Math Practice Test
Using 2 + 9x + 3 + 4x + 7=14, what is the correct answer when asked to combine like terms?
13x = 2.
Which of the following is a way that does NOT represent how 108 can be factored?
2>3rd power 3>2nd power
21 32 43 35 56 17 24 32 18 27 32 15 29 21 42 What is the mode for the data shown above?
32
Juan threw 12 red, 8 blue and 10 green diving sticks into the pool. The pool is very cloudy and you cannot see the color of the diving sticks. If Juan dives in what is the probability he will be able to find a blue diving stick first?
4/15
How many times larger is 4 x10>6 than 1 x 10>4?
400
The perimeter of a rectangle 108 cm. If the width is 24 cm. What is the area?
720 sq. cm
Which of the following statements best explains why the algebraic formula for the area of a triangle is 1/2 bh?
A parallelogram is composed of two congruent triangles, so the area of a parallelogram with the same base and height as the triangle can be divided by 2 to find the area of the triangle. every parallelogram is made up of two congruent triangles. The formula for the area of a parallelogram is b × h, so the area of each of the two congruent triangles is half the area of the parallelogram. Two congruent triangles can always be arranged to form a parallelogram with the same base and 73 Competency 005—(Probability and Statistics): The teacher understands concepts related to probability and statistics and their applications. the same height as the triangles. The area of the triangle will therefore be one-half as much as that of the parallelogram.
Which of the following geometric solids has five faces, eight edges and five vertices?
A rectangular pyramid a rectangular pyramid has one rectangular base and four triangular faces, eight edges and five vertices.
Ms. Foreman asks her students if there is a correlation between how many hours a student spends studying for a test and the test score they receive. Which graph is the best choice for showing this data?
A scatterplot is the only type of graph that is used to find a is there is a correlation between the data.
A teacher is working with a group of kindergarten students exploring the concept of one-to-one correspondence. Which activity would be most effective in developing this concept?
A student rolls a die and count outs enough plastic bears to correspond to the dots on the die rolled.
At teacher is planning to demonstrate the concept of division to students for the first time. Which of the following is the best way for a teacher to introduce this concept?
Act out a division problem using manipulatives.
A teacher is planning a math lesson on balancing equations to a group of sixth-grade math students. Which manipulatives would enhance the understanding of this concept?
Algebra balance scales
A fifth-grade teacher writes the problem 56 × 12 on the board. Students begin to solve the problem mentally, and as each student finds a solution, he or she signals the teacher with a thumbs-up signal. When almost every student has given a thumbs-up signal, the teacher has the following dialogue with a student. Teacher: "Billy, what answer did you come up with?" Billy: "792." Teacher: "Great job, Billy! That is the correct answer. Raise your hand if you found 792 to be the product, like Billy." Almost every student in the class raised a hand. The teacher writes the next problem on the board. Which of the following instructional adjustments can the teacher make to best assess all of the students' understanding of multiplying two-digit numbers?
Asking multiple students to share and defend their solutions before acknowledging the correct answer the discussion gives the teacher an opportunity to hear how students are solving the problem. It will also give students an opportunity to share before they know their answer is wrong.
Word problem: A paint store is having a sale, and for every gallon of paint a customer purchases, the customer will receive one additional gallon for free. Write an equation for p, the number of gallons of paint received, in terms of x, the number of gallons of paint purchased. A teacher asks students to solve the word problem shown. One student, John, says the answer is 2 + x = p. Which of the following activities will best help John recognize his misconception?
Creating a function table a function table is a table of ordered pairs that follow a rule. The table will help the student identify the pattern.
Which is the best problem-solving strategy to solve the problem below? While sorting coins into piles, Lekha put 7 coins in the first pile, 11 coins in the second pile, 15 coins in the third pile, and 19 coins into the fourth pile. If this pattern continues how many coins will be in the 13th pile?
Draw a table
Archimedes' Stomachion puzzle from about 200 B.C. in which a 12-by-12 grid is divided into 12 different polygons, is shown above. A third-grade teacher is using the puzzle to determine whether or not students are able to partition or decompose nonstandard polygons to find their areas. Of which of the following polygons should the students be asked to find the area in order to demonstrate this skill? Select all that apply.
Figure 1 Figure 5 Figure 8 Figure 1, Figure 5 and Figure 8 are nonstandard polygons, which are the focus of the lesson.
After teaching a lesson on how to compare fractions with unlike denominators, Ms. Bailey gives her class the following problem to solve: Order the following fractions from least to greatest: 1/2, 3/4, 1/4 She finds that her class is still having difficulty with this concept and plans to reteach this concept using a different strategy. Which type of assessment is Ms. Bailey using in her classroom?
Formative
. Students are working independently to solve the equation -4 + ? = -10. The teacher says the following to help them understand the problem. "If you owe somebody $4, you have a negative $4 balance with that person. If you borrow more money from the person, you will owe more and have a more negative balance with that person." After speaking with several students, the teacher finds that some of them are still having trouble with the concept of negative numbers. As a result, the teacher then reteaches the concept using a number line. Which of the following types of assessments has the teacher used?
Formative formative assessment involves teachers' adjusting their instruction based on their assessment of students. The teacher in the scenario has conversations with the students and teaches again based on what is observed.
When simplified which two of the following expression is equal? I. 2>3+ (1+5)>2+ 4>4 II. (2962-562) ×1/8 III. 1/2×3/4×(3√125+2>4) IV. (8 x 5).3 + 16
I & II
Students are given the equation y=3x. Choose which table illustrates this equation and correctly identifies it as additive or multiplicative? I. Additive II. Multiplicative III. Multiplicative IV. Additive x y x y x y x y 0 0 0 0 0 0 0 0 1 3 1 3 3 1 3 1 2 6 2 6 6 2
II
Word problem: Samantha' s Bakery sells cupcakes in packages of 12 and cookies in packages of 20. The bakery sold the same number of cupcakes and cookies yesterday. What is the minimum number of cupcakes that the bakery could have sold? A teacher creates the word problem shown for a math lesson. Based on the word problem, the lesson will most likely cover which of the following mathematics concepts?
Least common multiple finding the least common multiple will identify the smallest number of cupcakes sold. In fact, let x be the number of packages of cupcakes that were sold and y be the number of packages of cookies that were sold. The number of sold cupcakes will be 12x, and the number of sold cookies will be 20y. Clearly 12 divides 12x and 20 divides 20y. Since 12x = 20y, 20 must also divide 12x. Since 12 and 20 both divide 12x, 12x is a common multiple of 12 and 20. The problem asks for the minimum (or least) number of cupcakes that could have been sold, so the least common multiple must be found to answer the question.
Which statement describes the relationship of line n to line m? m n \ / \ / \90 \/ / \ / \ / \ / \
Line n is perpendicular to Line m
Celeste is buying erasers for 8 of her friends. There are 76 erasers left at the store. Which of the following approaches can Celeste use to determine the greatest number of erasers she can buy to give each of her friends the same number and have none remaining?
Making an organized list of the multiples of 8 to see which one is closest to 76 the approach described provides the correct answer of how many erasers Celeste should buy at the store, 72.
Which of the following statements does NOT show how math is connected to other disciplines?
Math is the manipulation of numbers and it is independent of other disciplines including, science and technology.
A teacher writes the following problem on the board. Furry Pets pet store has 20 animals, 2/5 of them are puppies. Pets Galore pet store has 12 animals, and 3/4 of them are puppies Which pet store has the most puppies? Which concept is he/she most likely teaching?
Multiplying fractions
During a lesson on addition, a first-grade teacher is having students concretely practice addition problems by using cubes. She then has her students draw a pictorial model of the problems. When will the teacher know to move her students to the abstract phase of use of math symbols?
Once a child has demonstrated that they have a solid understanding of the concrete and pictorial representations of a problem, a teacher can introduce the more abstract concept of math symbols.
In both figures shown, the scales are balanced. Which of the following scales is also balanced?
Option C is correct because of the following logic steps. Let's call the scale to the left scale 1 and the scale to the right scale 2. Step 1: In scale 1 substitute a cylinder and a cube in place of the triangle, as per the equality in scale 2. Step 2: Using the properties of equality, cancel a cylinder from both sides, obtaining a balanced scale, which will be called scale 3, with two cubes on a side and a cylinder on the other. 76 Step 3: In scale 2 substitute two cubes in place of the cylinder, as per equality in scale 3, obtaining a balanced scale with a triangle on one side and three cubes on the other. The latter balanced scale corresponds to the scale in Option C.
A first-grade teacher has set up the following math workstations for students to work in pairs. Station 1: Students toss 7 two-color counters from a cup and record the addition equation represented. They repeat the process ten times. Station 2: Each student builds a tower of 8 cubes using two different colors, and then records the addition equation that the colors represent. Students then exchange towers and record the addition equation for the new towers. Station 3: Students are provided with 9 counters each. One student hides some of the counters. The other student looks at how many counters remain present and determines how many are hidden. The students then record the equation that the missing counters represent. Which of the following relationships are the students most likely exploring in the stations?
Part-part-whole in the activity, the students are conceptualizing that a number is made up of two or more parts.
Which of the following activities is most effective in helping kindergarten students understand measurement of the lengths of small objects, such as pencils or cups?
Placing interlocking cubes next to the objects and counting the cubes. having the students count the number of interlocking cubes and placing the cubes next to each item provides a visual for the student to use in determining length.
Which of the following represents a fixed expense?
Rent
A teacher has introduced a token economy in her classroom during a unit on personal financial literacy. Students are assigned jobs and are given a salary. At the end of the unit, the students will be able to shop at the class store with the money they have earned. As part of the unit students will learn about different type of taxes. Which of the following types of taxes would be the most appropriate for students to learn about during this unit?
Sales tax and income tax
A kindergarten teacher is planning a lesson on nonstandard measurement. For the activity, they will measure items around the classroom with different items such as Unifix cubes, blocks, plastic teddy bears, and so on. Which of the following statements does NOT describe how this will strengthen mathematical understanding of measurement for her students?
Students need to experience measuring items with nonstandard units to build a foundation for using standard measurements. As well as understanding items have the attribute of being measured. Young students need foundational skills before using standard units.
Which of the following learning goals is most appropriate for a third-grade unit on money?
Students will be able to determine the value of a collection of coins and bills. this option correctly describes a Texas Essential Knowledge and Skill (TEK) for third grade math. A learning goal identifies what students will learn or be able to do as a result of instruction, not what they will be asked to do to demonstrate such learning.
Which of the following word problems matches the strip diagram drawn below? 56 4 N N N N N
Teresa has 56 pieces of candy and her sister gives her 4 more pieces. If she eats the same amount of candy each day for 5 days, how many pieces of candy will she eat each day?
Students use the relationship between skip counting and equal groups of objects to represent the addition or subtraction of equivalent sets, which builds a strong foundation for multiplication and division Which of the following is a learning goal for the Texas Essential Knowledge and Skills listed above?
The learner will use models to show 5 x 3 is the same as adding 5+5+5.
\ \ \---------\ \ \ /\ \ / \ \/ \ /\ /-- \/ \-------/ \ \ The graph above shows the population growth rate for the United States in the latter half of the 20th century. If this graph is used to predict the growth rate in the population for the next 50 years, which prediction is most likely correct.
The population growth of the United States will steadily decrease because the graph shows a steady decline.
Bag A contains 10 marbles of which 2 are yellow and 8 are blue. Bag B contains 8 marbles of which 5 are yellow and 3 are blue. A marble is pulled out of each bag. What is the probability that a yellow marble is drawn out of the bag?
The probability of drawing a yellow marble from bag A is 2/10 and from bag B 5/8. To find the probability of the combination you 2/10 x 5/8= 10/80. Then simplify to find that it equals 1/8.
3 × (2 + 6)>2 − 4 [3(2) + 3(6)]>2 − 4 (24)>2 − 4 576 − 4 572 A student simplifies the initial expression by applying the rule of order of operations. Which of the following best describes the student's error when simplifying the expression?
The student multiplied before simplifying within grouping symbols. the student multiplied before evaluating within the grouping symbol, violating the rule for order of operations: parentheses left to right, exponents left to right, multiplications or divisions left to right, additions or subtractions left to right.
Mr. Roberts asked his students to draw a model equal to ¼. He noticed some of his students drew the picture below. Which of the following is the error his students are making? ------------------ - \ \ - - \ \ - - \ \- - \ - -\ \ - - \ \- ------------------
The students did not understand that fractions are divided into equal parts.
After learning the theoretical probability of a two-sided coin landing on any one side, students work in groups to flip the coin several times and get the following results: 9 heads and 6 tails. Based on the scenario, which of the following observations made by students about probability is accurate?
The theoretical probability of a coin's landing on heads is less than the experimental probability obtained. the experimental probability and the theoretical probability of the coin's landing on heads are respectively 0.6 and 0.5. The theoretical probability is thus less than the experimental probability.
Which of the following statements is supported by this diagram? Venn Diagram (49) (1,7) (28, 14, 4, 2)
This Venn diagram is comparing factors of 28 and 49. It is easy to understand the GCF of 49 and 28 is 7.
The PTA at Fielder Elementary is having a pancake breakfast fundraiser. In two minutes, the PTA can cook 22 pancakes. They are planning to feed 538 people. If each person eats 3 pancakes what is the best estimate of how many minutes the PTA will be cooking?
This is a proportion question. The estimated number of pancakes needed is 3 *550=1650. It is better to round to the compatible number of 550 than 500 because that gives a more accurate estimate. Additionally, round 22 down to 20. Thus, 2/20=x/1650=165.
Ms. Ruiz, a 4th-grade math teacher, has a goal is to create a more engaging environment for math during a unit on data analysis. Which of the following activities would be most engaging for her students?
This lesson is hands-on and requires students to gather the data from an authentic source and build meaning for themselves as they answer the question presented. Students would be most engaged finding the statistics of bags of candy and answering the question as a class.
A teacher asks her students to prove that this shape is parallelogram. Blue Square Which of the following statements is correct?
This shape is a parallelogram because opposite sides and opposite angles are congruent.
A teacher begins a lesson with the following question. During a car race, 2 competitors, Car A and Car B, will stop to fill up the fuel tank. Car A will fill up every 4 laps and Car B will fill up every 5 Laps. When the race begins after how many laps will the cars meet at the fuel stations, if they travel the same speed? Which of the following topics will be covered in the math lesson?
To find when car A and B meet you must find the least common multiple. 4 8 12 16 20 24 5 10 15 20 25 At lap 20 is when they will meet.
man on horse filling all available spaces The picture above is tessellation, an arrangement of shapes closely fitted together, especially of polygons in a repeated pattern without gaps or overlapping. Which type of transformation is seen in the picture above?
Translation
Mr. Reyes class has collected 582 pieces of candy for prizes at the school carnival. The candy is going to be separated into bags with 7 pieces of candy in each bag. Which of the following equations represents the use of compatible numbers in estimating the amount of prizes bags?
Using compatible numbers means using friendly numbers so the problem can be done using mental math, Using 7 x8 =56 is the most correct and closet way to round.
Teresa, a fifth-grade student is asked to solve the following problem. Two groups of tourists each have 60 people. If 3/4 of the 1st group and 2/3 of the 2nd group board buses to the museum, how many more people board the 1st bus then the 2nd bus? Teresa's answer was 3/4=9/12 and 2/3=8/12. Then she subtracted 9/12-8/12=1/12. She stated 1/12 more people boarded bus A. Which of the following statements might explain why she may have difficulty solving this question?
Using the strategy to find common denominators helps her find a fractional however, she is unable to understand how to express the fractional amounts as part of a whole.
Represent and solve multiplication of a while number and a fraction that refers to the same whole using objects and pictorial models, including area models Which of the following is an example of a learning goal for the Texas Essential Knowledge and Skills listed above?
Working in pairs student will show two different ways to solve problems involving multiplication of fractions by either drawing area models, using number lines, fraction bars, or using Cuisenaire Rods.
Nicole solves the word problem below: Jack, Terence, Sharon, and Alex are neighbors. Jack is half as old as Sharon. Sharon is three years older than Alex. Alex's and Sharon's ages added together equal 17 years. Terence is eight years old. Who is the youngest? Her work is shown below Step 1: If the ages of Alex +Sharon =17. Then I need find ways to add up to 17.17=8+917=10 +717= 11 +6 Step2: Since Sharon is 3 years older than Alex I chooses 10 + 7. Sharon is 10 and Alex's is 7, because 7+3=10 Step3: Jack is ½ Sharon's age so she decides to do 10 = 5 Step4: Jack is the youngest because Terence is 8 and Alex is 7. Which of the following statements explains why Nicole's work is justified?
Yes, Nicole's work is justified because she shows evidence of her work and explains each step.
Paola weighs 119 pounds. Together, Paola and her baby sister, Ana, weigh 128 pounds. Which expression shows how many pounds, p, Ana weighs?
p=128-119
Mr. Sanchez displays this area model and asks students to propose a number sentence that is represented by this model. Which of the following student responses is the best answer? 2 blue large square blue boxes 10 rectangular green boxes 11 small squares 23 total boxes
the correct answer is 12 x 23=276. None of other equations can be represented by this model.
Identify relative units of sizes within the metric system and customary system Using the TEKS listed above, which idea listed below will help students understand this skill?
using 1-inch square tiles to measure objects will help student understand units of length of the customary system.
Time 12:05 A.M. 2:05 A.M. 4:05 A.M. 5:05 A.M. 6:05 A.M. Temperature 67 60 53 49.5 46 A cold front arrived at 12:05 A.M., and the subsequent temperatures were recorded in the table shown. If x represents the number of hours after 12:05 A.M., which of the following equations best represents the change in temperature as a function of time?
y = -3.5x + 67 the y-intercept represents the starting temperature, which was 67, and the slope represents the rate at which the temperature changed per hour, which was 60 − 67 = -3.5. 2-0
The table below shows a linear relationship between the variable x and y. Which equation below correctly identifies the relationship? x y 1 7 2 9 3 11 4 13
y=2x +5
