TExES Math 4-8 (115) common mistakes
TExES Math 4-8 (115) · Understand the traps and how to avoid them.
When dividing fractions, inverts the dividend instead of the divisor (rewriting 3/4 ÷ 1/2 as 4/3 × 1/2) or cross-multiplies and reports 3/8 for the quotient.
The 'keep-change-flip' chant was memorized as a sequence of gestures with no attachment to the meaning of division, so in memory the dividend and divisor become interchangeable.
What to do instead
Rebuild the operation from a quotient question the candidate can model: 'How many 1/2-cup scoops fit in 3/4 cup?' Draw both fractions on parallel number lines and count the jumps, then verify by multiplying (3/2 × 1/2 = 3/4). Train the estimate habit: because the divisor is less than 1, the quotient must exceed 3/4.
Computes percent change as new ÷ old (reporting 125% as the change from 100 to 125), and treats a 20% discount followed by a 20% markup as returning to the original price.
Percent is handled as a label stuck onto a number rather than as a comparison to an identified base, so the base of each successive percent is never named.
What to do instead
Force a multiplier and a base for every percent: 125/100 = 1.25, so the change is 1.25 − 1 = 25%; for the discount-then-markup case, 0.8 × 1.2 = 0.96, a 4% net decrease. Confirm with a bar model anchored on $100, which makes the shifting base visible.
Solving 2(x − 3) = 10 by subtracting 3 from both sides before dealing with the factor of 2, or by distributing to get 2x − 3.
Operations are undone in left-to-right visual order instead of reverse order of operations, and the distributive property is recalled as a rule rather than as an area relationship.
What to do instead
Practice both legitimate routes on the same equation and compare: divide both sides by 2 first (x − 3 = 5), or distribute fully (2x − 6 = 10). Draw the distribution as an area model split into 2x and 6, and always substitute the solution back into the original equation.
Computes slope as (x₂ − x₁)/(y₂ − y₁), or reports the y-intercept as the slope when a linear relationship is presented in a table or a context.
Slope lives in memory as a formula to be matched to two points rather than as a rate of change, and table columns are read in whatever order they appear.
What to do instead
Before touching a formula, write the rate as a sentence with units - 'dollars per hour,' 'feet per second' - and derive slope = Δy/Δx from that sentence. Use a quick rise/fall check: decide from the context whether the line should go up or down, then see whether the sign of the answer agrees.
Assumes doubling the side lengths of a rectangle doubles its area, and answers 'perimeter' when the question asks how much material is needed to cover a surface.
Length, area, and volume are all filed mentally under 'size,' and the exponent in the unit (cm vs cm² vs cm³) carries no operational meaning.
What to do instead
Make the scale factor explicit and dimensional - linear ×2, area ×2², volume ×2³ - and verify on grid paper or with unit cubes. Treat the unit as the deciding cue: read the units in the prompt before choosing a formula, and state the answer in squared or cubed units.
Converts 1.5 m² to 150 cm², or converts 2.5 hours to '2 hours 50 minutes.'
A conversion factor is applied as a single multiplication with no tracking of how many factors of the unit are present, and base-60 time is handled with base-10 habits.
What to do instead
Write the factor twice for square units: 1.5 m² × (100 cm/1 m)² = 15,000 cm². For time, convert to one unit before computing (2.5 h = 150 min) and never read the decimal digits as minutes. Finish with a rough-estimate check: square centimeters should be far more numerous, not fewer.
Adds probabilities of overlapping events (P(king or heart) = 4/52 + 13/52), or claims a tail is 'due' after five consecutive heads.
The addition rule is applied outside the mutually exclusive case, and independence is conflated with a belief that outcomes must balance out in the short run.
What to do instead
Redraw the sample space or a Venn diagram and subtract the overlap: 4/52 + 13/52 − 1/52 = 16/52. For independence, run a short simulation recording the flip that follows five heads; the observed proportion stays near 1/2, which confronts the 'due' intuition directly.
Reports the mean as the 'typical' value for a skewed data set or one containing an outlier, and reads a histogram bar height as if it were a data value.
Mean is over-generalized as 'the average' without ever comparing it to the median on skewed data, and the conventions of different graph types (bar chart vs histogram, frequency vs value) are not distinguished.
What to do instead
Always compute both mean and median on the same small skewed set and describe how the outlier pulls the mean. For any graph, restate aloud what each axis counts and what one bar represents before answering the item.
Answers a constructed-response item with the numeric result alone - no justification, no representation, no interpretation in context - and loses the communication and reasoning points even when the computation is right.
Preparation centers on procedural drills and multiple-choice formats, so explanation is treated as optional decoration rather than as a scored component of the response.
What to do instead
Rehearse a three-part template for every practice prompt: claim, evidence (computation or diagram), and interpretation back in the context of the problem. Score your own responses against the state rubric descriptors - clarity, accuracy, and use of representations - before checking the answer.
Responds to a scenario about a student misconception with 'the teacher should explain it more clearly' or 'assign more practice problems,' and classifies an ungraded exit ticket as a summative assessment.
Instructional items are answered from personal classroom memory rather than from a diagnostic-teaching framework, so terms like formative, summative, and CRA are recognized as vocabulary but not applied to the situation described.
What to do instead
For each scenario, name the specific misconception first, then select a move that surfaces it - a diagnostic question, a concrete or visual representation, or a student-to-student comparison of strategies. Classify assessments by purpose and use of results (informing instruction right now = formative) rather than by whether points are awarded.