EDEL 4370 Post Tests and Final Review

Emphasized counting concepts

1. Addition connected to forward counting 2. multiplication connected to skip counting from 0 3. Subtraction connected to backwards counting

Mod 2 misconceptions

1. Confusing base 60 with base 10 regrouping when adding 2. confusing base 60 with base 10 regrouping when subtracting 3. If it was 10:30am what time would be in 3 hours and 15 minutes

5 mod 1 methods

1. counting by ones 2. skip counting 3. counting with 10 frames 4. subtilizing 5. counting on a number line

when teaching it is important that you (2 things)

1. emphasize counting concepts 2. emphasize base 10 concepts

Mod 1 misconceptions/ types of errors

1. factual errors 2. procedural errors 3. conceptual errors

Mod 3 Misconceptions

1. fractions 2. numbers and operations 3. much more abstract than arithmetic

Addition and subtraction strategies

1. make 10 approach 2. place value approach 3. number line

4 counting techniques

1. number sequence 2. one to one correspondence 3. cardinality 4. Subtilizing

Regroup up to ______ AM/PM

12

time set model

H:Min:Sec (Base 60 time chart), digital clock

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 John in regard to rectangles? a. Below Level 0: Visualization b. Level 2: Informal Deduction c. Level 1: Analysis d. Level 0: Visualization e. None of these

Level 1: Analysis

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? a. Level 0 b. Level 1 c. Level 2 d. Level 3

Level 2

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

Level 2: Informal Deduction

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

None of these statements are true

linear model

continuous model, modeled by using number lines and lengths (ex, strip diagrams, bar diagrams, fraction tiles)

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

separate problem , compare problem

Mod 4 misconceptions

1. treats the denominator as a whole when it is broken into equal parts 2. shows the total object when you don't need to include that

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

122

What base is time in?

60

What is time?

A diration of events, count the space not the ticks, include colon (:) when under intervals

set model

A discrete model with which mathematical concepts can be modeled by using sets of objects. (ex. color counters, base 10 blocks)

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? a. part-part-whole problem b. separate problem c. join problem d. compare problem

Join problem, separate problem

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? a. Level 0 b. Level 2 c. Level 1 d. Below level 0

Level 0

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". What van Hiele level do you think is Jacob at in relation to Rhombi? a. Level 1 b. Level 0 c. Level 2 d. Level 3

Level 0

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?" 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? a. Level 0 b. Level 2 c. Level 3 d. Level 1

Level 1

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? a. None of these b. 4/9 c. 5/8 d. 5/16 e. 7/16

None of these

All of the following is true of all rhombi EXCEPT? (Pick as many as you think) a. Each diagonal bisects opposite angles. b. The two diagonals are perpendicular. c. All angles have the same measure. d. The two diagonals are the same length.

The two diagonals are the same length, all angles have the same measure

T/F: 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.

True

T/F: According to the van Hiele model instruction should be matched with the individual's van Hiele levels for learning to take place.

True

Level 0

Visualization- the children judges shapes by their appearance and what they look like Describe things using the names of shapes without talking about the attributes. name the shapes regardless of their orientation. separate shapes into categories of flats and solid, and group shapes that seem to look alike based on appearance.

part-part whole problem

When it gives the whole amount amount and the smaller amount

geometry

math concerned with shape, size, figures, and shapes

area model

modeled using shared regions

Level 1

Analysis- the child sees figures in terms of their parts and discovers properties of a class of shapes. For example, triangles have 3 sides, 3 angles, sides are straight etc. However, still think that squares and rectangles are different classes of shapes. experiment with shapes to discover attributes and form new shapes. think about shapes within shapes for the purpose of describing properties, and measuring distance and discoing attributes

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

I, II, and III

Measurement requires

1. selecting an attribute that you want to measure (length) 2. find a tool that has same attribute 3. Define a unit of measurement 4. create a one to one correspondence

Summary of Mod 2

1. sort shapes by their attributes and properties 2. compare and contrast shapes based on properties 3. make and test connectives about the properties of shapes

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

29

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

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

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?

A square

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

AD and BD are perpendicular

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? a. B = 6G b. 6B = G c. B = G + 6 d. B + 6 = G e. None of the answers given

B = 6G

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

Both diagonals have the same length

Sue is learning to count in her kindergarten classroom. She points to counting bears one at a time and says the sequence of number names. She says "one, two, three, four, five, ..." as she points to each bear. When her teacher asks Sue to show her the quantity 3. Sue points to the third bear. Which counting concept has Sue probably not yet have attained? a. subitizing b. one to one correspondence c. none of the answers given d. cardinality

Cardinality

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

Commutative Property

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? a. developing definitions for shapes b. All of these would be adequate for Cindy's level of geometric thought c. listing the properties of shapes d. identifying shapes based on their descriptions e. comparing shapes based on their properties

Developing definitions for shapes

T/F: According to the van Hiele model individuals can skip levels if they have advanced mathematical skills.

False

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? a. G=3-L b. G-3=L c. G=L-3 d. none of the above

G=L-3

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 a. If a and b is true, ABCD is a rectangle. b. If a and d is true, ABCD is a square. c. If a, b, and c are all true, ABCD is a square. d. If a and c is true, ABCD is a rhombus.

If a, b, and c are all true, ABCD is a square.

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 a. If statement 2 is true, then statement 1 is true. b. If statement 1 is true, then statement 2 is true. c. If statement 2 is false, then statement 1 is false. d. Statement 1 and 2 can both be true

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 rhombus. Statement 2: Figure A is a square. a. If statement 1 is false, then statement 2 is true. b. If statement 1 is true, then statement 2 is true. c. Statement 1 and 2 cannot both be true. d. Statement 1 and 2 cannot both be false. e. If statement 2 is true, then statement 1 is true.

If statement 2 is true, then statement 1 is true

Level 2

Informal Deduction- the child logically interrelates previously discovered properties. They can deduce properties of a figure and recognize classes. For example, by using the definition of a rectangle, a square is a rectangle because it has all the properties of a rectangle. create new shapes from existing shapes, understand that a square is a rectangle

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? a. Level 1: Analysis b. Level 3: Rigor c. Level 2: Informal Deduction d. It would be appropriate for all these levels e. Level 0: Visualization

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? a. Level 0: Visualization b. None of these c. Level 1: Analysis d. Level 2: Informal Deduction e. Below Level 0: Visualization

Level 0: Visualization

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? a. Level 2 b. Level 0 c. Level 1 d. Level 3

Level 1

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

Placing focus mainly on computations

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

Set model

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

Sometimes True

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

Statement 2 is true, then statement 1 is true

Which of the following word problems BEST illustrates what 1/4 divided 1/2 means? a. It takes 1/4 hour to fly 300 miles. How far can you fly in 1/2 hour? 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. You want to split 1/4 pie evenly between two families. How much pie should each family get? e. All of these

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)

Which of the following word problems BEST illustrates what 1/4 divided 2 means? a. It takes 1/4 hour to fly 300 miles. How far can you fly in 1/2 hour? b. All of these 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. You have $0.25 and may soon double your money. How much money would you end up with? e. You want to split 1/4 pie evenly between two families. How much pie should each family get?

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

Algebra

a branch of math that uses variables and rules for operations with variables

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? a. an analog clock and keep track of the time on piece of paper b. None of these methods c. a time line d. apply the make 60 approach and keep track of time

a time line

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? a. an analog clock and keep track of the time on piece of paper b. None of these methods c. a time line d. apply the make 60 approach and keep track of time

a time line

Variables

are letters or symbols used to represent quantities

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? a. measurement tool b. linear model c. set model d. area model

area model

Equal sign

balanced, What is on he left is the same as the right side

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? a. classifying different types of triangles based on their properties b. All of the above would be adequate for Billy c. drawing triangles d. sorting, identifying, and describing triangles

classifying different types of triangles based on their properties

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? a. compare problem b. part-part-whole problem c. separate problem d. join problem

compare problem, part-part-whole problem

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? 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.

comparing shapes according to their characterizing properties

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? a. manipulating and constructing geometric shapes b. comparing shapes according to their characterizing properties. c. identifying a shape in a simple drawing d. describing geometric shapes using standard and nonstandard language e. identifying a shape in a variety of orientations.

comparing shapes according to their characterizing properties

CRA approach

concrete- representational- abstract approach

Emphasized Base 10 concepts

counting in groups of 10 by powers of 10 (ones, tens, hundreds, thousands)

What does equal mean?

equal is not an operation. Subtraction and addition are operations.

The attributes of a time line is ____________ because the lengths represent the time.

equal lengths

Factual errors

errors due to a lack of factual information (e.g., vocabulary, digital identification, place value identification)

Conceptual Errors

errors due to misconceptions or a faulty understanding of the underlying principle and ideas connected to the mathematical problem (e.g., relationship among numbers, characteristics, and properties of shapes).

Procedural Errors

errors due to the incorrect performance of steps in a mathematical process (e.g., regrouping, decimal placement)

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? a. join problem b. separate problem c. compare problem d. part-part-whole problem e. not sure

join problem, compare problem

compare problem

larger amounts, smaller amounts, How many (looking for the difference)

The __________________ represent the number in a number line.

lengths

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? a. set model b. linear model c. area model d. metric model e. not sure

linear model

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? a. number of counters in sets and subsets b. weight of counters in sets and subsets c. length of counters in sets and subsets d. area of counters in sets and subsets

number of counters in sets and subsets

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? 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? a. part-part-whole problem b. separate problem c. join problem d. compare problem

part-part-whole problem, separate problem

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?" 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? a. sorting and resorting shapes by single attributes b. manipulating, coloring, folding, and constructing geometric shapes c. identifying a shape or geometric relation in a variety of orientations. d. identifying minimum sets of properties that describe a figure.

sorting and resorting shapes by single attributes

location

specify where objects are located in a plane or in 3D space.

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? a. None of these options b. take one half and divide by one fourth c. take one half and subtract one fourth d. take one half and multiply by 4 e. take one half and multiply by one fourth

take one half and multiply by one fourth

Which model emphasizes how many objects are in a set?

the set model

shapes and properties

the study of properties of shapes in two and three dimensions

transformations

the study of translations, reflections, and rotations. the study of symmetries, and the concept of similarity

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

the two diagonals are the same length

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

they have four right angles, opposite sides are parallel, the diagonals have the same length, the opposite sides have the same length

concrete approach

uses objects and manipulatives

An effective representation for addition that will help students later with measurement concepts related to length is to use which model: a. using a collection of objects and showing addition by joining sets of objects b. using areas on a 10 x 10 grid and showing addition by joining shaded regions c. using a number line and showing addition by joining distances of on a number line d. none of the answers given

using a number line and showing addition by joining distances of on a number line

A teacher is working with a group of students on exploring the concept of base 10 place value with numbers up to 120. Which of the following activities would be the most effective in helping the students grasp the concept of place value? a. using two hundreds chart with multiples of 10 up to a 120 highlighted b. using real world pennies, nickels, dimes, and dollar bills c. showing students how place value increase from right to left by powers of 10 d. using base 10 blocks

using base 10 blocks

representational or pictorial approach

visual models, drawings, and visual manipulatives

join problem

you are adding to or giving= an action

separate problem

you are taking away or giving away= an action

abstract approach

numbers and mathematical symbols (ex. 7, infinity, +, =).