core math

Mrs. Brooks is a first-grade mathematics teacher. She wants to incorporate workstations into her lesson. She sets up the following stations: Station 1: Students toss two dice and record the numbers on each die plus the sum of the two dice. They repeat the process ten times. Station 2: Students build a tower consisting of nine cubes and each cube must have either a red or blue color on a side. Students then count the number of red sides and blue sides on each side of the tower. Station 3: Two students place 13 marbles on the table. The students take turns removing from 1-12 marbles from the table and the other student has to figure out how many marbles the other student removed. The students then record the two numbers. Which of the following concepts is Mrs. Brooks most likely trying to explore with the workstations for her students?

Part-part-whole

In a kindergarten class, the students are lining up for lunch. The teacher begins calling the first four or five students to line up in boy-girl order. She stops after the fifth student and asks the question, "Class, who do you think I might pick to go next in line? Why?" What math concept is the teacher most likely teaching?

Patterns to make prediction

Which of the following activities is most effective in helping kindergarten students understand measurement of the lengths of small items, such as juice boxes or lunchboxes?

Placing same-size objects, such as Legos or cubes, next to the object and counting the number of objects

A teacher draws many variations of triangles on the board in front of the class. She then asks students to identify which triangles have acute angles, right angles, and obtuse angles. Which of the following is the teacher most likely trying to accomplish?

Reinforcing geometric definitions

Miguel is playing with his model cars. Which transformation is represented in the picture of his cars?

Rotation

Which of the following learning goals is most appropriate when teaching a class of third-grade students about money?

Students will be able to identify and determine the value of a specific coin or bill

Mrs. McCoy writes two equations on the board for her class. +5 - 5 = 0 -20 + 20 = 0 Which of the following properties of integers is Mrs. McCoy most likely trying to illustrate?

The additive inverse property

Ellie is getting a new rug for her room. Her old rectangular rug is 5 ft by 7 ft. Her new rug is circular with a diameter of 7 ft. How is the new rug related to the old one?

The new rug is about 3.5 ft² larger than the old one

Which statement about a rectangular prism and a rectangular pyramid is true?

The pyramid has triangular faces

A student is working through a double-digit multiplication problem and turns in the work pictured above. Which of the following best describes the student's error? (View attachment for larger image)

The student carried over the hundreds value from the 9 and 15 multiplication

A teacher is monitoring her class while the students are involved in a group activity exploring the size of angles in a set of triangles. She moves from group to group, pausing and watching the group dynamics. What the teacher is doing can best be described as:

informal formative assessment.

In a kindergarten class, two students have discovered that four butter tubs full of sand will fill a plastic pitcher. This learning is best described as:

informal non-standard measurement.

Which of the following is equivalent to the inequality? 5 > x -1

x < 6

If 15 ml is equivalent to ½ oz., which equation could be used to find x, the number of ml in 1 cup?

x = 15 • 8 ÷ ½

Which expression best represents y in terms of x? x: 1,2,3,4,5,6 y: -1,-3,-5,-7,-9,-11

y = 1 - 2x

Mr. Harris wants to divide a long string of gummy candy into pieces for his class. He folds the gummy candy in half and makes one cut along the end of the folded string so that he now has three pieces. He asks his students to create an equation so he can find out how many cuts he should make in the candy to have enough for all the students. Which of the following equations represents the data in the table attached? (View attachment for larger imag

y = 2x + 1

What equation describes the linear relationship shown in the above table? x: 2,6,9,12 y:7,19,28,2

y = 3x + 1

Which of the following equations is written in slope-intercept form?

y = 3x + 5

A heat wave began at 6:10 a.m. on a Tuesday morning. The temperatures were recorded by Mr. Davis' class. Mr. Davis asked his students to create an equation that represented the rise in temperature and would use x to represent the hours.

y = 3x + 70

Use the table to answer the question: Which of the following equations correctly models the relationship in the table x:1,3,5,9 y:-2,4,10,22

y = 3x - 5

Which of the following lists ALL the equations that are linear? (Select all that apply)

y = x - 2 y = x y = -3x - 5 y = -1/3 x - 5/3

Which of these equations does NOT pass through quadrants III or IV?

y = x²

Which of the equations, when graphed, will contain the ordered pair (1,1)? (Select all that apply)

y = x² y = -2x² + 3 y = x

If angle DEF is congruent to angle GHI, which of the statements is true?

∠G and ∠F are complementary

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

The Booster Club at Martin MS is selling spirit buttons for homecoming. The buttons cost $0.75 to make and will be sold for $2 each. How many buttons, b, must be sold to make a profit of $500?

$500 = $2b - $0.75b

A baseball mitt is on sale for 30% off. If the regular price is $78, what is the sale price, excluding tax?

$54.60

The graph above is a representation of the following situation: Marty purchased a car for $24,000; this included all interest, tax, and title fees. She made payments of $500 per month for 48 months until the car was paid off. What ordered pair would best represent point A at the top of the graph? (View attachment for larger image)

(0,24000)

Triangle ABC will be reflected across the line x = y. What are the coordinates of the reflection image of point A?

(1,-2)

Look at the coordinate grid above. Which ordered pair is between the x-axis and the line j?

(2, 3)

Mr. Andrews is in a city whose street grid can be represented by a coordinate plane. Mr. Andrews wants to walk from his current location at a local barbershop, represented on the coordinate plane as (1, 2), to his apartment. Mr. Andrews walks 5 blocks east, or to the right, and 1 block south, or down. Which of the following ordered pairs correctly depicts the location of Mr. Andrews' apartment?

(6, 1)

What is the degree of the monomial 66?

0

Which of the following lists all the factors of a composite number?

1, 5, 25

Jonathan is filling large cylindrical metal buckets with popcorn to sell as a money-raising project for new band uniforms. Which is closest to the volume of the bucket?

1.2 cu ft

Aaron went to sleep at 8:35 pm Tuesday night. He woke up at 7 am. How much sleep did he get?

10 hours, 25 minutes

On the number line above, what is the length of segment LQ?

10 units

Jamal went to bed at 9:38 pm and woke up at 10:15 am the next morning. How long did Jamal sleep?

12 hr 37 min

Simplify: 100 ÷ 4 × 5

125

Mrs. North's front yard is in the shape of a pentagon. The measure of 4 of its angles are: 90°, 110°, 120°, and 90°. What is the measure of the fifth angle?

130°

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

13:7

What is the area, in square units, of the figure above? (View attachment for larger image) 10,15,20

175

Simplify: 200 - 3(6 - 2)³ + 10

18

In the expression 3x² + 6x +3, what is the degree of 3x²?

2

What is the area, in square units, of the figure above? (View attachment for larger image) 8,5,4

26

The time allowed for Elliot's lunch was 11:42 am to 12:10 pm. How many minutes was lunch?

28 minutes

A pancake recipe requires 1 tablespoon of baking powder per 2 cups of flour. If 2 cups of flour make 4 pancakes, how many tablespoons of baking powder are needed to make 12 pancakes?

3

In the expression 3x² + 6x +3, how many terms are in the equation?

3

Simplify: 15 - 3(8 - 6)²

3

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

3/40

Above is a diagram of Tanya's new swimming pool. What is the perimeter of Tanya's pool?

30

If the pattern above is continued, how many blocks will be in the 7th term? x: 1,2,3,4, y:3,6,10,15

36

The ratio of Antone's height to arm span is the same as the ratio of his brother's height to arm span. About how tall is Antone? (View attachment for larger image) Antone: arm span (36in) height (x) Brother: arm span (56in) height (60in)

39''

If 2.54 cm = 1 in, about how many inches are in 1 meter?

39.4 in

How many terms are in the equation 4x - 4 = 6 * 9?

4

Becky arrived at her babysitting job Saturday morning at 9:15 am. She left at 1:30 pm. How many hours did she work?

4 hours, 15 minutes

What is the degree of the monomial 3x²y³?

5

Austin leaves his home and walks 3 blocks north, 5 blocks east, then 2 blocks south. What other route could he have walked that would have been a shorter distance but would have ended in exactly the same location?

5 blocks east, 1 block north

Jim wants to walk to Bill's house. To get to Bill's house, Jim walks 3 miles south and then walks 4 miles east. Jim wants to know how many miles he would have walked if he just walked in a straight line. How many miles would Jim have walked if he walked in a straight line to Bill's house?

5 miles

Danielle's 3rd-period class began at 10:43 am and ended at 11:38 am. How long was the class?

55 minutes

Mrs. Fields' science class takes care of a plant at school. The class is responsible for watering the plant and measuring its growth. The students' measurements are charted in the attached table. Which of the following equations relates the height of the plant, h, and the number of months, m, assuming a constant rate of growth? months: 1,2,3,4 height:8,13,18,23

5m + 3 = h

Which of the following correctly combines like terms for the following equation? 3x - 4 + 6x + 5 - 4x - 2 = 16

5x - 1 = 16

A school fundraiser is selling candy bars to raise money for a new gymnasium. If Billy sells a total of $650 worth of candy bars for $x per candy bar, which equation would be used to find out how many candy bars Billy sold?

650 / x

Simplify: 3 + 12 ÷ 3

7

The school day at Franklin Elementary begins at 7:45 am and goes until 3:04 pm. How long is the school day at Franklin Elementary?

7 hours, 19 minutes

Christopher had a basketball tournament on Saturday from 10:45 am to 6:15 pm. How long was the tournament?

7 hours, 30 minutes

Larry started the following number pattern: 900, 888, 876, 864, ... Which number could not be a part of Larry's pattern?

736

A small company employs 19 hourly wage workers. The hourly wage range is from $10 to $25 per hour. If three workers earn the median wage of $13.50 per hour, how many workers earn more than $13.50 per hour?

8

A teacher presents a right triangle to her class. She says the hypotenuse can be written as 4x + 30 or 6x + 14. What is the value of x?

8

Which of the following word problems is the correct question to be written and solved with the given equation? 8 - 5 + 3 = 6

8 birds were sitting on a fence. 5 birds flew away and 3 more birds landed on the fence. How many birds are on the fence now?

A teacher draws the grid above on the board without any "X"s in the grid. The teacher then writes the "X"s in the grid. The teacher asks the students to create an equation to represent the grid if the "X"s represent the blocks that have been removed from the grid. Which of the following is the best equation in response to the teacher's question? (View attachment for larger image) (15 x's) & 80 squares total

80 - 15

Use the protractor to read the measure of each angle. What is the measure of angle BAD?

90°

A student asks a teacher when would knowing the likelihood of a six being rolled on a dice be useful in real life. Which of the following examples would be the most appropriate response for the student?

A health insurance company estimating the expected number of payouts over the next fiscal year

A teacher provides students a table on the historical populations of the United States during the 19th century, divided by decade. Which of the following would be the most appropriate display for the information?

A line graph

A student asks the teacher why the area of a triangle is ½bh? Which of the following would be the most appropriate answer for the teacher to provide to the student?

A parallelogram is the combination of two congruent triangles and the area of a parallelogram is simply bh, so taking one half of the area of a parallelogram yields the area of a triangle

Which of the following geometric objects has five faces, eight edges, and five vertices?

A rectangular pyramid

A fifth-grade student was asked to multiply 15 and 35. His answer was: As his teacher, how would you begin remediation for this student?

A remedial lesson on place value

What is the 10th term of the geometric sequence 50, 40, 32, 25.6, 20.48,...?

A(10) ≈ 6.71

Given a₁ = 512, r = ½, and n = 6, what is the value of A(n)?

A(6) = 16

Given a₁ = 4, r = -5, and n = 7, what is the value of A(n)?

A(7) = 62,500

What is the 8th term of the geometric sequence -3, 6, -12, 24, -48,...?

A(8) = 384

Anytown School District provides a 50 multiple-choice question mathematics assessment to all 4th grade 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?

Accuracy

In a sixth-grade class, students are beginning a unit on algebraic reasoning. They are asked to measure the sides of several different squares and then determine the perimeter of the square. They are to record the information in a table like the one above. The purpose of this activity is for students to discover the relationship between perimeter of a square and the length of a side the square. At what level of Bloom's is this activity?

Analysis Level

Which of the following is the most appropriate learning progression through the levels of geometric thinking?

Analysis, Abstraction, Deduction

A fifth-grade teacher writes the problem 5(10-5) on the board. She asks students to solve the problem mentally and raise their hands when they find a solution. When all students have raised their hands, the teacher begins a dialogue with a student: Teacher: "John, what solution did you come up with?" John: "25" Teacher: "That is the correct answer! (to the class) Raise your hands if you thought 25 was the correct answer." Every student then raises their hands and the teacher writes a new problem on the board. Which of the following adjustments could the teacher make to best assess all the students' understanding of the concept?

Ask multiple students for their answers and allow them to explain how they found the answers prior to identifying the correct answer

Which of the above graphs best represents the equation y = x²? (View attachment for larger image)

c

A third-grade teacher wants to assess students' ability to calculate the area of nonstandard polygons. Which of the following figures would assess a student's ability to find the area of nonstandard polygons?

Figure 5

When asked to answer the question what is ½ ÷ 2; Jon answered 1. How could this problem be presented to Jon so that he would better understand the problem and how to answer it?

Have Jon draw a picture to represent ½ a pizza, then divide it into two equal parts. Ask him how much of the whole pizza each part represents.

In a first-grade class, the students have been working with manipulative materials and pictures as they investigate the concept of addition. Through both formative and summative assessments, the teacher has determined that the students are ready to move to more abstract (pencil and paper) ways to represent addition. How should she begin this process?

Have the children model pictorial representations of problems like 7 + 2 = 9 that include the numbers that represent each step

Which situation could best be represented by the equation: 12x = 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?

Maria baked 6 dozen cookies for her classmates. There are 28 students in her class, each child received 2 cookies and Maria gave 6 cookies each to her teacher and her principal. Which equation could be used to find C, the number of cookies she had left over?

C = 6 • 12 - (2 • 28 + 2 • 6)

A student walks into class and tells the teacher that a local candy store had a "buy one candy bar, get one candy bar free" promotion this weekend. The teacher asks the student how many candy bars she purchased, but the student was only able to remember how many candy bars she received. The teacher uses this opportunity to create a word problem for the class. She asks the class to create an equation that would help the student find out how many candy bars a person would receive (r) if for any candy bar they purchased (p), they received one candy bar for free. One student, Sally, says the equation would be 2p + 1 = r. Which of the following activities would best help Sally recognize the error in her answer?

Create a function table

A sixth-grade teacher is beginning a unit on probability. She utilizes the following steps in planning her unit: I. Determine the necessary prerequisite skills. II. Begin planning probability activities that involve the collection of data. III. Determine what the students already know by using a KWL chart. IV. Plan the final assessment for the unit. What is the best order for the teacher to organize these steps?

IV, I, III, II

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?

Length

A model of an equation is above. What is the value of M? m+M+m+m - 8 = m+1

M = 3

A student is instructed to draw a four-pointed geometric shape on an xy-plane. After the shape is drawn, the student is instructed to add 5 to each x-coordinate and add 3 to each y-coordinate. Which of the following did the student perform?

Translation

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?

Use pattern blocks to model fractions equivalent to ½ of the hexagon

In a sixth-grade class, students are beginning a unit on algebraic reasoning. They are asked to measure the sides of several different squares and then determine the perimeter of the square. They are to record the information in a table like this: What would be the best question to assess student understanding about this concept?

What is the relationship between the length of side of a square and its perimeter?

Jana is playing a game called Guess My Rule. Her friends choose a number (input), Jana subtracts 3 and tells her friends the result (output). The game continues until one of her friends can predict what their output number will be and can correctly state Jana's rule. Which graph correctly shows possible values of input/output for Jana's rule? (View attachment for larger image)

b

If -¼ is the 11th term in a geometric sequence where r = -½, then what is a₁?

a₁ = -256

If the 5th term in a geometric sequence where r = 3 is 162, then what is a₁?

a₁ = 2