Deck 8: Developing Concepts of Number

Question 1

That objects may be counted in any way is the idea behind which principle of counting?

A)abstraction principle
B)one-to-one principle
C)cardinal principle
D)order irrelevance principle

Answer 1

order irrelevance principle

Question 2

If a child recognizes that Keesha is taller than Kristen, which thinking/learning skill is she using?

A)sorting
B)seriation
C)grouping
D)sequencing

Answer 2

seriation

Question 3

When kindergarteners find two pencils with the same length, which thinking/learning skill are they using?

A)grouping
B)ordering
C)seriation
D)matching

Answer 3

matching

Question 4

If a child arranges beads on a string in the order: red, blue, green, red, blue, green, what thinking/learning skill or strategy is he using?

A)matching and discriminating
B)classifying, sorting
C)patterning
D)seriation

Question 5

Which of the following is not a feature of zero in the Hindu-Arabic system of numbers?

A)Zero is a placeholder.
B)Zero represents multiplication by 10.
C)Zero allows compact representation of large numbers.
D)Zero is the easiest number to multiply by in this system.

Question 6

Which of the following statements is not true about common counting errors?

A)Coordination errors occur when children fail to match objects with numbers.
B)Omission errors occur when one or more items are not counted.
C)Double counting errors occur when one or more items are counted more than once.
D)Geographic errors occur when children rearrange the objects being counted.

Question 7

Having children retell the events of a story uses which thinking/learning strategy?

A)classifying
B)matching
C)sequencing
D)seriation

Question 8

Skip counting is valuable in learning mathematics for all of the following reasons except :

A)skip counting is a precursor to multiplication.
B)skip counting encourages faster counting strategies.
C)skip counting encourages more flexible counting.
D)skip counting is faster than rote counting.

Question 9

Which of the following statements is not true of the decimal number system?

A)There are 9 symbols for the numbers in the system.
B)The value of a digit is determined by its position in a numeral.
C)Zero acts as a number and as a placeholder in the system.
D)Ten is the base number.

Question 10

Students who are said to have such strong visual images for numbers without having to count dots are said to have an ability called:

A)the stable-order principle.
B)subitizing.
C)the abstraction principle.
D)conservation.

Question 11

Algorithms are:

A)useful because they allow students to work out math problems without having to think.
B)meant to be used to solve math problems when everything else fails.
C)are step-by-step calculation procedures.
D)inventions of Greek mathematicians.

Question 12

Seriation is found in counting because:

A)the value of counting numbers increases by one.
B)counting numbers occur in a stable sequence.
C)counting numbers begin at one and continue to infinity.
D)counting numbers have a beginning and end.

Question 13

Given the following problem, determine which type of correspondence it illustrates.
If three pencils cost 25 cents, how many pencils will 75 cents buy?

A)one-to-one correspondence
B)one-to-many correspondence
C)many-to-one correspondence
D)many-to-many correspondence

Question 14

An error made when children count some items more than once is a violation of the:

A)abstraction principle.
B)stable-order principle.
C)one-to-one principle.
D)cardinal principle.

Question 15

Which principle of counting is that the number of a set is the number given to the last number counted?

A)stable-order principle
B)cardinal principle
C)order irrelevance principle
D)abstraction principle

Question 16

Number constancy (or conservation)has all of the following characteristics except:

A)students who do not possess number constancy or conservation cannot progress to more complex mathematical ideas.
B)students can only learn number constancy or conservation if allowed to use manipulatives.
C)students can be taught number constancy or conservation by their teachers and parents.
D)students can be interviewed using Piaget's protocol to determine if they understand conservation of quantities.

Question 17

The concept of even numbers can be developed with all of the following activities except :

A)counting eyes, ears, hands and feet.
B)skip counting by 2s.
C)starting at 1 and skip counting by 2s.
D)coloring in every other square on hundreds chart starting at 0.

Question 18

If children stand in three groups according to eye color, they are using which thinking/learning skill?

A)discriminating
B)sequencing
C)seriation
D)patterning

Question 19

Ordinal numbers are numbers used to:

A)designate location in a sequence.
B)tell how many objects are in a set.
C)identify.
D)name.

Question 20

Rational counting is valued more than rote counting because rational counting:

A)is faster than rote counting.
B)is easier than rote counting
C)has more meaning than rote counting.
D)is learned earlier than rote counting.

Question 21

Sample benchmarks for grade 1-counting and numbers: Which is the smallest number?

A)8
B)3
C)6
D)12

Question 22

What is the importance of number constancy or number conservation?

Question 23

Praxis: Mr. Kinski asks students to classify classroom objects into three groups. Which mathematical concepts and skills are the students using?

A)recognizing similarities and differences
B)counting
C)relating numbers to numerals
D)recognizing two-dimensional and three-dimensional shapes

Question 24

While participating in a Piaget-type interview on number, five-year-old Ryan seems puzzled about whether the red checkers and black checkers are the same. He pairs them up, rearranges them, and lines them again. This behavior is typical of a student who is:

A)a non-conserver.
B)a  conserver of number.
C)a transitional thinker.
D)an irrational counter.

Question 25

Sample benchmarks for grade 1-counting and numbers: Which is the largest number?

A)17
B)37
C)73
D)13

Question 26

Gelman and Gallistel (1978)found that counting was a complex cognitive task requiring five counting principles (abstraction, stable-order, one-to-one, order-irrelevance, and cardinal principles). Choose two of these principles and explain what they mean.

Question 27

Teacher Licensing Examination Questions
Praxis:  When Mrs. Rodriquez greets children by counting them first, second, third, fourth, and so on, which use of number is she demonstrating?

A)cardinal
B)nominal
C)counting
D)ordinal

Question 28

Explain the difference between rote counting and rational counting.

Question 29

Sample benchmarks for grade 1-counting and numbers: How many crayons are there?

A)9
B)5
C)7
D)8

Question 30

Explain how the place-value system of the Hindu-Arabic number system works.

Question 31

Give three characteristics of the Hindu-Arabic number system that make possible compact notation and efficient computational processes.

Question 32

Which of the following is not a sequence?

A)July, August, September
B)first, middle, last
C)1, 4, 9, 16, 25
D)John, Susan, Philip, Estela

Question 33

Describe activities related to the three thinking/learning skills (1. Matching and discriminating, comparing and contrasting; 2. Classifying, sorting, and grouping; 3. Ordering, sequencing, and seriation)for primary age and intermediate grade children. These might be from real life or from other content areas.

Question 34

Patterns can be represented in many ways. Which of the following is an ABAC pattern?

A)clap, snap, clap, stomp, clap, snap, clap, stomp, ……
B)bark, meow, bark, bark, meow, bark, ……
C)triangle, triangle, square, circle, triangle, triangle, square, circle, …….
D)head, shoulders, knees, toes, head, shoulder, knees, toes, …….

Question 35

Sample benchmarks for grade 1-counting and numbers: Which of the following number sets has all values in order from smallest to largest?

A)18, 14, 22, 53, 36
B)36, 18, 53, 14, 22
C)14, 18, 22, 36, 53
D)22, 14, 53, 18, 36

Question 36

Give three reasons why children's literature is helpful for promoting understanding of mathematical concepts.

Question 37

When Ms. Simmons asked students to arrange 24, 78, 16, 53, 34 from smallest to largest, which mathematical thinking skill is she asking students to use?

A)classification
B)sequence
C)patterning
D)matching

Question 38

Children demonstrate an early understanding of number by:

A)counting from 1 to 100.
B)recognizing the difference between ½ and ⅓.
C)recognizing which group of cookies is "more" or "less."
D)writing numerals 1 through 9.

Question 39

Praxis: Miss Shalabi asks students to extend the pattern made with the following attribute blocks.

Benito places a square and then a triangle at the end of the pattern. What response would be the best way to help Benito?

A)No, that is wrong. Put a circle and then the square and triangle.
B)Read the pattern with me. What pattern do you hear?
C)How many shapes are in the pattern?
D)Let me show you how to finish the pattern.

Question 40

Compare nominal, ordinal, and cardinal numbers. Give examples of each to illustrate the differences.

Question 41

Describe three ways that you could teach children to differentiate between even and odd numbers.

Question 42

Why is skip counting important for children to learn mathematical concepts?