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5th Grade Math AI Tutor
Mastering 33 Basic Math

Explain your answer

1. Logan Academy students take part in four field trips during the school year. They visit a library, a museum, a park, and a zoo. How many different ways can the four trips be ordered for the school year?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 5.MP.4 Model with mathematics. Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

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2. A number cube is labeled with the digits 1 through 6. The cube is tossed once. What is the probability that the cube will land on either a 4 or a 6?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 5.MP.4 Model with mathematics. Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Explain your answer

3. A dolphin was swimming at 20 feet below sea level. The it dove to 45 feet below its original position. Which integer represents the depth of the dolphin's dive?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations in Base Ten (NBT) 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, connecting objects or drawings to strategies based on place value, properties of operations, and/or the relationship between operations. Relate the strategy to a written form.

Explain your answer

4. Which of the following would be best displayed on a double-line graph?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 5.G.A.2: Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Explain your answer

5. What is the coordinate of point A?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 5.G.A.1: Understand and describe a coordinate system as perpendicular number lines, called axes, that intersect at the origin (0 , 0). Identify a given point in the first quadrant of the coordinate plane using an ordered pair of numbers, called coordinates. Understand that the first number (x) indicates the distance traveled on the horizontal axis, and the second number (y) indicates the distance traveled on the vertical axis.

Explain your answer

6. Grace measures a bean plant at the end of every week. At the end of week 1, the plant is 4 inches tall. It grows 1/2 inch each week for 5 more weeks. How tall is Grace's bean plant at the end of week 5?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations – Fractions (NF) 5.NF.A.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12).

Explain your answer

7. Ms. Cook's class bought 2 bags of concrete and some bricks to build a border for their class garden. The bricks cost $51. The total cost of the bricks and the concrete was $57. Which equations can be used to find the cost, b, of 1 bag of concrete?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 5.MP.4 Model with mathematics. Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Explain your answer

8. Look at the vertex-edge graph. Which statement about the graph is true? Click to see the vertex-edge graph

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 5.MP.4 Model with mathematics. Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Explain your answer

9. Students agree that the following equations using integers are true. Which statement about adding integers is not true? Click to see the list of equations.

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations in Base Ten (NBT) 5.NBT.B.5: Fluently add multi-digit whole numbers using a standard algorithm.

Explain your answer

10. Look at the graph. Which situation is best reprsented by the graph? Click here to see the graph.

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 5.G.A.2: Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Explain your answer

11. Sheri asks 83 students at school to choose the sports that they most enjoy watching. The students can choose from baseball, basketball, football, and soccer. The results are shown in the table. Which statement is a reasonable conclusion to make from the information in the table?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 5.MP.4 Model with mathematics. Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Explain your answer

12. Scott ran in a two-day race. The first day he ran 5 3/4 miles. The next day he ran 6 5/8 miles. How many total miles did Scott run?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations – Fractions (NF) 5.NF.A.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12).

Explain your answer

13. What is the solution to the equation 72,658 ÷ 313 = ?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations in Base Ten (NBT) 5.NBT.B.5: Fluently divide multi-digit whole numbers using a standard algorithm.

Explain your answer

14. To place 0.67, 3/4, and 34% in order from least to greatest. John changes 3/4 to 0.75 and 34% to 0.34. Then he uses the three decimals to correctly place the original numbers in order from least to greatest: 34% , 0.67, 3/4. Which problem is best solved by using this same strategy?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations in Base Ten (NBT) 5.NBT.B.7: Add, subtract, multiply, and divide decimals to hundredths, connecting objects or drawings to strategies based on place value, properties of operations, and/or the relationship between operations.

Explain your answer

15. What is the area of the shaded figure? Click to see the figure.

Augmented Reality to show the concept of Area, Perimeter, and Volume using Geogebra 3D AR

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations in Base Ten (NBT) 5.NF.B.4.c: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Explain your answer

16. The diagram below shows the length and width of the wall that Tara is going to cover with wallpaper. What is the least amount of wall paper Tara will need to cover the entire area of the wall?.

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations in Base Ten (NBT) 5.NF.B.4.c: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Explain your answer

17. Samantha and Pedro each have 2 fair number cubes. The faces of each cube are numbered 1 through 6. They each rolled their 2 number cubes 50 times and recorded the sum of the numbers rolled. Based on the data in the tables, which statement is not true?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 5.MP.7 Look for and make use of structure. Mathematically proficient students use structure and patterns to assist in making connections among mathematical ideas or concepts when making sense of mathematics. Students recognize and apply general mathematical rules to complex situations. They are able to compose and decompose mathematical ideas and notations into familiar relationships. Mathematically proficient students manage their own progress, stepping back for an overview and shifting perspective when needed.

Explain your answer

18. A diagram of Ryan's yard is shown. Which expression can Ryan use to find the total area of his yard?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Operations and Algebraic Thinking (OA) 5.OA.A.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them (e.g., express the calculation "add 8 and 7, then multiply by 2" as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product).

Explain your answer

19. What is the solution to the equation 5 + 9 x 21 = ?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Operations and Algebraic Thinking (OA) 5.OA.A.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them (e.g., express the calculation "add 8 and 7, then multiply by 2" as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product).

Explain your answer

20. Which list shows all of the prime numbers between 0 and 22?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Operations and Algebraic Thinking (OA) 5.OA.B.4: Understand primes have only two factors and decompose numbers into prime factors.

Explain your answer

21. Which number is closest to the answer to the problem 39 x 62 ?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations in Base Ten (NBT) 5.NBT.B.5: Fluently multiply multi-digit whole numbers using a standard algorithm.

Explain your answer

22. What is the next term in the pattern 1.25, 1.95, 2.65, 3.35, ...

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations in Base Ten (NBT) 5.NBT.B.7: Add, subtract, multiply, and divide decimals to hundredths, connecting objects or drawings to strategies based on place value, properties of operations, and/or the relationship between operations.

Explain your answer

23. Which value for x makes the number sentence true 3x + 10 = 19 ?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations in Base Ten (NBT) 5.NBT.B.5: Fluently add multi-digit whole numbers using a standard algorithm.

Explain your answer

24. Look at the number pattern. 1/4, 1 1/2, 2 3/4, 4, ... What rule is used to get the next term?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations in Base Ten (NBT) 5.NBT.B.7: Add, subtract, multiply, and divide decimals to hundredths, connecting objects or drawings to strategies based on place value, properties of operations, and/or the relationship between operations.

Explain your answer

25. Two angles of a triangle add up to 65°. What is the measure of the third angle?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 5.MP.6 Attend to precision. Mathematically proficient students clearly communicate to others using appropriate mathematical terminology, and craft explanations that convey their reasoning. When making mathematical arguments about a solution, strategy, or conjecture, they describe mathematical relationships and connect their words clearly to their representations. Mathematically proficient students understand meanings of symbols used in mathematics, calculate accurately and efficiently, label quantities appropriately, and record their work clearly and concisely.

Explain your answer

26. What is 3/5 written as a percent?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations in Base Ten (NBT) 5.NBT.A.3.a: . Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.

Explain your answer

27. Erika is baking cupcakes. The recipe calls for 1 1/4 cups of sugar for the batter, and 1 2/3 for the frosting. About how many total cups of sugar will Erika need for her recipe?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations – Fractions (NF) 5.NF.A.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12).

Explain your answer

28. What is the mean of the numbers listed 31, 42, 46, 47, 51, 51, 68 ?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 5.MP.6 Attend to precision. Mathematically proficient students clearly communicate to others using appropriate mathematical terminology, and craft explanations that convey their reasoning. When making mathematical arguments about a solution, strategy, or conjecture, they describe mathematical relationships and connect their words clearly to their representations. Mathematically proficient students understand meanings of symbols used in mathematics, calculate accurately and efficiently, label quantities appropriately, and record their work clearly and concisely.

Explain your answer

29. Roberto began his homework at 4:25 p.m. He finished it one and a half hours later. At what time did Roberto finish his homework?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 5.MP.4 Model with mathematics. Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Explain your answer

30. Which figure has only one pair of parallel sides? Click to see the figures

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Geometry (G) 5.G.B.4: Classify two-dimensional figures in a hierarchy based on properties.

Explain your answer

31. What is the solution to the expression 3 - 4(1/2) + 7 ?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations – Fractions (NF) 5.NF.A.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (e.g., 2/3 + 5/4 = 8/12 + 15/12 = 23/12).

32. Sand Dollar Elementary is planning a school field trip for its fourth and fifth grade students. The location that the students visit will depend on their names. The chart below shows the options for the field trip locations. Based on the information in the chart, which statement is not true?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Mathematics Practice 5.MP.4 Model with mathematics. Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. When given a problem in a contextual situation, they identify the mathematical elements of a situation and create a mathematical model that represents those mathematical elements and the relationships among them. Mathematically proficient students use their model to analyze the relationships and draw conclusions. They interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

33. What is the solution to the equation 7400.05 - 526.175 = ?

Explain your answer

SOURCE: Arizona Department of Education, Arizona Mathematics Standards 5th Grade, Sample Math Assessment Test Question
Arizona Mathematics Standards 5th Grade & Introduction to AZ Math Standard
Math Lesson Curriculum Aligned to AZ Standard for Number and Operations in Base Ten (NBT) 5.NBT.B.7: Add, subtract, multiply, and divide decimals to thousandths, connecting objects or drawings to strategies based on place value, properties of operations, and/or the relationship between operations.

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