Lessons · Teaching · turning a sentence into arithmetic
Turning a sentence into arithmetic
Most mathematics marks on this test are lost in translation rather than in calculation. A word problem is solved by naming the unknown, writing what the sentence says about it as an equation, solving, and then answering the question that was actually asked, which is often not the thing you solved for.
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
This is the skill that transfers, in both directions. It is what the test is really measuring, and it is what children find hardest, which means the way you learn it here is the way you will teach it. 'What are we looking for' is the first question in both rooms.
How to think about it
Read once for the situation and once for the numbers. Write down what the unknown is, in words and with a unit. Translate phrase by phrase: 'more than' is plus, 'less than' subtracts in the reverse order, 'of' multiplies, 'per' divides. Solve, then reread the question and answer that.
Worked example
'Five less than twice a number is 17': 2n - 5 = 17, so 2n = 22 and n = 11'Five less than' puts the 5 second. Written in reading order it would be wrong.
A shirt costs 40 after a 20 per cent discount: 40 / 0.8 = 50 was the originalDivide to undo, because 0.8 of the original is what you were given.
Two workers, one taking 6 hours and one 3, together do 1/6 + 1/3 = 1/2 of the job an hour, so 2 hoursRates add. Times do not.
Solve for x and then check what was asked: often it is x + 3, not xThis is the most expensive habit on the mathematics section and the easiest to fix.
Your turn
Name the phrase that reverses the order of a subtraction.
'Five than twice a number' puts the five second
Solve one, graded on the server
The trap
Starting to calculate before naming the unknown. The arithmetic then happens to whatever numbers are nearest, and the answer is a correct calculation of something nobody asked about.