Math Gace Practice Test Questions with Complete Solutions Latest Update 2025, Exams of Mathematics

Download Math Gace Practice Test Questions with Complete Solutions Latest Update 2025 and more Exams Mathematics in PDF only on Docsity!

Math Gace Practice Test Questions with Complete Solutions Latest

Update 2025

1/8-20% 2/5-30% 3/8-40% 4/5-50% 5/8-80%

How many fraction-percent equivalents are listed in the worksheet represented above? A. One B. Two C. Three D. Four - Correct AnswersB Students in a fourth-grade class are learning how to copy line segments and angles from their textbook onto a piece of paper. Which of the following tools is appropriate for the activity? Select all that apply. A. protractor B. A straightedge C. A geoboard D. A compass - Correct AnswersA. B. D. Which of the following activities will best help kindergarten students understand the concept of negative numbers? Watching a needle on a dial that shows how fast a wheel is turning B. Using a thermometer to illustrate extreme temperatures recorded at the South Pole

C. Moving the hands of a clock back an hour at the beginning of daylight saving time D. Placing money from a change purse into a piggy bank - Correct AnswersB Green - 32% Yellow-21% Violet-23% Blue-20% Red-? The circle graph above shows the distribution, in percents, of various colors of gems in a collection. What fraction of the collection is red? A. 2/ B. 4/ C. 2/ D. 4/25 - Correct AnswersA The Evergreen Shoe Factory received an order for 100 pairs of shoes. The factory ships shoes in cartons that each holds up to 12 pairs. How many cartons will the factory need to ship this order? Most of the fourth graders who worked on the problem above gave answers such as 8 R4, 8.333, and 8 1/3. These responses suggest that the students need practice in A. rounding down B. expressing remainders C. applying number sense D. using fractions rather than decimals - Correct AnswersC

Second-grade students are using a calculator to total the number of books in their classroom library. At one point, they mistakenly subtract 12 instead of adding 12. The calculator display shows a total of 57. What one operation can they do to correct the mistake? A. Add 12 B. Add 24 C. Subtract 12 D. Subtract 24 - Correct AnswersB "A retailer wants to determine the size most often purchased of a certain type of children's shoe to ensure that enough of that item is available to meet consumer demand. Sizes sold last month: 2, 2, 2, 3, 5, 5, 7, 8." A fifth-grade teacher poses the question above to the class during a lesson. The lesson most likely addresses which of the following concepts? A. Mode B. Median C. Mean D. Range - Correct AnswersA Which of the following activities requires a student to perform a mathematical computation at the most concrete level? A. Adding 2+ B. Joining two blocks and four blocks C. Adding two apples and four apples using pictures of the apples D. Solving X+4=6 - Correct AnswersB 19+17+15+13+7+5+3+

A teacher writes an addition problem on the board and asks students to think of other ways to write the sum, using a different operation. Which of the following represents the sum of the numbers shown using multiplication? A. 4× B. 4× C. 4× D. 4x21 - Correct AnswersC A fourth-grade class is discussing the problem shown. Sid is traveling by train from Little City to Big City. The train departs Little City at 8:30 A.M. and arrives in Big City at 9:15 P.M. How long does it take the train to travel from Little City to Big City? During the discussion, one student says, "All you have to do is subtract 830 from 915, and you have the answer! It's 85 minutes." For which of the following reasons is the student incorrect? A. The student did not consider how fast the train was traveling. B. The student used an inappropriate number-base system to calculate elapsed time. C. The student did not consider the distance between the cities. D. The student made a subtraction error in calculating elapsed time. - Correct AnswersB Which of the following is a nonmetric unit of measurement? Square meter B. Kilogram C. Centimeter D. Mile - Correct AnswersD Luis, Kristina, Mallory, and Hasan are four friends with pets. One has a horse, one a cat, one a white mouse, and one a rabbit. Mallory is allergic to cats and does not have one.

Luis has the smallest pet, and Hasan's pet sleeps standing up. Kristina does not have a rabbit. What is each friend's pet? A fourth-grade math teacher presents the problem above to the class. Which of the following problem-solving strategies is most likely to help the students solve the problem? A. Making a table B. Looking for a pattern C. Working backward D. Eliminating unnecessary information - Correct AnswersA Which of the following is the most appropriate strategy to use when first teaching primary- grade students the mathematical concept of regrouping? A. Using manipulatives and concrete materials B. Presenting mathematics problems devised from newspaper articles and advertisements C. Lecturing and allowing time for questions and answers D. Having students write a story about regrouping - Correct AnswersA A fifth-grade teacher has students cut some two-dimensional shapes from paper and then fold them into three-dimensional figures. Which of the following concepts are the students most likely exploring? A. Rotations B. Reflections C. Nets D. Tessellations - Correct AnswersC Fred, a student in a math class, showed the following solutions for two problems.

Problem: Dan cooked 60 of the 200 burgers at a company picnic. What percent of the burgers did he cook? Work: 200 × 0.60 = 120 Answer: 120% Problem: Tara watered 50 of the 180 plants in her mother's garden. What percent of the plants did she water? Work: 180 × 0.50 = 90 Answer: 90% Which of the following strategies could best help the student check answers to word problems and look for errors? A. Estimate the answer first, use an algorithm, and compare results. B. Practice multiplication with decimals outside the context of a word problem. C. Multiply the first digits and add the appropriate number of zeros. D. Complete the multiplication, then use division to check the answer. - Correct AnswersA How many different pairs of positive whole numbers have a product of 12? A. One B. Two C. Three D. Four - Correct AnswersC 29x

Before students in a fifth-grade class solve the problem above, the teacher has them use mental mathematics to compute 9×7,20×7,9×50, and 20×50. For which of the following reasons is it appropriate to have the students use mental mathematics that way? A. To reinforce the connection between multiplication and addition B. To practice rounding to the nearest 10 C. To introduce the associative property of multiplication D. To recall the partial products used in the algorithm - Correct AnswersD 25/10 =N A third-grade teacher asks students to write a word problem for the number sentence above, where N is the exact answer to the problem. Which of the following student responses best satisfies the conditions set by the teacher? A. A team of 10 students wins 25 movie tickets. How many tickets will each student get? B. Ten students tied for the winning prize of $25 in a contest. How many dollars will each student receive? C. Twenty-five children at a birthday party will eat 10 pizzas. How many slices will each child have? D. A tub of paint holds 25 gallons. How many 10 - pint cans can be completely filled with paint before the tub is empty? - Correct AnswersB The ability to skip count by tens is a benchmark mathematical skill for first- and second- grade students primarily because it A. serves as a conceptual foundation for multiplication B. shows an understanding of number and quantity C. familiarizes students with the concept of order of magnitude D. prepares students for reading and constructing scales and grids - Correct AnswersA

30/

53/

84/

75/

Third graders studying division were asked to solve and check the four division problems above and then write a story for each problem. Which of the following is the most likely reason for asking the students to write the stories? A. To have students demonstrate that division can mean partitioning a set of objects B. To have students practice division skills through drill-and-check exercises C. To help students write quotients that might contain a decimal D. To have students practice the strategy of solving a simpler problem than those presented - Correct AnswersA 65+28= 17+74= 45+15= The work of a student is shown above. The most likely reason for the error in the work is that the student has difficulty A. recalling addition facts B. recognizing an appropriate answer C. interpreting arithmetic symbols D. rounding up whole numbers - Correct AnswersB To introduce students to geometry, a first-grade teacher selects a variety of classroom objects having different shapes and passes them to the students. Which of the following concepts is most appropriate for the students to explore? A. Measurement of angles B. Plane and solid figures

C. Area and perimeter D. Reflection and rotation - Correct AnswersB Omar had 12 cookies. After he gave some of his cookies to Leah, he had 6 cookies left. How many cookies did he give to Leah? Which of the following best describes the problem type above? A. Result unknown B. Order unknown C. Start unknown D. Change unknown - Correct AnswersD Use the number line below to answer the question that follows. <0.....1/2.....1> A third-grade teacher gives students the following list of fractions: 4/8,7/8,11/8,7/12,and 9/12. How many of the fractions on the list can students correctly graph on the number line? A. Two B. Three C. Four D. Five - Correct AnswersC 5(6+4) =30+ = Which of the following properties of operations is illustrated in the example above? A. Commutative property B. Distributive property

C. Transitive property D. Reciprocal property - Correct AnswersB A kindergarten teacher shows students how to count objects in a set and then represent the number of objects with a numeral. The activity best fosters students' understanding of which of the following mathematical concepts? A. Identifying patterns and relationships B. Recognizing and naming numbers C. Comparing two- and three-dimensional shapes D. Applying the cardinality principle - Correct AnswersD Craig wants to buy 3 compact discs from a friend who is selling them for $14.49 each. Craig has $45 to spend. His sister says that is not enough money to buy all the compact discs. Is she right or wrong? A teacher poses the preceding word problem to fifth-grade students. Which of the following students has created an expression that will solve the problem? A. StudentA: 14.49 +3- 45 B. Student B: 45 - (3x14.49) C. Student C: (45-3)x 14. D. Student D: 45 - 14.99+3 - Correct AnswersB A third-grade student cuts out three pairs of rectangles, with the rectangles in each pair having equal size, and then glues the pieces together to make a box. The activity requires the student to demonstrate which of the following mathematical understandings? A. Number sense B. Data sense C. Spatial sense

D. Symbol sense - Correct AnswersC A kindergarten teacher asks questions that encourage students to think numerically and make quantitative judgments. In the morning, the teacher might ask students to figure out how many students are absent. During snack time, the teacher might ask students if there are enough snack cups for everyone in the classroom. During recess, the teacher might ask students to determine how many balls they take outside so they know how many balls to bring back inside. Which of the following mathematical concepts is the teacher most likely reinforcing? A. Classifying B. Ordering C. Patterning D. Counting - Correct AnswersD A teacher taps each child in line, calling out, "First, second, third, fourth." Which of the following types of numbers is the teacher using? A. Nominal B. Cardinal C. Ordinal D. Real - Correct AnswersC At the beginning of a unit on division, a third-grade teacher asks students working in groups to devise a method for dividing 156 gum balls equally among four people. The activity will most likely require students to use which of the following? Select all that apply. A. Cooperative learning B. Standard algorithms for division C. Guess and check

D. Estimation - Correct AnswersA, C, D Place the fractions in order from least to greatest.

1. 14/
2. 4/
3. 6/
4. 12/24 - Correct Answers3,1,2, A third-grade student uses the following strategy to begin solving an addition problem. 2106 ———- 2000 895 ———— 800 +309———+300= ?————— 3100 Which of the following best describes the strategy the student used? A. Rounding up B. Front-end estimation C. Regrouping D. Compatible numbers - Correct AnswersB Students place unit cubes in a rectangular solid until the base is covered. Students continue adding layers of cubes until the solid is filled to the top. Which of the following concepts does the activity address? A. Area B. Volume C. Perimeter D. Circumference - Correct AnswersB