Math Methods Test 3 (CH 12, 13, 14, 15)

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Which of the following is important to do before students learn the formal​ algorithms?

Address misconceptions.

Which of the following is a good explanation for how to add​ fractions?

Add​ equal-sized parts - finding a common denominator can help to solve the problem.

Lynne used the partitioning strategy to multiply 27 x 4. Which problem below shows this​ strategy?

27 x​ 4, 20 x 4 plus 7 x 4​ =

All the following are recommendations for effective fraction computation instruction except​:

Carefully introduce procedures

Establishing a culture where students are making their own conjectures develops their skills at justification. Which of the following would foster this​ culture?

Always, sometimes or never mathematical statements

A student​ says, "My answer must be wrong - my answer got​ bigger." Which of the following responses will best help the student understand why the answer got​ bigger?

Ask them to explain the meaning of 8​ ÷ 2, using cutting ribbon as a​ context, and then ask them to​ re-explain to you using 8​ ÷ 1/2​, still using cutting ribbon as a context.

Which of the following best describes how to teach multiplication involving a whole number and a​ fraction?

A​ "fraction times a whole​ number" and a​ "whole number times a​ fraction" are conceptually​ different, so they should be taught separately.

The way we write fractions with a top and bottom number is a convention. What method focuses on making sense of the parts rather than the​ symbols?

Begin by using words​ (i.e., one-fourth)

Which of the following statements about multiplication strategies is true​?

Cluster problems use multiplication facts and combinations that students already know in order to figure out more complex computations.

Which of the following strategies would you like students to use when determining which of these fractions is greater 7/8 or 5/7​?

Compare how far from 1

All the following are representative of how algebraic thinking is integrated across the curriculum except​:

Composing and decomposing shapes

All of the methods below would work to support​ students' knowledge about what is happening when multiplying a fraction by a whole number​ except:

Compute with a calculator

Locating a fraction on a number line can be challenging but is very important. Which is a common error that students make in working with the number​ line?

Count the tick marks that appear without noticing any missing ones

A critical aspect of understanding divisions of fractions​ is:

the divisor is the unit

The teachers have identified three manipulatives to use when teaching fractional concepts. Each teacher intended to select one manipulative to show each fraction model. Which teacher succeeded in selecting manipulatives for each​ type?

Denise selected​ tangrams, color​ tiles, and number lines.

What is the primary reason to not focus on specific algorithms for comparing two​ fractions?

Developing number sense about relative size of fractions is less likely

Marek was asked to multiply 34​ × 5. He​ said, "30​ × 5​ = 150 and 4​ × 5​ = 20, so I can add them to get​ 170." Which property did Marek use to solve this multiplication​ problem?

Distributive property of multiplication over addition

The goal is to rename a fractional amount. What is the concept that requires the use of many contexts and​ models?

Equivalent fractions

What is a problem with learning only designated​ (standard) algorithms for fraction​ operations?

Follow a procedure in a short​ term, but not retain

Language plays and important role in thinking conceptually about division. Identify the statement below that would not support students thinking about the problem 4​ ÷ 583.

Four goes into 5 how many​ times?

Which of the following analyzes how the pattern is changing with each new element in the​ pattern?

Geometric growing patterns

All of the following statements are​ research-based recommendations for teaching and learning about fractions except one. Which​ one?

Give greater emphasis to specific algorithms for finding common denominators

Research findings support all of the following fraction teaching ideas but one. Which of the following is the unsupported​ method?

Give students area models that are already partitioned and ask them to record the fractional amount shaded.

A fraction by itself does not describe the size of the whole. A fraction tells us​ only:

the relationship between part and whole.

Identify which statement below would not be considered a common or limited conception related to fractional​ parts?

Knowing that answers can be left as fractions rather than writing them as mixed numbers

When asked to solve the division problem 143​ ÷ 8, a student​ thinks, "What number times 8 will be close to 143 with less than 8​ remaining?" Which strategy is the student​ using?

Missing factor

What form of algebraic reasoning is the heart of what it means to do​ mathematics?

Noticing generalizations and attempting to prove them true

Which of the following best describes the relationship between iterating and​ partitioning?

Partitioning is finding the parts of a​ whole, whereas iterating is counting the fractional parts.

Arithmetic and algebra are closely connected. Identify the reason below that best describes​ why?

Place value and operations are generalized​ rules; a focus on algebraic thinking can help students make connections across problems and strengthen understanding.

Which instructional method does not support purposeful teaching of mathematical​ properties?

Providing opportunities for students to name and match properties to examples

Guiding students to develop a recording scheme for multiplication can be enhanced by the use of what​ tool?

Recording sheet with​ base-ten columns

When students use the break apart of decomposition strategy with​ division, what must they​ remember?

Remember that you cannot break apart the divisor

What division approach is good for students with learning disabilities that allows them to select facts the already​ know?

Repeated subtraction

Which of the following can be presented to students that will open opportunities for them to​ generalize?

Set of related problems

Which model below would not provide a clear illustration of equivalent​ fractions?

Show an algorithm of multiplying the numerator and denominator by the same number

Identify the example below that represents a​ relational-structural approach for the problem 8​ + 4​ = n​ + 5

Since 4 is one more than 5 on the other​ side, that means n is one less than 8

Providing students with many contexts and visuals is essential to their building understanding of equivalence. More examples of linear situations are needed to make comparisons more visible. Which of the following would not be best to model on a number​ line?

Slices of pizza eaten

Computational estimation refers to which of the​ following?

Substituting close compatible numbers for​ difficult-to-handle numbers so that computations can be done mentally

Which of the following options would be misleading for student understanding of​ fractions?

Tell students that fractions are different from whole​ numbers, so the procedures are also different.

There are multiple contexts that can guide students understanding of fractions. Which of the following would involve shading a region or a portion of a group of​ people?

part-whole

All the following are reasons that data and algebra are good topics to integrate except​:

There​ isn't enough time in the year to address​ everything, so it is more efficient to teach these two together. OR Real data can be gathered and used to see if the data​ covary, for example in a linear​ manner, which builds knowledge of both algebraic and statistics.

The benefits of using a rectangular area to represent multiplication of fractions include all the following except​ which?

They are easy for students to draw.

What statement below best describes​ functions?

They describe a relationship between two variables and may be linear or not.

When adding fractions with like denominators it is important for students to focus which key​ idea?

Units are the same

Teaching fractions involves using strategies that may not have been part of a​ teacher's learning experience. What is a key recommendation to teachers from this​ chapter?

Use multiple​ representations, approaches,​ explanations, and justifications

Algebraic thinking includes several characteristics. Which of the following statements is not a part of algebraic​ thinking?

Using manipulatives to reason about situations

Which of the following is not representative of the current thinking about arithmetic and algebra in the elementary​ classroom?

Variables are not appropriate for​ elementary-age students; a box is a more concrete representation.

Mathematical modeling is appropriate for investigating real challenges. Which of these examples requires some mathematical​ modeling?

What would be the better​ deal, buy-one-get-one half​ off, 25%​ off, buy-two-get-one-free?

When teaching computational​ estimation, it is important​ to:

accept a range of reasonable answers.

Proficiency with division requires​ understanding:

place​ value, multiplication, and the properties of the operations

Using contextual problems with fraction division works in providing students with an image of what is​ being:

shared or partitioned

Mixed​ numbers:

can be changed into fractions or​ "improper" fractions and added.

An important concept in working with repeating patterns is for the student to identify​ the:

core of the pattern

One way to effectively model multiplication with large numbers is​ to:

create an area model using​ base-ten materials.

Conceptualizing the symbol for equal as a balance can support​ students' understanding​ of:

equality or inequality.

A common misconception with set models​ is:

focusing on the size of the subset rather than the number of equal sets.

Writing fractions in the simplest terms means to write it​ so:

fraction numerator and denominator have no common whole number factors.

Mathematical models are useful in both real life and mathematics​ because:

models such as​ equations, graphs, and tables can be used to analyze empirical​ situations, to understand them​ better, and to make predictions.

Research recommends that teachers use one of the following to support​ students' understanding that fractions are numbers and they expand the number system beyond whole numbers.

number lines

Students need experiences with variables that​ vary, and pairs of variables that​ covary, early in the elementary curriculum. It is important to emphasize​ the:

variable stands for the number of.

Delia was asked to estimate 489​ + 37​ + 651​ + 208. She​ said, "400​ + 600​ + 200​ = 1200, so​ it's about​ 1200, but I need to add about 150 more for 80​ + 30​ + 50​ + 0.​ So, the sum is about​ 1350." Which computational estimation strategy did Delia​ use?

​Front-end

Children as early as first grade can explore functional thinking by​ using:

​input-output activities.


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