FAST Math Grade 4 common mistakes
FAST Math Grade 4 · Understand the traps and how to avoid them.
When comparing multi-digit whole numbers such as 5,099 and 5,149, the student picks the number with more visible digits or compares digits left to right without regrouping, choosing 5,099 as larger because 9 > 1 in the tens place.
Students learn place value as a labeling exercise (ones, tens, hundreds) but not as a magnitude system, so they compare the first place where digits differ without checking whether an earlier place already decided the comparison, or they treat 'more digits' as the only reliable cue.
What to do instead
Have the student write both numbers stacked with place-value headings and compare one column at a time from the left, stopping at the first difference. Practice with matched-digit pairs (5,099 vs 5,149) and unequal-length pairs (999 vs 1,002) so the student states the rule aloud: compare the highest place first; only if equal, move left to right.
The student subtracts without regrouping across zeros, writing 4,003 − 1,258 = 3,255 by borrowing 1 from the 4 and treating each zero as 10 without cascading the borrow.
The standard algorithm is memorized as a sequence of marks ('cross out, add ten') rather than as exchanging one unit for ten of the next smaller unit, and zeros give no visible digit to decrease, so the student either skips the borrow or borrows only once.
What to do instead
Use place-value blocks or a written exchange table to physically trade 1 thousand for 10 hundreds, then 1 hundred for 10 tens, then 1 ten for 10 ones before subtracting. Then have the student check every subtraction by adding the difference to the subtrahend, so an incorrect 3,255 is caught when 3,255 + 1,258 ≠ 4,003.
When multiplying a multi-digit number by a two-digit number, the student writes only one partial product, e.g. 34 × 26 = 204, forgetting to shift the second partial product one place left.
The student treats the algorithm as repeated single-digit multiplication and does not connect the '2' in 26 to 20, so the second row has no conceptual meaning and is dropped or written in the wrong column.
What to do instead
Before using the compact algorithm, have the student decompose the multiplier: 34 × 26 = 34 × 20 + 34 × 6, compute both partial products separately, and add them. Then show the same work in the stacked format with the zero written in the ones place of the second row, so the shift is visible rather than remembered.
The student adds or subtracts fractions with unlike denominators by operating on the numerators and denominators directly, writing 1/2 + 1/3 = 2/5.
Whole-number arithmetic is overgeneralized: the student sees two pairs of numbers and applies the familiar operation to each pair, without the idea that a fraction is a count of same-sized pieces and that only like-sized pieces can be combined.
What to do instead
Rebuild the idea with fraction strips or number lines: show that 1/2 and 1/3 are different-sized pieces, replace both with sixths (3/6 and 2/6), and only then add to get 5/6. Require the student to name the common unit before adding, and have them estimate first (1/2 + 1/3 is close to 1, so 2/5 is impossible).
When comparing decimals such as 0.7 and 0.65, the student says 0.65 is greater because 65 > 7, treating the digits after the decimal point as whole numbers.
Students transfer whole-number comparison rules to decimals and do not yet see decimals as fractions of a whole, so 'longer is bigger' and 'bigger digits mean bigger value' feel correct.
What to do instead
Have the student say the decimals in fraction form (0.7 = 7/10 = 70/100; 0.65 = 65/100) or place both on a hundredths grid or number line. Then compare with the same rule used for whole numbers, aligning by place value rather than by digit count.
Given a pattern rule such as 'add 5', the student continues the sequence correctly but cannot write the rule as an expression, or writes 5n when the sequence starts at 3 and the correct rule is 5n + 3 or 5(n − 1) + 3.
The student sees the recursive step (what to add each time) but not the relationship between position number and term, and has had little practice translating between a table, a verbal rule, and an expression.
What to do instead
Build a two-column table (position, value) and have the student test candidate expressions against the first three rows. Emphasize checking the starting value separately from the step, and require the student to explain in words what the expression does for position 1 before accepting it.
The student evaluates an expression with more than one operation strictly left to right, computing 4 + 3 × 5 as 35, or ignores parentheses in 3 × (8 − 2) and computes 3 × 8 − 2 = 22.
Left-to-right reading is deeply practiced from earlier grades, and the order-of-operations conventions feel arbitrary because the student has not seen why grouping changes the meaning of an expression.
What to do instead
Use a context that makes grouping visible, such as '3 bags of 8 apples minus 2 apples eaten', and have the student write the expression two ways to see they differ. Then practice a fixed routine: parentheses first, then multiplication and division left to right, then addition and subtraction left to right, with every step rewritten on a new line.
When converting measurements, the student multiplies when the conversion requires division (or reverses the factor), e.g. converting 3,500 milliliters to liters by writing 350,000 liters, or converting 2.5 meters to centimeters as 0.025.
The student memorizes conversion pairs as isolated facts ('kilo means 1,000') without a reference for which unit is larger, so the operation is guessed rather than reasoned from the relative size of the units.
What to do instead
Anchor each conversion to relative size: a liter is larger than a milliliter, so the number of liters must be smaller. Have the student state the direction in words before computing ('going from small units to large units, so divide'), then check with a benchmark such as 'a bottle of water is about 1 liter, so 3,500 mL is a few liters, not hundreds of thousands.'
When finding the area of a rectangle, the student adds the side lengths instead of multiplying them, or confuses area with perimeter and reports square units for a perimeter answer.
Area and perimeter are taught close together and both involve the same four side lengths, so the student retains the numbers but not which quantity each formula measures, and unit labels are treated as decoration.
What to do instead
Separate the two ideas physically: tile a rectangle with unit squares to count area and run a string around the edge to measure perimeter, recording both for the same rectangle. Require unit labels in every answer (square centimeters for area, centimeters for perimeter) and have the student explain in one sentence what each number measures.
When classifying a shape, the student says a square is not a rectangle, or identifies a figure as a rhombus only if it is drawn rotated in the familiar orientation, failing to recognize a square as a special rectangle and a rhombus.
Students learn shapes from prototypical pictures and treat category names as mutually exclusive labels, so a shape that looks like 'the square picture' cannot also belong to the rectangle category.
What to do instead
Sort the same set of shapes into overlapping categories and discuss the defining attributes (four right angles, four equal sides) rather than appearance. Show that a square satisfies every attribute of a rectangle and a rhombus, and rotate and resize shapes so orientation and proportions stop driving the classification.