Math Elementary Education 305 Content Area Exam

Dr. Abbott was performing surgery and at 90 minutes she was 60% of the way through. How many more minutes of surgery can she expect to perform?

a

54

b

60

c

36

d

135

b. 60 (cross multiply)

A student-athlete can run 10 yards in 6 seconds. Which expression shows the number of yards that can be run in s seconds?

a

6s

b

0.6s

c

0.6/s​

d. s/0.6​

d. s/0.6​

formula for mixed fractions

example: 3 ½ (A b/c) = a x c +b over c

Which of the following corresponds to the progression of stages of learning about a new mathematical concept from most basic to most advanced?

a

representational, abstract, concrete

b

concrete, abstract, rectangular

c

concrete, representational, abstract

d

abstract, rectangular, concrete

c. concrete, representational, abstract

A parent is complaining about the math homework. They feel that their ELL child is at a disadvantage because they cannot afford internet at home and the homework is best completed using online software. The teacher is providing students time in class to complete the work that requires online resources, however, this student has not been using it stating that he will do it at home. What is the best strategy the teacher should use to prepare for meeting with the parent?

a

Have the student write a note to the parent explaining why they are not completing work.

b

Open communication with the parents that does not involve educational jargon.

c

Offer that the student be exempt from doing any online work.

d

Videotape the student not using time wisely in class.

b. Open communication with the parents that does not involve educational jargon.

Maria has recently moved from Mexico City to the U.S. She is a secondary student who speaks little English, but who came from her school in Mexico City with excellent grades. Which of the following would be the most appropriate accommodation for Maria's math teacher to use with Maria?

a

Allow Maria to be an observer in math class for a few days until she feels a bit more at ease.

b

Make sure that Maria has all the materials she needs to complete the assigned tasks.

c

Pair Maria with another student who speaks Spanish, to clarify instructions in Spanish as needed.

d

Repeat the instructions that are given to the rest of the class more slowly and privately to Maria.

c. Pair Maria with another student who speaks Spanish, to clarify instructions in Spanish as needed.

A teacher of students from various socioeconomic backgrounds is teaching financial literacy. Which of the following strategies is best for reaching all of the students in the class?

a

Ask students what financial topics they need or want to learn about as a guide for lesson planning.

b

Use rigorous financial vocabulary to ensure depth and complexity in the lesson.

c

Have students create a budget based on their family's income.

d

Have students create budgets using different, randomized income levels and share their information with the class.

d. Have students create budgets using different, randomized income levels and share their information with the class.

Ms. Davis teaches a fifth-grade math class primarily composed of English language learners (ELL). Which of the following can support her ELL students?

Select all answers that apply.

a

Use gestures, pictures, and models to explain terms.

b

Speak loudly and slowly so they can hear each syllable separately.

c

Make a word wall.

d

Explain terms in long sentences.

a and c

A second-grade teacher is introducing the idea of adding different kinds of coins. Which would be the most effective beginning activity?

a

demonstrating how to add a nickel and a dime

b

providing the problem using numbers and words

c

having the students use coins to represent a problem

d

identifying a coin as a penny or not

c. having the students use coins to represent a problem

A second-grade teacher is introducing the idea of measuring using inches and centimeters. Which would be the most effective beginning activity?

a

having the students find what objects are roughly an inch long in the classroom

b

giving the students rulers to measure one irregular object in both units

c

asking each student to measure their hand in inches for homework

d

demonstrating conversion using linking cubes.

a. having the students find what objects are roughly an inch long in the classroom

inverse variation

one is decreasing and one is increasing

reflection

A geometric transformation over a line that that produces a mirror image of the original object or image

4 Quadrant Planes

(from right to left. 2,1,3,4)

Rotation

A geometric transformation consisting of a turn of a shape about a point, often the origin, (0, 0)

translation

moves the shape up/down or right/left still keeping its original figure

When working on solving an equation, Josef rearranged the terms on each side of the equation so:

Original equation: −2+3x=4−5x−2+3x=4−5x

New equation: 3x−2=−5x+43x−2=−5x+4

Which property did Josef use to allow him to make this change?

a

associative property of addition

b

addition property of equality

c

transitive property

d

commutative property of addition

commutative property of addition

says a+b=b+a

commutive property

does not change the sum, just changes the order

composite numbers

numbers with 2 digits

Write down a list of numbers from 1 to 50. Start by circling the number 2 and crossing out all of its multiples. Move to the next number that is not crossed out (3), circle it, then cross out all of its multiples. Continue this process until all numbers under 50 have been circled or crossed out.

A fifth-grade math teacher uses the steps above to help students understand a previously introduced concept. Which of the following best describes the content being addressed by the lesson?

a

cardinal numbers

b

ordinal numbers

c

whole numbers

d

prime numbers

d. prime numbers

A student was given the following equation:

4(2x+3)+8x=924(2x+3)+8x=92

In solving the problem for xx, the first step of a student's solution was: 4⋅2x+4⋅3+8x=924⋅2x+4⋅3+8x=92

Which of the following is the justification for this step?

a

distributive property

b

associative property of multiplication

c

additive identity property

d

multiplicative inverse property

a. distributive property

Which of the following equations represents the additive identity?

a

b+(a+c)=(b+a)+cb+(a+c)=(b+a)+c

b

d+e=e+dd+e=e+d

c

a+(−a)=0a+(−a)=0

d

c+0=cc+0=c

c+0=c

number plus zero equals the same number

The additive inverse property

The additive inverse property is that each number has an inverse that, when added to the number, equals 0: −a+a=0−a+a=0 and a−a=0a−a=0.

Which of the following algebraic equations shows the multiplicative inverse property?

a

38+27x2×72x−2=11883​+72​x2×27​x−2=811​

b

5x×(−5x)=15x×(−5x)=1

c

2x×(22)=2x2x×(22​)=2x

d

34−38x2×38x2=3443​−83​x2×83​x2=43​

a.

Which of the following is true of the associative property?

a

An example is: 123+(639+47)=(123+639)+47123+(639+47)=(123+639)+47

b

An example is: 10−(6−2)=(10−6)−210−(6−2)=(10−6)−2

c

It can only be applied to multiplication.

d

When multiplying and using the associative property, the number order can be re-arranged.

a

An example is: 123+(639+47)=(123+639)+47123+(639+47)=(123+639)+47

Which of the following is an example of the associative property of multiplication?

a

(2x3+6)+y=2x3+(6+y)(2x3+6)+y=2x3+(6+y)

b

(2x3+6)y=2x3y+6y(2x3+6)y=2x3y+6y

c

(2x3×6)+y=2x3+(6×y)(2x3×6)+y=2x3+(6×y)

d

(2x3×6)×y=2x3×(6×y)(2x3×6)×y=2x3×(6×y)

d. (2x3×6)×y=2x3×(6×y)

associative property of addition

allows the grouping of addends to change without changing the sum. different numbers in ( )

What is inversely proportional (graph/x and y chart)

Adding x and y across