4 mistakes learners make with circles, each one named and explained.
Area uses the radius squared; circumference uses the radius once.
2 pi r is worked out and given as the area of the circle.
Both formulas start with pi and use the radius, and there are only two of them to confuse.
Question. Radius 7 cm, pi = 3.14
A common answer. 2 x 3.14 x 7 = 43.96
The answer. 3.14 x 49 = 153.86
Why. Area needs the radius squared, which is what makes the unit cm squared.
Only one of the two formulas has a square in it, and it is the one that gives a squared unit.
The radius is doubled before being put into the area formula, in one place or both.
Circle questions give sometimes the radius and sometimes the diameter, so a conversion habit forms.
Question. Radius 7 cm
A common answer. using 14 in the formula
The answer. using 7
Why. The question already gave the radius, so nothing needed converting.
Read which one you were given before touching the formula. Convert only if you must.
Area is worked out as pi times r, with the square never applied.
The small raised 2 is easy to lose when copying the formula down.
Question. Radius 7 cm, pi = 3.14
A common answer. 3.14 x 7 = 21.98
The answer. 3.14 x 7 x 7 = 153.86
Why. Without the square the answer is a length, not an area.
Write the formula out in full before substituting. The square then cannot go missing.
The full circle area is worked out and the fraction for the angle is never applied.
Working out the circle is the substantial step, and it produces a complete-looking answer.
Question. A 90 degree sector, radius 6, pi = 3.14
A common answer. 3.14 x 36 = 113.04
The answer. 113.04 / 4 = 28.26
Why. 90 degrees is a quarter of the full 360.
Work out the fraction of 360 first and write it down. Then it cannot be forgotten.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.