7 mistakes learners make with number patterns, each one named and explained.
Find what happens between each pair of terms, then check it works for all of them.
A sequence whose gaps increase is continued with a constant step.
Most sequences met earlier do have a constant step, so it is the pattern the eye looks for first.
Question. A, C, F, J, O, ?
A common answer. T
The answer. U
Why. The gaps are 2, 3, 4, 5, so the next gap is 6.
Write the gaps underneath the sequence. If they are not all the same, they are a sequence too.
Grey is chosen for the missing cell when grey already sits in that row.
The eye checks that the pattern looks nice, not whether the row rule still holds.
Question. Each row and column has white, grey and black exactly once. Row 3 is black, blank, grey. What fills the blank?
A common answer. Grey
The answer. White
Why. The row already contains grey and black, so the only shade the rule allows is white.
Tick off what the row and column already contain before choosing.
One of the numbers already in the sequence is given as the next one.
The numbers on the page are the only ones available if the rule has not been found.
Question. 3, 4, 5, 6, ?
A common answer. 5
The answer. 7
Why. 5 has already appeared, and the sequence is increasing.
An increasing sequence never repeats. Check your answer is bigger than the last term.
The right shape appears in the wrong colour, or the right colour on the wrong shape.
Getting one rule right feels like the job done, and the second rule slips past.
Question. Row 3 uses hexagons and column 2 uses grey. What goes at row 3, column 2?
A common answer. A black hexagon
The answer. A grey hexagon
Why. The cell must obey its row and its column at the same time: hexagon from the row, grey from the column.
Every cell in a grid answers to its row and its column at once.
Row 3 times column 3 is answered with the value for a neighbouring cell.
Rows and columns are easy to swap or slip by one when the grid is only imagined.
Question. Each cell holds row times column stars. How many in row 3, column 3?
A common answer. 12, which is row 3 times column 4
The answer. 9
Why. The missing cell is row 3, column 3, so it holds 3 times 3. Reading a neighbouring cell gives a different number.
Point at the exact cell and say its row and column out loud before calculating.
The final step is twice the size of the earlier ones.
Continuing a pattern feels like it should accelerate, and the last term gets a bigger jump.
Question. 3, 4, 5, 6, ?
A common answer. 8
The answer. 7
Why. Each term goes up by 1, so the next is 7.
The next gap is the same as the last gap unless the gaps themselves form a pattern.
The pattern is continued with a step that does not match the earlier terms.
One glance at two terms gives a step, and it is not always checked against the rest.
Question. 2, 4, 6, ?
A common answer. 9
The answer. 8
Why. The step is 2 each time, so 6 becomes 8.
Work out every gap, not just the first. They have to agree before you use one.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.