Chapters 14-16

1) Estimating with fractions means that students have number sense about the relative size of fractions. All of the activities below would guide this number sense EXCEPT: a) Comparing fractions to benchmark numbers. b) Find out the fractional part of the class are wearing glasses. c) Collect survey data and find out what fractions of the class choose each item. d) Use paper folding to identify equivalence.

D

1) Fraction misconceptions come about for all of the following reasons. The statements below can be fraction misconceptions EXCEPT. a) Many meanings of fractions. b) Fractions written in a unique way. c) Students overgeneralize their whole-number knowledge d) Teachers present fractions late in the school year.

D

1) Models provide an effective visual for students and help them explore fractions. Identify the statement that is the definition of the length model. a) Location of a point in relation to 0 and other values. b) Part of area covered as it relates to the whole unit. c) Count of objects in the subset as it relates to defined whole. d) A unit or length involving fractional amounts.

D

1) What does a strong understanding of fractional computation relies on? a) Estimating with fractions. b) Iteration skills. c) Whole number knowledge. d) Fraction equivalence.

D

1) What does it mean to write fractions in simplest term? a) Finding equivalent numerators. b) Finding equivalent denominators. c) Finding multipliers and divisors. d) Finding equivalent fractions with no common whole number factors.

D

1) What is the definition of the process of partitioning? a) Equal shares. b) Equal-sized parts. c) Equivalent fractions. d) Subset of the whole.

D

12) Instruction on decimal computation has been dominated by rules. Identify the statement that is not rule based. A) Line up the decimal points. B) Count the decimal places. C) Shift the decimal point in the divisor. D) Apply decimal notation to properties of operations.

D

14) The estimation questions below would help solve this problem EXCEPT: - A farmer fills each jug with 3.7 liters of cider. If you buy 4 jugs, how many liters of cider is that? A) Is it more than 12 liters? B) What is the most it could be? C) What is double 3.7 liters? D) Is it more than 7 × 4?

D

18) The main link between fractions, decimals and percents are A) Expanded notation. B) Terminology. C) Equivalency. D) Physical models.

D

2) What is an early method to use to help students see the connection between fractions and decimals fractions? A) Show them how to use a calculator to divide the fraction numerator by the denominator to find the decimal. B) Be sure to use precise language when speaking about decimals, such as "point seven two." C) Show them how to round decimal numbers to the closest whole number. D) Show them how to use base-ten models to build models of base-ten fractions.

D

8) All of the statements below are true of this decimal fraction 5.13 EXCEPT: A) 5 + 1/10 + 3/100. B) Five and thirteen-hundredths. C) 513/100. D) Five wholes, 3 tenths and 1 hundredth.

D

9) Approximation with compatible fractions is one method to help students with number sense with decimal fractions. All of the statements are true of 7.3962 EXCEPT: A) Closer to 7 than 8. B) Closer to 7 3/4 than 7 1/2. C) Closer to 7.3 than 7 1/5. D) Closer to 7.4 than 7.5.

D

1) A _______ is a significantly more sophisticated length model than other models. a) Number line. b) Cuisenaire rods. c) Measurement tools. d) Folded paper strips.

A

1) All of the models listed below support the understanding of fraction equivalence EXCEPT: a) Graph of slope b) Shapes created on dot paper c) Plastic, circular area models d) Clock faces

A

1) The term improper fraction is used to describe fractions greater than one. Identify the statement that is true about the term improper fraction. a) Is a clear term, as it helps students realize that there is something unacceptable about the format. b) Should be taught separately from proper fractions. c) Are best connected to mixed numbers through the standard algorithm. d) Should be introduced to students in a relevant context.

A

1) What is it advisable to do when you are exploring decimal numbers? A) 10 to one multiplicative relationship. B) Rules for placement of the decimal. C) Role of the decimal point. D) How to read a decimal fraction.

A

15) Understanding where to put the decimal is an issue with multiplication and division of decimals. What method below supports a fuller understanding? A) Rewrite decimals in their fractional equivalents. B) Rewrite decimals as whole numbers, compute and count place value. C) Rewrite decimals to the nearest tenths or hundredths. D) Rewrite decimals on 10 by 10 grids.

A

7) A common set model for decimal fraction is money. Identify the true statement below. A) Money is a two-place system. B) One-tenth a dime proportionately compares to a dollar. C) Money should be an initial model for decimal fractions. D) Money is a proportional model.

A

Complete the statement, "Developing the algorithm for adding and subtracting fractions should..." A) Be done side by side with visuals and situations. B) Be done with specific procedures. C) Be done with units that are challenging to combine. D) Be done mentally without paper and pencil.

A

Estimation and invented strategies are important with division of fractions. If you posed the problem (1/6) ÷ 4 you would ask all of the questions EXCEPT: A) Will the answer be greater than 4? B) Will the answer be greater than one? C) Will the answer be greater than 1/2? D) Will the answer be greater than 1/6?

A

Identify the problem that solving with a linear model would not be the best method. A) Half a pizza is left from the 2 pizzas Molly ordered. How much pizza was eaten? B) Mary needs 3 (1/2) feet of wood to build her fence. She only has 2 (3/4) feet. How much more wood does she need? C) Millie is at mile marker 2(1/2). Rob is at mile marker 1. How far behind is Rob? D) What is the total length of these two Cuisenaire rods placed end to end?

A

This model is exceptionally good at modeling fraction multiplication. It works when partitioning is challenging and provides a visual of the size of the result. A) Area model. B) Linear model. C) Set model. D) Circular model.

A

What is helpful when subtracting mixed number fractions? A) Deal with the whole numbers first and then work with the fractions. B) Always trade one of the whole number parts into equivalent parts. C) Avoid this method until the student fully understands subtraction of numbers less than one. D) Teach only the algorithm that keeps the whole number separate from the fractional part.

A

What is one of the methods for finding the product of fractional problems when one of the numbers is mixed number? A) Change to improper fraction. B) Compute partial products. C) Linear modeling. D) Associative property.

B

1) All of the following are fraction constructs EXCEPT: a) Part-whole. b) Measurement. c) Iteration. d) Division.

C

1) Complete this statement, "Comparing two fractions with any representation can be made only if you know the..". a) Size of the whole. b) Parts all the same size. c) Fractional parts are parts of the same size whole. d) Relationship between part and whole.

C

1) How do you know that = ? Identify the statement below that demonstrates a conceptual understanding. a) They are the same because you can simplify and get . b) Start with and multiply the top and bottom by 2 and you get . c) If you have 6 items and you take 4 that would be . You can make 6 groups into 3 groups and 4 into 2 groups and that would be . d) If you multiply 4 x 3 and 6 x 2 they're both 12.

C

1) Locating a fractional value on a number line can be challenging but is important for students to do. All of the statements below are common errors that students make when working with the number line EXCEPT: a) Use incorrect notation. b) Change the unit. c) Use incorrect subsets. d) Count the tick marks rather than the space.

C

1) The following visuals/manipulatives support the development of fractions using the area model EXCEPT: a) Pattern blocks. b) Tangrams. c) Cuisenaire rods. d) Geoboards.

C

10) There are several common errors and misconceptions associated with comparing and ordering decimals. Identify the statement below that represents the error with internal zero. A) Students say 0.375 is greater than 0.97. B) Students see 0.58 less than 0.078. C) Students select 0 as larger than 0.36 D) Students see 0.4 as not close to 0.375

C

17) What is it that students can understand if they can express fractions and decimals to the hundredths place? A) Place value. B) Computation of decimals. C) Percents. D) Density of decimals.

C

19) The following are guidelines for instruction on percents EXCEPT: A) Use terms part, whole and percent B) Use models, drawings and contexts to explain their solutions. C) Use calculators. D) Use mental computation.

C

6) What is the most common model used for decimal fractions? A) Rational number wheel B) Base ten strips and squares. C) 10 × 10 grids. D) Number line.

C

A(n) ________ interpretation is a good method to explore division because students can draw illustrations to show the model. A) Area. B) Set. C) Measurement. D) Linear.

C

All of the activities below guide students to understand the algorithm for fraction multiplication EXCEPT: A) Multiply a fraction by a whole number. B) Multiply a whole number by a fraction. C) Subdividing the whole number. D) Fraction of a fraction- no subdivisions.

C

Identify the manipulative used with linear models that you can decide what to use as the "whole." A) Circular pieces. B) Number Line. C) Cuisenaire Rods. D) Ruler.

C

It is recommended that division of fractions be taught with a developmental progression that focuses on four types of problems. Which statement below is not part of the progression? A) A fraction divided by a fraction. B) A whole number divided by a fraction. C) A whole number divided by a mixed number. D) A whole number divided by a whole number.

C

Students are able to solve adding and subtracting fractions without finding a common denominator using invented strategies. The problems below would work with the invented strategies EXCEPT: A) 3/4 + 1/8 B) 1/2 + 1/8 C) 5/6 + 1/7 D) 2/3 + 1/2

C

To guide students to develop a problem-based number sense approach for operations with fractions all of the following are recommended EXCEPT: A) Address common misconceptions regarding computational procedures. B) Estimating and invented methods play a big role in the development. C) Explore each operation with a single model. D) Use contextual tasks.

C

1) Comparing fractions involves the knowledge of the inverse relationship between number of parts and size of parts. The following activities support the relationship EXCEPT: a) Iterating. b) Equivalent fraction algorithm. c) Estimating. d) Partitioning.

B

1) Counting precedes whole-number learning of addition and subtraction. What is another term for counting fraction parts? a) Equalizing. b) Iterating. c) Partitioning. d) Sectioning.

B

1) Teaching considerations for fraction concepts include all of the following EXCEPT: a) Iterating and partitioning. b) Procedural algorithm for equivalence. c) Emphasis on number sense and fractional meaning. d) Link fractions to key benchmarks.

B

1) The part-whole construct is the concept most associated with fractions, but other important constructs they represent include all of the following EXCEPT: a) Measure. b) Reciprocity. c) Division. d) Ratio.

B

1) The way we write fractions is a convention with a top and bottom number with a bar in between. Posing questions can help students make sense of the symbols. All of the questions would support that sense making EXCEPT: a) What does the denominator in a fraction tell us? b) What does the equal symbol mean with fractions? c) What might a fraction equal to one look like? d) How do know if a fraction is greater than, less than 1?

B

1) What is a common misconception with fraction set models? a) There are not many real-world uses. b) Knowing the size of the subset rather than the number of equal sets c) Knowing the number of equal sets rather than the size of subsets d) There are not many manipulatives to model the collections.

B

11) Understanding that when decimals are rounded to two places (2.30 and 2.32) there is always another number in between. What is the place in between called? A) Place value. B) Density. C) Relationships. D) Equality.

B

13) Decimal multiplication tends to be poorly understood. What is it that students need to be able to do? A) Discover the method by being given a series of multiplication problems with factors that have the same digits, but decimals in different places. B) Discover it on their own with models, drawings and strategies. C) Be shown how to estimate after they are shown the algorithm. D) Use the repeated addition strategy that works for whole number.

B

16) What is a method teachers might use to assess the level of their students understanding of the decimal point placement? A) Ask them to show all computations. B) Ask them to show a model or drawing. C) Ask them to explain or write a rationale. D) Ask them to use a calculator to show the computation.

B

20) Estimation of many percent problems can be done with familiar numbers. Identify the idea that would not support estimation. A) Substitute a close percent that is easy to work with. B) Use a calculator to get an exact answer. C) Select numbers that are compatible with the percent to work with. D) Convert the problem to one that is simpler.

B

3) The 10-to-1 relationship extends in two directions. There is never a smallest piece or a largest piece. Complete the statement, "The symmetry is around..." A) The decimal point. B) The ones place. C) The operation being conducted. D) The relationship between the adjacent pieces.

B

4) The following decimals are equivalent 0.06 and 0.060. What does one of them show that the other does not show? A) More place value. B) More hundreds. C) More level of precision. D) Closer to one.

B

5) Using precise language can support students' understanding of the relationship between fractions and decimal fractions. All of the following are true statements EXCEPT: A) 0.75 = 3/4. B) Five and two-tenths is the same as five point two. C) Six and three-tenths = 6 3/10. D) 7. 03 = 7 30/100.

B

All of the statements below are examples of estimation or invented strategies for adding and subtracting fractions EXCEPT: A) Decide whether fractions are closest to 0, (1/2), or 1. B) Look for ways different fraction parts are related. C) Decide how big the fraction is based on the unit. D) Look for the size of the denominator.

B

Different models are used to help illustrate fractions. Identify the model that can be confusing when you are learning to add fractions. A) Area. B) Set. C) Linear. D) Length.

B

What statement is true about adding and subtracting with unlike denominators? A) Should be introduced at first with tasks that require both fractions to be changed. B) Is sometimes possible for students, especially if they have a good conceptual understanding of the relationships between certain fractional parts and a visual tool, such as a number line. C) Is a concept understood especially well by students if the teacher compares different denominators to "apples and oranges." D) Should initially be introduced without a model or drawing.

B

Adding and subtraction fractions should begin with students using prior knowledge of equivalent fractions. Identify the problem that may be more challenging to solve mentally. A) Luke ordered 3 pizzas. But before his guests arrive he got hungry and ate 3/8 of one pizza. What was left for the party? B) Linda ran 1 (1/2) miles on Friday. Saturday she ran 2 (1/8) miles and Sunday 2 (3/4) miles. How many miles did she run over the weekend? C) Lois gathered (3/4) pounds of walnuts and Charles gathered (7/8) pounds. Who gathered the most? How much more? D) Estimate the answer to (12/13) + (7/8)

D

Based on students experience with whole number division they think that when dividing by a fraction the answer should be smaller. This would be true for all of the following problems EXCEPT: A) 1/6 ÷ 3 B) 5/6 ÷ 3 C) 3/6 ÷ 3 D) 3 ÷ 5/6

D

Common misconceptions occur because students tend to overgeneralize what they know about whole number operations. Identify the misconception that is not relative to fraction operations. A) Adding both numerator and denominator. B) Not identifying the common denominator. C) Difficulty with common multiples. D) Use of invert and multiply.

D

Each the statements below are examples of misconceptions students have when learning to multiply fractions EXCEPT: A) Treating denominators the same as addition and subtraction. B) Matching multiplication situations with multiplication situations. C) Estimating the size of the answer incorrectly. D) Multiplying the denominator and not numerator.

D

Linear models are best represented by what manipulative? A) Pattern Blocks. B) Circular pieces. C) Ruler. D) Number line.

D