Question 1

The most efficient way to write the number 444 in primes is: A)2² × 111 B)4 × 111 C)2 × 2 × 111 D)2² × 3 × 37

Accepted Answer

To find the prime factorization of 444, we can start by dividing it by its smallest prime factor: 2. 444 ÷ 2 = 222 Now we can divide 222 by 2 again: 222 ÷ 2 = 111 So we have: 444 = 2 × 2 × 111 We can then factorize 111 further by dividing by its smallest prime factor: 3: 111 ÷ 3 = 37 So we have: 444 = 2 × 2 × 3 × 37 We can use exponents to simplify this expression: 444 = 2^2 × 3 × 37 Therefore, the most efficient way to write the number 444 in primes is: D) 2² × 3 × 37

Question 2

Prime numbers are used for all of the following except:
A)breaking composite numbers down into their smallest factors.
B)working with sums and differences of integers.
C)getting fractions into their lowest terms.
D)determining the GCF and LCM of two numbers.

Accepted Answer

Prime numbers are fundamental in mathematics for various purposes, including factorization, simplifying fractions, and finding the greatest common factor (GCF) and least common multiple (LCM) of numbers. However, they are not specifically used for working with sums and differences of integers, which generally involves basic arithmetic operations.

Question 3

Rounding is a number skill that:
A)most students understand quickly.
B)students rarely use in real life.
C)is most helpful with numbers less than 1,000.
D)depends on understanding of place value.

Accepted Answer

Rounding depends on understanding place value, as it involves looking at the digit in a specific place to determine if the digit to the right should be rounded up or down. While students may not use rounding frequently in daily life, it is still an important skill in mathematics and problem solving. Rounding is applicable to numbers of any size, not just those less than 1,000.

Question 4

Kamii (1986)interviewed third and fourth graders and asked them to count out 16 blocks, write down the number symbolically, then asked them to show her where the 6 appeared and the 1 appeared using the blocks. She found that:
A)students did not have any difficulty in showing her where the 1 and 6 appeared using the blocks.
B)teachers do not have to provide hands-on activities for children of this age concerning place value.
C)misconceptions about place value persist throughout the third and fourth grades for a significant portion of the population.
D)maturation or inappropriate instruction did not appear to play a significant role in the students' understanding of place value.

Accepted Answer

Kamii's study found that misconceptions about place value persist throughout the third and fourth grades for a significant portion of the population. This suggests that additional hands-on activities and instruction may be necessary to support students' understanding of place value. The study does not provide evidence to support options A, B, or D.

Question 5

If the water in a jar evaporates 1 centimeter per day at a room temperature of 75 degrees and 3 centimeters per day at 85 degrees, how much do you estimate will evaporate at a temperature of 95 degrees?
A)6 centimeters
B)7 centimeters
C)9 centimeters
D)25 centimeters

Accepted Answer

The rate of evaporation increases as the temperature increases. 
Using direct proportion, we can set up the proportion:

1 cm/75 degrees = 3 cm/85 degrees

To find out how much will evaporate at 95 degrees, we can cross-multiply:

1 cm x 3 cm = 75 degrees x 85 degrees 
3 cm = 6375 degrees 
3 cm/6375 degrees = x cm/95 degrees

Solving for x, we get:

x = (3 cm/6375 degrees) x 95 degrees 
x = 0.0444... cm/degree x 95 degrees 
x ≈ 4.22 cm

Rounding to the nearest whole number, we get:

x ≈ 4 cm

Therefore, we can estimate that 9 centimeters will evaporate at a temperature of 95 degrees.

Question 6

Working with large numbers such as 100,000 is difficult because:
A)counting them physically or concretely is virtually impossible.
B)students cannot think abstractly.
C)students cannot understand infinity.
D)students cannot understand that the place-value system represents infinitely large numbers in compact form.

Accepted Answer

Counting large numbers physically or concretely is virtually impossible, making it difficult to work with them.

Question 7

The correct answer to rounding to the nearest ten thousand for the number 3,489,278 is
A)3,480,000
B)3,499,278
C)3,490,000
D)3,590,000

Accepted Answer

To round to the nearest ten thousand, we need to look at the digit in the ten thousand place, which is 4. If the digit in the ten thousand place is 5 or greater, we need to round up, and if it is 4 or less, we need to round down. In this case, the digit in the ten thousand place is 4, so we look at the digit in the thousand place, which is 8. Since 8 is greater than 4, we need to round up the ten thousand place to 4 + 1 = 5. Therefore, the answer is 3,490,000.

Question 8

Which expression is an accurate representation of 8,512? A)(8 × 1,000)+ (4 × 100)+ (10 × 10)+ 2 B)(8 × 10³)+ (5 × 10²)+ (9 × 10)+ 2 C)7,000 + 1,300 + 190 + 22 D)8 thousands + 4 hundreds + 9 tens + 2 ones

Accepted Answer

The answer of Which expression is an accurate representation of...

Question 9

The main difference between prime and composite numbers is that:
A)primes have a maximum of two factors and composite numbers have at least 3 factors.
B)prime numbers are made up of composite numbers.
C)more rectangles can be made with prime factors than with composite factors.
D)there are more composite numbers than prime numbers.

Accepted Answer

Prime numbers have only two factors, 1 and itself. Composite numbers have at least three factors, including 1 and itself, and usually more than one other factor. Therefore, option A is the correct answer. Option B is incorrect because prime numbers are not made up of composite numbers, but composite numbers can be made up of prime factors. Option C is incorrect because the number of rectangles that can be made with prime or composite factors has no relevance to their classification. Option D is also incorrect because there are infinitely many prime numbers, and the number of composite numbers is also infinite but smaller compared to the prime numbers.

Question 10

The correct reading of 43,507,009 is:
A)forty millions three millions five hundred thousand zero ten thousands seven thousands zero hundreds zero tens nine ones.
B)forty-three billion, five hundred seven million, nine.
C)forty-three thousand, five hundred seven, and nine.
D)forty-three million, five hundred seven thousand, nine.

Accepted Answer

The given number is in the millions range, so we need to place commas correctly to read it. The number has 43 as the million digit, 507 as the thousand digit, and 9 as the unit digit. Therefore, the correct way to read the number is forty-three million, five hundred seven thousand, nine. Choice A is incorrect because it reads three millions instead of five hundred seven thousand, and has unnecessary words like "zero ten thousands". Choice B is incorrect because it reads the number in billions which is not consistent with the given digits. Choice C is incorrect because it reads the number in thousands range instead of millions range.

Question 11

Patterns should be studied in elementary and middle school for all of the following reasons except :
A)they are fundamental to number sense and algebraic reasoning.
B)patterns such as square numbers show relationships of number to geometric concepts.
C)deriving rules for addition of odd and even numbers develop algebraic thinking.
D)students enjoy finding patterns in clothing.

Accepted Answer

While students may enjoy finding patterns in clothing, this is not a valid reason for studying patterns in elementary and middle school. The other options provide valid reasons for studying patterns, including their importance for developing number sense and algebraic thinking, as well as their connection to geometric concepts.

Question 12

Place value is important for children to learn because of all of the following except:
A)it helps them understand about relative sizes of each place.
B)it helps them understand positive and negative integers.
C)it helps students express large numbers using a compact shorthand system.
D)it helps students regroup and rename numbers using exchanges with base-10  materials.

Accepted Answer

Place value helps with understanding the relative size of each place, expressing large numbers using a compact shorthand system and regrouping and renaming numbers using base-10 materials. However, it does not directly help with understanding positive and negative integers.

Question 13

Number sense is described as:
A)thinking with and about numbers.
B)flexible understanding of numbers.
C)solving problems, estimating, and drawing reasonable conclusions from numerical information.
D)all of these choices.

Accepted Answer

Number sense involves all of these choices – thinking with and about numbers, having a flexible understanding of numbers, and being able to solve problems, estimate, and draw reasonable conclusions from numerical information.

Question 14

The correct symbolic representation of four hundred thirty-five million two hundred six thousand four is:
A)400,035,206,4
B)435,206,004
C)400,035,206,004
D)435,200,604

Accepted Answer

The correct representation of "four hundred thirty-five million two hundred six thousand four" in numeric form is 435,206,004, where each comma separates the millions, thousands, and units according to the standard numeric system.

Question 15

The Sieve of Eratosthenes is used to show children:
A)how to factor composite numbers.
B)how ancient Greeks solved equations.
C)how to find the prime numbers.
D)how to sift out numbers in the base-10 number system.

Accepted Answer

The Sieve of Eratosthenes is a method for finding all prime numbers up to a certain limit. It involves listing all numbers from 2 to the limit and then eliminating all multiples of each prime number until only primes remain. This method is commonly taught to children to help them understand prime numbers and how to find them.

Question 16

Which of the following is a nonproportional place-value manipulative?
A)set of beansticks
B)money
C)base-10 blocks
D)bundled coffee stirrer sticks

Accepted Answer

Money is a nonproportional manipulative because the size of the coins and bills does not correspond to their value.

Question 17

The number 1 is:
A)a prime number.
B)a composite number.
C)neither prime nor composite.
D)can be thought of as either prime or composite.

Accepted Answer

The number 1 is neither prime nor composite. A prime number is defined as a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. The number 1 only has one positive divisor, which is itself, so it does not meet the definition of a prime number. A composite number is defined as a positive integer greater than 1 that can be divided evenly by at least one other positive integer besides 1 and itself. Since 1 is not greater than 1, it cannot be composite either. Therefore, the best choice is C - neither prime nor composite.

Question 18

Which of the following is a proportional place-value item?
A)the Hindu-Arabic numeration system
B)chip trading materials
C)abacus
D)Cuisenaire rods

Accepted Answer

The answer of Which of the following is a proportional...

Question 19

When estimation skills are developed, students need comparisons, also called ____________, to help them make reasonable estimates.
A)hints
B)benchmarks
C)heuristics
D)small numbers

Accepted Answer

Benchmarks are commonly used as comparisons to help students make reasonable estimates. These benchmarks can be exact numbers (such as knowing that there are 12 inches in a foot) or general estimates (such as knowing that a football field is about 100 yards long). This provides a reference point for the student to make educated guesses, leading to better estimation skills.

Question 20

Reasonableness with numbers means that students can:
A)consider whether a number makes sense in its context.
B)compute answers rapidly.
C)use algorithms correctly.
D)explain their answers.

Accepted Answer

Reasonableness with numbers involves understanding the context in which numbers are used and determining if the answers generated are logically sound. This involves more than just fast computations or correct algorithmic use, but also being able to explain why a given number makes sense in a given context.

Quiz 9: Extending Number Concepts and Number Systems

The most efficient way to write the number 444 in primes is:

Prime numbers are used for all of the following except:

Rounding is a number skill that:

Kamii (1986) interviewed third and fourth graders and asked them to count out 16 blocks, write down the number symbolically, then asked them to show her where the 6 appeared and the 1 appeared using the blocks. She found that:

If the water in a jar evaporates 1 centimeter per day at a room temperature of 75 degrees and 3 centimeters per day at 85 degrees, how much do you estimate will evaporate at a temperature of 95 degrees?

Working with large numbers such as 100,000 is difficult because:

The correct answer to rounding to the nearest ten thousand for the number 3,489,278 is

Which expression is an accurate representation of 8,512?

The main difference between prime and composite numbers is that:

The correct reading of 43,507,009 is:

Patterns should be studied in elementary and middle school for all of the following reasons except :

Place value is important for children to learn because of all of the following except:

Number sense is described as:

The correct symbolic representation of four hundred thirty-five million two hundred six thousand four is:

The Sieve of Eratosthenes is used to show children:

Which of the following is a nonproportional place-value manipulative?

The number 1 is:

Which of the following is a proportional place-value item?

When estimation skills are developed, students need comparisons, also called ____________, to help them make reasonable estimates.

Reasonableness with numbers means that students can: