MCAS Math Grade 3 common mistakes
MCAS Math Grade 3 · Understand the traps and how to avoid them.
When multiplying to find an area or a total (for example 6 rows of 7 tiles), the student counts the squares one at a time or adds 7 six times instead of using the multiplication fact, and loses count partway through.
Grade 3 is where multiplication shifts from repeated addition and skip-counting to recalled facts. Students who still count by ones have no efficient strategy and run out of working memory, so they drop or double-count items.
What to do instead
Have the student draw an array, split it into two known facts (6 × 7 = 6 × 5 + 6 × 2), and connect the drawing to the fact. Practice a small set of facts with the commutative pair shown together (3 × 8 and 8 × 3) so the student sees the array rotate rather than relearn each fact.
On a division word problem such as '24 pencils shared equally among 4 tables,' the student divides in the wrong direction (4 ÷ 24) or multiplies 24 × 4, producing an answer that is larger than the starting number.
Students match the operation to keywords or to the first two numbers they see rather than to the structure of equal sharing or equal groups. They also lack a habit of checking whether the answer is reasonable.
What to do instead
Teach the student to name the unknown first: 'Am I finding the number in each group, or the number of groups?' Then have them act it out with counters or draw a bar model before writing an equation. Add a one-second sanity check: for sharing a set into groups, the answer must be smaller than the total.
When solving a two-step word problem, the student computes only the first step and reports that number as the answer, ignoring the remaining question.
Grade 3 problems often hide a second question in the final sentence. Students read for the first set of numbers, start computing, and never return to the full question text.
What to do instead
Have the student underline the question sentence before starting and restate it in their own words ('I need to find how many are left after...'). Then require a written plan with two numbered steps and a check that the final answer answers the underlined question.
The student finds the correct numerical answer but does not write the unit, or writes the wrong unit (says '7' when the question asks for minutes), and on multi-step problems labels an intermediate result as the final answer.
Students treat the number as the whole answer. In Grade 3, answers are graded on whether the quantity is identified correctly, and units are the cheapest evidence of that understanding.
What to do instead
Make 'number + unit + what it counts' a standing requirement (for example '7 minutes per lap,' not '7'). Have the student reread the question sentence and match their unit to the unit asked for before moving on.
When rounding 47 to the nearest ten, the student answers 50 correctly but then rounds 44 to 50 as well, or rounds 350 to 400 when asked for the nearest ten, because they look at the last digit only or round twice.
Students memorize 'five or more rounds up' without anchoring to the two nearest multiples of ten (or hundred) on a number line, so they misjudge which benchmark is closer and sometimes round a rounded number again.
What to do instead
Have the student place the number on a number line between the two candidate benchmarks and decide which is nearer before applying any rule. Explicitly forbid rounding twice: identify the place being rounded, then decide once using the digit to its right.
When comparing fractions with the same numerator (1/4 and 1/6), the student says 1/6 is larger because 6 is bigger than 4, or orders fractions by the size of the denominators.
Whole-number reasoning is overlearned and gets applied to fractions. Students have not built the idea that more parts means each part is smaller, because they have not seen the same whole partitioned different ways.
What to do instead
Have the student shade the same rectangle into fourths and sixths and compare the shaded pieces directly. Then state the generalization in words ('the more pieces I cut the whole into, the smaller each piece') and follow with same-denominator comparisons to contrast the two cases.
The student identifies 3/4 and 3/8 as equivalent because both have a 3, or places 1/2 and 2/4 at different points on a number line.
Students compare the written numerals rather than the quantities. Equivalence as 'same point on the number line' or 'same area' is not yet a working mental model.
What to do instead
Use fraction strips and a number line together: fold or shade to show 1/2 and 2/4 landing on the same point, and have the student generate equivalent fractions by repeatedly splitting each part. Require a drawing as justification before accepting an equivalence claim.
When finding the perimeter of a rectangle, the student adds only the length and width (giving 2 + 5 = 7 instead of 14), or when finding area, adds the sides instead of multiplying.
Students confuse the two measurements and do not connect perimeter to the distance around the boundary and area to the squares covering the region. They also forget that opposite sides are equal.
What to do instead
Have the student trace the boundary with a finger for perimeter and tile the inside with unit squares for area, on the same rectangle, and record both. Then write the formulas from the drawing (P = l + w + l + w, A = l × w) rather than from memory.
The student reads a scaled bar graph or picture graph as if each symbol or tick were one unit, reporting 4 when each symbol stands for 5 and the bar reaches 4 symbols.
Grade 3 introduces scaled graphs, but students carry over the Grade 2 habit of counting marks. The key is printed apart from the data, so it is easy to skip.
What to do instead
Require the student to write the key's value at the top of the page before answering any question, then annotate each bar with its true value. Practice with two graphs of identical shape but different keys so the student sees the key, not the height, determines the value.
When measuring an object with a ruler that does not start at zero, the student reports the ending mark as the length (reads 9 cm for an object spanning 2 cm to 9 cm), or lines the object up with the ruler's edge rather than the zero mark.
Students treat the ruler as a count of marks rather than a number line of distances. The zero point is assumed to be the physical end of the ruler.
What to do instead
Have the student measure the same object twice, once from zero and once starting at 2, and subtract to confirm the same length. State the rule as 'length is the distance between the endpoints,' and check that the object's left end sits exactly on a marked number.