Deck 12: Developing Understanding of Common and Decimal Fractions

Question 1

If a base-10 flat represents 1, then the unit represents:

A)0.01.
B)0.1.
C)0.001.
D)0.0001.

Answer 1

0.01.

Question 2

Cutting a piece of cloth that is 3 yards long into 5 equal-size pieces is a situation represented by:

A)Unit partitioned into equal-size parts
B)Set partitioned into equal-size groups
C)Expression of ratios
D)Indicated division

Answer 2

Indicated division

Question 3

According to the research by Hunting, children have the most difficulty showing fractions that are:

A)part of a set of discrete objects.
B)part of a whole.
C)ratios.
D)part of a continuous object such as a number line.

Answer 3

part of a continuous object such as a number line.

Question 4

Taking a cake and dividing it into 6 equal slices is a situation represented by:

A)unit partitioned into equal-size parts.
B)set partitioned into equal-size groups.
C)expression of ratios.
D)indicated division.

Question 5

When a toy model is built with a scale of
, this is an example of a situation represented by:

A)unit partitioned into equal-size parts.
B)comparison model.
C)expression of ratios.
D)indicated division.

Question 6

One of the difficulties children have when naming decimal numbers is that:

A)they usually require more words than whole numbers.
B)they require that every place be named unlike whole numbers that are named in groups of three.
C)there is an asymmetry of names for place values when comparing numbers left and right of the decimal point.
D)there is no consistent way to remember the names of the place values.

Question 7

Decimal fractions are similar to common fractions except that:

A)they are nonterminating, nonrepeating.
B)they have denominators that are powers of ten.
C)they are smaller than common fractions.
D)they cannot be converted into percentages.

Question 8

Equivalent fractions are best taught using:

A)units partitioned into equal-sized groups.
B)sets partitioned into equal sized groups.
C)comparison models.
D)ratio models.

Question 9

The purpose in using the terms common fractions and decimal fractions is to:

A)let children know that they are commonly found in nature.
B)help children understand that both types of numerals are used to represent fractional numbers.
C)help children distinguish between these completely different types of numbers.
D)decrease confusion about these complex numbers.

Question 10

The best way to teach children fractions and decimals is to:

A)teach them the rules first, then give them manipulatives to substantiate the rules.
B)allow them to work with manipulatives, then teach them the rules.
C)allow them to work with manipulatives, then have them make sketches, then to show them the rules.
D)teach them the rules, then have them make sketches, then give them manipulatives.

Question 11

Teaching children common and decimal fractions includes about common and decimal fractions includes all of the following except for :

A)it extends their understanding on number concepts beyond knowledge about whole numbers.
B)it allows children to represent many aspects of their environment that would be unexplainable with only whole numbers.
C)it helps them to improve their understanding of odd and even numbers.
D)it helps them to broaden their awareness of powers of numbers.

Question 12

Improper fractions are:

A)fractions greater than 1.
B)not equivalent to mixed numbers.
C)fractions that should not be used in elementary school settings.
D)algebraic fractions.

Question 13

If the largest base-10 cube (10 units × 10 units × 10 units)represents 1, then the small unit (1 unit × 1 unit × 1 unit)represents:

A)0.1.
B)0.001.
C)0.01.
D)0.0001.

Question 14

The concept of a fractional part of a set should only be introduced after children:

A)demonstrate that they can conserve number.
B)have a good grasp of whole numbers.
C)are skillful in counting objects in sets.
D)all of these options are correct.

Question 15

If a decimal is written as 1.0, this has the same meaning as all of the following statements except for:

A)It indicates that a unit has been separated into 10 parts and that all 10 parts are being considered.
B)It is equivalent to the common fraction 10/10, and the zero should not be omitted.
C)It is equivalent to 10 hundredths.
D)It indicates a precision of measurement.

Question 16

A unit fraction is one that:

A)is in the form 3/3.
B)has a numerator of 1.
C)that is the result of combining two or more fractions to get 1.
D)that is in the form 1:1.

Question 17

Round 34,567.32578 off to the nearest thousandth. The answer is:

A)34,567.325.
B)34,567.32600.
C)34,000.32578.
D)34,567.326.

Question 18

In order for children to fully understand rounding decimal fractions, they must have all of the following prerequisites except for :

A)they must know the names for each place value.
B)they must know the rules for when to go up to the next number and when to keep the same number.
C)they must understand numbers' relative positions on number lines.
D)they must understand the meaning of decimal fractions.

Question 19

If a child takes ½ of 12 cookies, this is an example of a situation represented by:

A)unit partitioned into equal-size parts.
B)set partitioned into equal-size groups.
C)comparison model.
D)indicated division.

Question 20

John was asked whether
Or

Was closer to

. Which of the following would be an accurate explanation?

A) is left of and is to the right of . Since 3 and 4 are one unit apart, their average would be , which would be halfway. So, and are the same distance from .
B)  is from ½ which is equivalent to . is from , which is equivalent to , so is larger than , is closer to .
C) is equivalent to and is equivalent to . Since  is equivalent to , is closer to .
D) is left of and is right of . is equivalent to 0.375 and is equivalent to 0.47, so is closer to .

Question 21

Which of these coins or units of currency will NOT help students understand decimal fractions?

A)5¢
B)1¢
C)10¢
D)$1

Question 22

Two different fractions each have a difference of 2 between their numerators and their denominators. All of the following are true except:

A)the fraction with the larger numerator is the larger fraction.
B)the fraction with the larger denominator is the larger fraction.
C)the fraction that has a terminating decimal is larger.
D)the fraction with the larger sum of numerator and denominator is the larger fraction.

Question 23

Compare
To

.

A)
B)
C)
D)

Question 24

Give four examples of manipulatives that can be used to introduce fractions to elementary children.

Question 25

A bag of marbles has 5 red, 4 blue, and 7 green marbles. Which of the following fractions is not a part-whole representation?

A)
B)
C)
D)

Question 26

Explain how you can use Cuisenaire rods and meter sticks to explain the connections between common fractions and decimal fractions.

Question 27

Decimal fractions are easier for children to understand than common fractions for the following reasons except:

A)decimal fractions are easier to read.
B)computations are easier with decimal fractions.
C)decimal fractions have only denominators of powers of 10.
D)decimal fractions are easier to place in order.

Question 28

Which of the following is equal to a quarter of a million?

A)40,000
B)250,000
C)2,500,000
D)

Question 29

Draw two different illustrations of improper fractions to explain why they are equivalent to mixed numerals.

Question 30

What is the best teaching sequence for teaching children about common fractions?

Question 31

Explain the differences between these two situations represented by common fractions: Unit partitioned into Equal-Size Parts versus Set partitioned into Equal-Size Groups. Give illustrations to show the differences.

Question 32

These manipulatives are appropriate for teaching decimal fractions except for:

A)Cuisenaire rods.
B)fraction strips.
C)fraction circles.
D)meter sticks.

Question 33

Compare 3.0 to 3. The following are true except:

A)they have the same value.
B)3.0 shows greater precision.
C)there is no difference.
D)3.0 may be a rounded value.

Question 34

Which of the following is not equivalent to the others?

A)
B)
C)
D)0.4

Question 35

What is the decimal equivalent of ⅞ ?

A)0.70
B)0.875
C)0.85
D)0.75

Question 36

Explain the differences between the comparison model and the expression of ratios situations for representing fractions. Give illustrations to show the differences.

Question 37

Why should a teacher use the terms common fractions and decimal fractions rather than just the terms fractions and decimals ?

Question 38

A cake was cut into eight pieces of equal size. Brandon ate three pieces of the cake. What fraction of the cake did Brandon eat?

A)
B)
C)
D)

Question 39

Which of the following has the fractions in ascending order?

A)
B)
C)
D)

Question 40

Explain what is meant by the indicated division representation of fractions.

Question 41

How would you help a child who thinks that when you multiply two numbers the result is always larger than either of the two factors?

Question 42

Shade ⅓ of the rectangle below.

Question 43

How would you explain to children the paradox that the finite space from 0 to 1 contains an infinite number of common fractions?

Question 44

For health reasons people should limit their efforts, for instance, during sports, in order not to exceed a certain heartbeat frequency. For years, the relationship between a person's recommended maximum heart rate and the person's age was described by the following formula: Recent research showed that this formula should be modified slightly. The new formula is as follows: A newspaper article stated: "A result of the new formula is that the recommended maximum number of heart beats per minute for young people decreases slightly and for old people it increases slightly." From which age onward does the recommended maximum heart rate increase as a result of the introduction of the new formula? Show your work.

Question 45

How would you explain to a child how to round a number to the nearest hundredths place? Use a specific example to help you explain the process you would go through.