MCAS Math Grade 4 common mistakes
MCAS Math Grade 4 · Understand the traps and how to avoid them.
When comparing two fractions with unlike denominators, the student compares the denominators and concludes the fraction with the larger denominator is larger (e.g., says 1/8 > 1/3 because 8 > 3).
The student has overgeneralized whole-number reasoning, where a bigger numeral means a bigger quantity, and has not yet built the idea that more equal parts means each part is smaller.
What to do instead
Have the student draw two same-size rectangles, split one into 3 parts and one into 8 parts, shade one part in each, and physically compare the shaded areas. Then state the rule in words: for the same numerator, the larger the denominator, the smaller the piece. Practice with unit-fraction cards sorted from least to greatest.
The student adds fractions with unlike denominators by adding numerators and adding denominators (2/3 + 1/4 = 3/7).
The student is treating the fraction bar as a separator between two independent whole numbers rather than as a single number, and has no mental image of adding lengths of equal-size pieces.
What to do instead
Use fraction strips or number lines to show that thirds and fourths cannot be combined until both are expressed in the same size piece. Have the student replace both fractions with equivalent fractions in twelfths, model the sum on a number line, and check reasonableness: 2/3 is already more than 1/2, so the sum must exceed 1/2, which 3/7 does not.
On a multi-step word problem, the student computes one operation, writes the result as the answer, and stops, ignoring the remaining condition (e.g., finds the total cost but never subtracts the amount already saved).
The student reads the problem once for numbers rather than for the question being asked, and has not been taught to identify the final question sentence and the hidden intermediate step before computing.
What to do instead
Require a three-line plan before any arithmetic: what is asked, what is known, what must be found first. Have the student restate the question in their own words and label each computed number with a unit and meaning ("$36 = total cost"). Then check the answer against the question sentence, not against the last number computed.
The student solves 4,203 − 1,568 and writes 3,365, borrowing from the 4 but not reducing it, or skipping the borrow across zeros in the tens and hundreds places.
The student performs regrouping as a ritual of crossing out digits without tracking that a borrowed ten must be removed from the column to its left, and zeros offer no visible digit to decrease.
What to do instead
Use base-ten blocks or place-value disks to physically trade one thousand for ten hundreds and one hundred for ten tens. Have the student say the regroup aloud ("I take one ten from the 2 tens, leaving 1 ten"). Then verify with addition: add the difference back to the subtrahend and confirm it equals the minuend.
The student multiplies 24 × 3 and gets 612 by multiplying digits and concatenating results (2×3=6, 4×3=12) instead of carrying.
The student is applying a digit-by-digit procedure without place value, so the 2 in 24 is treated as 2 ones rather than 2 tens, and the carried ten is dropped.
What to do instead
Model with an area model: split 24 into 20 + 3... actually 20 + 4, compute 20 × 3 = 60 and 4 × 3 = 12, and add to get 72. Have the student write the partial products in a two-row array before using the standard algorithm, and estimate first (24 × 3 is about 25 × 3 = 75) to catch the unreasonable 612.
When finding factors or multiples, the student lists only the pairs that come to mind (for 36: 1, 2, 3, 4, 6) and misses 9, 12, 18, and 36, or confuses factors with multiples.
The student searches randomly rather than systematically, and the vocabulary pair factor/multiple is not anchored to a concrete meaning.
What to do instead
Teach a systematic sweep: test divisors 1, 2, 3, ... and record each pair (1×36, 2×18, 3×12, 4×9, 6×6) until the pairs meet in the middle. Anchor the terms with a concrete sentence: factors divide into the number, multiples are what you get by skip-counting from it. Have the student sort a mixed list of numbers into factor/multiple columns.
The student classifies a shape as a rectangle or a square based on how it looks, and denies that a square is a rectangle or that a rotated square is still a square.
The student relies on a prototypical visual image of each shape rather than on the defining attributes (number of sides, right angles, equal sides, parallel sides), so a tilted or unusual orientation breaks recognition.
What to do instead
Have the student test each shape against a written attribute checklist rather than naming it by sight, and draw shapes in multiple orientations on grid paper. Explicitly build the hierarchy: a square has all the properties of a rectangle plus equal sides, so it belongs inside the rectangle category. Include non-examples (a rhombus with no right angles) to sharpen the boundary.
When measuring an angle with a protractor, the student reads the wrong scale and reports 130° for an acute angle, or aligns the vertex with the outer edge instead of the center mark.
The student has not learned to choose the scale based on whether the angle opens to the left or right, and does not use the size of the angle as a reasonableness check.
What to do instead
Establish a fixed routine: center mark on the vertex, zero line on one ray, then decide acute or obtuse first and pick the scale that matches. Have the student estimate the angle before measuring ("it's less than 90, so it must be the smaller number") and compare the protractor reading to that estimate.
The student computes the area of a rectangle by adding the side lengths (7 + 4 = 11 square units) or confuses area with perimeter and reports the wrong unit.
The student has memorized two formulas without attaching them to a model, so the operations and units are interchangeable in memory.
What to do instead
Have the student cover the rectangle with unit squares and count, establishing area as the number of squares covering the region. Contrast with walking the perimeter with a finger. Require the unit to be written and spoken: square units for area, units for perimeter. Then connect the count to the multiplication 7 × 4.
The student converts 3 kilograms to grams and writes 300 grams, or 2 meters to centimeters and writes 200 millimeters, misplacing the decimal by one place.
The student is recalling the metric prefixes as an undifferentiated list rather than as a structured sequence of powers of ten, and has no benchmark for how large a gram or centimeter is.
What to do instead
Build a prefix ladder (kilo, base, centi, milli) with the multiplication factor at each step and have the student move a token along it, multiplying or dividing by 10 each step. Anchor with benchmarks: a paper clip is about 1 gram, a meter is about a doorknob-to-floor height. Check the direction: a kilogram is bigger, so the number of grams must be larger.