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WinterProgress Monitoring and Instructional Strategies for 4.NF.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
- Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
- Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
- Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
- Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
Pose add/subtract fraction problems with the same denominator
Number Talks: Refer to Chapters 4 and 6 in Making Number Talks Matter by Cathy Humphreys and Ruth Parker
Choose fractions that highlight strategies for subtractions such as: Round the subtrahend to a multiple of 1, Decompose the subtrahend, Add instead, Find the same difference, Break apart by place
Choose fractions that highlight strategies for addition such as: Round and adjust, Take and Give, Start from the Left, Break One Addend Apart, Add up.
The Chocolate Bar Problem
Adding & Subtraction Fractions (like denominators)
Sense or Nonsense 1
Sense or Nonsense 2
Teaching Student-Centered Mathematics 3-5 (Van de Walle): In chapter titled Building Strategies for Fraction Computation activities: More Than Or Less Than One, The Gold Prize
Beyond Invert and Multiply: Chapter 2