Question 1
Question
What is it advisable to do when you are exploring decimal numbers?
Answer

10 to one multiplicative relationship.

Rules for placement of the decimal.

Role of the decimal point.

How to read a decimal fraction.
Question 2
Question
What is an early method to use to help students see the connection between fractions and decimals fractions?
Answer

Show them how to use a calculator to divide the fraction numerator by the
denominator to find the decimal.

Be sure to use precise language when speaking about decimals, such as “point
seven two.”

Show them how to round decimal numbers to the closest whole number.

Show them how to use baseten models to build models of baseten fractions.
Question 3
Question
The 10to1 relationship extends in two directions. There is never a smallest piece or a largest piece. Complete the statement, “The symmetry is around..”.
Question 4
Question
The following decimals are equivalent 0.06 and 0.060. What does one of them show that the other does not show?
Answer

More place value.

More hundreds.

More level of precision.

Closer to one.
Question 5
Question
Using precise language can support students’ understanding of the relationship between fractions and decimal fractions. All of the following are true statements EXCEPT:
Question 6
Question
What is the most common model used for decimal fractions?
Question 7
Question
A common set model for decimal fraction is money. Identify the true statement below.
Answer

Money is a twoplace system.

Onetenth a dime proportionately compares to a dollar.

Money should be an initial model for decimal fractions.

Money is a proportional model.
Question 8
Question
All of the statements below are true of this decimal fraction 5.13 EXCEPT:
Question 9
Question
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:
Question 10
Question
There are several errors and misconceptions associated with comparing and ordering decimals. Identify the statement below that represents the error with internal zero.
Answer

Students say 0.375 is greater than 0.97.

Students see 0.58 less than 0.078.

Students select 0 as larger than 0.36

Students see 0.4 as not close to 0.375
Question 11
Question
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?
Answer

Place value.

Density.

Relationships.

Equality
Question 12
Question
Instruction on decimal computation has been dominated by rules. Identify the statement that is not rule based.
Answer

Line up the decimal points.

Count the decimal places.

Shift the decimal point in the divisor.

Apply decimal notation to properties of operations.
Question 13
Question
Decimal multiplication tends to be poorly understood. What is it that students need to be able to do?
Answer

Discover the method by being given a series of multiplication problems with factors that have the same digits, but decimals in different places.

Discover it on their own with models, drawings and strategies.

Be shown how to estimate after they are shown the algorithm.

Use the repeated addition strategy that works for whole number.
Question 14
Question
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?
Answer

Is it more than 12 liters?

What is the most it could be?

What is double 3.7 liters?

Is it more than 7 x 4?
Question 15
Question
Understanding where to put the decimal is an issue with multiplication and division of decimals. What method below supports a fuller understanding?
Answer

Rewrite decimals in their fractional equivalents.

Rewrite decimals as whole numbers, compute and count place value.

Rewrite decimals to the nearest tenths or hundredths.

Rewrite decimals on 10 by 10 grids.
Question 16
Question
What is a method teachers might use to assess the level of their students understanding of the decimal point placement?
Answer

Ask them to show all computations.

Ask them to show a model or drawing.

Ask them to explain or write a rationale.

Ask them to use a calculator to show the computation.
Question 17
Question
What is it that students can understand if they can express fractions and decimals to the hundredths place?
Answer

Place value

Computation of decimals.

Percents.

Density of decimals.
Question 18
Question
The main link between fractions, decimals and percents are _______________.
Answer

Expanded notation.

Terminology.

Equivalency.

Physical models.
Question 19
Question
The following are guidelines for instruction on percents EXCEPT:
Answer

Use terms part, whole and percent.

Use models, drawings and contexts to explain their solutions.

Use calculators

Use mental computation.
Question 20
Question
Estimation of many percent problems can be done with familiar numbers. Identify the idea that would not support estimation.
Answer

Substitute a close percent that is easy to work with.

Use a calculator to get an exact answer.

Select numbers that are compatible with the percent to work with

Convert the problem to one that is simpler
Question 21
Question
Complete this statement, “A ratio is a number that relates two quantities or measures within a given situation in a..”.
Question 22
Question
What is the type of ratio that would compare the number of girls in a class to the number of students in a class?
Answer

Ratio as rates.

Ratio as quotients.

Ratio as partwhole.

Ratio as parttopart
Question 23
Question
What should you keep in mind when comparing ratios to fractions?
Answer

Conceptually, they are exactly the same thing

They have the same meaning when a ratio is of the parttowhole type.

They both have a fraction bar that causes students to mistakenly think they are
related in some way.

Operations can be done with fractions while they can’t be done with ratios.
Question 24
Question
In the scenario “Billy’s dog weighs 10 pounds while Sarah’s dog weighs 8 pounds", the ratio 10/8 can be interpreted in the following ways EXCEPT:
Answer

For every 5 pounds of weight Billy’s dog has, Sarah’s dog has 4 pounds.

Billy’s dog weighs 1 1/4 times what Sarah’s dog does.

Sarah’s dog weighs 8 out of a total of 10 dog pounds.

Billy’s dog makes up 5/9 of the total dog weight.
Question 25
Question
A _____________ refers to thinking about a ratio as one unit.
Question 26
Question
The following statement are ways to define proportional reasoning EXCEPT:
Answer

Ratios as distinct entities.

Develop a specialized procedure for solving proportions.

Sense of covariation.

Recognize proportional relationships distinct from nonproportional relationships.
Question 27
Question
Identify the problem below that is a constant relationship.
Answer

Janet and Jean were walking to the park, each walking at the same rate. Jean started first. When Jean has walked 6 blocks, Janet has walked 2 blocks. How far will Janet be when Jean is at 12 blocks?

Kendra and Kevin are baking muffins using the same recipe. Kendra makes 6 dozen and Kevin makes 3 dozen. If Kevin is using 6 ounces of chocolate chips, how many ounces will Kendra need?

Lisa and Linda are planting peas on the same farm. Linda plants 4 rows and Lisa plants 6 rows. If Linda’s peas are ready to pick in 8 weeks, how many weeks will it take for Lisa’s peas to be ready?

Two weeks ago, two flowers were measured at 8 inches and
12 inches, respectively. Today they are 11 inches and 15 inches tall. Did the 8inch or 12 inch flower grow more?
Question 28
Question
Covariation means that two different quantities vary together. Identify the problem that is about a covariation between ratio.
Answer

Apples are 4 for $2.00.

2 apples for $1.00 and 1 for $0.50.

Apples at Meyers were 4 for $2.00 and at HyVee 5 for $3.00.

Apples sold 4 out of 5 over oranges.
Question 29
Question
Using proportional reasoning with measurement helps students with options for finding what?
Answer

Conversions.

Similarities.

Differences.

Rates.
Question 30
Question
What is one method for students to see the connection between multiplicative reasoning and proportional reasoning?
Answer

Solving problems with rates.

Solving problems with scale drawings.

Solve problems with between ratios.

Solving problems with costs.
Question 31
Question
The following are examples of connections between proportional reasoning and another mathematical strand EXCEPT:
Answer

The area of a rectangle is 8 square units and the length is four units long. How long is the width?

The negative slope of the line on the graph represents the fact that, for every 30 miles the car travels, it burns one gallon of gas.

The triangle has been enlarged by a scale factor of 2. How wide is the new triangle if its original width is 4 inches?

Sandy ate 1/4 of her Halloween candy and her sister also ate 1/2 of Sandy’s candy. What fraction of Sandy’s candy was left?
Question 32
Question
Which of the following is an example of using unit rate method of solving proportions?
Answer

If 2/3 = x/15, find the cross products, 30 = 3x, and then solve for x. x = 10.

Allison bought 3 pairs of socks for $12. To find out how much 10 pairs cost, find that $12 divided by 3 is $4 a pair, and multiply $4 by 10 for a total of $40.

A square with a length of 2 inches was enlarged by a scale factor of 4 and is now 8 inches long.

If 5 candy bars cost $4.50, then 10 would cost $9. (Because 5 × 2 = 10, multiply $4.50 by 2).
Question 33
Question
Which of the following is an example of using a buildup strategy method of solving proportions?
Answer

Allison bought 3 pairs of socks for $12. To find out how much ten pairs cost, find that $12 divided by 3 is $4 a pair, and multiply $4 by 10 for a total of $40.

A square with a length of 2 inches was enlarged by a scale factor of 4 and is now 8 inches long.

If 5 candy bars cost $4.50, then 10 would cost $9. (Because 5 × 2 = 10, multiply $4.50 by 2).

If 2/3 = x/15, find the cross products, 30 = 3x, and then solve for x. x = 10.
Question 34
Question
A variety of methods will help students develop their proportional thinking ability. All of the ideas below support this thinking EXCEPT:
Answer

Provide ratio and proportional tasks within many different contexts

Provide examples of proportional and nonproportional relationships to students and ask them to discuss the differences.

Relate proportional reasoning to their background knowledge and experiences.

Provide practice in crossmultiplication problems.
Question 35
Question
Creating ratio tables or charts helps students in all of the following ways EXCEPT:
Answer

Application of build up strategy

Organize information

Show nonproportional relationships.

Used to determine unit rate.
Question 36
Question
What statement below describes an advantage of using strip diagrams, bar models, fraction strips or length models to solve proportions?
Answer

A concrete strategy that can be done first and then connected to equations.

A strategy that connects ratio tables to graphs.

A common method to figure out how much goes in each equation

A strategy that helps set up linear relationships.
Question 37
Question
Posing problems for students to solve proportions situations with their own intuition and inventive method is preferred over what?
Answer

Scaling up and down

Ratio tables

Graphs.

Cross products
Question 38
Question
Graphing ratios can be challenging. Identify the statement that would NOT be a challenge.
Answer

Slope m is always one of the equivalent ratios.

Decide what points to graph

Which axes to use to measure

Sense making of the graphed points.
Question 39
Question
When a teacher assigns an object to be measured students have to make all of these decisions EXCEPT:
Answer

What attribute to measure?

What unit they can use to measure that attribute?

How to compare the unit to the attribute?

What formulas they should use to find the measurement?
Question 40
Question
Identify the statement that is NOT a part of the sequence of experiences for measurement instruction.
Answer

Using measurement formulas

Using physical models

Using measuring instruments.

Using comparisons of attributes
Question 41
Question
All of the ideas below support the reasoning behind starting measurement experiences with nonstandard units EXCEPT:
Answer

They focus directly on the attribute being measured.

Avoids conflicting objectives of the lesson on area or centimeters.

Provides good rational for using standard units.

Understanding of how measurement tools work.
Question 42
Question
When using a nonstandard unit to measure an object, what is it called when use many copies of the unit as needed to fill or match the attribute?
Answer

Iterating

Tiling

Comparing.

Matching.
Question 43
Question
There are three broad goals to teaching standard units of measure. Identify the one that is generally NOT a key goal.
Answer

Familiarity with the unit.

Knowledge of relationships between units

Estimation with standard and nonstandard units

Ability to select and appropriate unit.
Question 44
Question
The Common Core State Standards and the National Council of Teachers of Mathematics agree on the importance of what measurement topic?
Answer

Students focus on customary units of measurement.

Students focus on formulas versus actual measurements.

Students focus on conversions of standard to metric.

Students focus on metric unit of measurement as well as customary units.
Question 45
Question
All of these statements are true about reasons for including estimation in measurement activities EXCEPT:
Answer

Helps focus on the attribute being measured.

Helps provide an extrinsic motivation for measurement activities.

Helps develop familiarity with the unit.

Helps promote multiplicative reasoning.
Question 46
Question
Young learners do not immediately understand length measurement. Identify the statement below that would not be a misconception about measuring length.
Answer

Measuring attribute with the wrong measurement tool.

Using wrong end of the ruler

Counting hash marks rather than spaces.

Misaligning objects when comparing
Question 47
Question
The concept of conversion can be confusing for students. Identify the statement that is the primary reason for this confusion.
Answer

Basic idea if the measure is the same as the unit it is equal

Basic idea that if the measure is larger the unit is longer.

Basic idea that if the measure is larger the unit is shorter.

Basic idea that if the measure is shorter the unit is shorter.
Question 48
Question
Comparing area is more of a conceptual challenge for students than comparing length measures. Identify the statement that represents one reason for this confusion.
Answer

Area is a measure of twodimensional space inside a region

Direct comparison of two areas is not always possible

Rearranging areas into different shapes does not affect the amount of area

Area and perimeter formulas are often used interchangeably.
Question 49
Question
As students move to thinking about formulas it supports their conceptual knowledge of how the perimeter of rectangles can be put into general form. What formula below displays a common student error for finding the perimeter?
Answer

P = l + w + l + w

P = l + w

P = 2l + 2w

P = 2(l + w)
Question 50
Question
What language supports the idea that the area of a rectangle is not just measuring sides?
Answer

Height and base.

Length and width

Width and Rows

Number of square units
Question 51
Question
Challenges with students’ use of rulers include all EXCEPT:
Answer

Deciding whether to measure an item beginning with the end of the ruler

Deciding how to measure an object that is longer than the ruler

Properly using fractional parts of inches and centimeters

Converting between metric and customary units
Question 52
Question
Volume and capacity are both terms for measures of the “size” of threedimensional regions. What statement is true of volume but not of capacity?
Answer

Refers to the amount a container will hold

Refers to the amount of space of occupied by threedimensional region

Refers to the measure of only liquids

Refers to the measure of surface area
Question 53
Question
The statements below represent illustrations of various relationships between the area formulas? Identify the one that is NOT represented correctly
Answer

A rectangle can be cut along a diagonal line and rearranged to form a nonrectangular parallelogram. Therefore the two shapes have the same formula.

A rectangle can be cut in half to produce two congruent triangles. Therefore, the formula for a triangle is like that for a rectangle, but the product of the base length and height must be cut in half

The area of a shape made up of several polygons (a compound figure) is found by adding the sum of the areas of each polygon

Two congruent trapezoids placed together always form a parallelogram with the same height and a base that has a length equal to the sum of the trapezoid bases. Therefore, the area of a trapezoid is equal to half the area of that giant parallelogram, ½ h (b1 +b2).
Question 54
Question
What is the most conceptual method for comparing weights of two objects?
Answer

Place objects in two pans of a balance.

Place objects on a spring balance and compare

Place objects on extended arms and experience the pull on each.

Place objects on digital scale and compare.
Question 55
Question
Identify the attribute of an angle measurement
Answer

Base and height

Spread of angle rays

Unit angle

Degrees.
Question 56
Question
Steps for teaching students to understand and read analog clocks include all of the following EXCEPT:
Answer

Begin with a onehanded clock.

Discuss what happens with the big hand as the little hand goes from one hour to the next

Predict the reading on a digital clock when shown an analog clock.

Teach time after the hour in oneminute intervals
Question 57
Question
All of these are ideas and skills for money that students should be aware of in elementary grades EXCEPT: