1 of 159

Grades 4-12�CogAT�Orientation

Levels 10 through 17/18

Here is where your orientation begins

2 of 159

Table of Contents

Teacher and Student Directions
Verbal
Quantitative
Nonverbal

3 of 159

Teacher and Student Directions

01

4 of 159

Whoa! What’s CogAT?

The CogAT (Cognitive Abilities Test) is an ability test that measures cognitive development through learned reasoning and problem-solving abilities through three batteries.

The test is comprised of three sections:

Verbal: Measures a child’s ability to remember, understand, make inferences and judgments about words; contains picture/word analogies

Quantitative: Determining relationships and patterns between numbers

Nonverbal: Determining relationships between shapes and figures

5 of 159

Teacher Directions Part 1

Welcome to CogAT Orientation. Please use these slides as presented. Do not edit or alter activity content in any way in order to ensure all students receive the same instruction and experience. The exercises are designed as a guided practice and do not require explicit instruction.

Some instructions may indicate “filling in the circle” should you choose to use the printed student booklets. Use of the student booklets is optional and not required to achieve the benefit of the practice activities. If the booklets are not used, the scripted directions may be modified as needed to reflect the method of student response.

6 of 159

Teacher Directions Part 2

This slideshow will introduce your students to the thinking skills and question format they may see in online testing. You may complete this as a whole class or push out as asynchronous work in order to meet the needs of your students. It is broken down into three parts: Verbal, Quantitative, and Nonverbal.

You will see red Stop Signs indicating natural stopping points.

Extra Thinking Activities: Give students paper and scissors to fold then cut into squares, rectangles, circles, triangles, hearts, etc.

7 of 159

Student Directions

Welcome to CogAT Orientation. This slideshow will introduce you to the thinking skills and questions you may see in online testing. You may complete this as a whole class or work independently to understand and complete the tasks. It is broken down into three parts: Verbal, Quantitative, and Nonverbal.

You will see red Stop Signs showing you when to stop.

8 of 159

Whoa! What’s CogAT?

The CogAT (Cognitive Abilities Test) involves solving brain puzzles to determine how your brain learns best.

The test has three parts:

Verbal: Picture/word puzzles

Quantitative: Number puzzles

Nonverbal: Shapes and figure puzzles

9 of 159

Beverly Sills

“You may be disappointed if you fail, but you’ll be doomed if you don’t try.”

10 of 159

Verbal

02

Verbal Analogies & Verbal Classification

11 of 159

Verbal Analogies

What is the relationship between oven and heat?

Which of these relates to a speaker in the same way that an oven relates to heat?

Part 1: Overview of Verbal Analogies

An analogy draws parallels between objects or ideas. Analogies can be about simple concepts such as “Brothers are boys just like sisters are girls” or complex concepts such as “Friendships are like glass. Once broken, they are hard to fix.” Successful learners habitually reason by analogy. Good analogies allow them to use what they already know when they are trying to understand new ideas. Reasoning by analogy requires attending carefully to the ways that two things are similar. Then this relationship is mapped onto a different pair of objects or ideas.

In this test, students answer questions that look like this.

When practicing the Verbal Analogies questions, encourage students to use these strategies:

Make a sentence that describes the potential relationship, substituting words for the symbols. For example, use “is related to” in place of the arrow, and “in the same way” in place of the colon. Oven is related to heat in the same way that speaker is related to…?
Generate a possible answer and look for it among the answer choices, testing for the relationship that matches best.

Students at this level tend to make the following common mistakes:

Students may ignore the relationship between the first two words and simply choose an answer that is associated with the third word. For example, the student might pick radio because a radio has a speaker.
Students might examine only some of the answer choices and then choose an answer that only partially satisfies the analogy. For example, the student may pick voice, which partially captures the idea of something the speaker emits, but the speaker emits sound in general, and voice is only part of that sound. Thus, sound is a better answer.

12 of 159

Each question has three words and a missing fourth word.

You must decide which choice is the missing word.

Practice Question 1

Part 2: Verbal Analogies Practice Test Script

The following script covers many issues that will help students do their best on the test. Read aloud the text printed in bold italics: these are directions to the students. Directions for you are in parentheses and should NOT be read aloud. Feel free to modify the script to ensure that students understand what they are supposed to do and how to do it.

(Make sure each student has a practice booklet. Then SAY:)

Open your practice booklet to page 1.

(Check that all students have the correct page.)

For each question in the Verbal Analogies test, you must figure out the relationship between the first pair of words. Then think about the third word. Choose the answer that relates to the third word in the same way that the first word relates to the second word.

P1

Let’s do the first practice question.

13 of 159

Start by looking at first two words.

The arrow between them means that they go together in some way.

Practice Question 1

14 of 159

Then look at the second word and the answer choices.

One of these will be connected to the color black in the same way that snow is connected to the color white.

Practice Question 1

15 of 159

Circle your answer.

Practice Question 1

16 of 159

How do the first two words go together?

Which answer choice has the same relationship with the second word?

Practice Question 2

17 of 159

Check your answer!

Practice Question 2

(Encourage responses. If someone chooses the correct answer, sound, SAY:)

You chose sound because a speaker produces or puts out sound like an oven produces or puts out heat. You’re right. That is the best answer.

(If someone chooses music, SAY:)

Music is too specific because it is only one type of sound put out by a speaker.

(If someone chooses radio, SAY:)

Radio isn’t the answer because it does not relate to speaker in the same way that oven relates to heat. A radio has a speaker, but it is not produced by a speaker.

(If someone chooses voice, SAY:)

Voice is too specific because it is only one type of sound put out by a speaker.

(If someone chooses stage, SAY:)

Stage isn’t the correct answer because it is not put out by a speaker, but used as a place to set a speaker.

(Check to make sure that all students have selected answer choice J.)

18 of 159

How do the first two words go together?

Which answer choice has the same relationship with the second word?

Practice Question 3

P3

Look at the third practice question. Listen carefully while I solve this question. I will tell you how I answer the question so you can answer similar questions.

First I’ll read the analogy. Animals are related to a zoo in the same way that art is related to…. Hmmm, let me think now. How are animals and a zoo connected?

Animals can live at a zoo. So where does art live? Well, art doesn’t really live, so the rule must be something else.

First I want to look at all the answer choices to see if they can help me decide what might relate to art in the same way that animals relate to a zoo.

Well, art can be displayed (or shown) or it can be a type of display. But that doesn’t really describe the same relationship of animals and a zoo.

An exhibition is a public display of art. A zoo is where animals are kept for public display. That might work, but let me look at the rest of the answer choices first.

A museum is a home for art like a zoo is a home for animals. Also, a museum allows for the public display of art like animals are publicly displayed in a zoo. I think museum is the best answer yet. But I still want to look at the other choices.

A fair might have art for sale, but zoos don’t usually sell animals to people, so that relationship doesn’t work.

A vault may hold art, but it usually has other important things as well. It is not designed just for art. A zoo is designed to hold animals, so vault doesn’t seem like the right answer.

19 of 159

Check your answer!

Practice Question 3

20 of 159

Can you try this one on your own?

First look at the relationship between the first two words. Then consider a similar relationship for the third word.

Practice Question 4

21 of 159

Which answer choice relates to seldom in the same way that many relates to often?

Practice Question 4

How is often related to many?

(Encourage responses. Call on a few students to answer. The correct answer is something like “Often describes something that happens a lot, and many shows that there are a lot of something. Often describes time and many describes amount.” Wait for a correct answer, then SAY:)

You are correct. Often is a term for something that happens a lot, and many is a term for having a lot of something. Often describes a high frequency and many describes a high number. Which answer choice relates to seldom in the same way that many relates to often?

(Encourage responses. If someone chooses the correct answer, few, SAY:)

Yes, few is a term for a small number of something like seldom is a term for something that happens a small number of times. I have few absences because I seldom miss school. But I have many books because I often read. Often and many describe large amounts, but seldom and few describe small amounts.

22 of 159

Check your answer!

Practice Question 4

23 of 159

Can you try this one on your own?

First look at the relationship between the first two words. Then consider a similar relationship for the third word.

Practice Question 5

24 of 159

Which answer choice relates to diner in the same way that fare relates to cab?

Practice Question 5

25 of 159

Check your answer!

Practice Question 5

26 of 159

Can you try this one on your own?

First look at the relationship between the first two words. Then consider a similar relationship for the third word.

Practice Question 6

27 of 159

Which answer choice relates to soaked in the same way that dry relates to arid?

Practice Question 6

28 of 159

Check your answer!

Practice Question 6

29 of 159

Verbal Classification

How do these three words go together?

Which one of these words belongs in the same group?

Part 1: Overview of Verbal Classification

The Verbal Classification test requires students to infer how several words are alike and then pick the answer choice that belongs in the same category. Typically, there are many ways that the concepts or objects expressed by the words could be alike. Some categories capture relatively superficial similarities such as “All of the words are colors” whereas other categories capture unique similarities such as “All of the words are pastels.” As students mature cognitively, they are able to detect more abstract and nuanced similarities. Using language to make more refined inferences is essential for learning, comprehension, and question solving. Teaching students strategies for making better inferences will improve their skills in these and many other domains.

In this test, students answer questions that look like this.

When practicing the Verbal Classification questions, encourage students to use these strategies:

Think of a rule or category that describes the similarities among the first three words. For example, all of the words refer to pieces of clothing.
Test the rule on each answer choice, eliminating answer choices that do not fit the rule. Only one answer choice should fit the inferred rule or category.
Look for a more precise rule or category if more than one answer choice fits the rule. It is important to find the rule that most precisely describes the words. For example, “pets” is more precise than “animals”, and “dresses” is more precise than “clothing.”

Students at this level tend to make the following common mistakes:

Students might select a word or object that reminds them of one of the words or objects in the first row, often relying only on appearance. For example, a student may pick “scarf” because it begins with an “s” like the words in the first row in the question above.
Students may find a rule or category that fits more than one option and not go back to determine a more narrow or precise rule. For example, “clothing” describes all of the answer choices above, so a more precise rule is required.
Students might choose an answer that is the name of the category and not another member of the category. For example, suppose that one of the options were “clothing”. Students may select this as the answer because they recognize the first three words as articles of clothing.

30 of 159

Each question has a top row with several words and a bottom row of answer choices.

You must decide which answer choice goes with the words in the top row.

Practice Question 1

31 of 159

Start by looking at the top row.

All of the words go together in some way. What do these all have in common?

Practice Question 1

32 of 159

Then look at the bottom row with the answer choices.

One of these will be connected to the objects in the top row in a way the others are not.

Practice Question 1

33 of 159

Circle your answer.

Practice Question 1

34 of 159

How do the words in the top row go together?

Which answer choice is most similar to the words in the top row?

Practice Question 2

35 of 159

Check your answer!

Practice Question 2

(Encourage responses. If someone chooses the correct answer, strawberry, SAY:)

You chose strawberry because it is a flavor of ice cream like the words in the top row. You’re right. That is the best answer.

(If someone chooses sherbet, SAY:)

Sherbet is a category or type of cold, creamy dessert like ice cream, but it is not the best answer because it is not a flavor of ice cream.

(If someone chooses cone, SAY:)

Cone isn’t the best answer. Although a cone holds ice cream, it is not a flavor of ice cream.

(If someone chooses twist, SAY:)

Twist is two flavors of ice cream mixed together, so it cannot be the right answer.

(If someone chooses sundae, SAY:)

A sundae is a dessert made from ice cream, but it is not a flavor of ice cream.

(Check to make sure that all students have selected answer choice L.)

36 of 159

How do the words in the top row go together?

Which answer choice is most similar to the words in the top row?

Practice Question 3

P3

Look at the third practice question. Listen carefully while I solve this question. I will tell you what I am thinking so you will know how to answer similar questions.

First, I’ll look at the words in the top row.

They are shirt, socks, and skirt. Let me think, how are these three words like each other?

All of the words start with “s” and have five letters. But is there another way that they are alike?

I know. All three words are types of clothing. Maybe that’s the right rule. Let me look at the answer choices in the bottom row.

Well, scarf starts with an “s” and has five letters, so it could work. But I should look at all of the answer choices before picking one.

A coat is a piece of clothing. So, coat might be a good answer if the rule is types of clothing.

Gloves are also clothing. I probably need to look at how the things in the top row are alike again. But first I’ll look at the other two words.

Pants are also clothing. A hat is also a piece of clothing. Now I really need to look at what makes the words in the top row alike. I need to find a more precise rule for grouping the words in the top row.

A shirt, socks, and a skirt are all pieces of clothing. What else do they have in common?

I know! You could wear all of them when you change out of your pajamas before leaving for school. They are important/ primary pieces of clothing. The shirt covers the upper body, the

socks cover feet, and the skirt covers legs. You would need to wear all of them to school.

(Point to the answer choices as you SAY:)

Now, I can look at the words in the bottom row.

Scarf is not the best answer because you can go to school without a scarf. It is not an important or necessary piece of clothing. What about the coat? You might need a coat in winter, so maybe it is the best answer. I am going to look at the other choices again before I choose an answer.

Gloves are not as important to wear as a coat is, so they are not the best answer. The next choice is pants. Pants are more important than a coat because boys cannot go to school without pants. Pants are an important primary piece of clothing. Pants are the best answer now. The last choice is hat, which is not as important to wear as pants.

37 of 159

Check your answer!

Practice Question 3

38 of 159

Can you try this one on your own?

First look at what the words in the top row have in common. Then consider which answer choice also fits this category. If more than one answer choice seems to fit, then look for a more specific rule connecting the top row.

Practice Question 4

39 of 159

Which answer choice best fits the top row?

Practice Question 4

40 of 159

Check your answer!

Practice Question 4

41 of 159

Can you try this one on your own?

First look at what the words in the top row have in common. Then consider which answer choice also fits this category.

Practice Question 5

42 of 159

Which answer choice best fits the top row?

Practice Question 5

How are the three words in the top row like each other?

(Encourage responses.)

All of the words in the top row are names of things that carry many people at the same time. A bus takes many people around town or from city to city. A train takes many people on short or long trips. And an airplane flies many people from one airport to another. Which word in the bottom row belongs in the same group?

(Encourage responses. If someone chooses the correct answer, ship, SAY:)

You are correct. But why did you pick the ship?

(Encourage responses.)

Ship is the best answer because it takes many people from place to place.

(If someone chooses any of the other answer choices, SAY:)

Why did you pick the ?

(Allow the student to share their reasoning.)

Well, the isn’t the right answer because it does not transport many people at the same time.

43 of 159

Check your answer!

Practice Question 5

44 of 159

Can you try this one on your own?

First look at what the words in the top row have in common. Then consider which answer choice also fits this category.

Practice Question 6

45 of 159

Which answer choice best fits the top row?

Practice Question 6

46 of 159

Check your answer!

Practice Question 6

47 of 159

48 of 159

Quantitative

03

Number Analogies, Number Puzzles, & Number Series

49 of 159

Number Analogies

What rule explains how to transform 7 into 14 and 9 into 18? The rule must work on both pairs of numbers.

Apply the same rule to figure out the missing number.

Part 1: Overview of Number Analogies

An analogy draws parallels between objects or ideas. Successful learners habitually reason by analogy. Good analogies allow students to use what they already know when they are trying to understand or remember new ideas. Reasoning by analogy requires attending carefully to the ways in which two things are similar. Then this relationship is mapped onto something new.

Performance on this test predicts mathematics achievement because discovering quantitative patterns and relationships is at the core of learning mathematics.

Each question on the Number Analogies test presents two pairs of numbers. To solve the questions, students must find a rule that transforms the first number in each pair into the second number. The same rule must work for both pairs of numbers. Then the student uses the rule to generate the missing number in the third pair. Most questions require only one rule, but some questions use two rules such as adding and then doubling. Students are allowed to use scratch paper on the actual test. Items in the test look like this.

When practicing the Number Analogies questions, encourage students to use these strategies:

Think of a rule that describes how to transform the first number into the second number in the first two pairs. For example, the second number is double the first.
If more than one rule works, then try the simplest rule first.
Apply the same rule to the third pair of numbers to determine the missing number.

Students at this level tend to make the following common mistakes:

Students may use the wrong arithmetic operation. For example, the student might add instead of subtract.
Students might find a rule that works with only one of the pairs and not both. For example, in the sample question above, a student may remember that adding 7 to 7 will make 14. Although this rule does not work for the second pair, the student may simply add 7 to 1, and marks the answer as 8.

50 of 159

Each question has a five numbers and a missing sixth number.

You must decide which answer choice is the missing number.

Practice Question 1

51 of 159

Start by looking at the first two sets of numbers.

The arrow between them means that they go together. Something changed between the first and second number.

Practice Question 1

52 of 159

Then look at the last number set and the answer choices.

The number 16 will have to change in the same way that the 9 and the 17 changed.

Practice Question 1

53 of 159

Circle your answer.

Practice Question 1

54 of 159

What rule do the first two pairs of numbers follow?

Which answer choice has the same relationship?

Practice Question 2

55 of 159

Check your answer!

Practice Question 2

56 of 159

Can you try this one on your own?

First figure out what rule the first two pairs of numbers follow. Then use the same rule on the third number.

Practice Question 3

57 of 159

What is the missing number?

Practice Question 3

58 of 159

Check your answer!

Practice Question 3

59 of 159

Can you try this one on your own?

First figure out what rule the first two pairs of numbers follow. Then use the same rule on the third number.

Practice Question 4

60 of 159

What is the missing number?

Practice Question 4

61 of 159

Check your answer!

Practice Question 4

62 of 159

The rule for these numbers has two steps.

Can you figure out the relationship between the sets of numbers?

Practice Question 5

63 of 159

Check your answer!

Practice Question 5

64 of 159

Can you try this one on your own?

Practice Question 6

First figure out what rule the first two pairs of numbers follow. Then use the same rule on the third number.

65 of 159

What is the missing number?

Practice Question 6

66 of 159

Check your answer!

Practice Question 6

67 of 159

Number Puzzles

Which number should go in the square with the question mark?

Part 1: Overview of Number Puzzles

The Number Puzzles test requires the student to solve simple equations by choosing an answer that makes the numbers on both sides of the equal sign the same amount. To answer the questions in this test, the student must find the missing number that goes in the square with the question mark. This test measures understanding of mathematical identities.

In this test, students are asked to solve problems that look like this.

When practicing the Number Puzzles questions, encourage students to use these strategies:

Perform the necessary calculations to make both sides of the equal sign total the same amount in each row of the question.
Substitute numbers for shapes wherever possible. For example, in the above sample question, the second row shows that the diamond is equal to 5. The number 5 can replace the diamond in the top row.
Use scratch paper to keep track of each step in the solution.

Students at this level tend to make the following common mistakes:

Students may work from the top down rather than from the bottom up. Solving the simple identities in the second and third lines is necessary before one can solve the identity in the first line.
Students might use the wrong arithmetic operation. For example, the student may add numbers instead of subtracting them.
Students may solve the question for a shape other than the square with the question mark. For example, in the sample question above, the student might solve for the diamond and choose 5.

68 of 159

Each question has an equation with numbers on both sides of an equal sign.

You must decide which number goes in the box with the question mark.

Practice Question 1

69 of 159

The two sides of the equal sign must total the same amount.

Because the right side of the equal sign has only a 3, the numbers on the left side must also equal 3.

Practice Question 1

70 of 159

Circle your answer.

Practice Question 1

71 of 159

Which number goes in the box with the question mark?

This one has multiple steps. To figure out the answer, you need to substitute the diamond in the equation with its value.

Practice Question 2

72 of 159

To help figure out the answer, put the value of the diamond in place of the diamond.

Practice Question 2

5

73 of 159

Check your answer!

Practice Question 2

74 of 159

Which number goes in the box with the question mark?

This time, there are two steps to figure out the value of the diamond.

Practice Question 3

75 of 159

Replacing the diamond with its value will help you figure out the answer.

Practice Question 3

14

76 of 159

Check your answer!

Practice Question 3

77 of 159

Can you try this one on your own?

Remember to start at the bottom and figure out the value of the diamond first. Then you can substitute the value of the diamond to figure out what goes in the box with the question mark.

Practice Question 4

78 of 159

Which number goes in the box with the question mark?

Practice Question 4

4

79 of 159

Check your answer!

Practice Question 4

80 of 159

This one has two shapes to substitute for numbers.

Remember to start at the bottom. Use the circle to figure out the value of the diamond. Then you can figure out what number goes in the box with the question mark.

Practice Question 5

81 of 159

Substituting the circle with 5 allows us to determine the value of the diamond.

Practice Question 5

5

82 of 159

Then substituting the diamond with 17 allows us to figure out the answer.

Practice Question 5

5

17

83 of 159

Check your answer!

Practice Question 5

84 of 159

Can you try this one on your own?

Practice Question 6

Start at the bottom and figure out the values of the circle and diamond first.

85 of 159

Which number goes in the box with the question mark?

Practice Question 6

6

3

86 of 159

Check your answer!

Practice Question 6

87 of 159

Number Series

Which number should come next to continue the pattern?

Part 1: Overview of Number Series

The Number Series test requires the student to discover the pattern in a series of numbers and then infer the simplest logical extension of the pattern from the choices available. The questions in this subtest follow various kinds of patterns, so it is important to consider different patterns for each question. Students will be allowed to use scratch paper in the actual test.

In this test, students are asked to solve problems that look like this.

When practicing the Number Series questions, encourage students to use these strategies.

Look for repeating patterns in groups of adjacent numbers. If this is not successful, then look for patterns in every other number or every third number. For example, every other number in the series 4 3 5 4 6 increases by one.
Apply the rule to determine which number will come next in the series.
Eliminate answer choices that do not fit the rule.
If more than one rule applies, use the simplest rule to decide what comes next (in most cases, alternate rules lead to the same answer).

Students at this level tend to make the following common mistakes.

Students might use the wrong arithmetic operation. For example, the sample question above has a pattern that has two steps – first subtract1 then add 2. The student might confuse the two steps and add instead of subtract.
Students may try to use the same pattern for every question and not attempt to find a new pattern for each question.

88 of 159

Each question has numbers that form a pattern.

You must decide what number comes next to continue the pattern.

Practice Question 1

Part 2: Number Series Practice Test Script

The following script covers many issues that will help students do their best on the test. Read aloud the text printed in bold italics: these are directions to the students. Directions for you are in parentheses and should NOT be read aloud. Feel free to modify the script to ensure that students understand what they are supposed to do and how to do it.

(Make sure each student has a practice booklet. Then SAY:)

Open your test booklet to page 4.

(Check that all students have the correct page.)

In these questions, you must figure out what the pattern is for each series of numbers. Then choose the number that comes next in the pattern.

P1

Let’s do the first practice question together.

(Point to the top row of numbers as you SAY:)

Look at the series of numbers in the top row. What pattern do the numbers in the series follow?

(Encourage responses.)

89 of 159

What is the pattern?

Practice Question 1

+ 4 =

The pattern is to add 4 to each number. So what comes next?

90 of 159

Circle your answer.

Practice Question 1

91 of 159

Which number comes next?

What is the pattern here?

Practice Question 2

92 of 159

Check your answer!

Practice Question 2

93 of 159

Which number comes next?

What is the pattern here?

Practice Question 3

94 of 159

Check your answer!

Practice Question 3

95 of 159

Can you try this one on your own?

What is the pattern here?

Practice Question 4

96 of 159

Which number comes next?

If the pattern is confusing, try breaking it down into groups.

Practice Question 4

Which number will come next in the series?

(Encourage responses.)

How did you solve this question?

(Encourage responses. If there are students who don’t understand how to solve the question, go through the process as follows.)

Look at the first three numbers: 1, 2, 3. Then look at the next three numbers: 2, 4, 6. How do the numbers in each set of three go together?

(Encourage responses.)

The second number in each set is the first number multiplied by 2. In the first set, the second number is 2, which is the same as 1 multiplied by 2. In the second set, the second number is 4, which is the same as 2 multiplied by 2.

The third number in each set is the first number multiplied by 3. In the first set, the third number is 3, which is the same as 1 multiplied by 3. In the second set, the third number is 6, which is the same as 2 multiplied by 3.

The last number in the series is 3. Which number must come next to continue the pattern?

(Encourage responses.)

97 of 159

Check your answer!

Practice Question 4

98 of 159

This pattern is a little more complicated.

Look at the relationship between each two numbers. What pattern do you notice?

Practice Question 5

99 of 159

Numbers are added each time, but the numbers added are what make the pattern.

Which number should be added next?

Practice Question 5

+ 5 =

+ 4 =

+ 3 =

+ ?

100 of 159

Check your answer!

Practice Question 5

101 of 159

Can you try this one on your own?

Practice Question 6

What is the pattern here?

102 of 159

Which number comes next?

Practice Question 6

- 7 =

+ 6 =

- 5 =

- 4 =

+ 3 =

- 2 =

Which number will come next in the series?

(Encourage responses.)

How did you solve this question?

(Encourage responses. If there are students who don’t understand how to solve the question, go through the process as follows.)

Look at the top row of the question. What pattern do the numbers in the series follow?

(Encourage responses. Then point to the series and examine each successive pair of numbers. Write the operation that changes the first into the second in the space between them.)

In this series, sometimes the numbers increase and sometimes the numbers decrease. The first two numbers are 13 and 6. To go from 13 to 6, we subtract 7.

To go from 6 to 12, we add 6. Then, we subtract 5. To go from 7 to 3, we subtract 4. Then, we add 3. To go from 6 to 4, we subtract 2.

So the pattern is: subtract 7, add 6, subtract 5, then subtract 4, add 3, subtract 2.

The operation that we use to change numbers follows this pattern: subtract, add, subtract, (Pause), subtract, add, subtract, and so on. So which operation do we use next?

(Encourage responses.)

To continue the pattern, we must subtract. But how much should we subtract?

(Encourage responses.)

The amount by which the numbers change also follows a pattern. That pattern is: 7, 6, 5, 4, 3, 2, and so on. So, these numbers are decreasing by 1 every time.

In this problem, we have to use both patterns to find the next number. Which number will come next in the series?

(Encourage responses.)

103 of 159

Check your answer!

Practice Question 6

104 of 159

105 of 159

Nonverbal

04

Figure Matrices, Paper Folding, & Figure Classification

106 of 159

Figure Matrices

Which answer choice shows what would happen if the new arrow changed in the same way as the first arrow?

Part 1: Overview of Figure Matrices

An analogy draws parallels between objects or ideas, for example, “up is to down as left is to right.” Analogies can be about simple things “A tadpole is like a fish” or complex concepts “Friendships are like glass. Once broken, they are hard to fix.” Successful learners habitually reason by analogy. Good analogies allow them to use what they already know to understand or remember new ideas. Reasoning by analogy requires attending carefully to how two things are similar and then applying these relationships to something new.

The Figure Matrices test is like the Verbal Analogies and Number Analogies tests except the questions use figures or shapes rather than words or numbers.

In this test, students are asked to solve problems that look like this.

When practicing the Figure Matrices questions, encourage students to use these strategies:

Carefully examine the first two figures and think of a rule (and say it silently) that describes the relationships between them. For example, flip the first figure to get the second one.
Apply the rule to the third figure to determine the missing figure.
Test the rule on each answer choice, eliminating answer pictures that do not fit the rule.
Look for a more precise rule if more than one answer choice fits the rule.

Students at this level tend to make the following common mistakes:

Students may choose an answer choice that looks like the figure in the bottom row. For example, in the sample question above, students might select the first answer choice.
Students might infer the wrong relationship between the first two figures. Putting the rule into words will help them to be more precise.
Students may overlook or forget a critical feature of the figures in the top row. Using language to describe the rules will help them remember them.
Students might select an answer choice before checking all the answer choices.

107 of 159

Each question has three pictures and a question mark.

You must decide which answer choice goes where the question mark is.

Practice Question 1

108 of 159

Start by looking at the top two pictures.

The arrow between them means that they go together in some way.

Practice Question 1

109 of 159

Then look at the bottom row and the answer choices.

One of these will be connected to the first shape in the same way the shapes in the top row are connected.

Practice Question 1

110 of 159

Let’s look at each choice one at a time.

Think about how it relates to the first picture.

Practice Question 1

111 of 159

Circle your answer.

Practice Question 1

112 of 159

How do the first two pictures go together?

Which answer choice has the same relationship with the bottom picture?

Practice Question 2

P2

Let’s do the second practice question.

(Point to the large box as you SAY:)

The large box has two rows. We must decide which answer choice goes in the space with the question mark.

(Point to the top row as you SAY:)

Look at the top row of the large box. The first picture shows a white square and a dark square. The second picture shows a dark square and a white square.

How do these pictures go together?

(Encourage responses.)

The squares in the second picture are the same but are in the opposite order.

(Point to the bottom row as you SAY:)

The shapes in the bottom row must go together in the same way.

In the first picture we see a dark circle and a white circle. What shapes should go in the space with the question mark?

(Encourage students to say the rule. Then point to the answer choices as you SAY:)

Which answer choice shows that?

(Encourage responses.)

113 of 159

Check your answer!

Practice Question 2

114 of 159

How do the first two pictures go together?

Which answer choice has the same relationship with the bottom picture?

Practice Question 3

P3

Let’s do the third practice question.

(Point to the top row as you SAY:)

Look at the two shapes in the top row of the question. How do these shapes go together?

(Encourage responses.)

The second shape looks like the first one but with the middle cut out.

(Point to the bottom row of the question as you SAY:)

The two shapes in the bottom row of the question must go together in the same way.

Look at the dark square in the bottom row. How would the square look if we cut out the middle?

(Encourage responses. Then point to the answer choices as you SAY:)

Which answer choice shows that?

(Encourage responses. Then point to the second, fourth, and fifth answer choices as you SAY:)

These three answer choices have the middle cut out, so which do we choose? We need to find another rule so we can decide which answer choice is correct.

(Point back to the top row as you SAY:)

Do you notice anything else about the part that was cut out of this shape?

(Encourage responses.)

The part that was cut out is the same shape as the part that is still there. So which answer choice should we choose?

�(Encourage responses.)

115 of 159

Check your answer!

Practice Question 3

116 of 159

How do the first two pictures go together?

Which answer choice has the same relationship with the bottom picture?

Practice Question 4

P4

Let’s do the fourth practice question.

(Point to the top row of the question as you SAY:)

Look at the pictures in the top row. Both pictures show squares with hearts in three corners. How do these pictures go together?

(Encourage responses. Note that there are several different rules that would produce this change. For example, the single heart moves to the empty space. Or the single heart switches corners. Or the entire picture was flipped about the vertical axis.)

The second picture looks like the first one but it has been flipped over.

(Demonstrate with your hand. If necessary, draw 3 hearts on a transparent sheet and flip it. Then point to the bottom row as you SAY:)

The two pictures in the bottom row must go together in the same way. What would happen if we flipped the picture in the first box?

(Encourage responses. Then point to the answer choices as you SAY:)

Which answer choice shows that?

(Encourage responses.)

117 of 159

Check your answer!

Practice Question 4

118 of 159

Can you try this one on your own?

First determine the relationship between the top two pictures. Then examine the answer choices to figure out which choice has the same relationship with the bottom picture.

Practice Question 5

119 of 159

Which answer picture is correct?

Practice Question 5

120 of 159

Check your answer!

Practice Question 5

121 of 159

How do the first two pictures go together?

Which answer choice has the same relationship with the bottom picture?

Practice Question 6

P6

Let’s do the last practice question.

(Point to the top row as you SAY:)

Look at the boxes in the two pictures in the top row of the question. Each box is divided into four boxes with shapes inside. How are the pictures the same? How do they differ?

(Allow students time to study the pictures. Then encourage responses. Try to get students to focus on what changes and what stays the same between the two pictures.)

The second picture looks like the first except the square and triangle changed places inside the box. The diamond and the circle stayed in the same place.

(Point to the bottom row of the question as you SAY:)

The two pictures in the bottom row of the question must go together in the same way. So what shapes must stay the same?

(Encourage responses. Point to the two X’s as you SAY:)

The two X’s must stay in the same place in the answer. Which answer choices show this?

(Encourage responses.)

Only the second and fourth answer choices show the X’s in the same place. This tells us that the other answer choices cannot be correct. We do not need to look at them again.

What must happen to the other two shapes in the picture? Do you remember the rule?

(Encourage responses.)

Those shapes must switch places. Which answer choice shows this?

(Encourage responses.)

122 of 159

Check your answer!

Practice Question 6

123 of 159

Paper Folding

The paper is folded in half and a circle is cut out of it.

Which answer choice shows how the paper will look when it is unfolded?

Part 1: Overview of Paper Folding

The Paper Folding test requires that the student imagine what happens to a sheet of paper after it is folded and a piece is cut out of it. The first pictures show how the paper is folded. The student must understand how these pictures describe the folding of an actual piece of paper. Then a circle is cut through all the layers of paper at that point. The student must then reverse the process to infer how the piece of paper will look when it is unfolded. Logical thinking can assist in solving most questions. For example, if the paper is folded in half and a hole is cut through both layers, then the unfolded paper must have two holes.

This practice test is designed to teach students (a) how to imagine the correspondence between the pictures in the test booklet and the actual folding, cutting, and unfolding of a piece of paper and (b) how to use logical thinking to help them solve the problems. The practice session begins with demonstrations that use real paper to help explain the diagrams. Whenever students are confused by a question, it is helpful to ask them to solve the question using an actual piece of paper.

In this test, students are asked to solve problems that look like this.

When practicing the Paper Folding questions, encourage students to use these strategies:

Imagine how the cut-out will be reflected on the other side of the paper each time it is unfolded.
Use logical reasoning to say how many holes or cut-outs should be on the unfolded paper. For example, if the paper is folded once and a hole is cut in it, then there will be a hole in each layer of the paper. So there will be two holes in the unfolded paper.
Examine all of the answer choices before picking one.
When confused, model the problem using a square sheet of paper.

Students at this level tend to make the following common mistakes:

Students might select the first answer that looks right without considering other answers.
Students may ignore the angle of the fold. Diagonal folds can be particularly challenging for some students.
Students might forget to reason about the approximate location of the holes when unfolding the paper.
Students may ignore the number of holes that must appear on the answer. For example, in the sample question above, the student might forget that there were two layers of paper that were cut and select the second answer choice.

124 of 159

In these questions, an imaginary piece of paper is folded in half, cut, and then unfolded.

You must decide what the paper will look like when it is unfolded.

Practice Question 1

Part 2: Paper Folding Practice Test Script

The following script covers many issues that will help students do their best on the test. Read aloud the text printed in bold italics: these are directions to the students. Directions for you are in parentheses and should NOT be read aloud. Feel free to modify the script to ensure that students understand what they are supposed to do and how to do it.

(Find a SQUARE piece of paper and scissors. Crease the paper down the middle so it folds easily. Hold up the piece of paper as you SAY:)

Watch me fold this square piece of paper in half and cut a hole.

(Fold the paper in half and cut a hole in the location shown in the first practice question below.)

How will the paper look if I unfold it?

(Encourage responses. Then unfold the paper and show the students how it looks.)

(Make sure each student has a practice booklet. Then SAY:)

Open your practice booklet to page 3.

(Check that all students have the correct page.)

Each of these questions shows a piece of paper being folded. Then, a piece is cut out of the folded paper. You must imagine how the paper will look when it is unfolded.

P1

Let’s do the first practice question.

(Point to the pictures in the top row as you SAY:)

Look at the pictures in the top row. They show a square piece of paper folded in half, then a hole is cut through the paper. This is like what I just showed you.

What will the paper look like when we unfold it?

(Encourage responses.)

125 of 159

Remember the cut was made through both layers of paper.

The final picture shows what it looks like after the cut is finished.

Practice Question 1

126 of 159

Circle your answer.

Practice Question 1

127 of 159

What will the paper look like when it is unfolded?

Remember that the cut goes through both layers of paper.

Practice Question 2

128 of 159

Check your answer!

Practice Question 2

129 of 159

Can you try this one on your own?

How many times is the paper folded? So how many holes should there be?

Practice Question 3

130 of 159

What will the paper look like when it is unfolded?

Practice Question 3

131 of 159

Check your answer!

Practice Question 3

132 of 159

Can you try this one on your own?

How many times is the paper folded? So how many holes should there be?

Practice Question 4

133 of 159

What will the paper look like when it is unfolded?

Practice Question 4

What will the paper look like when we unfold it?

(Encourage responses.)

How did you solve this question?

(Encourage responses. If there are students who don’t understand how to solve the question, go through the process as follows.)

After two folds, the two holes are cut through four layers of paper, so the answer should have two holes on each of the four parts of the paper or eight holes.

The holes will flip over the fold each time we unfold the paper. What will the paper look like after we unfold it the first time? (Pause.) The paper will be folded in half like it is in the second picture in the top row.

Where will the holes be on this piece of paper that is folded in half? They will make the pattern shown in answer K, but on the half-sheet of paper.

Now imagine unfolding the paper a second time so that it makes a square again. Now what pattern will the holes make?

134 of 159

Check your answer!

Practice Question 4

135 of 159

Can you try this one on your own?

Practice Question 5

Look very carefully at the position of the fold. Some of the cuts will go through only one layer of paper, and some cuts will go through more than one layer.

136 of 159

What will the paper look like when it is unfolded?

Practice Question 5

137 of 159

Check your answer!

Practice Question 5

138 of 159

Can you try this one on your own?

Practice Question 6

The position of the fold makes this problem a little tricky. Which parts of the paper have multiple layers to cut through, and which do not?

139 of 159

What will the paper look like when it is unfolded?

Practice Question 6

140 of 159

Check your answer!

Practice Question 6

141 of 159

Figure Classification

How are these shapes like each other?

Which one of these shapes belongs in the same group?

Part 1: Overview of Figure Classification

The Figure Classification test requires the student to find the object that is most similar to three initial objects. Students must discover rules that describe how the objects are alike then test these rules until they find a set of rules that fit one and only one answer choice. Each question uses a new set of rules that create a novel problem, so during this practice test students should focus on learning general techniques for testing classification rules, not memorizing specific rules.

In this test, students will solve questions that look like this.

When practicing the Figure Classification questions, encourage students to use these strategies:

Think of (and say silently) a rule that describes the similarities among the first three pictures. For example, all of the shapes have stripes.
Test the rule on each answer choice, eliminating answers choices that do not fit the rule.
Look for a more precise rule if more than one answer choice fits the rule.

Students at this level tend to make the following common mistakes:

Students might overlook a critical feature of the first three pictures. For example, in the sample above, the student may notice the exterior shape, but ignore the shading.
Students may choose an answer based on only part of the first three pictures. For example, the student might select the first or third answer choice because it has the same shape as one of the first three pictures.
Students might select an answer choice before checking all the answer choices.

142 of 159

Each question has a group of pictures with something in common.

You must decide which answer picture on the right goes with the three objects on the left.

Practice Question 1

143 of 159

Start by looking at the pictures to the left of the line.

How are they like each other?

Practice Question 1

144 of 159

Then look at the answer choices on the right side of the line.

One of them will be similar to the shapes on the left.

Practice Question 1

145 of 159

Circle your answer.

Practice Question 1

146 of 159

How do the pictures on the left go together?

Which answer choice is most similar to the objects to the left of the line?

Practice Question 2

P2

Let’s do the second practice question.

(Point to the first three pictures as you SAY:)

Look at the first three pictures. How are these three pictures like each other?

(Encourage responses.)

All three have a square and a triangle inside.

Now look at the answer choices on the other side of the question.

(Point to the answer choices as you SAY:)

Which ones have a square and a triangle?

(Encourage responses. Then point to the first and third answer choices as you SAY:)

The first and third answer choices both have a square and a triangle. We need another rule to decide which one is correct.

(Point back to the first three pictures as you SAY:)

How else are the first three pictures the same?

(Encourage responses.)

The square and triangle are next to each other in all three pictures. So which answer choice should we choose?

147 of 159

Check your answer!

Practice Question 2

148 of 159

How do the pictures on the left go together?

Which answer choice is most similar to the objects to the left of the line?

Practice Question 3

P3

Let’s do the next practice question.

Look at the first three pictures. How are they like each other?

(Encourage responses.)

All three have a big shape in the middle and two small shapes that are the same: one on the top and one on the bottom.

Now look at the answer choices on the other side of the question.

(Point to the answer choices as you SAY:)

Which ones have a big shape in the middle and small shapes on the top and bottom?

(Encourage responses. Then point to the second, third, and fourth answer choices as you SAY:)

These three do. We need to find another rule to decide which answer choice is correct.

(Point back to the first three pictures as you SAY:)

How else are these three pictures the same?

(Encourage responses.)

The small shapes are the same shape as the big shape and they go the same direction as the big shape. Which answer choice shows this?

(Encourage responses.)

149 of 159

Check your answer!

Practice Question 3

150 of 159

Can you try this one on your own?

First determine what the three pictures on the left have in common. Then find the answer choice that follows the same rule.

Practice Question 4

151 of 159

Which answer picture goes with the first three shapes?

Practice Question 4

152 of 159

Check your answer!

Practice Question 4

153 of 159

Can you try this one on your own?

First determine what the three pictures on the left have in common. Then find the answer choice that follows the same rule.

Practice Question 5

154 of 159

Which answer picture goes with the first three shapes?

Practice Question 5

155 of 159

Check your answer!

Practice Question 5

156 of 159

Can you try this one on your own?

First determine what the three pictures on the left have in common. Then find the answer choice that follows the same rule.

Practice Question 6

157 of 159

Which answer picture goes with the first three pictures?

Practice Question 6

158 of 159

Check your answer!

Practice Question 6

159 of 159

You’re finished! Way to go!

If you have questions, please ask your teacher or your school’s Advanced Learning Teacher.