Deck 13: Extending Understanding of Common and Decimal Fractions

Question 1

Given the problem below, which of the following is not a correct strategy to illustrate this problem?
Juan practiced piano for ¾ hour on Tuesday, Wednesday, and Thursday. How long did he practice altogether?

A)Take 3 fraction strips 1 unit long and mark off  ¾ of each strip. Lay the pieces together end to end and then separate them into halves and fourths. Add all the halves together and fourths together until all possible wholes and fractions are left.
B)Use a clock to mark off the ¾ hours, starting at 12:00 and continuing around the clock marking off ¾ portions until ending up at 2:30.
C)Using a number line, starting at 0, marking off the number line in fourths, then marking off ¾ units three times.
D)Use fraction squares, shade in ¾ on each, then adding together the pieces, forming wholes and fractional parts.

Answer 1

Use a clock to mark off the ¾ hours, starting at 12:00 and continuing around the clock marking off ¾ portions until ending up at 2:30.

Question 2

Common fractions with denominators of factors of 2s and 5s only are known as:

A)repeating decimals.
B)terminating decimals.
C)both repeating and terminating decimals.
D)neither repeating nor terminating decimals.

Answer 2

terminating decimals.

Question 3

The statements below concerning the greatest common factor (GCF)are all true except for :

A)the name for the GCF causes confusion because many times this "greatest" number can be smaller than any of the numbers under consideration.
B)the GCF is used to find the common denominator of fractions.
C)Venn diagrams can be used to illustrate the GCF of two or more numbers.
D)two numbers must have a GCF.

Answer 3

the GCF is used to find the common denominator of fractions.

Question 4

Which model for subtraction of common fractions is illustrated by the problem below?
Mykala bought 4¾ pounds of chicken and cooked 2½ pounds. How much chicken does she have left?

A)takeaway
B)comparison
C)completion
D)whole-part-part

Question 5

Tyrone asked Mr. Jones what the answer to 0.7 × 0.3 would be. Which of the following is the best method that Mr. Jones could use to help Tyrone understand this problem conceptually?

A)Mr. Jones could tell him to count the number of decimal places to the right of each decimal, then to multiply the two numbers as if they were whole numbers, and count back that number of places from the right.
B)Mr. Jones could tell him to use base-10 pieces for each decimal, by laying down 7 longs 3 times, then to go back one decimal.
C)Mr. Jones could tell him to change each decimal into fractions, multiply out the fractions, then change back into decimals.
D)Mr. Jones could tell him to add 7 tenths three times, then to divide by one tenth.

Question 6

Children learn the rule "Multiplication makes bigger, division makes smaller" when working with whole numbers (with the exception of products and quotients with 0 and 1). All of the following mathematical statements concerning fractions violate this rule except for :

A)⅔ × ¾
B)⅔ × 24
C)⅔ ÷  ¾
D)1⅔ × 24

Question 7

What is a correct expansion of 37.206?

A)(3 × 10²)+ (7 × 10⁰)+ (2 × 10¹)+ (6 × 10³)
B)(3 × 10)+ (7 × 10⁰)+ (2 × 1)+ (0 × 10⁻¹)+ (6 × 10⁻²)
C)(3 × 10¹)+ (7 × 10⁰)+ (2 × 10⁻¹)+ (6 × 10⁻³)
D)(3 × 10)+ (7 × 1)+ (2 × 0.1)+ (6 × 0.01)

Question 8

The following statements below concerning the least common multiple (LCM)are all true except for:

A)The LCM is used to find the common denominator of fractions.
B)The LCM of 24, 36, and 70 is 2³ × 3² × 5 × 7.
C)The LCM is used to reduce fractions down to lowest terms.
D)The LCM is confusing to children because this "least" number can be larger than any of the numbers under consideration.

Question 9

A half-gallon of milk is poured into 16 equal-sized containers. Which of the following is true with respect to this statement?

A)This is an example of the partitive model.
B)This is an example of the repeated addition model.
C)This is an example of the measurement model.
D)The correct mathematical statement for this situation is ½ × 16.

Question 10

Which model for subtraction of common fractions is illustrated by the problem below?
Deshawn walks 1½ miles around the track while Sam walks 1⅞ miles around the track. How much farther does Sam walk than Deshawn?

A)takeaway
B)comparison
C)completion
D)whole-part-part

Question 11

Research has shown that:

A)it is more difficult for students to learn rote procedures once they have acquired conceptual understanding.
B)it makes no difference for students in the long run whether conceptual practice or rote practice comes first.
C)it is more difficult for students to acquire conceptual understanding once they have learned rote procedures.
D)it is more difficult for students to acquire conceptual understanding if they simultaneously learn the comparable rote procedures.

Question 12

A student multiplied 5½ × 3¼, but was not sure of his answer. Which of the following mathematical statements that he listed on his paper has the same meaning as the given problem?

A)(5 × 3)+ (½ × ¼)
B)(5 + ½)× 3 × ¼
C)(5 × ½)+ (3 × ¼)
D)(5 + ½)× (3 + ¼)

Question 13

The following have the value of 3.6 except for :

A)36 × 0.1
B)0.4 × 9
C)120 × 0.03
D)72 × 0.5

Question 14

Which of the following situations is the correct problem for the mathematical statement 0.8 ÷ 0.2?

A)Mary has 0.8 of a yard of cloth and wants to make 2 headbands out of the cloth.
B)Jim has 0.8 of a meter of molding and needs as many 0.2 meter pieces he can cut as possible.
C)Nicole has 0.2 of a dollar and wants to increase it to 0.8 of a dollar.
D)David wants 0.2 of a 0.8 square foot piece of metal for a dog house roof.

Question 15

Adding fractions should be introduced in which order (from least to most complex)?

A)like denominators, unlike denominators, one denominator that is a multiple of another
B)unlike denominators, one denominator that is a multiple of another, like denominators
C)like denominators, one denominator that is a multiple of another, unlike denominators
D)unlike denominators, like denominators, one denominator that is a multiple of another

Question 16

Which model for subtraction of common fractions is illustrated by the problem below?
Emily has ⅝ cup of flour but needs 1¼ cups to make bread. How much more flour does she need?

A)takeaway
B)comparison
C)completion
D)whole-part-part

Question 17

The density property refers to:

A)the thickness of the width of a number line.
B)the property that states that there is always another number between any two numbers.
C)the necessity for students to recognize how dense the curriculum is when learning about fractions.
D)the equivalency of fractions to decimals.

Question 18

John wants to get ⅔ of his money out of the bank, but he has to pay his brother ⅙ of that. Which of the following statements shows what John would have left of the amount he took out of the bank, after paying his brother?

A)⅔ - ⅙
B)⅔ × ⅙
C)1 - (⅔ × ⅙)
D)⅔ × ⅚

Question 19

"Lining up the decimal points" is the rote rule that children learn when adding and subtracting decimal fractions. The reasoning behind this rule is:

A)children are following the "one place value at a time" rule when adding and subtracting, similar to what they followed with whole numbers.
B)children will not add together or subtract the wrong numbers.
C)that base-10 blocks won't be necessary for conceptual understanding in this case.
D)that real-life examples won't be necessary for conceptual understanding in this case.

Question 20

The correct sequence when adding fractions is:

A)working with fractions with like denominators, then mixed numerals with unlike denominators, then fractions with like denominators.
B)working with fractions with unlike denominators, then working with fractions with like denominators, then working with mixed numerals.
C)working with fractions with unlike denominators, then working with mixed numerals with like denominators, then working with fractions with like denominators.
D)working with fractions with like denominators, then fractions with unlike denominators, then working with mixed numerals.

Question 21

A)
B)
C)
D)

Question 22

Some teachers say that using manipulatives for teaching fractions just confuses children and that they do just fine learning the traditional algorithms. Do you agree or disagree with these statements? Why or why not?

Question 23

How could you convince children that they need to have common denominators when adding and subtracting common fractions?

Question 24

Which of these fractions is a terminating decimal?

A)
B)
C)
D)

Question 25

A)
B)
C)
D)

Question 26

Everett found out that the exchange rate between Singapore dollars and South African rand was:
1 SGD = 4.2 ZAR
Everett changed 3,000 Singapore dollars into South African rand at this exchange rate. How much money in South African rand did Everett get?

Question 27

4.8 ÷ 0.2 =

A)0.24
B)240
C)24
D)2.4

Question 28

9.6 × 4.23 =

A)40.68
B)4.068
C)406.8
D)4068.0

Question 29

What is the progression you should use to teach children to add and subtract fractions? Use examples to illustrate the progression.

Question 30

Why is the expansion of decimals important for upper elementary children?

Question 31

Mason is 50 inches tall and is growing at the rate of
 inch per month. Owen is 47 inches tall and is growing at the rate of

Inch per month. If they continue to grow at these rates for the next four years, in how many months will they be the same height?

A)24 months
B)30 months
C)36 months
D)42 months

Question 32

How could you explain the density property to children?

Question 33

Explain how you would help children make the transition between common fractions and decimal fractions.

Question 34

12 - 8.34 =

A)4.66
B)3.66
C)4.34
D)6.34

Question 35

A)
B)
C)
D)

Question 36

What is the least common multiple (LCM)for 36 and 48?

A)288
B)144
C)192
D)576

Question 37

A)
B)
C)
D)

Question 38

In which of these pairs of numbers is 2.25 larger than the first number but smaller than the second number?

A)1 and 2
B)2 and
C)
D)

Question 39

On the number line given here, what number would be located at point P?

Question 40

4.5 + 6.23 + 8.25 + 6 =

A)19.58
B)20.58
C)21.98
D)24.98

Question 41

Sketch models to convince children that the expressions below are equal to their correct answers.
(a)
(b)
(c)
(d)
What is the value in making sketches such as these?

Question 42

Explain how GCFs and LCMs are related to common fractions.

Question 43

A student solved

 by subtracting 6 - 4 to obtain 2 and

 to obtain

. She then subtracted

 to get

. Is this a legitimate algorithm? Will it always work? Explain why or why not.

Question 44

Use pattern blocks to make a design in which ⅓ is made of trapezoids. Trace your design. Shade the trapezoids.

Question 45

Performance Task: Using Pattern Blocks and Tangrams
Use pattern blocks or tangrams to complete each performance task.
Use pattern blocks to make a design in which 1¼ is green. Trace your design. Shade the green part.

Question 46

Give several examples of how calculators can be beneficial when teaching common fractions and decimal fractions.

Question 47

Illustrate and describe how tangrams can be used to develop the concepts of ½ and ¼ .

Question 48

Represent ⅓ and ⅔ using pattern blocks.