NB Grade 7 Math common mistakes
NB Grade 7 Math · Understand the traps and how to avoid them.
When subtracting a negative integer, the student changes the sign of the second number but then subtracts, writing 5 - (-3) = 2 instead of 8.
The student treats every minus sign as 'take away' and has not connected subtracting a negative to moving right on a number line or to adding the opposite.
What to do instead
Have the student rewrite every subtraction as addition of the opposite before calculating: 5 - (-3) becomes 5 + 3. Model both expressions on a vertical number line, then practise mixed integer subtraction with the rewrite step shown.
The student evaluates 3 + 4 × 2 as 14 by working strictly left to right, or evaluates 2 + 3² as 25 by squaring the whole sum.
The student sees arithmetic as a chain of equal-priority steps and has not internalised the hierarchy of operations, especially exponents and multiplication before addition.
What to do instead
Require the student to bracket the operation that happens first before calculating: 3 + (4 × 2) and 2 + (3²). Use a four-step checklist (brackets, exponents, multiply/divide left to right, add/subtract left to right) and compare wrong and right results side by side.
The student adds fractions by adding numerators and denominators, writing 1/2 + 1/3 = 2/5.
The student applies whole-number addition rules to fraction notation and does not yet see fractions as quantities measured in same-sized parts.
What to do instead
Use fraction strips or number lines to show that halves and thirds are different-sized parts, so they must be converted to a common denominator. Have the student estimate first (about 0.8), then calculate 3/6 + 2/6 = 5/6 and check the estimate.
When calculating a percent increase, the student finds the amount of increase and stops, or subtracts the percent from the original number as though percent were a whole-number amount.
The student memorises 'find the percent of a number' as the only percent procedure and does not distinguish the part from the new total.
What to do instead
Use a two-column organizer: original amount, increase or decrease amount, new amount. Require a sentence answer such as 'The price rises by $12, so the new price is $72.' Practise with percent bars before moving to multiplication by a decimal factor.
Solving 2x + 3 = 11, the student divides both sides by 2 first, producing x + 3 = 5.5, or moves +3 to the other side without changing its sign.
The student applies inverse operations in the order they appear rather than undoing operations in reverse order, and treats equation solving as symbol moving rather than maintaining balance.
What to do instead
Model the equation with algebra tiles or a balance scale: undo the added 3 first, then divide the remaining 2x by 2. Require the student to record the inverse operation beside each step and substitute the answer back to verify.
Given a table of values, the student states the pattern rule by comparing only the first two rows, or reads a graph's vertical intercept as the rate of change.
The student looks for a quick single-step rule and does not check whether the same change repeats across all rows or connect slope to change per unit.
What to do instead
Require calculation of first differences for every consecutive pair before naming a rule, and check the rule against at least three rows. For graphs, have the student build a table from plotted points and describe change in y per 1 unit of x before identifying the starting value.
The student uses the diameter as the radius in A = πr², or uses the circumference formula when asked for area, producing an answer twice or half the correct size.
The student memorises formulas as letter patterns without attaching each symbol to a measured feature of the circle, and does not distinguish linear from square units.
What to do instead
Have the student label the radius and diameter on a diagram before choosing a formula, and write the formula in words: area equals pi times radius squared. Require units in every answer (cm versus cm²) and a reasonableness check comparing the answer to a square drawn around the circle.
Calculating the volume of a cylinder, the student multiplies radius by height times pi without squaring the radius, or adds the areas of faces instead of multiplying base area by height.
The student confuses surface area and volume procedures and memorises formula strings without understanding that volume counts congruent layers.
What to do instead
Build volume with stacked layers: find the base area first, then multiply by the number of layers (height). For a cylinder, calculate r² explicitly before multiplying by π and h. Have the student state whether the question asks about covering (area) or filling (volume) before starting.
Reflecting a point across the x-axis, the student changes the x-coordinate, or plots (3, 5) by moving 3 units up and 5 units right.
The student confuses which axis is horizontal and which coordinate controls each direction, and memorises reflection rules without visualising the flip.
What to do instead
Require plotting on a labelled grid and physically folding the paper along the axis to see where the image lands. Reinforce the order: x is horizontal first, y is vertical second. Have the student state the rule in words: across the x-axis, x stays and y changes sign.
Asked for the median of a data set, the student gives the middle number without ordering the values first, or reports the mean when the question asks which measure best represents typical data.
The student treats all 'average' questions as mean calculations and skips the ordering step that defines the median.
What to do instead
Require rewriting the data in order from least to greatest before locating the middle, and show that an even count needs the mean of the two middle values. Compare mean and median on a set with an outlier so the student can explain which is more representative.