Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
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.
[divider] [/divider]Students are able to…
- Decompose and compose fractions, including fractions greater than one, and mixed numbers into unit fractions and fractions with the same denominator using models and pictures prior to moving to an algorithm.
- Understand that the denominator names the unit being added or subtracted. Just as they added 1 teddy bear to 3 teddy bears when they were in the primary grades, they are now adding 1 “sixth” to 3 “sixths”.
- Use words, pictures, and/or numbers to explain any algorithm used to regroup fractions or add and subtract fractions and mixed numbers.
- Use a variety of materials to model and describe various situations involving adding and subtracting fractions and mixed numbers.
- Explain their thinking using models, pictures, numbers and words.
[divider] [/divider]Students are able to…because teachers…
- Provide students with manipulatives including fraction tiles, number lines and area models to use as they solve problems involving addition and subtraction of fractions.
- Provide opportunities for students to compose and decompose fractions, including fractions greater than 1 and mixed numbers, into unit fractions and fractions with the same denominator using concrete and pictorial representations, words, and numbers.
- It is important to provide students ample opportunity to experience tasks oriented around the two bullets above (components “a.” and “b.” of the standard) before moving to using procedural algorithms to solve word problems involving addition and subtraction of fractions and mixed numbers. This will help build a strong conceptual foundation that students will need in 5th grade when working with unlike denominators.
- Provide activities that make connections between addition and subtraction of fractions to addition and subtraction of whole numbers.
[divider] [/divider]Questions to ask students:
- Ask students to decompose a fraction like 4/3 into a sum of fractions in more than one way.
- Sample answer that indicates understanding: 1/3 + 1/3 + 1/3 +1/3 or 2/3 + 2/3 or 1/3 + 3/3 or 2/3 + 1/3 + 1/3 including the rearrangement of the addends.
- Sample answer that indicates an incomplete understanding or a misconception: An incomplete or inaccurate list of number sentences.
- Ask students to explain and/or model how to find the difference between two fractions or mixed numbers like 2 3/4 – 1 2/4.
- Sample answer that indicates understanding: Student can use fraction strips, number lines, drawings, or words to describe the process of subtracting both whole and fourths to arrive at a difference of 1 1/4.
- Sample answer that indicates understanding: Student can use fraction strips, number lines, drawings, or words to describe the process of subtracting both whole and fourths to arrive at a difference of 1 1/4.
- When would renaming a mixed number into fractions greater than one make the problem easier to solve?
- Sample answer that indicates understanding: Student should be able to share with you an example of an expression where renaming would help to find the sum or difference such as: 2 and 3/10 – 1 and 7/10 and one where renaming is not needed such as: 1 and 3/4 – 1 and 1/4.
- When you add two fractions with same denominator why does the sum also have the same denominator?
- Sample answer that indicates understanding: The denominator names the unit or the size of the pieces. The size of the pieces does not change when you add them.
- Sample answer that indicates an incomplete understanding: They just always stay the same or my teacher told me that they always stay the same.
[divider] [/divider]FSA Notes
Cognitive Complexity Level: 2: Basic Application of Skills & Concepts
Achievement Level Descriptors:
2-adds and subtracts fractions with like denominators by joining and separating parts referring to the same whole; decomposes a fraction into a sum of fractions with the same denominator in more than one way and records and represents the decomposition using an equation
3- adds and subtracts fractions and/or mixed numbers with like denominators, in mathematical and real-world context, by replacing each mixed number with an equivalent fraction, without regrouping, and by using the properties of operations and the relationship between addition and subtraction; decomposes a mixed number into a sum of fractions with the same denominator in more than one way and records and justifies the decomposition
4- adds and subtracts mixed numbers with like denominators, in mathematical and real-world context, by replacing each mixed number with an equivalent fraction, with regrouping, and by using the properties of operations and the relationship between addition and subtraction
5- solves multi-step word problems involving addition and subtraction of fractions and/or mixed numbers
Assessment Limits:
Denominators of given fractions are limited to: 2, 3, 4, 5, 6, 8, 10, 12, 100.
Mixed numbers and fractions must contain like denominators.
Items must reference the same whole.
Visual fraction models are limited to circular models, rectangular models, and number line models.
[divider] [/divider]Additional Resources:
Additional in depth content knowledge
Video: Decomposing fractions within word problems
Adding and subtracting mixed numbers using equivalent fractions
K-5 Progression of standards leading up to and including adding and subtracting fractions
Comparing strategies for adding and subtracting mixed numbers (not always renaming mixed numbers)
[divider] [/divider]Sample Formative Assessment Tasks:
[divider] [/divider]Resources/Tasks to Support Your Child at Home
Find fractions in magazines or recipes and have your child decompose them as many different ways as they can. For example: 1 3/4 can be broken down to 4/4 + 3/4 or 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4+ 1/4
Learnzillion – “Decompose fractions into…” https://goo.gl/S1P9X9
Learnzillion- “Add and subtract fractions…” https://goo.gl/9mHnM8
Learnzillion “Add and subtract mixed numbers…”- https://goo.gl/94Xwil
Practice adding fractions with like denominators with an interactive number line: http://www.visualfractions.com/AddEasy/addlines.html
Play Fruit Splat Fraction Addition: https://goo.gl/F7FWzB
Math Man is a “Pac-man” style game. Practice adding and subtracting fractions with like denominators: https://goo.gl/Hgsuap
Get cooking! Involve your child in helping with following a recipe using fractions. Before they combine dry ingredients, such as three-fourths cup of flour and one-fourth cup of sugar, ask them to think about how many total cups they will have of dry ingredients.
Khan Academy Practice Addition and Subtraction Word Problems (like denominators) – https://goo.gl/pkgArS