Math Chapters 12-17

Why are five views that algebra should be included in school?

-Algebra is a study of patterns and relationships -Algebra is a way of thinking -Algebra is an art, characterized by order and internal consistency. -Algebra is a language that uses carefully defined terms and symbols. -Algebra is a tool.

In modular arithmetic, 5 (mod 8) + 4 (mod 8) =:

1 (mod 8)

Which of the following lists all the factors of 18?

1, 2, 3, 6, 9, and 18

The Fibonacci Sequence begins with 1, 1, 2, 3, 5, 8, and 13, and continuesinfinitely. What are the next two numbers in the Fibonacci Sequence?

21, 34

Which of the following is NOT an example of representing the problem below?Mary had 5 dogs and John has 8 dogs. How many more dogs does John have thanMary?

3 (This option gives the answer, as opposed to representing the problem)

How are variables used as placeholders?

3 + r = 7

What two numbers come next in the pattern? 6, 7, 9, 12, 16, 21, 27, 34, ____,___

42, 51

What is a ratio fraction?

6/10 may mean 6 boys to 10 girls in a class.

Eight grams is equal to all of the following EXCEPT: 800 centigrams 80 kilograms 8000 milligrams 80 decigrams

80 Kilograms

A visual representation of data that includes the minimum value, maximum value,median, and interquartile range is known as

A box plot

Which is an example of a real or concrete graph?

A graph of favorite fruits that uses whole apples and oranges placed in a grid on the floor

Which type of display would be most appropriate for depicting how the number ofdaylight hours changes over a period of weeks?

A line plot

All of the following statements regarding units of measurement are true EXCEPT: Standard units are needed to communicate effectively. A smaller unit gives a less exact measurement. Units may be combined or subdivided to make other units. Units must match the attribute that is being measured.

A smaller unit gives a less exact measurement.

What is a proportion?

A statement that two or more ratios are equal or "the same". For instance, the ratios 2"3 and 4:6 are proportional.

What is a part-whole?

A whole has been partitioned into equal parts. The fraction 3/5 means that a whole has been partitioned into 5 equal parts, three of which are being considered.

A student is shown a rectangle divided into 5 equal sections. Two of the sectionsare shaded, and the student is asked to identify the fraction that is indicated by theshaded region. Which meaning of fractions is being emphasized?

A. part-whole

Examining locations and movements provides young learners with opportunities: To explore ideas related to positive and negative numbers To develop understanding of positional vocabulary such as "above," "below," "behind," and "between" To develop skills connected to other subjects, such as map skills All of the above

All of the above

If you were a principal, which of the following explanations of why your students did not study geometry do you think he should not accept? I never liked geometry so I do not teach it. I think geometry is not important for elementary students, they can learn it in high school. I always save geometry to the end of the year and do it if I have time. All of these.

All of these

Which of the following is NOT a true statement? All congruent shapes have equal areas. All regions with the same area are congruent. The formula for the area of a parallelogram is the same as the formula forthe area of a rectangle. The formula for the surface area of a solid depends on the area of two-dimensional regions.

All regions with the same area are congruent.

Taking one unit (such as a Unifix cube) and moving it along an object is called:

An iteration

Children should begin their study of fractions by: Learning that it takes two whole numbers to represent a part of a whole. Learning what it means to share equally or partition. Learning the names for the top number (numerator) and the bottom number(denominator). Learning that halves mean part of a whole

B. Learning what is means to share equally or partition

A student is asked how 4 cookies could be divided evenly among 5 people. Whichmeaning of fractions is being emphasized?

B. Quotient

What are partitioning models of fractions?

Basically sharing among a certain number of people.

A parent asks you why you are including drawing three-dimensional shapes in the fifth-grade. Which of the following do you think would be the best reason to give the parent? Because the fifth-grade teacher did it last year and I am following her lead. Because there are questions on the state test that requires identifying three-dimensional shapes from drawings. Because developing visualization of objects is an important aspect of understanding the world around you. Because the students really enjoy drawing and I do also.

Because developing visualization of objects is an important aspect of understanding the world around you.

Which of the following graphs is likely to be introduced late in elementary school?

Box Plots

The fraction c/d does NOT mean: c groups of 1/d c divided by d 1/d of c c parts of d

C parts of d

Which of the following is NOT true? Every whole number can be represented by a fraction. Every fraction can be represented with symbols in more than one way. Between any two whole numbers, there is a whole number. Between any two fractions, there is a fraction.

C. Between any two whole numbers there is a whole number

A word problem indicates that in a classroom, there are 5 girls and 7 boys. The teacher and students represent this relationship as 5/7. Which meaning of fractions is being emphasized?

C. Ratio

A young learner is looking at an empty shoe box and a zip-lock bag full of pennies. Without lifting either item, the student states that the shoebox is heavier. What is the likely reason for this?

Children often think that a heavier item weighs more

Which of the following statements is true?

Children should study three dimensional shapes because they are in the world around them.

A student is estimating the length from her desk to the classroom door. She thinks,"The length from my desk to the teacher's desk is about six feet, and the length from the teacher's desk to the door is about seven feet. My desk is about 13 feetfrom the classroom door." Which strategy of measurement estimation is the studentlikely using?

Chunking

Young learners should begin geometry by: Studying the definitions of two-dimensional shapes so they can identify them. Making models of three-dimensional shapes. Comparing three-dimensional objects on common properties. Making models of two-dimensional shapes.

Comparing three-dimensional objects on common properties.

A student knows that he is four feet tall. He lies down on the classroom rug andstates, "This rug is a little longer than me, so it must be about five feet long."Which strategy of measurement estimation is the student likely using?

Comparing to a referent

Knowing that a region can be cut and rearranged without changing the area is: A misconception because cutting and rearranging a region would changethe area Conservation of area An ability that students typically develop in high school Unable to be confirmed without carefully measuring the lengths of all sides

Conservation of Area

Histograms are typically used to display:

Continuous Data

Strong understanding of benchmark fractions such as ¼, 1/3, and ½ can facilitate students': Checking the reasonableness of computations with fractions Identifying fractions that are near 0 or near 1 Estimating answers All of these

D. All of these

Which of the following are NOT types of models of the part-whole meaning of fractions?

D. Parts

What are routine problems?

Exercises for practicing computation, build algebraic understanding.

T/F A rhombus is a parallelogram with exactly two sides congruent.

False

T/F An explicit equation lets you calculate the value of one term only if you know thevalue of the previous term

False

T/F Direct comparison of length involves measuring two objects with a ruler and determining which measurement is greater.

False

T/F If a whole number is divisible by 3, then it must be an odd number

False

T/F The Common Core State Standards for Mathematics recommends that comparing fractions with different denominators should be a focus of grade 3.

False

T/F The number 51 is prime.

False

T/F The recommendations for teaching statistics proposed by the Common Core StateStandards and the American Statistical Association are nearly identical.

False

T/F To nurture understanding in learners, it is recommended that teachers use numberwords (such as "3 over 5") rather than fraction words (such as "three-fifths."

False

T/F Between two whole numbers there are an infinite number of other whole numbers.

False. There are a limited amount of whole numbers, but an unlimited number of fractions.

Which of the following represents the typical order of steps involved in statisticalanalysis?

Formulate questions, collect data, analyze data, and interpret results

Elementary school teachers might use a game like "Guess My Rule" to exposestudents to which algebraic concept?

Functions

What are the three different uses of variables?

Generalizations, placeholder, and formulas/functions.

Which of the following is not a cogent reason to study geometry in elementaryschool? Geometry engages children in different ways than number work. Geometry can help develop other skills such as following directions. Geometry can be used to teach other mathematical topics. Geometry is in the textbook we are using.

Geometry is in the textbook we are using.

It is sufficient to disprove a conjecture to: Give an example that shows the conjecture can be true. Give an example of when the conjecture is not true. Give examples showing it is true for lots of different numbers Give another conjecture that is true.

Give examples showing it is true for lots of numbers.

The largest number that will divide into 16 and 24 with no remainder is 8. Withregard to 16 and 24, 8 is the:

Greatest Common Factor

Measurement should be an integral part of the elementary mathematics curriculum because

It helps children with other mathematics concepts and procedures.

A young student states that a shape is a rectangle because it looks like a door. The student's level of understanding most closely reflects which modified Van Hiele level?

Level 1

A student holds a paper rectangle and states, "If I fold this down the middle, onehalf lies on top of the other half." This student's statement reflects knowledge of:

Line Symmetry

What are nonroutine problems?

Look for patterns, puzzling, require algebraic approach.

Model vs symbol vs word

Model is a picture or representation. Symbol is 2/5 word is two-fifths.

Using cubes to create a sequence of three-dimensional shapes of increasing size isan example of

Modeling

The numbers 5, 10, 15, 20, 25, and 30 are all:

Multiples of 5

Which is NOT a correct way to divide 12 by ¾? Divide 12 by 3 and multiply that quotient by 4. Divide 12 by ¼ and divide that quotient by 3. Multiply the 12 by 3 and divide that product by 4. Multiply the 12 by 4 and divide that product by 3

Multiply the 12 by 3 and divide that product by 4

Why should number theory be incorporated into the elementary school curriculum?

Number theory opens the doors to many mathematical conjectures. Number theory provides an avenue to extend and practice mathematicalskills. Number theory offers a source of recreation

Which of the following is the best reason to include number theory topics in teaching upper elementary school students? Number theory has many applications in the real world. Number theory is essential for algebra. Number theory provides a way to differentiate instruction. All of these.

Number theory provides a way to differentiate instruction.

What are benchmark fractions?

Ones that are easy to work with and remember.

Which is NOT a correct way to find 2/5 of 20? Partition the 20 into 2 equal groups and multiply the number in a group by5. Partition the 20 into 5 equal groups and multiply the number in a group by2. Find 1/5 of 20 and double the answer. Divide 20 by 5 and multiply the quotient by 2.

Partition the 20 into 2 equal groups and multiply the number in a group by 5.

What are some models of part whole fractions?

Region model - A rectangle with 5 pieces, 2 of which are shaded for 2/5. Length model - Folding a long, thin strip of paper into pieces. Set model - a set of 15 objects represent a fraction Area model - more general version of region model. Parts must be equal in area but not necessarily congruent.

Which of the following is NOT a part of the measurement process? Comparing an object to a unit. Comparing two objects. Reporting the number of units only to tell the size of an object. Reporting the object being measured and the units used.

Reporting the number of units only to tell the size of an object.

What are quotient fractions?

Represent a division problem

What are equivalent fractions?

Represent the same amount.

Assuming each model is the whole, which of the following is the most complicatedmodel for ¾?

See Photos

In one method of data collection, random number tables or devices such as coins,dice, spinners, or computer programs are used to model real-world occurrences.This method of data collection is known as:

Simulation

A translation of a shape is also known as a:

Slide

Which of the following is always true if only whole numbers are being used? All open sentences have a solution. No open sentence has more than one solution. Some open sentences may have no solution. Some open sentences have an infinite number of solutions.

Some open sentences have an infinite number of solutions.

The numbers 4, 9, 16, and 25 are all:

Square Numbers

A group of students create a bar graph in which colored squares represent theirchoices of after-school activities. This graph would be classified as:

Symbolic

Which of the following statements is false? The CCSSM includes some geometry objectives in elementary school. The CCSSM includes no geometry objectives in elementary school. The CCSSM emphasizes arithmetic more than geometry. The CCSSM emphasizes transformations of geometric shapes in the lowergrades

The CCSSM includes no geometry objectives in elementary school.

In a stem-and-leaf plot, the stem would be most likely to represent

The first digit of a value

In statistics, the whole group being studied is known as:

The population

Which of the following is a true generalization? The sum of an even and an odd number is an even number. The difference between two odd numbers is an odd number. The product of an even and an odd number is an even number. The quotient of an even number divided by an even number is an even number

The product of an even and odd number is an even number.

T/F A recursive expression is an expression that tells how to find the value of a term given the value of the previous term.

True

T/F All squares are rectangles.

True

T/F An isosceles triangle has at least two congruent sides

True

T/F Children who say taller container holds more than shorter containers may befocusing on height not capacity.

True

T/F In a probability problem, the set of all possible outcomes is called the samplespace

True

T/F In the study of fractions, the concept of equivalence focuses on differentrepresentations of the same amount.

True

T/F In the study of time, two attributes of events that can be measured are time of occurrence and length of duration.

True

T/F Research supports having students go through a writing process when analyzingdata, similar to process used in language arts.

True

T/F The ones digit of an even number must also be an even number.

True

T/F The probability of any event must fall between 0 and 1

True

The attribute that measures "how much space a three-dimensional figure takes up"is:

Volume

All of the following statements regarding units of measurement are true EXCEPT: A unit must remain constant. A measurement must include both a number and a unit. One unit may be more appropriate than another to measure an object. When a larger unit is used, more units are required to measure an object.

When a larger unit is used, more units are required to measure an object.

What is a function?

When two sets of numbers are related in a way that each number in the first set is related to only one number in the second set.

What are properties of numbers in relation to algebra?

You can use number properties to promote algebraic thinking.

Which of the following is NOT a recommended site for developing algebraicthinking for elementary school students?

algebraic sections of a curriculum

How are variables used as generalizations?

any number subtracted from itself is zero (a - a = 0)

In the equation W + 4 = 11, how is the variable used?

as a placeholder

Finding a rule that generates a pattern is a type of

generalizing

When asked how to find the area of a rectangle, a student replies A= B x H. Howare the variables used in the student's response?

in a formula

In the equation A - A = 0, how is the variable used?

in a generalization

A student was asked if it is true that when two numbers are multiplied, the answer is always larger than either of the numbers. She disproved it by providing an example. Which example might she have provided? 5 x 8 = 40 50 x 2 = 100 ½ x 1/3 = 1/6 8 x 8 = 64

½ x 1/3 = 1/6