CogAT Grade 3 cheat sheet

Analogy format is A : B :: C : ?. The relationship between A and B must hold in the same direction and same category between C and the answer.

Common analogy bridges: category-to-member (fruit : apple), function (knife : cut), part-to-whole (wheel : car), opposite (hot : cold), degree (warm : hot), and worker-to-tool (painter : brush).

In a classification (odd-one-out) item, find the single shared property that three or four words have and one lacks; the lacking word is the answer. Test each word against a candidate rule before choosing.

Classification rules to test in order: same category (all are birds), same function, same part of speech, same number of syllables, or same word class such as all being verbs.

Sentence-completion items: read the whole sentence, predict a word for the blank before looking at options, then pick the option closest in meaning to your prediction.

Verbal opposites (antonyms) are graded by degree: choose the option that is truly opposite, not merely unrelated or a weaker version. 'Cold' is a better opposite of 'hot' than 'cool' is.

A word ladder or letter-pattern item uses alphabet position: A=1 through Z=26. Consecutive letters (+1), alternating (+2, -1), and reverse order (Z to A) are the most frequent patterns.

In verbal analogies, keep the grammatical form consistent: if A and B are both nouns, C and the answer should also be nouns. A shift in part of speech signals a wrong choice.

Number series: compute the difference between consecutive terms first. A constant difference means addition/subtraction; a constant ratio means multiplication/division.

Two-level series: if the first differences form their own pattern (e.g., +2, +3, +4), the rule is a growing difference, not a constant one.

Alternating series: if odd-positioned and even-positioned terms each follow separate rules, split the series into two sub-series before solving.

Number analogy (A : B :: C : ?): identify the operation linking A to B (e.g., x3, +7, square), then apply the same operation to C.

Equation balance: whatever operation is applied to one side of an equals sign must be applied to the other side. Use inverse operations to isolate the unknown.

Place-value rule: in a multi-digit number, each position is worth 10 times the position to its right (ones, tens, hundreds). Reading digits by place value solves many puzzle items.

Pattern rules with shapes and numbers: count sides, corners, or objects in each figure and look for a constant sum, constant product, or a sequence across figures.

Estimation check: before committing to an answer, round the numbers to the nearest ten and confirm the answer is in the right range. Answers far outside the estimate are wrong.

Figure analogy (A : B :: C : ?): describe exactly what changed from A to B (rotation, size, shading, added part, flipped), then apply that same change to C.

Rotation vs. reflection: a 90-degree rotation moves a shape to a new orientation; a reflection creates a mirror image. Check whether a distinctive feature (a notch, dot, or arrow) ends up on the same side or the opposite side.

Paper folding and punching: unfold step by step in reverse order. Each fold doubles the number of holes, and holes appear as mirror images across each fold line.

Figure classification: find the property shared by the majority of figures (number of sides, symmetry, open vs. closed, curved vs. straight lines, shading) and pick the figure that does not share it.

Series of figures: track one attribute at a time across the sequence (position, count, size, shading, orientation) and find which attribute changes in a repeating cycle.

Symmetry check: a line of symmetry divides a figure into two identical halves. A figure can have zero, one, or many lines of symmetry; count them to classify.

Matrix puzzles (3x3): examine each row and each column for a consistent rule (same shape appears once per row, or the third figure is a combination of the first two).

Embedded figures: a target shape hidden inside a larger drawing keeps its exact size and orientation; look for the same angles and side lengths, not a rotated or resized version.