4.NF.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Formative Assessment Rubric
A. Understand addition and subtraction of fractions as joining and
separating parts referring to the same whole.
B. 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.
C. 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.
D. 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.
Learning Targets
About the Math
Addition and subtraction of fractions with like denominators can easily be solved using an algorithm of adding or subtracting the numerators and keeping the same denominator. However, prior to this, students need instruction on the conceptual understanding of adding and subtracting fractions and what a reasonable answer looks like. Questions such as will the answer when you add 7/8 + 3/8 be more or less than a whole and why? should be part of instruction. Concrete materials
should be used to introduce addition and subtraction prior to moving to the algorithm.
denominator
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Formative Assessment Rubric
A. Understand addition and subtraction of fractions as joining and
separating parts referring to the same whole.
B. 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.
C. 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.
D. 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.
Learning Targets
- I can use models to add and subtract fractions.
- I can use visual models to decompose a fraction. For example, 7/12 = 4/12 + 1/12 + 1/12 + 1/12.
- I can add or subtract mixed numbers.
- I can solve word problems with fractions
About the Math
Addition and subtraction of fractions with like denominators can easily be solved using an algorithm of adding or subtracting the numerators and keeping the same denominator. However, prior to this, students need instruction on the conceptual understanding of adding and subtracting fractions and what a reasonable answer looks like. Questions such as will the answer when you add 7/8 + 3/8 be more or less than a whole and why? should be part of instruction. Concrete materials
should be used to introduce addition and subtraction prior to moving to the algorithm.
- Students need to see that a fraction can be decomposed just like whole numbers. There are many different ways to decompose a fraction. Understanding this helps students see the value of fractions and enhances their fraction sense.
- 7/10 = 1/10 + 1/10 +1/10 + 1/10 +1/10 + 1/10 + 1/10 or 3/10 + 3/10 + 1/10 or 5/10 + 2/10 or 4/10 + 2/10 + 1/10.
- A mixed number is a whole number and a fraction. Students need to see that 3 ¼ is the same as 3 + ¼. This can be connected to the previous standard of decomposing fractions.
- Drawing a picture and writing an equation are two effective strategies when solving word problems with fractions. Writing an equation helps students translate word phrases into numbers. Encourage students to use these two strategies instead of looking for key words. Looking for key words should be avoided because key words can indicate different operations depending on the context in the problem.
denominator