Mathematics Institute for Learning Disabilities and Difficulties


MSTAR Interventions

Key Ideas

  • Fractions are related to a whole. (See Lessons 1 and 6.)
  • Fractional parts of a whole are equal in area. (See Lessons 1 and 6.)
  • A set or collection of objects can be considered a whole. (See Lesson 2.)
  • Fractions can be used to describe parts of sets or collections of objects. (See Lesson 2.)
  • Given a unit length, as the number of parts (unit fractions) needed to make 1 whole increases, the size of each unit part decreases. (See Lesson 3.)
  • Given a unit length, as the number of parts (unit fractions) needed to make 1 whole decreases, the size of each unit part increases. (See Lesson 3.)
  • All of the parts are selected for fractions equal to 1, so the numerator (number of selected parts) is the same as the denominator (type of parts). (See Lesson 4.)
  • Fractions can be greater than 1. (See Lesson 5.)
  • For fractions greater than 1, the numerator is larger than the denominator. (See Lesson 5.)
  • Fractions are equivalent if they represent the same amount of area. (See Lesson 7.)
  • Equivalent fractions represent the same value (position on the number line). (See Lessons 7 and 8.)
  • An infinite number of fractions can represent the same position on the number line. (See Lesson 8.)
  • Equivalent fractions name the same number. (See Lessons 9, 11, and 13.)
  • Equivalent fractions can be represented by many different models. (See Lessons 9 and 11.)
  • Multiplying by 1 (applying the identity property of multiplication) requires that the same operation be performed on the numerator and the denominator. (See Lessons 10 and 12.)
  • A tool to find equivalent fractions is the multiplication table. (See Lessons 10 and 12.)
  • Creating equivalent fractions by multiplying or dividing requires that the same operation be performed on the numerator and the denominator. (See Lesson 13.)
  • Fractions can be compared, using equivalent forms of fractions. (See Lesson 14.)
  • Fractions can be ordered, using equivalent forms of fractions and a number line. (See Lesson 14.)
  • Mixed numbers are representations of fractions greater than 1 that include a whole number and a fraction. (See Lesson 15.)
  • Mixed numbers and fractions greater than 1 can be compared and ordered by creating an equivalent fraction and using a number line. (See Lesson 15.)