Free ParaPro Core Plus (Math Version 1) Questions and Answers — Questions and Answers
Question 1: The addition of three two-digit numbers is demonstrated below using the usual addition technique. <br> <br> 4z <br> 27 <br> +x5 <br> y14 <br> <br> If x, y, and z each represent a different digit from 0 to 9, what is the value of (x)(y)(z)?
- 76
- 114
- 15
- 8 (Correct answer)
Correct answer: 8
First, analyze the units column: z + 7 + 5 results in a units digit of 4, meaning z + 12 ends in 4. This implies z must be 2 (2 + 12 = 14), with 1 carried over to the tens column. Next, for the tens column: the carried-over 1 + 4 + 2 + x results in a tens digit of y and a units digit of 1. So, 7 + x must equal 11 (since x is a single digit), making x = 4 and y = 1. Since x=4, y=1, and z=2 are all different digits, the value of (x)(y)(z) is 4 * 1 * 2 = 8.
Question 2: A pupil is unsure about how to approach the subsequent difficulty. What is the best course of action to take?
- Multiply by the reciprocal of the second fraction (Correct answer)
- Find a common denominator
- Cross factor the 4 and the 8
- Multiply the numerators first
Correct answer: Multiply by the reciprocal of the second fraction
When dividing fractions, the standard procedure is to 'keep, change, flip.' This means you keep the first fraction as it is, change the division operation to multiplication, and then flip the second fraction (find its reciprocal). Therefore, multiplying by the reciprocal of the second fraction is the correct and most fundamental step to solve a fraction division problem.
Question 3: David, a tutor, decides to buy five calculators at a store for $7.50 each with the intention of giving one to each of his students. The following day, he learns that the same calculator has dropped in price to $5.00 and that he would only have three tutoring clients rather than five. He returns the five calculators and replaces them with three new ones at a discounted price. To calculate the amount he should get back from the store, he applies the following phrase. <br> <br> (5 x $7.50) – (3 x $5.00) <br> <br> Which of the following expressions could David also have used?
- 3 ($7.50 - $5.00) + 2 x $7.50 (Correct answer)
- 5 ($7.50 -$5.00)
- $7.50 - $5.00
- (5 x $7.50) - $5.00
Correct answer: 3 ($7.50 - $5.00) + 2 x $7.50
David's initial expression calculates the total money spent minus the total cost of the new purchase. The equivalent expression, 3 ($7.50 - $5.00) + 2 x $7.50, breaks down the refund differently. It accounts for the savings on the three calculators he ultimately kept (paying $5.00 instead of $7.50) and adds the full refund for the two calculators he returned without replacement. Both methods correctly calculate the total amount of money David should receive back from the store.
Question 4: Which of the following may y be if its value is between 0.0078 and 0.01?
- 0.081
- 0.0099 (Correct answer)
- 0.1076
- 0.016
Correct answer: 0.0099
To determine which value for 'y' is between 0.0078 and 0.01, we need to compare each option. The number 0.0099 is greater than 0.0078 (since 99 is greater than 78 in the thousandths and ten-thousandths places) and also less than 0.01 (which can be written as 0.0100). Therefore, 0.0099 is the only option that falls within the specified range.
Question 5: Shaun is unsure of which digit, out of 514.196, belongs in the tenth place. How might he find it with the aid of a paraprofessional?
- It’s the last digit
- It’s the digit immediately to the left of the decimal point
- It’s the digit immediately to the right of the decimal point (Correct answer)
- It’s the digit two places to the left of the decimal point
Correct answer: It’s the digit immediately to the right of the decimal point
In the decimal number system, place values to the right of the decimal point represent fractions. The first digit immediately to the right of the decimal point holds the 'tenths' place value. For example, in 514.196, the digit '1' is in the tenths place, representing one-tenth (1/10).
Question 6: To the nearest hundredth, what is 317.93371?
- 317.9
- 317.94
- 317.934
- 317.93 (Correct answer)
Correct answer: 317.93
To round a number to the nearest hundredth, you need to look at the digit in the thousandths place. In the number 317.93371, the digit in the hundredths place is 3, and the digit in the thousandths place is also 3. Since the thousandths digit (3) is less than 5, we keep the hundredths digit as it is and drop all subsequent digits. Therefore, 317.93371 rounded to the nearest hundredth is 317.93.
Question 7: Raymart and Adam both achieved high scores in their favorite video game, "Space Attack," with 139,750 and 99,190 points respectively. Which of the following best represents the difference in points between Raymart and Adam?
- 5,900 points
- 410,000 points
- 59,000 points
- 41,000 points (Correct answer)
Correct answer: 41,000 points
To find the difference in points, subtract Adam's score from Raymart's score: 139,750 - 99,190 = 40,560. Among the given options, 41,000 points is the closest and best representation of this difference. The question asks for what 'best represents' the difference, implying an approximation.
Question 8: How might someone helping a pupil explain how to solve the following puzzle to them? <br> <br> 421.45 Ă— 10.09 is approximately equal to:
- Round the two numbers to the one’s column and then multiply (Correct answer)
- Multiply the two numbers and then round the answer to the one’s column
- Round the two numbers to the hundred’s column and then multiply
- Multiply the two numbers and then round the answer to the hundred’s column
Correct answer: Round the two numbers to the one’s column and then multiply
To approximate the product of two numbers, a good strategy is to round each number to a simpler place value *before* performing the multiplication. Rounding 421.45 to the nearest one's column gives 421, and rounding 10.09 to the nearest one's column gives 10. Multiplying these rounded numbers (421 x 10 = 4210) provides a quick and reasonable approximation, making the calculation much easier to perform mentally or quickly.
Question 9: A paraprofessional offers the following word puzzle assistance to a group of children. <br> <br> "A store employee does not add tax to food purchases. For a gallon of milk, she charges $3.21, and for two pounds, $2.40. a box of cereal, and $3.68 for an apple. The cereal is discounted by $0.75 thanks to a customer's coupon. What are the grocery costs?” <br> <br> Which of the following statements would correctly solve the problem?
- Multiply $2.40 by 2. Add that total to $3.21 and $.3.68. Then subtract $0.75
- Add $3.21, $2.40, $3.68, and $0.75 together
- Add $3.21, $2.40, and $3.68. Then subtract $0.75 (Correct answer)
- Multiply $2.40 by 2. Add that total to $3.21 and $3.68
Correct answer: Add $3.21, $2.40, and $3.68. Then subtract $0.75
To calculate the grocery costs, one must first sum the prices of all purchased items: the milk ($3.21), the cereal ($2.40), and the apple ($3.68). After totaling these amounts, the customer's coupon discount of $0.75 for the cereal should be subtracted from the sum. This sequence of operations accurately reflects the transaction to determine the final grocery cost.
Question 10: A visual organizer for planning, making forecasts, and linking old and new information
- Story Map
- Hundred Chart
- KWL Chart (Correct answer)
- Venn Diagram
Correct answer: KWL Chart
A KWL chart is a specific type of graphic organizer used to help students engage with new material. It prompts them to record what they **K**now about a topic before learning, what they **W**ant to know, and finally, what they **L**earned after instruction. This structure makes it ideal for planning, making forecasts, and linking new information to existing knowledge.
Question 11: Reading's ultimate goal
- Fluency
- Conferencing
- Comprehension (Correct answer)
- Application
Correct answer: Comprehension
While fluency, decoding, and application are crucial components of reading, the ultimate and overarching goal of reading is comprehension. Comprehension refers to the ability to understand, interpret, and make meaning from the text, allowing readers to grasp the message, connect ideas, and learn new information effectively. Without comprehension, reading is merely decoding words without true understanding.
Question 12: The first letter of a word
- Prefix (Correct answer)
- Affix
- Suffix
- Preview
Correct answer: Prefix
A prefix is a morpheme (a meaningful unit of language) that is attached to the beginning of a word. It modifies the meaning of the word's root or stem. For example, in the word 'unhappy,' 'un-' is the prefix that changes the meaning of 'happy' to its opposite.
Question 13: When reading aloud with a partner, students alternately read different passages and ask and respond to text-related questions.
- Partner reading (Correct answer)
- Choral reading
- Frustrations reading level
- Phonemic wareness
Correct answer: Partner reading
Partner reading is a collaborative reading strategy where two students take turns reading passages aloud from the same text. During this activity, they also engage in discussions, ask each other questions, and respond to text-related prompts, which helps to improve fluency, comprehension, and engagement with the material. This description directly aligns with the definition of partner reading.
Question 14: A grid with the numbers 1–100 is a good place value strategy.
- Drafting
- Kwl chart
- Place value
- Hundred chart (Correct answer)
Correct answer: Hundred chart
A hundred chart is a visual tool, typically a grid displaying numbers from 1 to 100, that is widely used in elementary mathematics education. It serves as an excellent strategy for teaching place value by visually representing the sequence and relationships between numbers, helping students understand patterns, counting, and basic arithmetic operations.
Question 15: The significance of a digit's place in a number.
- Ratios and Proportions
- Place Value (Correct answer)
- Factors and Multiples
- Whole Numbers
Correct answer: Place Value
Place value is a fundamental concept in mathematics that refers to the value a digit holds based on its position within a number. For instance, in the number 345, the digit '3' represents 3 hundreds, '4' represents 4 tens, and '5' represents 5 ones, illustrating how the position of each digit determines its specific value.
Question 16: The vertical axis of a coordinate grid.
- Place Value
- Conferencing
- Y Axis (Correct answer)
- Prefix
Correct answer: Y Axis
In a Cartesian coordinate system, which is commonly used for graphing, the vertical line is known as the Y-axis. This axis typically represents the dependent variable and is used to measure vertical distance or position from the origin.
Free ParaPro Core Plus (Math Version 1) Questions and Answers
The addition of three two-digit numbers is demonstrated below using the usual addition technique.
4z
27
+x5
y14
If x, y, and z each represent a different digit from 0 to 9, what is the value of (x)(y)(z)?