Evidence: find the reason the passage gives
Learn to answer “why did the character do that?” questions with the reason the passage states, and to reject reasons that only sound sensible in real life.
Start sample lessonTACHS Course: Free Sample Lessons
Sample chapters from the full TACHS course, grouped by section. Each one teaches a question type and ends with a practice question.
Updated October 3, 2026
Reading
main idea · author’s purpose · factual and inferential comprehension · evaluation · vocabulary in context
Character motivation: explain the choice and the plan it replaced
Learn to explain why a character makes a choice by linking the goal, the problem and the detail the character notices, and use the same close reading for detail, inference and ending questions on a story.
Start sample lessonMain idea in a science passage: name the process and its limits
Learn to find the main idea of a how-it-works passage by labeling each paragraph, and to sort wrong choices into too narrow, too broad and contradicted.
Start sample lessonPersuasive passages: pin down exactly what the writer proposes
Learn to find the proposal in an argument passage, measure its exact size and limits, and use it to answer questions about objections, support, references and tone.
Start sample lessonFigurative language: what an image brings with it
Learn to read an image in a poem by asking what feeling or quality the comparison carries, checking it against the lines nearby, and using the same habit for small actions, contrasts and endings.
Start sample lessonSequence in directions: number the steps, then find the gap
Learn to answer order questions about a set of directions by numbering the steps and using two anchors, and to handle if-steps, purpose questions and pointing phrases in the same passage.
Start sample lessonComparing viewpoints: find the one question two speakers answer differently
Learn to sum up each speaker in a discussion, separate what they agree on from what they dispute, and read polite concessions without mistaking them for a change of mind.
Start sample lessonCharacter motivation: read the narration right after the wish
Learn to find why a character first wants something by reading the narration that follows the wish, and to connect that motive to the setting, the final action and the story's resolution.
Start sample lessonMain idea in an informational passage: find the point the facts serve
Learn to find the main idea of a fact-filled passage by locating the general statement the examples support, and to keep detail, term, comparison and main idea questions separate.
Start sample lessonDetails in a notice: match the rule to the exact question
Learn to find one specific rule in a notice full of times, places and requirements, and to read the small words like must, may, only and but that decide who a rule covers and what it allows.
Start sample lessonComparisons in a personal story: what the object gives the narrator
Learn to read a narrator's comparison by asking what the second thing provides and what the narrator is going through, then follow that comparison to the story's later scenes and central insight.
Start sample lessonAuthor's purpose: name the verb and the exact object
Learn to state a persuasive writer's purpose as a verb plus an exact object, use what the writer keeps to rule out extreme choices, and apply the writer's own rules to new examples.
Start sample lessonCause and effect: trace the chain back to its first link
Learn to follow a chain of causes in a science or engineering passage, pick the link the question asks about, and tell a cause from an analogy or a limit the writer adds.
Start sample lessonLinked images in a poem: name the family the words share
Learn to explain what a group of related images adds to a poem by naming the real things they describe and the family of ideas they come from, and to track how a speaker's understanding changes.
Start sample lessonCharacter motivation: what outweighs the easy choice
Learn to explain a choice that costs a character something by weighing the temptation against the commitment, and to read the gestures, setting details and ending that show which one wins.
Start sample lessonComparison passages: sort what is shared from what differs
Learn to answer questions about a passage that compares two things by sorting shared features from the one difference the writer stresses, and by checking both halves of every two-part choice.
Start sample lessonPurpose of a letter: find the request and keep its size
Learn to label the parts of a letter, find the request that is its main purpose, and avoid choices that make the request larger or harsher than the writer does.
Start sample lessonMain idea of an interview: find the thread in every answer
Learn to find the main idea of an interview by labeling each answer and stating the thread they share, and to spot choices that fit one exchange, take a creative topic literally or reverse the speaker.
Start sample lessonWords with several meanings: let the sentence choose
Learn to pick the meaning of a word with several definitions by checking the word's job in the sentence and testing each meaning in place, whether the choices come from a dictionary entry or a most-nearly-means question.
Start sample lessonTone: compare the size of the language with the size of the problem
Learn to name a writer's tone by comparing how big the language is with how big the problem is, and to tell when the joke is on the narrator.
Start sample lessonWritten Expression
passage organization · sentence revision · clarity and effective expression · standard English · line-error identification
Subject-verb agreement: find the real subject
Match every verb to its true subject, even when a phrase full of other nouns sits between them.
Start sample lessonParagraph openings: choose the sentence that covers it all
Pick a first sentence that announces what the whole paragraph is about and fits every sentence that follows.
Start sample lessonParagraph conclusions: end with what the paragraph showed
Choose a closing sentence that sums up what the paragraph actually showed, without adding a new cause, a bigger claim or a new topic.
Start sample lessonSupporting details: pick the fact that proves the point
Choose an added sentence that gives real support for a paragraph's main point, not just more information on the same topic.
Start sample lessonSentence insertion: find the gap where every clue fits
Place a new sentence by matching its clue words to the sentences around it, so it comes after what it refers to and before what it must precede.
Start sample lessonSentence order: match each event, then follow the steps
Put a list of events in the order a paragraph requires by matching each event to its sentence and asking what had to happen first.
Start sample lessonSentence deletion: cut the sentence with no job
Spot the one sentence that does not help a paragraph do its job, even when it mentions the same place, people or object.
Start sample lessonTransitions: name the link before you choose
Choose a transition by first deciding how two sentences connect: result, contrast, example, replacement, response to a problem or time.
Start sample lessonSentence combining: join without changing the facts
Merge two short sentences into one that keeps every fact, keeps each describing word on the right noun and adds no new meaning.
Start sample lessonClear pronouns: replace it, they or this with the exact noun
Work out exactly what a vague pronoun refers to and choose the replacement that makes the reference explicit.
Start sample lessonAgreement in error lines: check every subject and verb
Check each line for a subject and verb that disagree, including tricky singular words, and know when to choose No error.
Start sample lessonVerb tense: keep the timeline straight
Spot verbs that jump to the wrong time or use the wrong form, including had with the earlier past event and irregular forms like had gone.
Start sample lessonSentence boundaries: catch comma splices and fragments
Tell a complete sentence from a fragment, spot two sentences joined by only a comma, and check that semicolons have a complete thought on both sides.
Start sample lessonPossessives and apostrophes: show who owns what
Place the apostrophe correctly for one owner, several owners and plurals like children, and know when no apostrophe belongs at all.
Start sample lessonSpelling: check each word against its pattern
Use a handful of spelling patterns to catch a misspelled word in a set of lines, and to trust hard words that are spelled correctly.
Start sample lessonCapitalization: names get capitals, general words do not
Decide which words need capitals and which stay lowercase, including tricky pairs like north and the North or history and History 8.
Start sample lessonPronoun case: subject or object
Choose between subject pronouns like he and object pronouns like him, especially when the pronoun is paired with another name.
Start sample lessonModifiers: put the description next to what it describes
Keep describing phrases next to the words they describe, so each revision says what the writer means.
Start sample lessonParallel structure: keep matching items in the same form
Keep every item in a list, or in a pair like not only and but also, in the same grammatical form, and recognize a sentence that needs no change.
Start sample lessonMathematics
number sense and operations · algebraic patterns · data analysis · probability and statistics · geometry · measurement
Percent change: sale prices, increases and working backward
Learn to find a sale price, a percent increase or decrease, and an original price, using one idea: every percent is taken of a starting amount.
Start sample lessonFractions of what remains: multiply what is kept
Track an amount through two fraction changes, decide when to multiply and when to subtract, and work back to the starting amount.
Start sample lessonMoney with decimals: find the total, then the change
Find totals and change with dollars and cents, work back to an item's price from a receipt, compare pack prices and count how many items a budget buys.
Start sample lessonDiscount, then tax: chain the multipliers and undo them
Turn a discount and a tax into multipliers, combine them, and work backward to a starting price or a missing percent.
Start sample lessonThree-part ratios: find the value of one part
Use a three-part ratio to find any group's share, the total, or a new ratio, starting from whatever number the question gives.
Start sample lessonConstant rates: find the amount for one unit of time
Use a unit rate to find distances, times and amounts, including trips with stops, machines working together and average speed.
Start sample lessonTemperature changes: move along the number line
Track rises and falls through zero, find the size of a change, work back to a starting temperature, and use a steady hourly change.
Start sample lessonOrder of operations: exponents before products before sums
Evaluate expressions with exponents, products and negative bases in the right order, and spot the step where a wrong answer went off track.
Start sample lessonIdentical groups: use the greatest common factor
Recognize when a grouping question calls for the greatest common factor, find it, and tell it apart from fixed-contents questions where leftovers are allowed.
Start sample lessonTwo pricing plans: set the costs equal
Write each plan as a fixed fee plus a rate, find where two plans cost the same, and decide which plan is cheaper or how much one costs more.
Start sample lessonBudget limits: the greatest whole number that fits
Write a budget as an inequality, solve it, and round correctly, including fees, extra people, change and the greatest price.
Start sample lessonArithmetic sequences: the first term plus the steps
Find any term of an adding pattern, find which term has a given value, and work with two known terms, figure differences and short sums.
Start sample lessonMean questions: work with the total
Turn a mean into a total to find a missing value, add or remove a value, correct a mistake, or combine two groups.
Start sample lessonMedian: sort, count, then find the middle
Find the median of an odd or even set, see how adding or replacing a value changes it, and find a missing value from a known median.
Start sample lessonTwo draws without replacement: update the bag
Find the probability of two draws in a row when the first item is not put back, including one of each, at least one, and draws with replacement.
Start sample lessonScale drawings: multiply by the scale, then convert units
Use a map or drawing scale to find real lengths, drawing lengths and real areas, and convert between centimeters, meters and kilometers.
Start sample lessonPerimeter and area: solve for the sides first
Use a perimeter or area to find unknown side lengths, then the other measure, and count perimeter on a grid figure.
Start sample lessonArea of combined shapes: subtract or split
Find the area of shapes built from rectangles by subtracting a cut-out or splitting into pieces, including borders, joined tiles and missing side lengths.
Start sample lessonPacking cubes: count by edges, then multiply
Count how many cubes fit in a box by counting along each edge, handle leftover space, and work backward to a box size.
Start sample lessonAbility
figure matrices · paper folding · figure classification
Matrices: track a turning figure
Learn to measure how far a figure turns across a row and down a column, then use both turns to build the missing cell, dot included.
Start sample lessonMatrices: follow a dot that wraps
Learn to name a dot's square in its small grid, measure how it moves across and down the matrix, and wrap it around an edge without losing count.
Start sample lessonMatrices: combine dots by overlay
Learn to read a six-circle figure as a list of dark spots, confirm the overlay rule from a shared spot, and build the missing figure one position at a time.
Start sample lessonMatrices: dots that cancel
Learn the cancel rule, where a circle dark in both of the first two figures turns white, and build the missing figure one position at a time.
Start sample lessonMatrices: one of each, three ways
Learn to split each cell into shape, shading and dot count, solve each feature on its own, and reject choices that get two of three right.
Start sample lessonPaper folding: one vertical fold
Learn to unfold a single up-and-down crease by flipping each hole across it, keeping its height and its distance from the crease.
Start sample lessonPaper folding: one horizontal fold
Learn to unfold a single side-to-side crease by flipping each hole straight up or down across it, keeping its column and its distance from the crease.
Start sample lessonPaper folding: two folds, four holes
Learn to undo two perpendicular folds one at a time, last fold first, so a single punch becomes four holes placed by two mirror lines.
Start sample lessonPaper folding: two folds the same way
Learn to undo two parallel folds, the quarter-width crease first and the center crease second, so the four holes land at their true, uneven spacing.
Start sample lessonPaper folding: diagonal folds and layers
Learn to unfold a corner-to-corner crease by trading a hole's row and column, and to check how many layers a punch really goes through when a second fold covers only part of the paper.
Start sample lessonClassification: find the mirror line
Learn to find the mirror line the three examples share, then check every dot in a choice for a partner directly across that line.
Start sample lessonClassification: compare inside and outside counts
Learn to count the dots inside and outside each outline, test simple rules until one fits all three examples, and ignore the outline's shape.
Start sample lessonClassification: a dot on the crossing
Learn the two conditions these figures share, a true crossing and a dot exactly on it, and test both in every choice while ignoring length and angle.
Start sample lessonClassification: match each shape to its shading
Learn to find the shape-to-shading pairing that every example keeps, ignore the changing counts and positions, and check every symbol in a choice.
Start sample lessonClassification: link sides to dots
Learn to turn each example into a pair of numbers, sides and dots, find the fixed difference, and count the answer polygon's sides without slipping.
Start sample lesson