Deck 9: Extending Number Concepts and Number Systems

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

Answer 1

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.

Answer 2

working with sums and differences of integers.

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.

Answer 3

depends on understanding of place value.

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.

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

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.

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

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

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.

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.

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.

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.

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.

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

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.

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

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.

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

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

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.

Question 21

What is one of the main reasons students have trouble understanding place value?

Question 22

The Ben Franklin Bridge was 75 years old in 2001. In what year was the bridge 50 years old?

A)1951
B)1976
C)1984
D)1986

Question 23

Explain the differences between proportional and nonproportional models for the base-10 system and give two examples for each. Why would a teacher ever use nonproportional models?

Question 24

A new hybrid car claims to have an excellent energy rating. Janice kept track of her mileage of 3,279 and gasoline consumption of 46 gallons. Based on this information, what would be a reasonable estimate of the actual miles per gallon (mpg)?

A)under 40 mpg
B)about 50 mpg
C)over 60 mpg
D)nearly 80 mpg

Question 25

Stickers come in small booklets of 100 and in rolls of 1,000. On the store shelf, there are 6 booklets and 4 rolls of stickers. How many stickers are on the shelf?

A)1,100
B)4,600
C)6,400
D)10,000

Question 26

TIMSS: Which of these is the largest number?

A)2,735
B)2,537
C)2,573
D)2,753

Question 27

Explain the essential role that number sense and number awareness plays in elementary mathematics.

Question 28

What is the total if you add 14, as shown below?

A)244
B)249
C)251
D)377

Question 29

Teacher Licensing Examination Questions
NAEP: What number is 100 more than 5,237?

A)5,238
B)5,247
C)5,337
D)6,237

Question 30

Explain the role that prime and composite numbers play in helping children develop number sense.

Question 31

Explain the role of rounding and estimation in helping to develop number sense.

Question 32

By how much will the value of the number 4,372 increase if the 3 is replaced with a 9?

A)6
B)60
C)600
D)6,000

Question 33

The prime factorization of 12 is:

A)2 × 3
B)2 × 2 × 3
C)12 × 1
D)6 × 2

Question 34

Explain why looking for patterns and relationships is fundamental to helping children develop number sense, particularly in middle school.

Question 35

Give three ways you could use real-life examples in your class to help children to understand large numbers.

Question 36

Grade-Level Tests Given by States
Based on the key below, which pattern equals 352?

A)
B)
C)
D)

Question 37

Weather records in a city show the coldest recorded temperature was −20°F, and the hottest was 120°F. Which of the following number lines represents the range of recorded actual temperatures in this city?

A)
B)
C)
D)

Question 38

Why should a child understand the base-10 numeration system?

Question 39

The correct answer to rounding to the nearest ten for the number 4,157 is:

A)4,150.
B)4,200.
C)4,000.
D)4,160.

Question 40

The goal of teaching children to estimate is so that they:

A)will get the exact answer.
B)develop number sense.
C)can win guessing contests.
D)can count quickly.

Question 41

Performance Assessment Place Value. Observe students playing the bankers game or other trading activities. Determine whether students are proficient with the trading process for trading up and for trading down.

Question 42

Give two reasons why integers are difficult for elementary students.

Question 43

Place-Value Mats. Have students display on place value mats several different numbers in base-10 using proportional (flat, rods, units)and non-proportional materials (chips).