CogAT lessonsQuantitative Battery
CogAT number analogies
Two pairs of numbers, each turned into the next by the same rule, then a third number. Your child finds the rule and uses it on the third number.
What your child sees
Grade 4, a question like this one
[ 10 → 31 ] [ 4 → 13 ] [ 12 → ? ]
Find the rule that turns each first number into the second. Which number should replace the question mark?
- A37
- B36
- C33
- D38
- E112
Kindergarten to Grade 2, read aloud
Look at the boxes in the top row. Something changes from the first box to the second. Which box below shows the same change for the bottom row?
- A
- B
- C
Show the answer and whyHide the answer
Count each box in the top row
4, then 3.
Say the change
The second box has one fewer.
Count the bottom box
2. Make the same change.
Final answer
The box with 1.
Remember
Count the things in each top box, then say the change: one more, two fewer, the same.
Up to Grade 2 the numbers are groups of pictures to count, the directions are read aloud, and there are three choices.
Worked example
The same question, one step at a time.
- 1Look at the first pair: 10 becomes 31. Think of rules that could do that.
- 2Test each rule on the second pair: 4 becomes 13. Only "multiply by 3, then add 1" works for both.
- 3Use the same rule on 12.
- 4Final answer: 37.
Common traps
Every wrong choice is built from a mistake children really make.
Only the first step
From Grade 5 many rules take two steps, such as multiply by 3 and then add 1. Doing only the first step gives a choice that is close.
In the example: choice B (36).
Adding the gap
10 becomes 31 is a jump of 21, but adding 21 does not work on the second pair. Test every rule on both pairs.
In the example: choice C (33).
Using the rule twice
The rule turns the third number into the answer once. Using it again on the answer gives a much bigger choice.
In the example: choice E (112).
Where it is on the test
Number analogies is one of the three parts of the Quantitative Battery. Up to Grade 2 it is a picture version, read aloud with no time limit.
| Grade | Part | Questions | Time |
|---|---|---|---|
| Kindergarten (Level 5/6) | Number analogies | 14 | No time limit |
| Grade 1 (Level 7) | Number analogies | 16 | No time limit |
| Grade 2 (Level 8) | Number analogies | 18 | No time limit |
| Grade 3 (Level 9) | Number analogies | 18 | 10 minutes |
| Grade 4 (Level 10) | Number analogies | 18 | 10 minutes |
| Grade 5 (Level 11) | Number analogies | 18 | 10 minutes |
| Grade 6 (Level 12) | Number analogies | 18 | 10 minutes |
| Grade 7 (Level 13/14) | Number analogies | 18 | 10 minutes |
| Grade 8 (Level 13/14) | Number analogies | 18 | 10 minutes |
Counts and times are Riverside Insights’ published figures.
Try it
Ten free Quantitative Battery questions, new every time, with the score at the end. You will be asked to make a free account.
The other parts of the Quantitative Battery
CogAT® is a registered trademark of Riverside Assessments, LLC. Scholar Tests is not affiliated with or endorsed by Riverside Insights or any school district. Our practice questions are written by us in the style of the published CogAT question types; they are not real CogAT questions, and a practice score is not a CogAT score.