Reading first
How should a student read a CML word problem?
Since reading comprehension is built into the divisions, our method starts with the words: read, restate in your own words, then solve, then answer the exact question asked. The method and its steps are ours.
- Read once for the story. Who is doing what? Do not touch the numbers yet.
- Read again for the question. Underline what is being asked: how many, how much more, which day, what fraction.
- Restate it in one sentence of your own. "There are some apples; a third were eaten and 10 are left; find the start." If you cannot restate it, read again.
- Solve with a picture or a short list. Bars, a table or a number line, whichever fits.
- Answer the underlined question. Check units and whether the answer is a sensible size for the story.
Worked example 1 (ours, grade 4): what is really asked. A basket held some apples. Lucy ate 2 and gave away 3. Then she bought twice as many as she had left, and now has 30. How many apples were in the basket at first? Restate: "after eating and giving away, some number remained; that number tripled to 30." Buying twice as many as she had means she now has three times as many, so before buying she had 10. Add back the 5 she ate or gave away: 15 at first. The phrase "twice as many as she had left" is where readers go wrong, treating 30 as only double.
Worked example 2 (ours, grade 5): time, read carefully. A movie started at 6:45 pm and ended 1 hour 55 minutes later. Sam left 30 minutes before the end. How long did Sam watch? Restate: "the movie lasted 115 minutes; Sam missed the last 30." So Sam watched 85 minutes, or 1 hour 25 minutes. The clock times are a distraction; the question never asks when anything ended. Readers who compute 8:40 pm first have done extra work that may hide a slip.
Worked example 3 (ours, grade 6): two conditions. I am thinking of two consecutive odd numbers. Their product is 143. What is their sum? Restate: "two odd numbers in a row multiply to 143; add them." 143 is close to 12 x 12 = 144, so try the odd numbers on either side of 12: 11 x 13 = 143. The sum is 24. Estimating with a square nearby is the key move, and it only appears once the student has restated the two conditions.
Why restating works
Most lost points in reading-heavy contests come from solving a different problem from the one asked. Restating in one sentence forces the student to decide what the problem is before spending any time on numbers.
Five minutes a question is enough time to do this properly. Students who skip it to save time usually lose more than they save.
From Euclidean to Pythagorean
A student moving to the Pythagorean division meets longer sentences and more conditions. The method does not change; the restatement just gets more careful.
We practice by giving the same math in a short and a long wording, so students learn that the words, not the numbers, set the difficulty.
