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Other fraction prompts

  
This prompt comes from division = subtraction? on Don Steward's website. Students verify the equation is true before using its structure to find more examples. After a period of exploration, students might attempt to generalise before changing the prompt to explore multiplication and addition.
  
Students verify the truth of the inequality, using a number line or converting to equivalent fractions, before exploring other examples in which the numerators and denominators on the left-hand side have differences of two. As the inquiry develops, students often seek an inequality that reverses the symbol while maintaining the condition that the right-hand fraction should in the 'middle' of the other two. (That the fraction is not half way between the other two, despite both numerator and denominator being exactly in the middle, can form the topic for an interesting discussion based on the concept of a fraction.)