Learn · Check · Practice

The math mistake atlas

A wrong answer is a place to start. Find the step that went wrong, work through the correction, and try it again.

Kindergarten

Skipping or counting an object twice

Touch or mark one object for each number word. Spreading a group out does not change its count.

Mixing up one more and one less

More and less describe opposite directions. Start at the number, then make exactly one step.

Giving the total instead of the missing part

The blank is one part of the total, not the whole group. Use the known part to find what is missing.

1st Grade

Adding digits instead of their place values

A digit in the tens place represents groups of ten. Its value changes when it moves to another place.

Using the same addend twice when making ten

Making ten uses part of an addend. Only the leftover part should be added afterward.

Reversing subtraction in a fact family

Addition allows the two parts to swap places. Subtraction begins with the total when finding a missing part.

2nd Grade

Writing digits instead of expanded values

Expanded form shows the value contributed by each place. Empty places still need zeros in standard form.

Forgetting the regrouped ten in addition

Ten ones become one ten. That ten must be included when adding the tens column.

Subtracting the smaller digit from the larger

Subtraction keeps its direction. Exchange a ten for ten ones rather than reversing a difficult column.

3rd Grade

Dropping a zero from a number

A missing expanded-form term can still need a zero in the written number. Check the place-value columns.

Adding the factors instead of multiplying

Multiplication counts equal groups. One additional group contributes the group size, not just one.

Counting number-line marks instead of intervals

The denominator counts equal spaces in one whole. The zero mark is a starting point, not an extra part.

4th Grade

Leaving out a partial product

Every part of one factor multiplies every part of the other. A rectangle split into regions helps keep track.

Changing only one part of a fraction

Multiplying numerator and denominator by the same nonzero value preserves the fraction. Subtracting the same number does not.

Confusing area with perimeter

Area measures the inside with square units. Perimeter measures the boundary with length units.

5th Grade

Counting the same volume twice

A total height or a missing notch can make a solid look larger than it is. Label each separate prism before multiplying.

Doing every operation from left to right

Reading order and calculation order are different. Group the operations before computing them.

Adding or subtracting the denominators

A denominator names a part size. Adding differently sized pieces requires a common size first.

6th Grade

Reversing a unit-rate calculation

The requested unit tells you the division order. Cost per pen is cost divided by pens.

Keeping a negative sign on absolute value

Absolute value is a distance from zero. Evaluate the expression inside first, then take that distance.

Using the same operation to undo an equation

Undo addition with subtraction and multiplication with division. Check by substituting into the original equation.

7th Grade

Dividing x by y instead of y by x

In y = kx, k tells how much y there is for each one of x. Reversing the quotient changes the meaning.

Moving the wrong way with negative numbers

A rise moves right on a number line even when the starting value is negative. A decrease can cross zero.

Using the new value as the percent-change base

Percent change compares a difference with the original amount. A discount amount is also different from the final price.

8th Grade

Dropping variable terms or forcing a solution

Collect variable terms with balanced operations. If variables cancel, decide whether the remaining statement is true.

Reversing just one subtraction in slope

Both coordinate differences must use the same point order. A line going down as x increases has negative slope.

Adding squares when finding a missing leg

The hypotenuse is already the sum-of-squares side. Subtract the known leg’s square before taking a square root.

9th Grade

Changing only one side of an equation

An equation remains balanced only when equivalent operations are performed on both sides.

Treating function notation as multiplication

f(3) asks for the output at input 3. It does not mean f times 3; negative inputs also need parentheses.

Swapping slope and intercept

The coefficient of x is the rate of change; the constant is the output when x is zero.

10th Grade

Mixing up complementary and supplementary angles

Complements sum to 90 degrees; supplements sum to 180 degrees. Choose the total before subtracting.

Using the wrong total for triangle angles

An ordinary plane triangle has interior angles totaling 180 degrees. Equal base angles share the remaining total.

Confusing the midpoint and the distance

A midpoint averages coordinates. A distance measures a length and uses both coordinate differences.

11th Grade

Losing restrictions when canceling factors

Cancel common factors, but keep exclusions from the original denominator. Simplification does not fill a hole in the domain.

Treating a logarithm as division

A logarithm asks for an exponent. Rewrite the statement as a power of the base.

Adding instead of multiplying in a geometric sequence

A geometric sequence has a constant ratio. Its sum is the total of terms, not simply the next term.