Worked examples
Three worked Hunter-style math examples
Problems we invented at a strong grade 6 level. They are not Hunter questions and are not taken from either Hunter sample exam.
Example 1: parts of a whole, in two steps. A jar holds red, blue and green marbles. One third are red, one quarter are blue, and the remaining 20 are green. How many marbles are in the jar? Reasoning: red and blue together are 1/3 + 1/4 = 4/12 + 3/12 = 7/12. So green is 5/12 of the jar, and 5/12 of the total is 20, which makes 1/12 equal to 4 and the whole jar 48. Check: 16 red, 12 blue, 20 green, total 48. A five-choice list would likely include 60, the answer for someone who treats green as one third.
Example 2: a fraction of a fraction. Lena cuts a ribbon in half and gives one half away. She cuts the rest into four equal pieces and uses three of them. What fraction of the original ribbon did she use? She kept 1/2, and used 3/4 of that: 3/4 x 1/2 = 3/8. The common slip is answering 3/4, which is the fraction of the kept half, not of the whole ribbon. Reading the last words of the question again, "of the original ribbon", saves the point.
Example 3: a repeating pattern. The digits 1, 4, 2, 8, 5, 7 repeat forever: 142857142857... What is the 1,000th digit? The block has 6 digits, so divide: 1,000 = 6 x 166 + 4. After 166 full blocks we need the 4th digit of the block, which is 8. Hunter’s own description mentions recognizing "patterns and relationships"; finding the cycle length and using the remainder is the whole idea.
What the examples share
Each needs only grade 6 content, but each is two or three steps, and each has one tempting wrong answer that a careless reader would choose from five options.
None needs a calculator, but all of them need clean written working, because a jumbled page makes it easy to lose a twelfth or a remainder.
How we teach from them
Before writing, the student says the plan aloud: "add the known parts, find what is left, scale up." Next, one number is swapped for a new one and the student works it through once more, which tests the method rather than the memory.
Last, we write the five choices ourselves and ask the student which wrong answers a rushed reader would pick. Knowing the traps is half of avoiding them.
