are learning basic statistics. They first learn to determine mean, median, and mode by traditional methods. Then students are taught how to enter data into Excel to determine the same information. Several students do not have Excel available at home. How should Mrs. Rogers accommodate these students?

A mathematics teacher is beginning a unit on multiplication of fractions. Which of the following is the least appropriate way to model this process?

Mr. Zammit is teaching his class about shapes. One of his students incorrectly labels all rectangles as squares and all rectangular prisms as cubes. Which of the following should Mr. Zammit do in this situation?

Select all answers that apply.

The Payday Lending industry has faced increased criticism and scrutiny for which of the following practices?

Ms. Smith is beginning a unit on area and perimeter. She begins the unit with an activity that requires students to use a list of formulas provided to find areas of several different quadrilaterals and triangles. The entire class is having difficulties with this assignment. What should Ms. Smith do to remedy the situation?

A teacher is teaching his students about converting between units. He gives the students a project where they have to build a map of a room using units of their choice to appropriate scale. He gives students rulers, measuring tape, and assorted objects like shoes and sticks to make their model. He finds that many students are confused by the assignment. Select all of the following that will improve the activity.

Select all answers that apply.

Mrs. Matthews is teaching her sixth-grade class about areas of regular geometric figures. How should she best introduce this topic to her students?

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?

A fifth-grade teacher is beginning a unit on equivalent fractions with her students. If this is an introductory lesson, which of the following activities would be the most effective in helping the students understand the concept of equivalent fractions?

Mrs. Herschend decided not to give a test about ratios and instead had her students do a project to display their knowledge. She has decided that she will do this for every unit going forward. What is the main disadvantage to this approach?

Which of the following questions can be used to demonstrate the interdisciplinary connections between math and other subjects?

Which of the following are variable expenses?

Select all answers that apply.

The mathematics teacher and art teacher work together to create an interdisciplinary lesson using tessellations, which are basic geometric shapes set to a repeating pattern. The students cover a large piece of poster board with the patterns they create. Which of the following mathematical concepts is most closely reflected in this activity?

Mr. Feeny has been teaching fifth-grade math for thirty years. He will only accept answers from his students that follow his algorithmic procedures. If a student determines a correct solution by any method other than the way they were taught in class they will not receive credit. How could Mr. Feeny improve his teaching practice?

A sixth-grade teacher discovers that each student in his class receives an allowance from their parents. Which of the following examples would best demonstrate to the students the power of saving their allowance instead of spending all of their allowance?

Mr. Sexton has been trying a variety of teaching methods to engage his class, but it seems to make things more out of control. How can he increase engagement while maintaining an orderly classroom?

Joshua is learning about volumes of three-dimensional figures. First, his teacher explains what volume is. Then, she writes the formula for area of a cube on the board v = s3. Next, she has the students recite "the volume of a cube is the side length cubed". Finally, she has students take six-sided dice of various sizes and measure them to determine their volume. Which best describes the teaching method is the teacher attempting to use?

Ms. Miller is a student teacher in a fourth-grade classroom. She has heard that group work is important so she wants to plan for group activities. On her first day student teaching, she briefly says "today we'll be doing group work about fractions" before she sends the students to stations. How could she best improve her teaching?

A parent is complaining about the math homework. They feel that their ELL child is at a disadvantage because they cannot afford internet at home and the homework is best completed using online software. The teacher is providing students time in class to complete the work that requires online resources, however, this student has not been using it stating that he will do it at home. What is the best strategy the teacher should use to prepare for meeting with the parent?

Interest is best defined as:

Mrs. Adamson's student asks her how much space a cube takes up. Mrs. Adamson said to answer this question, the student would need to calculate the volume of the cube. Which of the following measurable attributes is the formula for a cube based upon?

Which of the following is NOT considered a benefit of cash?

Two color counters are often used to model addition and subtraction of integers. The red counters represent negative integers; the yellow represent positive integers.

If the counters above were used to model the addition, what would be the result?

What learning progression should be used when teaching math concepts to third-grade students?

There are 110 people in line to ride the Shark Splash roller coaster. The ratio of girls to boys in line is 6 to 14. How many people in line are boys?