Figure Matrices Test

[Alexia Borson]

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In this post, we start with an overview of "Figure Matrix" question types. We also provide a sample question, accompanied by tips and strategies that student can use to perform successfully on "Figure Matrix" questions during the official CogAT exam.

The CogAT Form 7 levels reflect the age of the student taking the test, so, for example, Level 5/6 is taken by five and six year olds in Kindergarten, and Level 9 is taken by nine year olds in third grade (and so on). **However, we always recommend asking your school/school district which level of test is used for gifted or classroom assessments.

In the top row, there are two figures that go together in a certain way. They go together because the figure on the right is the same shape as the one on the left, but is a different color: black instead of white.

The subtests use geometric shapes and figures which have unlikely been seen by the students in their formal schooling. There is no reading required among the questions in the CogAT Nonverbal test. These three subtests are: Figure Matrices, Paper Folding, and Figure Classification. These three subtests combined make up the CogAT Nonverbal score.

Each question in this subsection portrays a 2 x 2 matrix. As in the Picture/Verbal Analogies in the CogAT Verbal Battery and the Number Analogies in the CogAT Quantitative Battery, the students must determine the relationship between the pictures in the two boxes in the top row and apply the same relationship in the bottom row. However, the Figure Matrices utilizes spatial forms. In all levels, students are presented with pictures in the matrices. This sub-test presents a relationship that is not always clear. Therefore, developing the skill to decipher the relationship is crucial to solve these types of questions. Below, you can see an example of two Figure Matrices questions from a Level 9 and Level 10 CogAT test:

The correct answer is B. In the above analogy, as you move across the rows, the figures rotate clockwise 90 degrees (1/4 of a circle). Additionally, the colors of the figures are inversed. Parts of the figure which are white become black and parts of the figure which are black become white. The answer will exhibit the above analogous properties.

Tip: It is sometimes helpful to look at one part of the figure. For example, look at the single square in the top analogy. Observe how it rotates 1/4 of a circle in a clockwise direction and changes colors from black to white.

In the left frame there is a circle with a vertical and a horizontal line inside. In the next frame (on the right), the circle shrinks and, in the center, overlaps the lines.

The same pattern should occur in the bottom row:

In the left frame, there is a diamond with two diagonal lines. In the next frame, the diamond should shrink and overlap the diagonal lines in the center of the frame.

Answer choice A is incorrect as the diamond is transparent and the lines can be seen.

For Level 5/6 - Level 8, students must determine how a piece of paper will look once folded. In Levels 9 and up, the questions may include hole punching and require students to determine how the paper will appear when it is unfolded. This sub-test measures the spatial capabilities of a student. The ability to unfold the paper and foresee the resulting image can be indicative of a strong analytical mind. Below, you can see two examples of a Paper Folding questions from the CogAT test:

The correct answer is C. First the paper was folded diagonally from the upper-left corner to the lower-right corner. Then it was folded again from the lower-left corner to the upper-right corner. Then three holes in different shapes were punched out. Therefore, when the paper is unfolded the holes will mirror each other across the diagonals of the page like this:

To solve this question look for the answer choices in which the holes do not mirror each other in the right way. Answer choices B and D can be eliminated in this way. Next, focus on the area of each remaining answer choice that appears in the rightmost frame of the question series (in this case the triangular area on the right side) and eliminate all choices that are different. Answer choice A can be eliminated as the circular hole is under the pentagon hole but should be above it. E can also be eliminated as the pentagon has been rotated. We are left with C as the only correct answer.

Like the Picture/Verbal Classification in the CogAT Verbal Battery, students are presented with three figures and the student is to select the answer choice that is supposed to be the fourth figure of the set by determining how the figures and shapes are similar. The idea is to develop the skill of recognizing patterns and applying them to make a smart choice. Below, you can see an example of two Figure Classification questions from the CogAT test:

The correct answer is A. In this question the three figures are all circles. The only answer choice that is a circle is A. The rest of the answers are all shapes that are different than the shapes in the question. Therefore, A is the correct answer.

In this blog, we will look deeper into the figure matrices section from the nonverbal battery. This subset requires children to analyze visual patterns and make logical deductions. In this area, the fourth graders are presented with a grid containing shapes, with one element missing. Their task is to identify the underlying pattern or relationship among the given shapes and choose the correct missing element from a set of options.

These figure analogies require the same thought processes as picture and number analogies. Still, in the CogAT Nonverbal Battery, students must identify relationships between spatial forms instead of dealing with verbal or quantitative concepts. By studying and identifying distinct points of relation between previous figures, students can assess possible answer choices.

Students must envision the outcome of folding a piece of paper, making cuts or hole punches in some manner, and then unfolding it. The testing.com website has a fun, animated game to help students with this subtest. This section consists of 10 questions and takes approximately 10 minutes to complete.

Sample Question- On the top row, you will see how a square piece of paper is folded sometimes once, sometimes more then once. Holes are then punched in the paper after it has been folded. Choose the answer in the second row that shows how the folded piece of paper would look after it is unfolded.

These questions require the same thought processes as picture classification, except instead of inferring relationships between pictures, students infer relationships between shapes and figures. They then must find the answer on the bottom that belongs with the group on top.

The Raven's Progressive Matrices (RPM) Test is a high-level, non-verbal assessment tool. Administered chiefly by Pearson, this abstract reasoning test is regarded as a reliable estimate of fluid intelligence (You might even see it referred to as Raven's IQ Test).

The questions in this Raven's assessment test include a 3X3 matrix. You must identify the pattern and select the missing element which completes the bottom right slot. We will start out with an easy example, and then move on to more challenging progressive matrices. The advanced progressive matrices will be interspersed with tips and insights on the Raven's progressive matrices test.

The positioning of the small black square inside the large square corresponds with the position of the figure in the matrix: All the figures in the leftmost column have their black square on the left, the middle column in the middle, and the right column on the right. All the figures in the top row have their squares on top, the middle row in the middle, and the bottom row at the bottom. The bottom-right figure should, therefore, have its black square at the bottom-right corner.

The third (rightmost) image in the first two rows is the result of adding a diagonal line pattern to the top half of the first images in those rows. Thus, the third image of the bottom row must also be the result of adding a diagonal line pattern to the top half of the first image in the bottom row.

Recurring patterns may include figures (such as circles, triangles, and rectangles), moving clockwise/anti-clockwise, the direction of lines, and changing colours (mostly black or white). For Raven's Assessments, there will usually be one recurring pattern along the rows and another along the columns.

The second image in each row is the result of moving the three shapes in the first image in each row closer together, and the third image in the first two rows is the result of placing the shapes from the first image in each row inside each other. Thus, the third image in the bottom row must have the shapes from the first image in the bottom row inside each other.

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