i-Ready Diagnostic Number and Operations Questions and Answers 1 — Questions and Answers
Question 1: A school is planning a field trip for 848 students from three different grade levels: 287 third-graders, 312 fourth-graders, and 249 fifth-graders. To get a quick, reasonable estimate of the total number of students, which calculation is most appropriate?
- 300 + 300 + 250 (Correct answer)
- 200 + 300 + 200
- 280 + 310 + 240
- 287 + 312 + 249
Correct answer: 300 + 300 + 250
The goal is a quick and reasonable estimate, which involves using 'friendly numbers' that are easy to calculate mentally. Rounding 287 to 300, 312 to 300, and 249 to 250 (rounding to the nearest 50 or 100) provides an easy calculation (300+300+250 = 850) that is very close to the actual total of 848. Option D is the exact calculation, not an estimate.
Question 2: An educator asks a student to describe the value of the digit 3 in the number 53,981. The student replies, 'The 3 is in the thousands place.' Which statement best describes the student's understanding?
- The student correctly identified the place of the digit.
- The student confused the digit's place with its value. (Correct answer)
- The student does not understand place value beyond the hundreds place.
- The student correctly identified the value of the digit.
Correct answer: The student confused the digit's place with its value.
This is a common misconception where a student confuses a digit's 'place' with its 'value'. The student correctly identified the name of the place (thousands), but the question asked for the value, which is 3,000.
Question 3: A student solves the problem 8 x 27 by breaking it into (8 x 20) + (8 x 7) to make the calculation easier. Which mathematical property is the student using?
- The Commutative Property of Multiplication
- The Associative Property of Multiplication
- The Distributive Property (Correct answer)
- The Identity Property of Multiplication
Correct answer: The Distributive Property
The Distributive Property states that multiplying a number by a sum is the same as multiplying the number by each addend separately and then adding the products. In this case, the student distributed the 8 across the sum of (20 + 7).
Question 4: Which of the following fractions is NOT equivalent to 3/4?
- 9/12
- 12/16
- 6/8
- 8/12 (Correct answer)
Correct answer: 8/12
To find an equivalent fraction, you must multiply or divide both the numerator and the denominator by the same non-zero number. 9/12 (x3), 12/16 (x4), and 6/8 (x2) are all equivalent to 3/4. The fraction 8/12 simplifies to 2/3, which is not equivalent to 3/4.
Question 5: A student was asked to add 14.7 and 2.35. The student incorrectly aligned the numbers and got an answer of 3.82. What is the primary conceptual error in the student's work?
- The student added from left to right instead of right to left.
- The student failed to align the numbers by their decimal point. (Correct answer)
- The student made a calculation error when adding 7 and 5.
- The student forgot to carry over a value to the next column.
Correct answer: The student failed to align the numbers by their decimal point.
The fundamental rule for adding or subtracting decimals is to align the decimal points vertically. This ensures that digits with the same place value (tenths, hundredths, etc.) are added together. The student's error came from right-aligning the numbers as if they were whole numbers, which leads to adding digits from different place values.
Question 6: Which statement accurately describes the relationship between the numbers 6 and 24?
- 6 is a multiple of 24.
- 24 is a factor of 6.
- 6 is a factor of 24, and 24 is a multiple of 6. (Correct answer)
- 6 and 24 share no common factors other than 1.
Correct answer: 6 is a factor of 24, and 24 is a multiple of 6.
A factor is a number that divides evenly into another number (24 ÷ 6 = 4), so 6 is a factor of 24. A multiple is the result of multiplying a number by an integer (6 x 4 = 24), so 24 is a multiple of 6.
i-Ready Diagnostic Number and Operations Questions and Answers 1
A school is planning a field trip for 848 students from three different grade levels: 287 third-graders, 312 fourth-graders, and 249 fifth-graders.
To get a quick, reasonable estimate of the total number of students, which calculation is most appropriate?