Grade 8 B.E.S.T. benchmarks

The first skill, classifying numbers, starts with one value and a reasoned verdict. It moves on to picking the only irrational value out of four, selecting every irrational value in a list, sorting values into Rational and Irrational columns, and a dropdown with three choices: an integer (a whole number, in FAST practice), rational but not an integer, or irrational. Harder items hide the answer behind a simplification (√11 · √11 is 11, and √121 + √9 is 14), ask which set of three numbers contains only irrationals, or quote a student's claim such as "√64 is rational" to judge.

The second skill, estimating and locating, asks which two consecutive integers a root lies between, what it rounds to, and which of four lettered points on a number line best shows it, including negative values such as −√41. Other items shade an interval on a number line and ask which roots belong in it, or show a student's worked estimate and ask for the step with the first error.

Wrong answers come from real mistakes: calling every radical irrational (or every one rational), taking 22/7 as exactly π, reading a repeating decimal as irrational, reading the radicand's digits as the value (√42 placed at 4.2), halving the radicand, and rounding a negative value toward zero. In FAST practice each wrong answer is tagged with the mistake it stands for, and a teacher's FAST practice report lists the mistakes a class makes most. A lint rule fails any reasoned item that does not give each verdict exactly two options.

In the plotting skill, students drag a point to √49 or to √16 + 5, pick which lettered point sits at √36, choose the best tenth-mark estimate for −√10, bracket √30 between two integers, and select the roots that fall in a shaded interval. A reverse item shows a plotted point that stands for √? and asks for the radicand.

The ordering skill asks for the correctly ordered list, fills ordered slots from dropdowns, matches each value to its rank, and plots a whole set in order. The comparing skill asks for the right symbol, the one true statement among four, the greatest or least value, and which range a radical falls in. Both skills include a student's worked ordering or claim to check, such as "√45 > 6.7", which is settled by squaring: 6.7² = 44.89, and 44.89 is less than 45.

Distractors follow real errors: comparing radicands instead of values (50 against 7 when the question is √50 against 7), reading √n as n/2, rounding π to 3, putting −√30 to the right of −5, confusing square and cube roots, and rounding an estimate the wrong way. FAST practice adds two-part items that compute and then compare, such as a 196-square-foot patio's side against a 15-foot board, or depth markers at −√34, −5.4 and ∛(−125) feet.

In the evaluating skill, students find values such as 13⁻², (3/5)⁻² and (−2)⁻³, combine like bases first (5⁻² · 5⁴, or 3⁴ ÷ 3⁷), pick out every expression in a set that equals 1, match expressions to values, and plot a value such as (−2)⁻¹ = −0.5 on a number line. When the prompt asks for a fraction, only a fraction scores: 0.125 is not accepted for 1/8.

In the rewriting skill, students choose the single power equal to 3² ÷ 3⁶, report the net exponent and the matching reciprocal in two dropdowns (6⁴ · 6⁻⁷ = 6⁻³ = 1/6³), select every expression equal to 4⁻², distribute a power over a product or quotient, and simplify chains such as (2³)² ÷ 2⁴. Both skills include a student's worked solution with one wrong step to find, and claims to judge, such as "2⁻⁴ < 0".

The distractors are the classic slips: turning a negative exponent into a negative number (13⁻² as −169), multiplying the base by the exponent (1/26), ignoring the negative sign (169), forgetting to flip a fraction, multiplying exponents that should be added, and treating 11⁰ as 0. Every practice, quiz and FAST question brings in a negative exponent, in the expression given or in the one the student produces, as FDOE's limit requires. FAST practice adds two-part items, such as combining a scale factor of 6² · 6⁻⁵ into one power and then giving its value.

In the converting skill, students write 4,500,000 as 4.5 × 10⁶ and 6.02 × 10⁵ as 602,000, repair an improper form such as 64 × 10⁴ by choosing a new coefficient and exponent, pick out the expressions that are proper scientific notation, select every form equal to a value, and plot a value such as 3.5 × 10¹ on a number line. A worked-solution item shows a student who wrote 7,100,000 as 71 × 10⁵ and asks where the first error is.

In the comparing skill, students find how many times larger 6 × 10⁸ is than 6 × 10⁵, then work with unequal coefficients and negative exponents, with sets where they first find the greatest and least, with matching, with estimates made by rounding each coefficient (a galaxy's stars against a star cluster's), and with the reverse question: which number is 4 × 10³ times as large as 1.5 × 10⁻²?

Wrong answers come from an exponent off by one, a coefficient outside 1 to 10 (45 × 10⁵), the wrong sign on the exponent for a small number, moving the decimal the wrong way, adding exponents when dividing, dividing the smaller number by the larger, subtracting the coefficients, and reporting only the difference of the exponents. FAST practice adds a typed answer in scientific notation for a 4.28-trillion-dollar valuation, a red blood cell 0.0000062 meters across, and an item where the student plots the exponent of the factor on a number line.

In the adding and subtracting skill, students start with matching exponents (3 × 10⁵ + 2 × 10⁵), then align a gap of one or two (6.8 × 10⁷ − 5 × 10⁵), pick the coefficient and exponent from dropdowns, match expressions to values, find a missing addend, and plot a sum on a number line scaled in units of 10⁴. When a sum appears in a story, the story says what it means: two legs of one trip, or a city's population plus its new residents.

In the multiplying and dividing skill, students find products and quotients such as (4 × 10³)(3 × 10³) = 1.2 × 10⁷, chain two operations, solve for a missing factor, select every expression equal to a target, and plot the exponent of a result on a number line. Both skills include worked solutions with one wrong step, and the adding skill also has claims to judge, such as "3 × 10⁵ + 2 × 10⁵ = 5 × 10¹⁰".

Distractors are the known slips: adding exponents when adding numbers, adding without aligning, keeping the smaller exponent, leaving 10.1 × 10⁵ unnormalized or shifting the exponent the wrong way when renormalizing, multiplying exponents in a product, and dividing in the wrong order. FAST practice adds two-part items that carry the first answer forward: a space probe's distance, then the same number as a standard numeral, or a reporter's "4,000 times as many people" claim checked against a computed 3 × 10³.

Most items are one step: the total mass of 3 × 10⁶ bacteria at 2 × 10⁻¹² grams each, the combined population of two towns, the number of seconds a coolant leak lasts. Harder items chain two operations, convert units (a marathon's 4.2 × 10⁴ meters into kilometers), or apply repeated growth (a colony of 2.5 × 10⁵ cells that doubles 3 times).

Other formats ask the student to select every true statement about two values (Miami-Dade County's 2.7 × 10⁶ people against a neighboring county's 8 × 10⁵), match labelled calculations to their values, find the two values whose product is a target, plot the result of a product or quotient (a season's total attendance) on a number line scaled in units of 10⁵, or find the first wrong step in a student's solution.

Distractors come from adding the coefficients in a product (5 × 10⁻⁶ for the bacteria), dropping the sign of an exponent, converting units in the wrong direction, forgetting to renormalize, reporting the full calculator display, and rounding away digits the measurements do support. FAST practice adds two-part items: a backup split across 6 × 10³ drives, then whether one drive can hold its share, and a wire measured to 2 significant figures, cut into pieces, then reported at the right precision.

The core item is one expression to evaluate, from 3² + √16 at the start to (−1/2)³ · 16 + √81 + 12 or (2/3)² · √81 − ∛(−125) at the top. Students type the value, pick it from four, or plot it on a number line. Other formats ask which expressions equal a target (2 · √16, √64 and 4² − 2 · √16 all equal 8), match expressions to values, find which of four expressions is greatest or least, and choose the values of two expressions from dropdown menus.

Word problems put the same arithmetic in a setting, such as a square garden with an area of 64 square feet and a border along all four sides, or a temperature that rises 3³ degrees and then falls 4 · √64 degrees. A worked-solution item shows a student who wrote −3² = 9 and asks for the first wrong step.

Distractors come from the order-of-operations slips students make: squaring a leading negative (−3² as 9 instead of −9), working left to right past a multiplication, reading √n as n/2, multiplying a coefficient into the radicand, dropping the sign of a negative cube root, and taking √(6² + 8²) as 6 + 8. Negative exponents appear too, as in 2⁻² · 12 + 1 and (−2)⁻³ · 16, with the slips of reading 2⁻² as −4 or as a negative number. FAST practice adds two-part items, such as evaluating a temperature model and then judging a claim that it predicts a rise.

The benchmark is practiced as two skills: organized lists and tables, and tree diagrams. Items ask how many outcomes the sample space has, which list is complete (the wrong lists miss an outcome, include one that cannot happen, or list one twice), and how many outcomes meet a condition: at least one tail, two different sections, a sum of 7. Tree items count end branches, and the hardest run the counting backward: a spinner spun twice gives 36 end branches, so how many sections does it have?

Four list-and-table items show the sample space as a table for the student to read (two of them with one cell left empty). The other lists and every tree are described in words ("organized in a table with Roll 1 as rows"), and the explanation writes out the whole sample space; no item draws a tree. Card items use small sets such as {A, K, Q, J} or letter cards (X, Y, Z), and some dice have 4 or 8 sides. Wrong answers come from adding the stage counts instead of multiplying, counting only the first stage, counting every branch segment instead of the end branches, merging outcomes that differ only in order, and leaving one favorable outcome out. Error-analysis items name the student's slip.

FAST practice adds a coin flipped six times, a table of two marble draws from five colors, a prize wheel spun twice, and multipart items that build a list and then test a claim about it.

Simple predictions multiply a probability by the number of trials: a wheel with two blue sections in six, spun 42 times. Compound predictions first find the probability of a two-part result (two red marbles, two spades, exactly one head in three flips) and then multiply by the number of times the experiment is repeated. Reverse items run it backward: about 9 bonus results on a spinner with 3 of its 20 sections marked, so about how many spins?

Select-all and matching items check several predictions from one setup (rain on about 7 of 28 days, no rain on about 21). Wrong answers are misconceptions, not near misses: using the probability that the event does not happen, assuming 1/2 for any two-way question, forgetting to scale by the number of trials, using one trial's probability for a two-part experiment, and reporting the favorable count as the prediction. Error-analysis items give a student's prediction and ask which of these produced it.

FAST practice adds a spinner built to model a player who makes 55% of her penalty kicks, a deck of 20 numbered cards with events matched to predicted counts, and five-flip experiments repeated 160 times.

Most items enumerate: list the sample space, count the favorable outcomes, and divide. Coins are flipped two to five times; dice, spinners, marbles and cards are used twice. Harder events include a product of 12 or a product that is a multiple of 5. Marble and card draws with replacement multiply the probability of each draw (neither of two draws yellow is 4/5 × 4/5), and "at least one" events use the complement, 1 minus the probability of none.

Select-all items have the student pick the favorable outcomes from a list, matching items pair events with probabilities, and ranking items ask which of four events is most or least likely. Error-analysis items give a student's answer and ask which mistake produced it: treating outcomes that differ only in order as one outcome, finding the probability that the event does not happen, using one flip's probability for the whole experiment, adding the outcomes of each stage instead of multiplying, or leaving a favorable outcome out. Answers are fractions, decimals or percents, and a typed answer must be in the form the stem asks for: "as a decimal" rejects the fraction, and "in simplest form" rejects an unsimplified fraction.

FAST practice adds a standard 52-card deck with an event of exactly one spade in two draws, five-flip coin experiments, an eight-sided die, answers given as percents and decimals, and a dropdown that builds a fraction in simplest form.

The easiest questions apply one law once, such as x³ · x⁴ or (x³)⁴, and ask for the simplified monomial or just its exponent. Middle questions bring in coefficients and negative exponents, such as 5p⁻⁴ · 4p¹⁰ or (2x⁴y)³. The hardest chain a power rule with a product or quotient, such as (2x³)² divided by 4x², or work backward to a missing exponent, as in xⁿ · x⁴ = x¹⁰. Students choose from four answers, type an exponent or coefficient, select every equivalent expression, or match expressions to their simplified forms. There are no figures: the benchmark is symbolic.

Wrong answers come from the rule mix-ups students actually make: multiplying the exponents in a product, adding them in a power of a power, keeping the larger exponent, leaving the coefficient alone in (2x⁴y)³, or multiplying the coefficient by the power instead of raising it. Error-analysis questions show a student's result, such as 8x¹⁵ for 2x³ · 4x⁵, and ask for the statement with the right verdict and the right rule. Every option states the result its own rule gives, and each verdict appears twice. The two "correct" options both reach the student's result: the student's own rule and a true but partial check when the student is wrong, or the right rule and a wrong rule that happens to agree when the student is right, as multiplying the exponents does for 3x² · 5x². A lint rule checks the two-per-verdict split, so the answer cannot be found by spotting the odd one out.

FAST practice adds two-part items that put the power rules in a setting: a square rug whose side is x⁷, a cube whose edge is 3p⁴, a prism whose height is 4u⁻². Part A asks for the simplified power and Part B uses it, for example to compare the rug's area with a second rug's. FDOE lists this benchmark as a mathematical context only, so these settings go beyond the FAST's format.

Most questions ask for the product directly: pick it from four choices, type one coefficient of the result (the b in ax² + bx), or fill in each term. Difficulty climbs from a whole number times a binomial, such as 5(3x + 4), to a monomial with x that produces an x² term, such as 3x(2x − 7), to fraction and decimal factors such as (2/3)x(12x − 9). Other questions ask students to select every expression equal to a product, match products to their expanded forms (two products on each board share a sign pattern, so the signs alone never place them), or distribute and then combine like terms, as in 6(x − 4) + 3x.

Distractors come from the slips students make with the distributive property: multiplying only the first term (4x + 3 for 4(x + 3)), adding instead of multiplying (6x + 13 for the area of a 6 by x + 7 rectangle), losing a sign on one term, and writing x · x as x instead of x². Error-analysis questions show a student's product, such as −2x² + 14x for −2x(x + 7), and ask which statement describes the mistake. An error choice appears only when that slip is possible for the expression shown, so a sign-error option never shows up for a product with no negatives. There are no figures on this benchmark.

FAST practice keeps the same product forms and adds area settings, such as a patio 3x feet wide and 4x − 2.5 feet long with a 1-foot strip along one 3x-foot side set aside for a drain, plus a reverse item: the product is −5x² + 30x, and the student finds the monomial that was multiplied by (x − 6). FDOE lists this benchmark as a mathematical context only, so these settings go beyond the FAST's format.

Questions build from finding the greatest common factor of the two terms, to writing the factored form, to checking factorings someone else wrote. Students pick the factored form from four choices, type it, fill in the factor and the two terms, select every product that multiplies back to the expression, select the expressions whose greatest common factor is exactly a given value, or match expressions to factored forms. Difficulty climbs from whole-number factors (6x + 9), to factors that include a power of x (36x³ + 48x² as 12x²(3x + 4)), to negative leading terms and fraction coefficients such as (3/2)x² + (1/2)x. Some questions use an area: a patio of x² + 5x square feet with one side x feet long, and the student finds the other side.

Wrong answers follow the classic mistakes: factoring out a common factor that is not the greatest, dividing only one term by the factor (3(2x + 9) for 6x + 9), subtracting the factor instead of dividing, dividing the coefficients but not the powers of x, and a sign error inside the parentheses. Error-analysis items describe these slips in words, and an error choice is offered only when it could actually happen for that expression.

A few questions ask only for the greatest common factor of the two terms, typed as a number or a monomial, such as 4 for 8x + 20 or 9x² for 27x⁴ + 45x². FAST practice follows the same range and adds a fundraiser's revenue expression to factor and a question about whether 4x(10x + 6) is completely factored. FDOE lists this benchmark as a mathematical context only, so these settings go beyond the FAST's format. Every question on this benchmark uses the single variable x.

Most questions give an equation and ask for x, typed, chosen from four values, or plotted on a number line. Difficulty grows with the moves needed: a product and a constant, as in 4 + 2(x − 3) = 18, then like terms or a fraction to clear, then variables on both sides with fractions, such as (1/2)x + 3 = (1/4)x + 7. Other questions turn the task around: pick the equation whose solution is x = −2, select the valid steps for solving 2(3x − 3) = −12, or find the constant c that makes 3(x + 2) + 2x = 5x + c true for every x.

For solution counts, students classify single equations, sort sets into one solution, no solution and infinitely many, and choose a reason, such as "no solution, because the x-terms cancel and leave 6 = 3, which is false." In the plain how-many questions the choices are no solution, infinitely many solutions and two "exactly one solution" choices with different values of x. How an equation looks does not give its count away: some with a product on each side have no solution, and some with like terms to combine have exactly one.

Distractors come from the usual slips: distributing to the first term only, moving a constant without changing its sign, adding the x-term from the other side instead of subtracting it, and subtracting the coefficient instead of dividing by it. Error-analysis questions show a student's numbered steps and ask for the first wrong step or the description of the slip.

FAST practice adds two-part items built on two plans that reach the same value: a climbing-gym season pass against a punch card, one tank filling while another drains, and two plans for 3D-printer time with decimal hourly rates. Part A solves the given equation for where they match and Part B uses it.

Students solve and state the solution, type the boundary value, test which listed values make the inequality true, and judge statements about the solution: did the symbol flip, is the circle open or closed, which way does the graph shade. The symbol flips in some of those items and not in others. Graphing items give an empty number line where the student places the boundary, sets the circle open or closed and shades a direction, and all three must be right. Other items run the other way: a graph is shown and the student picks the inequality it solves. Number lines follow our grid design rules (tick limits, the boundary on a tick, boundaries placed at different spots along the line), which the content lint checks.

Difficulty climbs from a positive coefficient, such as 2x + 3 > 11, to a negative one that forces the flip, such as −3x − 4 < 11, to fraction and decimal coefficients such as −(3/4)x + 2 > −7.

Wrong answers are the errors the benchmark is built to catch: keeping the symbol when dividing by a negative, reversing it when dividing by a positive, switching between strict and inclusive, moving the constant the wrong way, and distributing to only the first term. Error-analysis questions give a student's answer, such as x < −3 for −2x + 5 > 1, and ask which slip produced it. In a story, no choice uses a negative number of hours, days or items.

Both banks use settings, such as a phone plan or a cooling freezer, and FAST practice adds two-part items where Part A finds the boundary and Part B describes the graph or decides whether a value fits, such as whether 24 half hours of parking stays within a 28-dollar limit.

Students solve x² = p and x³ = q directly, choosing or typing the solutions, and some questions plot the solution on a number line. Square questions ask for every real solution, or for the positive or the negative one; cube questions stress the single real root, including negative cubes such as x³ = −64. Harder questions run the idea backward (which equation has the solutions ±13?), judge claims about how many solutions there are, or match values to their roots, with one extra root that fits no row so that sorting by size does not finish the match. Word versions state the equation in a sentence ("when a number is cubed, the result is −64") or use the area of a square or the volume of a cube, where only the positive root makes sense as a length, and some then ask for the perimeter.

Distractors target the mistakes students make: giving only the positive root of x² = 49, halving instead of taking a square root (±24.5 for x² = 49), dividing by 3 instead of taking a cube root (9 for x³ = 27), giving ±5 for x³ = −125, and writing √144 = ±12, which mixes up the two solutions of x² = 144 with the square root symbol, which names only the positive root.

FAST practice adds two-part items in settings: the side of a square patio and then the edging around it, the side of a square mural panel, and a sandbox whose area is 9 times larger, where a classmate claims the side is 9 times longer too.

Students pick the pair that solves the system from four candidates, often framed as four students each naming an answer; answer Yes or No for each equation and then conclude; select the true statements about pairs and equations; or sort pairs into "only the first equation", "only the second", "both" and "neither". Harder items use fraction slopes and negative coordinates, or list four pairs and ask the student to type one coordinate of the pair that solves the system. Every equation, in every question, is in slope-intercept form, as on the FAST. A few grid items ask the student to test four listed pairs and plot the one that solves the system.

The main distractor is a pair that fits one equation only. Reasoned questions add the claim a student makes after checking one equation ("(3, −3) is a solution because it makes y = 2x − 9 true") and ask for the right verdict and reason. Every such item offers the same four choices, whether the claim is right or wrong: correct because the pair makes both equations true, correct because it makes the tested equation true, incorrect because it misses the other equation, and incorrect because it misses the tested one. Every student-claim item offers the same four choices, whether the claim is right or wrong: correct because the pair makes both equations true, correct because it makes the tested equation true, incorrect because it misses the other equation, and incorrect because it misses the tested one. Practice and quiz questions do not ask students to solve a system from scratch; solving by graphing is MA.8.AR.4.3.

FAST practice adds settings, such as two vendors' prices for custom buttons, two kayak shops' fees and two water tanks, one draining and one filling, and two-part items that substitute a value into one equation and then judge the pair against the whole system. FDOE lists this benchmark as a mathematical context only, so these settings go beyond the FAST's format.

Graph questions draw both lines on a coordinate plane and ask for the number of solutions, sometimes naming the equations and sometimes showing the graph alone. Every multiple-choice count question whose choices carry no reason offers the same four: no solution, infinitely many, one solution at a y-intercept, and one solution at a point off the y-axis. When the lines cross, the key names the crossing, always a grid point, so the student has to find where the lines meet, not just whether they do.

Symbol questions compare slopes and intercepts: select every system with a given count, sort four systems into the three counts, or build a system, such as finding b so that y = 3x + b and y = 3x − 7 are the same line, or reading one line off a graph and finding the slope or y-intercept the other line needs. Reasoned questions give a student's claim, such as infinitely many solutions because both lines cross the y-axis at the same point, and ask for the right verdict and reason. Their four choices cross the two verdicts with two facts that are both true of the graph: one about the slopes, which decides the count, and one about the y-intercepts, which does not. Their choices pair each verdict with a true slope fact, which decides the count, or a true intercept fact, which does not.

Distractors come from the usual confusions: any two lines must cross, equal slopes mean the same line, comparing intercepts instead of slopes, and reading a y-intercept as the solution.

FAST practice adds a parallel pair on a graph, a line given only as a graph beside an equation that writes the same slope as a decimal, two lines that only meet off the edge of the graph, and two-part items such as two tanks draining at the same rate from different amounts, where Part A writes one tank's equation and Part B gives the count and what it means. FDOE lists this benchmark as a mathematical context only, so these settings go beyond the FAST's format.

Graph-and-solve items give an empty plane and two equations, such as y = x + 1 and y = −x + 5, and the student draws both lines. Most choice and typed items come with a blank graphing workspace beside the equations. Read-the-graph items show both lines drawn and ask for the solution or one coordinate. Settings include two plants growing, two tanks filling or draining, and two gym memberships.

Special systems appear too: parallel lines with no solution, and two equations for the same line with infinitely many, decided by comparing slopes and intercepts. Same-line pairs write the slope as a fraction in one equation and a decimal in the other, such as 3/2 and 1.5, never as a scaled equation, and some parallel pairs mix notations too. Other items select true statements or match systems to solutions.

Wrong answers come from careless graph reading: the coordinates switched, (7, 3) for (3, 7); a point on only one of the lines; a y-intercept taken as the crossing; a coordinate with the wrong sign. Error-analysis items mark a student's point on the drawn system and ask which slip it shows; exactly one statement fits the marked point. Explanations, bank and FAST, solve by graphing: draw each line from its intercept and slope, read the crossing, check it in both equations. Two practice and quiz questions cross between gridlines, at (4/3, 8/3) and (4/3, 11/3), and ask for the closest ordered pair to the tenth; the rounded grid point is a wrong choice.

FAST practice adds a crossing near (1.7, 4.3), with the grid point (2, 4) as a trap, and two-part items: two plants reaching the same height, two camera rentals, and two gym plans whose lines cross at a negative number of months, which the student has to interpret.

Graph items draw the line and mark the y-intercept and one more point, sometimes unlabeled so students read the coordinates from the grid. The hardest items in this skill drop the graph and give two points that are not on the y-axis. Table items show a linear table, sometimes without an x = 0 row. Description items state a starting amount and a rate, such as a 100-gallon tank that loses 4 gallons per hour, and name both variables. Students choose the equation from four, type it, fill in m and b, select true statements about a line, or match tables, lines and descriptions to equations. When lines or descriptions are matched to equations, the numbers alone do not decide the match: the lines share one y-intercept, or two descriptions use the same two numbers in swapped roles, such as 3x + 15 beside 15x + 3.

Every question states that the relationship is linear, as FDOE requires of its descriptions. Distractors come from real slips: they swap the slope and the intercept (y = 25x + 8 for a 25-dollar joining fee plus 8 dollars a month), flip the sign of a decreasing rate, use run over rise, or take the y-value of a row other than x = 0 as b. Error-analysis questions show a student's equation and ask which of these went wrong.

Typed equations accept equivalent spellings, such as (3/4)x, 3/4x and 0.75x. A check confirms that every accepted spelling equals the key, and every one is run through the real grader. A slope typed as a fraction in simplest form must be in simplest form.

FAST practice adds two-part items where Part A writes the equation and Part B uses it: a savings jar after 7 weeks, whether a draining tank is empty after 16 hours, and a drone's altitude given at minutes 4 and 10, where b has to be worked back.

Graph questions draw the line on a coordinate plane with two marked points. Some label the points; others leave them unlabeled, and the student reads the coordinates off the grid. Table questions give a linear table in a setting, such as a savings balance by week, and two-point questions give the points in words. Written descriptions state a rate as "7 kilometers each hour", "every 3 weeks" or "from 68 degrees to 44 degrees over 12 hours". Answers are typed, chosen from four, built in dropdowns (rise, run, slope), or plotted: given a slope and one point, the student plots a second point on the line.

Difficulty climbs from whole-number slopes to negative and fractional ones, then to reverse problems such as finding k when the line through (3, k) and (7, 18) has slope 2. Slope-triangle questions draw two triangles on one line and ask either why they give the same slope (the triangles are similar) or which calculation shows it, using the rise and run read off each triangle.

Distractors come from real slips, such as the reciprocal (run over rise), the opposite sign, the rise alone without dividing by the run, and subtracting the coordinates in opposite orders. Error-analysis questions show a student's slope work and ask which of these went wrong. A lint rule flags any wrong choice equal in value to the key, such as 0.75 beside 3/4, and a slope the stem asks for in simplest form is graded in simplest form.

FAST practice puts half its graphs in settings (a savings account, a burning candle, a draining aquarium) and adds two-part items that find a rate from a description and then interpret it or judge a claim, such as a pump that moves 30 liters every 4 minutes where a classmate says the slope is 30.

The core items give an empty coordinate plane and ask the student to draw the line with the line tool: from an equation such as y = −(3/4)x + 5, from a table, or from a situation such as a fuel tank that holds 16 gallons while the engine uses 3 gallons every 2 hours. They are graded on slope and intercept, so any two correct points count. Windows keep both axes in view and stay within our grid design rules, which the content lint checks.

Other items break the graphing move into steps: find the y-intercept point (and not confuse (0, 5) with (5, 0)), step the slope from (0, b) to the next lattice point, decide which points lie on the line, or choose the description that matches a table, such as plotting (0, 2) and then going up 3 and right 1. Some ask for the x-intercept or for y at a given x. Difficulty climbs from whole-number slopes to fractions and negative intercepts, and to tables that start away from x = 0.

Wrong answers and wrong graphs come from real slips, such as plotting the intercept on the x-axis, reading the slope as the intercept, swapping rise and run, and stepping the wrong way for a negative slope. Error-analysis items draw a student's incorrect graph and ask what went wrong.

FAST practice adds lettered candidate points for the y-intercept on a drawn plane, an error-analysis graph of y = −(5/2)x + 9 stepped down 2 and right 5, and two-part items such as a water cooler that loses 6 liters every 4 days, where the student finds the slope and then judges a classmate's graphing move.

Most questions give a model such as g = −6t + 50, with each variable defined (g is gallons of water left, t is minutes), and ask what −6 or 50 means. Answers are chosen from four statements, picked in a dropdown, typed as a number, matched, or selected from a list of true interpretations. Typed questions ask for a quantity in the setting, such as the gallons in a tank when it started filling or by how many centimeters the snow depth changes each hour. Tables and graphs appear too: students compute the rate from two readings, or find the starting value from a table that does not show the start by working back from the rate. Line-of-fit questions give the fitted equation, and some also show the scatter plot with its trend line. Conversion questions use F = (9/5)C + 32 or F = 1.8C + 32, the reverse (Celsius from Fahrenheit) and kelvins.

Difficulty climbs from reading a coefficient to computing a rate from a table or graph, using the slope over an interval (how much a plant's height changes over 4 days), comparing two plans' rates, and working a starting value back from a later reading.

Distractors are the slips students make, such as the slope read as the starting amount and the intercept read as a rate, the direction of change reversed, the rate not multiplied over an interval, rise and run switched, and the x-intercept read as the starting value. Claim questions give a student's interpretation, such as "the tank fills 8 gallons each minute" for g = 5t + 8, and ask for the right verdict with the right reason.

FAST practice adds two-part items that find a rate and then use or judge it: a savings table, a sunflower measured at weeks 2 and 8, and a technician who says a tank drops 4 centimeters a minute when the table shows 14 centimeters every 4 minutes.

In the function skill, students judge a single relation with a reasoned verdict, apply the vertical line test to plotted points and curves (a circle among them), select the ordered pairs that break the rule, and sort several relations into functions and non-functions. Constraint items ask which output keeps {(2, 7), (5, 3), (2, a)} a function, or for the smallest whole number that can be a new input. Claims to judge include "not a function, because the output 8 appears more than once."

In the domain and range skill, students list the domain and range of a set, table or mapping, find the greatest range value or count the distinct ones, write the domain and range of a graphed segment, ray or V-shaped graph as inequalities, find the range of a graph that rises and then falls, check statements about a ray, match relations to their domains, and use a rule such as y = 2x + 1 to move between domain and range.

Distractors follow real confusions: calling a repeated output a violation, missing the repeated input, calling a circle a function because it is one connected curve, swapping domain and range, listing a repeated value twice, listing every number in the relation as both, flipping ≤ and <, and reading a range from the two ends of a graph instead of its lowest or highest point. FAST practice adds two-part items: find the one output that keeps a relation a function and then say why, or find the fewest pairs to remove when one input has three different outputs.

In the graph skill, students judge a plotted graph with a reasoned verdict (a straight line, a curve, a corner, a horizontal line), match descriptions of graphs to Linear or Nonlinear, pick every table that could be linear, pick true statements about a linear graph (such as which way it runs from left to right), and judge claims such as "not linear, because it does not pass through the origin." In the equation skill, they judge equations such as y = 3x + 7 and y = 4 · 3ˣ + 5, pick the linear ones from a list that includes y = x², y = 8/x and y = 5, and match each equation to its reason ("x is in a denominator").

In the table skill, students diagnose a table, pick every table that could be linear, find the row that breaks the constant rate, and complete a dropdown argument: two rates, then a verdict. Other items find the one plotted point that keeps a graph from being linear, count the linear equations in a list that includes a standard-form equation such as 4x + 2y = 10, or enter the input of the one table row whose output breaks a constant rate.

Distractors come from believing a line must pass through the origin or must rise, rejecting a horizontal line, calling a V-shaped graph linear, reading 4 · 3ˣ + 5 as slope 4 and intercept 5, comparing output changes without checking the input steps, checking only the first pair of rows, and missing a repeated input. FAST practice adds two-part items: count the different rates of change between consecutive rows, then say whether the table could be linear and why (a food drive's cans, the seats left during ticket sales, and a bricklaying table with a proposed new row).

Questions present the relationship four ways. Equations range from y = 4x to forms that must be rearranged first, such as 2y = 6x or y − 6 = 2x. Tables ask the student to compute y/x for each row. Graphs show the line on a coordinate plane, and the student checks where it crosses the y-axis. Written situations, such as a taxi with a 3-dollar flat fee plus 2 dollars per mile, turn on whether there is a starting amount. Students answer with a reasoned choice, select every proportional equation from a list, sort equations into proportional and not proportional, or complete a sentence with dropdowns.

Some questions add a computation, and the typed answer carries the verdict: the student decides whether the relationship is proportional, then enters its constant of proportionality k if it is or its y-intercept b if it is not, from a table or from an equation to rearrange, such as 3y = 5x + 6. Others ask for the value of b that makes y = 18x + b proportional, or solve for k in y = kx + (k − 3). Every yes-or-no item offers two options for each verdict, each with a reason, so the answer cannot be found by spotting the odd verdict out; a lint rule checks that split. There are no graphing tasks here, since drawing a line belongs to MA.8.AR.3.4.

FAST practice follows the same mix and adds a comparison across forms (an equation against a list of points) and a situation where a capacity, a truck that holds 850 pounds, is the distractor rather than a starting value.

Most items show a real-world graph with labeled axes, such as the water in a tank, a hiker's elevation or the line at a food truck. Students say whether a quantity is increasing, decreasing or constant, find when it stops increasing or how many hours in all it decreases, choose the description that tells the story in order, and match each part of a story or each interval to its behavior. A few items use a smooth curve, such as a kite's height or a tossed ball's height, and ask where it rises or falls.

Claim items quote a student's reasoning to judge, such as "increasing on this interval, because the graph is at its highest there" or "she stopped walking, because the graph goes down." Sketch items turn a story (a candle burning down, a tank that fills, holds and drains, a drone that climbs and hovers) into its graph.

Distractors come from reading the highest part of a graph as increasing, reading a falling distance-from-home graph as standing still, reading a flat piece as decreasing, merging two intervals across a turn, reading the graph right to left, and counting the intervals instead of adding their lengths. FAST practice adds items such as counting how many separate times a hiker's elevation rises. Every interval, in the questions and in the explanations, is named in words or by its endpoints on the graph, never with an inequality.

The benchmark is practiced as two skills, constructing scatter plots and constructing line graphs. The hands-on items give the data as a list or a table and have the student plot the points on an interactive coordinate grid: plant height by day, a used car's age and price, a reservoir's weekly level with values below zero. Around them sit the construction decisions: which variable goes on which axis, which ordered pair a row of a table produces, how many points the plot needs, and which start value and tick spacing fit the data on a grid of a given size.

Other items judge a finished display: a scatter plot with one point plotted with its coordinates reversed, a student's plot that may have its axes swapped or its points joined, and a student's line graph with mistakes to find, such as the days running right to left. Line-graph items also read the display, finding the change from one time to the next or the coldest day. Wrong answers come from swapping x and y, joining scatter-plot points in order, a scale that cuts off data or leaves most of the grid empty, and treating a category such as genre as a number.

A few older items practice skills next to construction rather than construction itself, such as naming the quadrant a point falls in or reading a value from a steady change; they stay until a later wave replaces them. FAST practice adds multipart line-graph items, such as a class's running total of books read and a club balance that starts below zero.

The benchmark is practiced as two skills, describing the association and identifying outliers. Every item shows a scatter plot in a real-world context. Describing items ask for its direction and form by choosing a combined label, filling menus, selecting words, choosing the statements the plot supports, or marking statements about it true or false. No item asks the student to judge strength (strong, moderate or weak), which the FAST will not ask either.

Outlier items ask students to pick the outlier, say whether there is one and how many there are, decide whether the most extreme point is the outlier, mark which of several points on a plot are outliers, and reason about removing one: which association the other points show, how the mean of y changes, how the slope of the line of best fit changes. Wrong answers come from reading a falling trend as positive, calling a curve linear, calling a clear trend no association, and picking the point with the greatest x or y as the outlier.

The generators draw each plot from its keyed answer and then check it, and refuse to build an item that fails: a plot keyed as a linear association has to measure a correlation of at least 0.9 while its points stay visibly scattered, so it cannot be read as no association; a plot keyed as no association has to measure at most 0.2. Every keyed outlier sits far from the pattern of the other points. FAST practice adds multipart items (find the outlier, then say why it is one) and a select-all with two outliers.

The judging items show a scatter plot with a line a student drew and ask whether it is a good line of fit, with the reasons students actually give: it passes through the first and last points, it touches every point, or it has about as many points on each side. Other items ask how a student's line should move (up, down, steeper or flatter) to fit better, what sign the slope of the fitted line has, and which points lie above or below a given line.

A second group works with a line of fit once it exists: interpret its slope and y-intercept in context (a used car's predicted price falls by about 1,200 dollars per year of age), predict a value from its equation, read a value off a drawn line of fit, or find the x that gives a predicted y. No item asks the student to write or determine the equation of a line of fit. Besides the line-of-fit grid items, other grid items plot the point a given line predicts.

Wrong answers come from requiring the line to pass through the endpoints or every point, reading a falling trend as a positive slope, moving a line the wrong way, reading a slope as a starting value, reading the line at the wrong place, and reading a plotted point instead of the line. FAST practice uses the same forms and adds a comparison of two students' lines for one plot.

The benchmark is practiced as three skills: finding the hypotenuse, finding a missing leg, and solving real-world problems (a ladder against a wall, a kite string, a drone tether, a ramp, the diagonal of a screen or a garden). Early items show the triangle with its known sides labeled and ask for one length. Harder items give a leg as two segments laid end to end, ask for c² or the perimeter instead of c, make the student recognize which side in a story is the hypotenuse, or add a second step, such as how far a ladder's base slides out when its top drops from 12 ft to 5 ft.

Figures are right triangles with the known sides labeled and the unknown marked x. Some items draw the triangle on a plain grid so the legs are counted, and a few have the student plot the length on a number line. Wrong answers come from real slips: adding the legs instead of their squares, subtracting the lengths, stopping at c² without taking the square root, adding the squares when the hypotenuse is given (so the "leg" comes out longer than the hypotenuse), and echoing the longest given side. Error-analysis items show a student's four steps in order and ask where the first mistake is, such as writing 5² + 7² as 10 + 14, or which steps hold a new mistake.

FAST practice adds multipart items where the length found in Part A feeds Part B: how much guy line is left on a coil, whether a ladder reaches a window sill, how many seconds a diagonal shortcut across a lawn saves. The templates refuse to build any item whose radicand is over 225, and the FDOE coverage check fails any item on this benchmark that draws a coordinate plane.

Most questions give two points, usually drawn on a coordinate plane with the segment between them, and ask for the distance. Supporting items isolate one step: name the two leg lengths, plot the right-angle vertex that takes one point's x-coordinate and the other's y-coordinate, or select every pair of points exactly 10 units apart. Harder items run the theorem backward (a point moves 12 units right, then straight up until it is 13 units from where it started: plot where it stops) or combine several distances into a perimeter or a path length.

Grid items have the student plot a point on an interactive coordinate plane; the finished right triangle appears in the explanation, never in the prompt. Wrong answers come from adding the legs instead of their squares (4 + 7 = 11 in place of √65), subtracting the squares, forgetting the square root, and taking the longer leg as the distance. Error-analysis items show a student's steps, and a common first error is adding the leg lengths before squaring them.

FAST practice adds map settings where each unit is a kilometer, a hiking trail made of three straight segments, the fourth vertex of a tilted square, and "correct answer and correct reasoning" items that ask whether two segments are the same length. The templates refuse to build any item whose radicand is over 225.

The benchmark is practiced as two skills. For the Triangle Inequality, students test sets of three lengths, write the range for a missing third side as a compound inequality (8 < x < 52), find the largest or smallest whole-number third side, count how many whole-number lengths are possible, pick the value that cannot be the third side, graph one bound with an open circle on a number line, and find the smallest possible perimeter. For the converse, they compare a² + b² with c², sometimes with the sides listed out of order, and decide between a right triangle, a triangle that is not right, and no triangle. A few items draw a triangle ABC on a coordinate plane with no side horizontal or vertical, so a square corner cannot be judged by eye: the student reads each squared side length off the grid (the horizontal change squared plus the vertical change squared) and applies the converse.

Most items are text, since the three numbers are the whole problem. Contexts include fencing a garden, sewing a sail and a carpenter checking a square corner with sides of 30, 40 and 50 cm. Many items ask for the verdict and the reason together (two "yes" options and two "no" options, each with its reason), so a student cannot guess the verdict and skip the reasoning. Wrong answers come from adding all three sides, checking the wrong pair of sides, accepting two sides that add to exactly the third, treating "the sides add to more than the longest" as proof of a right angle, taking the wrong side as c, thinking a right angle needs a horizontal or vertical side, and doubling instead of squaring (4² + 5² written as 8 + 10).

FAST practice uses the same forms at FAST length, including matching sets of sides to whether they can form a triangle, a statement about which side the right angle sits opposite, and a tilted triangle on a coordinate plane to test with the converse.

The benchmark is practiced as two skills: complementary and supplementary angles, and vertical and adjacent angles. D1 items work with numbers only: the complement, supplement or vertical angle of one measure, or the missing part of a straight line or of a larger marked angle. D2 brings in expressions such as (x + 16)° and (2x + 10)°, and D3 is mostly algebra: write the equation, solve for x and substitute. Some items state the relationship in words or as a ratio, and a few chain two facts (the supplement of one of a pair of vertical angles is 145°).

Angle diagrams label every angle the item names: with its measure, an expression, its name (∠2), or a question mark for an unknown the stem does not name. Every item that writes an angle as an expression ends with an angle measure, as FDOE requires, though x may be asked along the way. Wrong answers come from using 180° for a complementary pair or 90° for a supplementary one, making vertical angles add to 180°, reporting x when the angle was asked, substituting x into the wrong expression, and sign slips when combining terms. Error-analysis items show a student's four steps and ask where the first mistake is.

Some items have the student plot a missing angle on a number line. Matching items mix complements and supplements row by row, so size order does not solve them. FAST practice adds multipart items (x in Part A, the larger angle in Part B), three expressions and a 96° angle around a point, and a ramp, a road fork, railroad tracks and a folding fan. FDOE lists this benchmark as a mathematical context only, so these stories, like the roads and fans in the practice questions, go beyond the FAST's format.

The benchmark is practiced as two skills, interior angles and exterior angles. Early items give two interior angles on a triangle figure and ask for the third, or give the two remote interior angles and ask for the exterior angle. Later items label the angles with expressions such as (2x + 10)°, (3x − 5)° and (x + 25)°, use isosceles triangles with equal base angles, give the remote angles in a ratio, or use the fact that a triangle's three exterior angles sum to 360°. Settings include roof trusses, sails, kite frames and A-frames. FDOE lists this benchmark as a mathematical context only, so these settings go beyond the FAST's format.

Triangle figures label each angle with a number, an expression or a question mark, and exterior-angle figures extend one side. The most common wrong answer on exterior angles is 180° minus the two remote angles, which is the third interior angle, not the exterior one, and the interior angle next to the exterior angle is offered as a choice too. Other wrong answers come from mishandling the isosceles case, reporting x instead of the angle, and moving a constant the wrong way when solving. Error-analysis items give a student's claim ("the exterior angle is 55° because the angles of a triangle add to 180°") with two verdicts and two reasons to choose from.

FAST practice adds a matching task that classifies triangles from their three angles, a select-all of which angle sets can belong to a triangle, and a missing exterior angle plotted on a number line.

Items move from counting to computing to working backward. First comes how many triangles the diagonals from one vertex make, and the angle sum that follows. Then each interior angle of a regular polygon (a regular 24-gon has angles of 165°) and each exterior angle. Reverse items give the sum (1,980°) or one interior angle (150°) and ask for the number of sides. A few D3 items write each interior angle and each exterior angle as expressions, such as (12w − 24)° and (6w + 6)°, and ask for the interior angle: the two add to 180°.

Practice and quiz questions draw polygons of up to ten sides with every vertex lettered; the FAST drawings letter only vertex A and go up to 11 sides. Sum and each-angle items draw every diagonal from vertex A, and triangle-count items leave the diagonals for the student to picture. Items that ask for the number of sides are never drawn, since the drawing would give the answer away. Wrong answers come from counting n triangles instead of n − 2 (a student multiplies 30 × 180 for a 30-gon), using n − 3, the number of diagonals, reporting the exterior angle as the interior angle, and treating 360° as every polygon's sum. Grid items plot a polygon as a point such as (sides, triangles) on a coordinate plane.

Matching items pair each polygon with a different kind of fact (an angle sum, one exterior angle, a triangle count, one interior angle), so no column lines up with the rows by size. FAST practice adds everyday regular shapes (a quilt block, a serving tray, a cake pan drawn with its diagonals), a comparison of two polygons where one has 4 more sides, and a select-all of which values can be the interior angle sum of a regular polygon. FDOE lists this benchmark as a mathematical context only, so these shapes, like the stop sign, the octagonal picture frame and the floor tile in the practice questions, go beyond the FAST's format.

Most questions show a figure and its image on a plain grid and ask for the move that connects them: which transformation it is, how far and which way a translation went, which drawn line is the mirror, or what angle and direction a turn has. Where the choices name transformations, they often mix translations, reflections, rotations and sometimes a dilation, since telling them apart is the skill. Harder questions put several labeled lines, numbered figures or labeled points on the grid, and the student has to find the one that fits. The benchmark is practiced as three skills, identifying translations, reflections and rotations, and each skill still offers the other moves as wrong answers.

Wrong answers come from the mistakes students really make: calling a rotation a reflection because the image faces a new way, reading a translation as a reflection, turning the wrong direction, counting a translation backward from the image to the preimage, swapping the left-right and up-down counts, counting grid lines instead of the gaps between them, and choosing a mirror line that touches the figure or runs the way the point moved.

The student always identifies a move and never performs one: no question states a move and asks where a point lands. Where a question draws a figure, it draws the image too. FAST practice adds a lineup of five numbered copies of one figure (which ones are translations?), matching three images of one point to the drawn lines it was reflected across, and a two-part item that asks for a slide and then for the slide back. Lint rules fail any item whose text or explanation shows an ordered pair, a vector, an (x, y) rule or a coordinate word (origin, x-axis, y-axis, quadrant, coordinate), any item that chains two moves, keys a dilation, or states a move and asks where a point lands, and the FDOE coverage check fails any item that draws a coordinate plane.

Questions give a preimage and its image, either as matching side lengths in the text or as a figure on a plain grid, and ask for the scale factor. Scale factors include whole numbers, fractions such as 5/2 and 2/5, and 1, the same-size copy and the only case where the image is congruent. Some items reverse the direction and ask what scale factor maps the image back onto the preimage. Others ask what the scale factor means: enlargement or reduction, which statements are true of the image when k = 2, whether the image is similar, and whether it is congruent.

Settings include enlarged photos, copier enlargements and reductions, a projector, a scale model and a scale drawing of a machine part. Wrong answers come from the additive slip ("the image side is 4 ft longer, so the scale factor is 4"), the inverted ratio (preimage over image), the change divided by one of the lengths (reading growth as the scale factor), and, on a figure, the ratio of two sides that do not match. On a same-size copy with number choices, the wrong answers come from 0 ("nothing changed"), the two lengths added, and a guess that a dilation must double or halve. No option is negative. Error-analysis items give a student's claim and four reasoned options, two agreeing and two disagreeing.

FAST practice follows the same pattern and adds a resized logo, a triangle whose image side is a decimal and whose answer must be typed as a fraction, and a perimeter that changes from 12 units to 28 units. A lint rule fails any item whose text or explanation shows an ordered pair, an (x, y) rule, or the words origin, x-axis, y-axis, quadrant or coordinate, and any item that asks for a length, mentions area or chains two moves, and the FDOE coverage check fails any item on this benchmark that draws a coordinate plane.

The benchmark is practiced as four skills, one for each kind of move. Forward items give a point or a polygon and a move and ask for the image: its coordinates, one coordinate, or the vertices plotted on an interactive coordinate plane. Many items show the preimage on the plane without printing its coordinates, so reading the plane is part of the task. Reverse items give the image and the move and ask for the preimage, or give both points and ask what connects them: which line is the mirror, which rotation about the origin maps (−2, 9) to (9, 2), what scale factor maps (−10, 6) to (−5, 3).

Descriptive items ask what the move does: every x-coordinate increases by 5, the image is congruent to the preimage, P′ is farther from the origin than P. Scale factors include fractions and decimals such as 1/2, 3/2 and 2.5. Wrong answers are the slips students make: a dropped sign, x and y swapped, clockwise read as counterclockwise, reflecting across the wrong axis or across an axis instead of the given line, translating the wrong way, and adding the scale factor instead of multiplying. Error-analysis items quote a student's method in words and ask whether it works.

FAST practice adds plotting a whole preimage quadrilateral from its image, and multipart dilation items that carry the scale factor into a second question. A lint rule fails any item that gives a transformation as an (x, y) rule, names a rotation angle without a direction, shortens a direction to CW or CCW, rotates about a point other than the origin or by an angle other than 90°, 180°, 270° or 360°, rotates or dilates in a stem that never names the origin, centers a dilation away from the origin, reflects across a slanted line such as y = x, or chains two moves in its text. The FDOE coverage check requires a coordinate plane in at least a quarter of the items.

Most items are indirect measurement: a person and a flagpole casting shadows at the same time of day, a mirror on the ground that shows the top of a tree, a model sail and the real sail, or two right triangles laid out beside a pond or river to measure across it. Others work with two similar triangles directly: find a missing side, find the scale factor in both directions, decide whether two triangles are similar by checking all three ratios, or find a side of the small triangle cut off by a segment parallel to the base. Select-all items check facts about a similar pair: the scale factor, equal angles, the larger perimeter, and congruence.

Some shadow problems and triangle pairs are drawn with their measurements on the figure, marked as not to scale, so the numbers, not a ruler, decide the answer. Grid items draw a right triangle and ask the student to plot the third vertex of a similar triangle that shares one vertex with it. Wrong answers come from a proportion whose parts do not correspond (height over shadow on one side, shadow over height on the other), the additive slip ("the extra 6 feet of shadow adds 6 feet to the height"), stopping at the cross product, adding the scale factor instead of multiplying, and calling triangles similar because two ratios match. Error-analysis items show a student's work and ask whether it is right, with two verdicts and two reasons.

FAST practice adds a roof truss drawn to scale with a brace parallel to its base, a tent whose cross bar is parallel to its base, two ladders leaning at the same angle, and a triangular banner whose scale factor comes from one pair of sides. A lint rule fails any item whose given lengths use two different units, or whose stem describes a rectangle, a photo, a poster, a map or a dilation from the origin.