1 · Find the question first
Read the last sentence before you start working. "How many are left?", "how many more?", and "how many in all?" need different steps from the same numbers.
Underline the unit the answer needs (minutes, dollars, boxes). A correct number in the wrong unit is still a wrong answer.
2 · Problems with several steps
"A theater has 18 rows of 24 seats. 350 tickets are sold. How many seats are empty?" Step 1: 18 × 24 = 432 seats. Step 2: 432 − 350 = 82 empty.
Write each step's answer down. The trap choices are usually the answer to step 1.
3 · Ratios as parts
"The ratio of cats to dogs at a shelter is 2 to 3. There are 40 animals." Each group of 5 animals has 2 cats and 3 dogs. 40 ÷ 5 = 8 groups, so 16 cats and 24 dogs.
4 · More than, less than: tape diagrams
"Kim has 3 times as many stamps as Joe. Together they have 48." Joe is 1 box, Kim is 3 boxes, 4 boxes = 48, so 1 box = 12. Joe has 12 and Kim has 36.
Drawing the boxes turns a hard sentence into one division.
5 · Sum and difference
"Two numbers add to 40 and differ by 6." Take away the difference: 40 − 6 = 34. Split it: 17. The numbers are 17 and 23.
6 · Ages
Everyone gets older at the same rate. If Mom is 30 years older than Ana now, she is 30 years older in 5 years too.
"Dad is 4 times as old as Sam, and Dad is 27 years older." 4 parts − 1 part = 3 parts = 27, so 1 part = 9. Sam is 9 and Dad is 36.
7 · What to do with a remainder
"130 students, 30 per bus." 130 ÷ 30 = 4 R10. Ten students still need a seat, so 5 buses: round up.
"$130, shirts cost $30. How many can you buy?" Only 4: round down. "How much money is left?" The remainder: $10.
8 · Working backwards
"Rosa spent half her money on a book, then $6 on lunch, and had $9 left. How much did she start with?" Undo each step from the end: 9 + 6 = 15, and 15 was half, so she started with $30.
9 · Try the answer choices
When an equation feels hard, test the choices. "A number times itself, plus the number, is 42." Try 6: 36 + 6 = 42. Done.
Start with a middle choice. If it is too big, the answer is smaller, and you have ruled out two choices at once.
10 · Estimate to rule things out
"Which is closest to 49 × 21?" 50 × 20 = 1,000. You do not need the exact answer (1,029) to pick the choice near 1,000.
Ask whether the answer should be more or less than the numbers you started with. That removes impossible choices fast.
11 · "Must be true" questions
Some ISEE questions ask which statement must be true. A statement that is true for one example is not enough; it has to work for every case the problem allows.
Test a choice with two quick examples. If one example breaks it, cross it out.
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