Math final

According to the van Hiele model individuals can skip levels if they have advanced mathematical skills. Select one: True False

False

According to the van Hiele model an individual's levels of geometric thought are dependent of the types of instruction and activities that the individual has been exposed to and has engaged with. Select one: True False

True

According to the van Hiele model instruction should be matched with the individual's van Hiele levels for learning to take place. Select one: True False

True

Using grid paper Julie shades a rectangle that is 8 units wide and 12 units long. Randy shades a rectangle that is 4 units wide and 6 units long. Randy wants to create a rectangle that has the same area as Julie's. In order to do this, he decides to extend the length of his original rectangle by X units long. What is the length of X? Select one: a. 18 units b. 12 units c. 24 units d. 4 units

a. 18 units

Lily uses 9 units, 4 flats, and 7 rods to represent a whole number. If she subtracts 8 units, 2 flats, and 4 rods, what does the result represent? Select one: a. 231 b. 123 c. 321 d. 312

a. 231

Suppose that you are given the following growing pattern: 1, 3, 5, 7, 9, ... What is the 15th term of this sequence? Select one: a. 29 b. 28 c. 39 d. None of the answers given

a. 29

William is practicing skip counting by 3. He skips six times and ends at 29, which process below could be used to find the number William started with? Select one: a. 29 - 6 x 3 b. 29 + 6 x 3 c. (29 - 3) x 6 d. (29-6) x 3 e. cannot be determined

a. 29 - 6 x 3

Sally is comparing the fractions 3/8 and 1/2. Which of the following statement(s) are TRUE? Select one or more: a. 3/8 < 1/2 because when you cross multiply 8 x 1 is larger than 3 x 2. b. 3/8 < 1/2 because the numerator three is larger than the numerator one c. 3/8 < 1/2 because the denominator eight is larger than the denominator two d. 3/8 < 1/2 because four eighths is more than three eighths

a. 3/8 < 1/2 because when you cross multiply 8 x 1 is larger than 3 x 2. d. 3/8 < 1/2 because four eighths is more than three eighths

William uses 3 units, 5 flats, and 5 rods to represent a whole number. If he subtracts 9 rods and 2 units, what does the result represent? Select one: a. 461 b. 164 c. 614 d. 146

a. 461

Just after Valentine's Day, Ms. Kay gives her class with 24 students the following mathematics question to solve: During Valentine's Day, each student in our class exchanged a Valentine's card with every student in the class. How many cards were exchanged in total in our class? What is the solution for this problem? Select one: a. 552 b. 576 c. 542 d. 529 e. 532

a. 552

Using grid paper Sylvia shades a rectangle that is 12 units wide and 8 units long. Billy begins to create a rectangle that is 16 units wide that he will shade. How long must Billy's rectangle need to be in order for his rectangle to be equal in terms of area with Sylvia's rectangle? Select one: a. 6 units b. 12 units c. 80 units d. 120 units

a. 6 units

Sandy lives 19 miles directly North of Cindy. Sue lives 65 miles directly South of Cindy. How far apart do Sue and Sandy live from each other? Select one: a. 84 miles b. 46 miles c. 19 miles d. 74 miles

a. 84 miles

Suppose that 6 pieces of candy represent 2/3 of a whole bag of candy. How many pieces of candy were in the whole bag? Select one: a. 9 pieces of candy b. None of these c. 3 pieces of candy d. 4 pieces of candy e. 12 pieces of candy

a. 9 pieces of candy

What problem type(s) does the word problem below illustrate? "Luck, Mike, and Sally are friends that collect Pokemon card. Luck has 18 Pokemon cards. Mike has 9 more cards than Luck. If Mike gives 7 of his cards to Sally, how many cards does Mike have now?" Select one: a. Compare and Separate b. Join and Part-part-whole c. None of the answers given d. Separate and Join Incorrect e. Compare and Join

a. Compare and Separate

Using the statements below which conclusions can you make EXCEPT for: Statement 1: Figure A is a rectangle Statement 2: Figure A is a parallelogram Select one: a. If statement 2 is true, then statement 1 is true. b. Statement 1 and 2 can both be true c. If statement 1 is true, then statement 2 is true. Incorrect d. If statement 2 is false, then statement 1 is false.

a. If statement 2 is true, then statement 1 is true

Using the statements below which conclusions can you make: Statement 1: Figure A is a parallelogram Statement 2: Figure A is a rhombus Select one: a. If statement 2 is true, then statement 1 is true. b. If statement 1 is false, then statement 2 is true. c. Statement 1 and 2 cannot both be true. d. If statement 1 is true, then statement 2 is true. e. Statement 1 and 2 cannot both be false.

a. If statement 2 is true, then statement 1 is true.

One of your students says that he has found an easier way to do addition. For example, 32 + 27 + 46. Using the meaning of place value he explains that this sum is the same as saying that you have 9 tens and 15 ones. Then, since 15 ones is one ten and 5 ones, he explains that you can regroup to make a total of 10 tens and 5 ones. Then since 10 tens is one hundred, you have 105. What are your thoughts on his reasoning process? Select one: a. It is mathematically correct and works when adding all whole numbers. b. While it works with some numbers, it does not work when adding all whole numbers. c. It is not mathematically correct. d. I do not know if it is mathematically correct.

a. It is mathematically correct and works when adding all whole numbers.

Philip says that he has found an easier way to multiply single digit and multidigit whole numbers. For example, to find 8 x 243 he multiplies 8 times 200, 8 times 40, and 8 times 3. He then adds those partial products together What are your thoughts on his reasoning process? Select one: a. It is mathematically correct and works when multiplying all whole numbers. b. While it works in this case, it does not work in general when multiplying all whole numbers. c. It is not mathematically correct. d. I do not know if it is mathematically correct.

a. It is mathematically correct and works when multiplying all whole numbers.

Your students are working on whole number subtraction with "regrouping." You have given them the problem: 36 -19 One of your students says she has come up with a much simpler method. She explains that 6 - 9 equals -3, and 30 - 10 equals 20, and -3 + 20 equals 17. What do you think about this student's solution method? Select one: a. It is mathematically correct. b. While it works in this case, it does not work in general. c. It is not mathematically correct. Incorrect d. I do not know if it is mathematically correct.

a. It is mathematically correct.

Cindy's fifth grade teacher asks her to describe a triangle. Cindy says "a triangle is a closed shape that has three straight sides and three angles." What van Hiele level do you think is Cindy at in regard to triangles? Select one: a. Level 1 b. Level 0 c. Level 3 d. Level 2

a. Level 1

When calculating two-digit addition, such as 12 + 15, Mary, Jacob, Mark, and Fanni proposed the following solution methods: Mary: Subtract 8 from 15 and join it with 12 to make 20. Then add 7. Jacob: Subtract 5 from 12 and join it with 15 to make 20. Then subtract 7. Mark: Add 2 and 5 to make 7 in the ones place of the solution. Then add 1 and 1 to make 2 in the tens places of the solution. Fanni: Add 1 and 1 to make 2 in the tens place of the solution. Then add 2 and 5 to make 7 in ones place of the solution Which of the above methods are mathematically correct? Select one or more: a. Mary's method b. Jacob's method c. Mark's method d. Fanni's method

a. Mary's method c. Mark's method d. Fanni's method

Problem type(s) where no change in quantities is described include: Select one or more: a. Part-part-whole b. Compare c. None of the answers given d. Join e. Separate

a. Part-part-whole b. Compare

What problem type(s) does the word problem below illustrate? "Jenny has some marbles. She gave Kate 13 marbles. Now Jenny has 19 marbles. How many marbles did Jenny give away?" Select one: a. Separate b. None of the answers given c. Part-part-whole d. Join e. Compare

a. Separate

Which of the following are properties of all rectangles? Select one or more: a. The opposite sides have the same length. b. They have four right angles. c. Opposite sides are parallel. d. The diagonals have the same length.

a. The opposite sides have the same length. Correct b. They have four right angles. Correct c. Opposite sides are parallel. Correct d. The diagonals have the same length. Correct

All of the following is true of all rhombi EXCEPT? Select one or more: a. The two diagonals are the same length. b. The two diagonals are perpendicular. c. All angles have the same measure. d. Each diagonal bisects opposite angles.

a. The two diagonals are the same length c. All angles have the same measure.

A class of third grade students are learning about elapsed time. For example, it is now 9: 30 am. What time will it be in 3 hours and 45 minutes? One student says that it will be 12:75 am. What do you think about this? Select one: a. This is not mathematically correct b. I think it is mathematically correct c. I do not know if this is mathematically correct or not d. It works in this case, but I'm not sure it would work in general

a. This is not mathematically correct

Suppose that Carol is at a van Hiele level 0 with her understanding of triangles, which of the shape below might Carol say is NOT a triangle? Select one: a. X b. W c. Z d. V e. All of the above

a. X

Which approach below do you feel would be MOST effective for teaching children how to solve the question below? A birthday celebration begins at 9:30 A.M. If it lasts 5 hours and 45 minutes, when will it be over? Select one: a. a time line b. apply the make 60 approach and keep track of time c. an analog clock and keep track of the time on piece of paper d. None of these methods

a. a time line

A teacher is working with a group of first grade students on exploring the concept of counting by twos. Which of the following activities would be the most effective in helping the students grasp the concept of counting by twos? Select one: a. coloring in the even numbers on a hundreds chart b. estimating the number of chocolate chips in a bag c. writing the numerals two through one hundred on dry-erase boards d. putting one bean in each square of a grid containing ten squares

a. coloring in the even numbers on a hundreds chart

What problem type(s) is represented in the word problem below? A day prior to his birthday Robert had 7 toy cars left in his collection. This year his parents gave him some more toy cars for his birthday. He now has 19 toy cars. If his parents gave him 3 more toy cars this year than last year, how many toy cars did his parents give to him last year? Select one or more: a. join problem b. part-part-whole problem c. Not sure d. compare problem e. separate problem

a. join problem d. compare problem

How many times must you regroup to find 303 divided by 3? Select one: a. no regrouping is required b. once c. twice d. three times

a. no regrouping is required c. twice

A teacher is working with a group of elementary students and wants to teach the parts of whole definition of fractions by using color counter. Which attribute of color counters should the teacher emphasize? Select one: a. number of counters in sets and subsets b. length of counters in sets and subsets c. area of counters in sets and subsets d. weight of counters in sets and subsets

a. number of counters in sets and subsets

What problem types are represented below? Rachel had sixteen dollars. For her birthday she got twenty-eight more dollars but spent twenty-five on a new pair of shoes. How much money does she have now? Select one or more: a. separate problem b. part-part-whole problem c. join problem d. compare problem

a. separate problem c. join problem

Suppose that you are given the following growing pattern: 14, 26, 38,... Which of the following processes could be used to find whether 60 is a term in the sequence? Select one or more: a. subtract 12 from 60, then repeatedly continue to subtract 12 from the result. If 14, 26, and 38 are part of that sequence, then 60 is a term of the pattern. b. subtract 14 from 60, then divide that difference by 12. If the quotient is a whole number, then 60 is a term in the sequence. c. using the equation 14 + 12n = 60, solve for n. If n is a whole number, then 60 is a term in the sequence. d. using the equation 14 + 12(n-1) = 60, solve for n. If n is a whole number, then 60 is a term in the sequence. e. subtract 14 from 60, then repeatedly continue to subtract 14 from the result. If 14, 26, and 38 are part of that sequence, then 60 is a term of the pattern.

a. subtract 12 from 60, then repeatedly continue to subtract 12 from the result. If 14, 26, and 38 are part of that sequence, then 60 is a term of the pattern. b. subtract 14 from 60, then divide that difference by 12. If the quotient is a whole number, then 60 is a term in the sequence. d. using the equation 14 + 12(n-1) = 60, solve for n. If n is a whole number, then 60 is a term in the sequence.

Suppose that you are given the following growing pattern: 1, 5, 9, 13, 17, ... Which of the following processes could be used to find the 15th term of this sequence? Select one or more: a. using the expression 1 + 4(n-1) substitute 15 for n and solve b. add four to 17, then continue to add four to the previously found term fifteen more times c. multiply 4 times 10, then add that to 17 d. add four to 17, then continue to add four to the previously found term nine more times e. using the expression 1 + 4n substitute 15 for n and solve

a. using the expression 1 + 4(n-1) substitute 15 for n and solve c. multiply 4 times 10, then add that to 17 d. add four to 17, then continue to add four to the previously found term nine more times

Suppose that you are given the following growing pattern 14, 26, 38, ... Which of the following numbers is a term in the pattern? Select one: a. 79 b. 122 c. 131 d. 80 e. None of the answers given

b. 122

Ms. Roberts is working with her 5th grade students to develop expressions based on problem situations. She poses the following scenario: Billy has six times as many books as George. What expression can be used to represent this situation? Use the variable B to represent the number of books that Billy has and the variable G to represent the number of books that George has. Which of the following expressions could be used? Select one: a. 6B = G b. B = 6G c. B = G + 6 d. None of the answers given e. B + 6 = G

b. B = 6G

All of the following is true of all parallelogram except? Select one: a. Opposite sides have the same length. b. Both diagonals have the same length. c. Two diagonals bisect each other. d. Opposite angles have the same measures.

b. Both diagonals have the same length.

Using the statements below, which conclusions can you make? Statement 1: Figure A is a rhombus. Statement 2: Figure A is a square. Select one: a. If statement 1 is true, then statement 2 is true. b. If statement 2 is true, then statement 1 is true. c. Statement 1 and 2 cannot both be false. d. If statement 1 is false, then statement 2 is true. e. Statement 1 and 2 cannot both be true.

b. If statement 2 is true, then statement 1 is true.

A third grade teacher poses an elapsed time problem to her students. She asks them to find the time 4 hours and 30 minutes before 2:45 AM. One student, Shelby, excitedly explains that she has figured out a new way of solving this problem. She explains that because she has to cross the midnight or noon time marks, she makes 2:45 into 14:45 by adding 12 to the hours, and then subtracts 4 from the 14 and 30 from forty-five to get 10:15 PM. What do you think about Shelby's reasoning? Select one: a. I do not know if this is mathematically correct or not. b. It is mathematically correct c. This is not mathematically correct. d. It works in this case, but I'm not sure it would work in general.

b. It is mathematically correct

Celia states that she has found an easier way to divide fractions. For example, suppose that she is given 2 and 1/2 divided by 1/4. She says "2 and 1/2 is like $2.50 and 1/4 is like a $0.25, therefore this question is really like asking how many quarters there are in $2.50." What do you think about Celia's reasoning? Select one: a. It works in some cases, but it would not work in general. b. It is mathematically correct for all cases. c. I do not know if this is mathematically correct. d. This is not mathematically correct for any cases.

b. It is mathematically correct for all cases

One of your students comes to class excited. She tells you that she figured out a theory that you never taught in class. She explains that she discovered that as the perimeter of a closed figure increases, the area also increases. What do you think about her theory? Select one: a. It is never true b. It is sometimes true c. It is always true

b. It is sometimes true

In a mathematics lesson on counting, Teacher A asked her students to write a sequence of numbers that represents skip counting by 5. Here are three sequences from Katie, John, and Wendy. Katie: 11, 15, 19, 23... John: 6, 11, 16, 21... Wendy: 1, 5, 10, 15... Whose answer best represent the ideas of skip counting by 5? Select one: a. Katie b. John c. Wendy d. Sam e. None of the responses

b. John

Mrs. Lee showed Figure A to her 2nd grade student, Jacob, and he said, "It is a square". When she turned the square 45 degrees (Figure B), Jacob said, "Now it is a rhombus because it looks like a diamond". square and rhombus What van Hiele level do you think is Jacob at in relation to Rhombi? Select one: a. Level 2 b. Level 0 c. Level 1 d. Level 3

b. Level 0

Asking children to list all the properties of squares would be LEAST appropriate for children at which level of van Hiele's model for squares? Select one: a. Level 1: Analysis b. Level 0: Visualization c. Level 3: Rigor d. It would be appropriate for all these levels e. Level 2: Informal Deduction

b. Level 0: Visualization

Sylvia can name and recognize a rectangle by its appearance but sometimes struggles when the shape's sides are not oriented parallel to her. What level of van Hiele is she in regard to rectangles? Select one: a. Level 1: Analysis Incorrect b. Level 0: Visualization c. Level 2: Informal Deduction d. None of these e. Below Level 0: Visualization

b. Level 0: Visualization

Fifth grade teacher, Mr. Flores, showed a figure below to his class and asked, "What is this? and how would you describe it to your friends?" a rectangle Erick answered, "It is a rectangle and it has four sides, closed, two long sides, two shorter sides, opposite sides parallel, and four right angles..." What van Hiele level do you think is Erick at in regard to rectangles? Select one: a. Level 2 b. Level 1 c. Level 0 d. Level 3

b. Level 1

Ian described a rhombus as "a parallelogram with two adjacent sides congruent". What van Hiele level do you think is Ian at in regard to rhombi? Select one: a. Level 3 b. Level 2 c. Level 1 d. Level 0

b. Level 2

Raymond, a third grade student, took a piece of paper and divided it into 6 equal-sized regions. He then shaded two of the regions green. Jian, another third grade student, took a piece of paper the same size as Raymond's and divided it into 12 equal-sized pieces. He then shaded four of the regions blue. You tell the class that both Raymond and Jian have shaded fractional parts of their paper. You then ask the class whether Raymond or Jian shaded more of their piece of paper. Bobby says that "Jian shaded more because he shaded 4 regions." How do you think about Bobby's reasoning? Select one: a. I do not know if this is mathematically correct. b. This is not mathematically correct c. It is mathematically correct. d. It works in this case, but it would not work in general.

b. This is not mathematically correct

You are teaching multiplication by 10. One of your students, Andrew, says that all you have to do is add a 0 to the right of the last digit of any number to get the answer. What do you think about Andrew's solution and process? Select one: a. It is mathematically correct and works for all numbers. b. While it works with some numbers, it does not work with all numbers. c. It is not mathematically correct for any numbers. d. I do not know if it is mathematically correct.

b. While it works with some numbers, it does not work with all numbers.

Which of the following word problems BEST illustrates what 1/4 divided 2 means? Select one: a. It takes 1/4 hour to fly 300 miles. How far can you fly in 1/2 hour? b. You want to split 1/4 pie evenly between two families. How much pie should each family get? c. All of these d. You have $0.25 and may soon double your money. How much money would you end up with? e. You are making some homemade taffy and the recipe calls for 1/4 cups of butter. How many sticks of butter will you need? (Each stick = 1/2 cup)

b. You want to split 1/4 pie evenly between two families. How much pie should each family get?

Which of the following methods would feel MOST comfortable with to solve the following question? Sally begins a trip at 9:30 A.M. If she travels for 5 hours and 45 minutes, when will the trip be over? Select one: a. a time line b. apply the make 60 approach and keep track of time c. None of these methods d. an analog clock and keep track of the time on piece of paper

b. apply the make 60 approach and keep track of time

Ian described a rhombus as "a parallelogram with two adjacent sides congruent". Which instructional activity is appropriate to Ian according to van Hiele theory (in relation to rhombi) EXCEPT for? Select one: a. working on a geoboard, change a quadrilateral to a trapezoid, trapezoid to parallelogram, parallelogram to rectangle. b. comparing shapes according to their characterizing properties. c. identifying minimum sets of properties that describe a figure. d. working with and discussing situations that highlight a statement and its converse.

b. comparing shapes according to their characterizing properties.

Just after Valentine's Day, Ms. Kay gives her class with 24 students the following mathematics question to solve: During Valentine's Day, each student in our class exchanged a Valentine's card with every student in the class. How many cards were exchanged in total in our class? Which of the following are mathematically correct ways of solving? Select one or more: a. have them count every card that was exchanged b. have them add all the cards that each student gave to all the other students c. have them use multiplication d. none of the answers provided

b. have them add all the cards that each student gave to all the other students c. have them use multiplication

How many times must you regroup to find 1001 - 301? Select one: a. no regrouping is needed b. once c. twice d. three times e. four times

b. once

The expression 80n could be used to represent the following scenarios? Select one: a. the cost of each candy bar in a pack of 80 candy bars where the total cost of the pack is n cents b. the total cost in cents of n candy bars at a cost of 80 cents for each candy bar c. an increase of 80 cents in the cost of a candy bar that originally cost n cents. d. a decrease of 80 cents in the cost of a candy bar that originally cost n cents e. the cost of each candy bar in a pack of n candy bars where the total cost of the pack is 80 cents

b. the total cost in cents of n candy bars at a cost of 80 cents for each candy bar

Rachel had sixteen dollars. For her birthday she got twenty-eight more dollars but spent twenty-five on a new pair of shoes. How much money does she have now? Select one: a. $23 b. $69 c. $19 d. $24

c. $19

What fractional part of the set of dots is red? (Check all that apply) A set of 12 dots. Dots are divided into 4 smaller sets consisting of three dots each. The dots in one of the four equal-sized sets is red. The rest are black. Select one or more: a. 3/9 b. 1/3 c. 1/4 d. 3/12

c. 1/4 d. 3/12

George had 25 pencils. Thirteen are red and the rest are yellow. George gives eight of his yellow pencils away. How many yellow pencils does George have now? Select one: a. 20 pencils b. 30 pencils c. 4 pencils d. 5 pencils

c. 4 pencils

By how much will the value of 4,372 increase if the 3 is replaced with a 9, the 7 replaced with an 8, and the 2 is replaced with an 8? Select one: a. 17 b. 988 c. 616 d. 900 e. none of the answers given

c. 616

A day prior to his birthday Robert had 7 toy cars left in his collection. This year his parents gave him some more toy cars for his birthday. He now has 19 toy cars. If his parents gave him 3 more toy cars this year than last year, how many toy cars did his parents give to him last year? Select one: a. 25 toy cars b. none of the answers given c. 9 toy cars d. 15 toy cars e. 29 toy cars

c. 9 toy cars

A class of third grade students are learning about elapsed time. For example, it is now 9: 30 am. What time will it be in 3 hours and 45 minutes? One student says that it will be 12:75 am. Which of the following responses BEST matches how you would respond? Select one: a. I'd discourage him from using it because it would confuse the rest of the class. b. I'd tell him that I'd like him to concentrate on learning the standard way of doing it. c. I'd ask him to explain how he figured this out and why he thinks it works. d. I'd praise him, but point out that while his method works in this case, it might not always work. e. I'd let him add time this way

c. I'd ask him to explain how he figured this out and why he thinks it works

ABCD is a quadrilateral. All of the following is true except? a. ABCD is a parallelogram b. Angle A is 90 degrees c. AB ≃AD d.AC ≃BD Select one: a. If a, b, and c are all true, ABCD is a square. b. If a and b is true, ABCD is a rectangle. c. If a and d is true, ABCD is a square. d. If a and c is true, ABCD is a rhombus.

c. If a and d is true, ABCD is a square.

One of your students said, "If 7 divided by 0, the result should be 7 because if you divide by nothing, you don't divide and so you would still have 7." What are your thoughts on his reasoning process? Select one: a. It is mathematically correct and I can explain why. b. It is mathematically correct but I cannot explain why. c. It is mathematically incorrect and I can explain why. d. It is mathematically incorrect but I cannot explain why.

c. It is mathematically incorrect and I can explain why. d. It is mathematically incorrect but I cannot explain why.

William says that he has discovered a method that always works when comparing fractions. He states that he just looks at the denominator and "the fraction with the larger denominator is smaller because the whole is divided into more pieces, therefore each piece is smaller. " What do you think about William's reasoning? Select one: a. It is mathematically correct and works for all cases. b. This is not mathematically correct for any cases. c. It works in some cases, but it would not work in general. d. I do not know if this is mathematically correct.

c. It works in some cases, but it would not work in general

What problem type(s) does the word problem below illustrate? "Stella has some dolls. Her parents gave her 8 more dolls on her birthday. Now Stella has 23 dolls. How many dolls did she have before her birthday?" Select one: a. Compare b. None of the answers given c. Join d. Part-part-whole e. Separate

c. Join

Joan recognizes the properties of a square and a rectangle but makes the observation that "a square is not a rectangle because a rectangle has two long sides and two short sides." What level of van Hiele is Joan in regard to rectangles? Select one: a. Level 0: Visualization b. Below Level 0: Visualization c. Level 1: Analysis d. None of these e. Level 2: Informal Deduction

c. Level 1: Analysis

Cindy is comparing the fractions 3/12 and 5/20. Which of the following statement(s) are TRUE? Select one: a. 3/12 < 5/20 because the 15 is smaller than the 120 when you multiply b. 3/12 < 5/20 because the numerator 5 is larger than the numerator 3 c. None of these statements are true d. 3/12 > 5/20 because the denominator 12 is smaller than the denominator 20

c. None of these statements are true

All of the following are effective methods for helping children understand the meaning of the equal sign EXCEPT: Select one: a. Placing focus on the relationship between the expressions on each side of an equation b. Rearrange equations to where the unknown is not always on the right hand side of the equal c. Placing focus mainly on computations d. Using a scale balance to represent the relationship between the right and left hand side of an equation

c. Placing focus mainly on computations

Which of the following is true for both an isosceles trapezoid and a rectangle? Select one: a. Each diagonal bisects opposite angles. b. Adjacent sides are congruent. c. The two diagonals are the same length. d. Opposite sides are parallel. e. The two diagonals are perpendicular.

c. The two diagonals are the same length

You give your students the following equation and ask them to solve: "Blank box minus eight equals 21" One of your students, Sammy, says "the blank box is 13 because 21 - 8 equals 13." What are your thoughts on the Sammy's reasoning? Select one: a. I think it is mathematically correct. b. It works in this case, but I'm not sure it would work in general. c. This is not mathematically correct. d. I do not know whether this is mathematically correct or not.

c. This is not mathematically correct

Which of the following word problems BEST illustrates what 1/4 divided 1/2 means? Select one: a. You want to split 1/4 pie evenly between two families. How much pie should each family get? b. You have $0.25 and may soon double your money. How much money would you end up with? c. You are making some homemade taffy and the recipe calls for 1/4 cups of butter. How many sticks of butter will you need? (Each stick = 1/2 cup) d. All of these e. It takes 1/4 hour to fly 300 miles. How far can you fly in 1/2 hour?

c. You are making some homemade taffy and the recipe calls for 1/4 cups of butter. How many sticks of butter will you need? (Each stick = 1/2 cup)

A teacher is working with a group of elementary students and wants to teach the concept of fractions using fraction circles. Which representational model would be MOST appropriate when using this tool? Select one: a. linear model b. measurement tool c. area model d. set model

c. area model

The relations below demonstrate what property of addition and multiplication of real numbers a, b, and c? (a + b) + c = a + (b + c) OR (ab)c = a(bc) Select one: a. inverse property b. not sure c. associative property d. commutative property Incorrect e. identity property

c. associative property

What problem type(s) are represented below: At the school carnival, Carol sold 3 times as many raffle tickets as Sam. If the two of them sold 152 tickets all together, how many raffle tickets did Carol sell? Select one or more: a. join problem b. separate problem c. compare problem d. part-part-whole problem

c. compare problem d. part-part-whole problem

What problem type(s) are represented below: Julia has 25 kittens. Eight are male and the rest are females. She gives four of the female kittens to her friend. How many female kittens does she have left? Select one or more: a. join problem b. compare problem c. part-part-whole problem d. separate problem

c. part-part-whole problem d. separate problem

An effective representation for addition that will help students later with measuring length is to: Select one: a. use a collection of objects and show addition by joining sets of objects Incorrect b. use areas on a 10 x 10 grid and show addition by joining shaded regions c. show addition by joining distances of on a number line d. none of the answers given

c. show addition by joining distances of on a number line

Alice gave ½ of her candy to Billy. Billy gave 1/4 of the candy that he received from Alice to Carter. How could you find what fraction of Alice's candy Carter received? Select one: a. take one half and divide by one fourth b. None of these options c. take one half and multiply by one fourth d. take one half and subtract one fourth e. take one half and multiply by 4

c. take one half and multiply by one fourth

How many times must you regroup to find 110 divided by 5? Select one: a. no regrouping is needed b. once c. twice d. three times e. four times

c. twice

At the school carnival, Carol sold 3 times as many raffle tickets as Sam. If the two of them sold 152 tickets all together, how many raffle tickets did Carol sell? Select one: a. 38 tickets b. none of the answers given c. 25 tickets d. 114 tickets e. 50 tickets

d. 114 tickets

Randy has 15 puppies. Josie has 4 more puppies than Randy. If Josie gives 6 of his puppies away, how many puppies does Josie have now? Select one: a. 19 puppies b. 17 puppies c. 25 puppies d. 13 puppies e. Not sure

d. 13 puppies

Sally is learning to skip count by four. If 1 is the first number in the sequence, what is the fifth number in the sequence? Select one: a. 20 b. 21 c. 19 d. 17

d. 17

George begins a trip at 9:30 A.M. If he travels for 5 hours and 45 minutes, when will the trip be over? Select one: a. None of these b. 4:15 PM c. 2:15 PM d. 3:15 PM e. 2:45 PM

d. 3:15 PM

uppose that you have a square ABDC. All of the following relationships are true in all squares EXCEPT? Select one: a. AC and CD have the same length b. All angles are 90 degrees c. AD and BC are perpendicular d. AD and BD are perpendicular

d. AD and BD are perpendicular

Ms. Sierra is working with her 5th grade students to develop expressions based on problem situations. She poses the following scenario: Gary works three hours less than Landry. What equation can be used to represent this situation? (Let G represent the number of hours worked by Gary and L represent the number of hours worked by Landry.) The most common answers that your students come up with are: Equation 1: G=3-L Equation 2: G-3=L Equation 3: G=L-3 Which equation is correct? Select one: a. G-3=L b. G=3-L c. None of the above d. G=L-3

d. G=L-3

One of your students said, "If 7 divided by 0, the result should be 7 because if you divide by nothing, you don't divide and so you would still have 7." Which of the following responses are mathematically correct? Select one or more: a. I would explain that if zero is the size of the groups you want to divide seven objects into, then you still have seven, so the answer is seven. b. I would explain that if zero is the number of the groups you want to divide seven objects into, then you are still left with the one group having seven objects, so the answer is one. c. I would explain that if zero is the number of the groups you want to divide seven objects into, then you are still left with the one group having seven objects, so the answer is seven. d. I would explain that there is no answer because there is no number times zero that will give you seven. e. I would explain that the answer cannot be seven because seven divided by one is seven. f. I would explain that any number divided by 0 is "undefined" and that is a rule that they will need to remember.

d. I would explain that there is no answer because there is no number times zero that will give you seven. e. I would explain that the answer cannot be seven because seven divided by one is seven. f. I would explain that any number divided by 0 is "undefined" and that is a rule that they will need to remember.

Your class is learning the parts of a whole definition of fractions. Scott, a second grade student, is asked to explain what the 5 in the fraction 2/5 means. He says that the "5 is the whole." How would you respond to Scott? Select one: a. I'd ask him to explain how he figured this out and why he thinks it works for all fractions. b. I'd tell him that I'd like him to concentrate on learning the standard parts of a whole definition of fractions c. I'd praise him, but point out that while this explanation works in this case, it might not always work for all fractions. d. I'd let him use this explanation, as it works for all fractions. e. I'd discourage him from using this explanation because it would confuse the rest of the class.

d. I'd let him use this explanation, as it works for all fractions.

Skip counting is important in the development of fluency in which of the following skills: I. calculation II. number sense III. multiplication and division Select one: a. II and III b. I and III Incorrect c. I and II d. I, II, and III

d. I, II, and III

Problem type(s) where a change in quantities is described include: Select one or more: a. Compare b. None of the answers given c. Part-part-whole d. Join e. Separate

d. Join e. Separate

Billy's fifth grade teacher asks him to describe triangles. Billy says "a triangle is a shape that looks like a mountain." Which van Hiele level do you think is Billy at in regard to triangles? Select one: a. Below level 0 b. Level 2 c. Level 1 d. Level 0

d. Level 0

Luke makes the observation that "all squares are rectangles, but not all rectangles are squares." Select one: a. Level 1: Analysis b. Level 0: Visualization c. None of these d. Level 2: Informal Deduction e. Below Level 0: Visualization

d. Level 2: Informal Deduction

Suppose that Andrew is at a van Hiele level 1 with his understanding of rectangles, which of the following shape might Andrew say is NOT a rectangle? Select one: a. K b. J c. L d. M

d. M

What problem type(s) does the word problem below illustrate? "There are 18 students in Miss Lily's class. Eight are boys and the rest are girls. If three girls transferred to another school this semester. How many girls are there in Miss Lily's class now?" Select one: a. Compare and Separate b. Compare and Join c. Part-part-whole and join d. Part-part whole and Separate

d. Part-part whole and Separate

A teacher is working with a group of first grade students on exploring the concept of ten. Which of the following activities would be the most effective in helping the students grasp the concept of grouping by ten? Select one: a. Coloring in the even numbers on a hundreds chart b. Estimating the number of chocolate chips in a bag c. Writing the numerals for one to ten on dry-erase boards d. Putting one bean in each square of a grid containing ten squares

d. Putting one bean in each square of a grid containing ten squares

When you divide a fraction by another fraction the answer is always smaller than one. Select one: a. Always True b. Not Sure c. Never True d. Sometimes True

d. Sometimes True

You give your second grade students to following equation: "18 plus 17 equals blank box plus 29" George says "Twenty-nine is two more than 27, so the missing number must be two more than 18" What do you think about George's reasoning? Select one: a. I think it is mathematically correct. b. I do not know if this is mathematically correct or not. c. It works in this case, but I'm not sure it would work in general. d. This is not mathematically correct.

d. This is not mathematically correct

Bobbie is learning to count in his kindergarten classroom. He points to counting bears one at a time and says the sequence of number names. He says "one, two, three, four, five, ..." as he points to each bear. When his teacher asks him to show her the quantity 4. Bobbie points to the fourth bear. Which counting concept has Bobbie probably not yet have attained? Select one: a. one to one correspondence b. none of the answers given c. subitizing d. cardinality

d. cardinality

Billy's fifth grade teacher asks him to describe triangles. Billy says "a triangle is a shape that looks like a mountain." All of the following instructional activities are aligned with Billy's level of geometric understanding and would be appropriate for his level of geometric thought Billy EXCEPT? Select one: a. sorting, identifying, and describing triangles Incorrect b. drawing triangles c. All of the above would be adequate for Billy d. classifying different types of triangles based on their properties

d. classifying different types of triangles based on their properties

The relations below demonstrate what property of addition and multiplication of real numbers: a + b = b + a OR ab = ba Select one: a. inverse property b. not sure c. associative property d. commutative property e. identity property

d. commutative property

What problem type(s) is represented below: Randy has 15 puppies. Josie has 4 more puppies than Randy. If Josie gives 6 of his puppies away, how many puppies does Josie have now? Select one or more: a. not sure b. join problem c. part-part-whole problem d. compare problem e. separate problem

d. compare problem e. separate problem

A teacher is working with a group of elementary students and wants to teach the concept of fractions using fraction tiles. Which representational model would be MOST appropriate when using this tool? Select one: a. not sure b. metric model c. area model d. linear model e. set model

d. linear model

An effective representation showing the relationship between addition and multiplication is using equal-sized groups of objects being combined to form a larger group. Which representational model is this? Select one: a. linear model b. none of the answers given c. area model d. set model

d. set model

Fifth grade teacher, Mr. Flores, showed a figure below to his class and asked, "What is this? and how would you describe it to your friends?" a rectangle Erick answered, "It is a rectangle and it has four sides, closed, two long sides, two shorter sides, opposite sides parallel, and four right angles..." Which instructional activity is appropriate to Erick's van Hiele geometry thinking level in relation to rectangles? Select one: a. manipulating, coloring, folding, and constructing geometric shapes b. identifying minimum sets of properties that describe a figure c. identifying a shape or geometric relation in a variety of orientations. d. sorting and resorting shapes by single attributes

d. sorting and resorting shapes by single attributes

Suppose you have a balanced scale. On the left side we have two cube weights and one cylinder weight. On the right side you have four cube weights. The weights on the scale are balanced. If each cube weight weighs 3 pounds and each cylinder weight weighs N pounds. Which of the following processes could be used to represent the solving for the weight of the cylinder? Select one: a. subtract two 3-pound cubes from the left hand scale b. subtract two 3-pound cubes from the right hand scale c. add two 3-pound cubes to the left hand scale d. subtract two 3-pound cubes from both sides

d. subtract two 3-pound cubes from both sides

Julia has 25 kittens. Eight are male and the rest are females. She gives four of the female kittens to her friend. How many female kittens does she have left? Select one: a. 33 kittens b. 21 kittens c. 17 kittens d. 18 kittens e. 13 kittens

e. 13 kittens

A boy in your first grade class identifies a square as a rectangle. How would you respond? Select one: a. I'd tell him that a rectangle has 2 longer and 2 shorter sides while sides of squares are all equal. b. I'd check to see whether this is okay. c. I'd ask him why he is calling the shape a rectangle. d. I'd praise him. e. I'd ask him, "What's a rectangle? What's a square?" and have the child remember the difference.

e. I'd ask him, "What's a rectangle? What's a square?" and have the child remember the difference.

A third grade teacher poses an elapsed time problem to her students. She asks them to find the time 4 hours and 30 minutes before 2:45 AM. One student, Shelby, excitedly explains that she has figured out a new way of solving this problem. She explains that because she has to cross the midnight or noon time marks, she makes 2:45 into 14:45 by adding 12 to the hours, and then subtracts 4 from the 14 and 30 from forty-five to get 10:15 PM. Which of the following responses BEST matches how you would respond? Select one: a. I'd let her subtract time this way. b. I'd discourage her from using it because it would confuse the rest of the class. c. I'd ask her to explain how she figured this out and why she thinks it works. d. I'd tell her that I'd like her to concentrate on learning the standard way of doing it. e. I'd praise her, but point out that while her method works in this case, it might not always work.

e. I'd praise her, but point out that while her method works in this case, it might not always work.

William says that he has discovered a method that always works when comparing fractions. He states that he just looks at the denominator and "the fraction with the larger denominator is smaller because the whole is divided into more pieces, therefore each piece is smaller. " How would you respond to William? Select one: a. I'd discourage him from using this explanation because it would confuse the rest of the class. b. I'd let him use this explanation, as it works for all fractions. c. I'd discourage him from using this explanation because it would confuse the rest of the class. d. I'd tell him that I'd like him to concentrate on learning the standard methods for comparing fractions. e. I'd praise him, but point out that while this explanation works in some cases, it might not always work for all fractions.

e. I'd praise him, but point out that while this explanation works in some cases, it might not always work for all fractions.

Three elementary teachers are having a discussion on effective methods for helping children conceptualize the meaning of the equal sign. Mr. A has his students solving equations such as 4 + 5 = ___ - 1. Mr. B has his students solve equations that look like 7 + 5 = ____. Mr. C has his students solve equations that look like 7 + ___ = 13. Mr. D has his students work with a balance where they add and subtract values from both sides and keep the scale balanced. Whose method would LEAST likely help students build a good understanding of the equal sign? Select one: a. Mr. C b. None of the answers given c. Mr. A Incorrect d. Mr. D e. Mr. B

e. Mr. B

Suppose that you have a closed number line having the length of one unit. The number line is divided into 8 segments that are equal in length. A red dot appears in the middle of the fifth segment. What location on the would the red dot represent? Select one: a. 5/8 b. 4/9 c. 5/16 d. 7/16 e. None of these

e. None of these

Using the times given in the analog clocks below, how much time has passed between the start and end times? (Assume that times are during the same day) Select one: a. 8 hours and 15 minutes b. 3 hours and 45 minutes c. 8 hours and 15 minutes d. 4 hours and 15 minutes e. None of these

e. None of these

Four students are discussing fractions as parts of a whole in real world contexts specifically, with the gender makeup of the 25 students in class. Student A proposes, we can use the fraction 13/12 since "13 is the number of boys in class and 12 is the number girls in class." Student B says that we can use the fraction 12/13 since "fractions are parts of a whole and the bigger number is always used in the denominator." Student C insists that "The whole in this context could be 25 because that is the total number of students in the class. So, we can use the fraction 12/25 for girls and 13/25 for boys." Student D responds, "I think you all are right." Which student(s) do you think is/are correct when using fractions to represent the gender make up of the class? Select one: a. Student B b. Student D c. Student A d. None of the students e. Student C

e. Student C

A class of third grade students are learning about elapsed time. For example, solving problems like: "It is now 7:30 am. What time will it be in 2 hours and 45 minutes?" One student says that it will be 9:75 am. What do you think about this? Select one: a. None of these b. I think it is mathematically correct. c. It works in this case, but I'm not sure it would work in general. d. I do not know if this is mathematically correct or not. e. This is not mathematically correct.

e. This is not mathematically correct.

Mrs. Lee showed Figure A to her 2nd grade student, Jacob, and he said, "It is a square". When she turned the square 45 degrees (Figure B), Jacob said, "Now it is a rhombus because it looks like a diamond". square and rhombus All of the following instructional activities would be appropriate for Jacob's van Hiele level of geometry thinking (in relation to Rhombi) EXCEPT for? Select one: a. identifying a shape in a variety of orientations. b. manipulating and constructing geometric shapes c. describing geometric shapes using standard and nonstandard language Incorrect d. identifying a shape in a simple drawing e. comparing shapes according to their characterizing properties.

e. comparing shapes according to their characterizing properties.

Cindy's fifth grade teacher asks her to describe a triangle. Cindy says "a triangle is a closed shape that has three straight sides and three angles." All of the following activities are aligned with Cindy's level of geometric thought and would be helpful for Cindy EXCEPT? Select one: a. listing the properties of shapes b. All of these would be adequate for Cindy's level of geometric thought c. comparing shapes based on their properties d. identifying shapes based on their descriptions e. developing definitions for shapes

e. developing definitions for shapes