Lessons · Teaching · number and quantity, at the level this test asks
Number and quantity, at the level this test asks
The number questions cover fractions, decimals and percent; ratio and proportion; integers and the order of operations; and exponents and roots at a basic level. This is secondary-school arithmetic, not the elementary content you will teach, and the difference shows up most in percent change and in ratios with three parts.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
Candidates who have just prepared for an elementary content examination arrive here confident and lose marks, because 'find 30 per cent of 80' and 'a price rose 30 per cent then fell 30 per cent, what happened' are different questions. The second one is this test, and the answer is not zero.
How to think about it
Turn every percent question into a multiplication by a decimal. A rise of 30 per cent multiplies by 1.30 and a fall of 30 per cent multiplies by 0.70. For ratios, add the parts to get the number of shares and divide the total by that, rather than reasoning part by part.
Worked example
30 per cent of 80 is 0.30 x 80 = 24One multiplication. The word 'of' is the multiplication sign.
Up 30 per cent then down 30 per cent: 1.30 x 0.70 = 0.91, so 9 per cent below the startNot back where it started, and this is the most tested trap in the family.
Share 350 in the ratio 2 : 3 : 2, so seven shares of 50: 100, 150 and 1002 + 3 + 2 = 7 and 350 / 7 = 50. Add the parts first, always.
A percentage increase is the change over the ORIGINAL, not over the new numberFrom 40 to 50 is 10 / 40 = 25 per cent. From 50 to 40 is 10 / 50 = 20 per cent. The same gap, two answers.
Your turn
Name what a 30 per cent rise multiplies a number by.
A rise of 30 per cent multiplies by
Solve one, graded on the server
The trap
Averaging percentages. Two classes, one scoring 60 per cent and one 80 per cent, do not average 70 per cent unless the classes are the same size. The average of percentages is only the percentage of the whole when the groups match.