Milestone Teachers

Free teacher guides · Grades 2-4 math

Math Misconception Guides

A wrong answer is often a rule the student is following. These guides name sixteen of those rules in fractions and place value, show the exact wrong answer each one gives, and give you a short small-group reteach for each.

Milestone Teachers - written by an Ontario Certified Teacher

The 8 Fraction Misconceptions in Grades 3-4 (and how to reteach each one)

Eight misconceptions, each with the exact wrong answer, a to-scale diagram, a 10-second tell, a 3-step reteach and the research source.

  1. Counting unequal parts as if they were equal Wonky
  2. Counting tick marks instead of jumps on a number line Tik
  3. Thinking a bigger denominator means a bigger fraction Biggy
  4. Ignoring the size of the whole Wholey
  5. Adding the same number to the top and bottom to make an equivalent fraction Polly
  6. Gap thinking: the same number of missing pieces means equal Gappy
  7. Adding the numerators and adding the denominators Stacker
  8. Thinking bigger numbers make a bigger fraction Grower

Read the fractions guide

The 8 Place Value Misconceptions in Grades 2-4 (and how to reteach each one)

Eight misconceptions, each with the exact wrong answer, a to-scale diagram, a 10-second tell, a 3-step reteach and the research source.

  1. Writing each part of a number name in full Hundry
  2. Leaving out the zero that holds an empty place Skippy
  3. Reading a digit at its face value Facer
  4. Reading base-ten groups in the order they sit Shuffy
  5. Cramming ten or more into one place instead of trading Crammy
  6. Comparing numbers by the first digit only Firsty
  7. Comparing numbers by the last digit only Lasty
  8. Rounding by chopping off the end Choppy

Read the place value guide

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