5.NF.1 and 5.NF.2
Conceptua: Addition and Subtraction of Fractions and Mixed Numbers
Suggested Pacing Includes a review of:
- adding and subtracting like fractions (Big Idea 3)
- equivalency (Big Idea 5)
- adding and subtracting with uncommon denominators (Big Idea 6)
***Note: If you are using this guide to support intervention for Grade 6 students you may wish to take more time with above mentioned concepts. This guide accelerates to adding and subtracting of mixed numbers (Big Idea 7). Grade 7 and Grade 8 students should be able to move fairly quickly to Big Idea 7 and will likely need the above review.
Prior to starting this work, students could create their “fraction kit” by folding fraction strips. They created fraction kits last year in 4th grade so this work would be a nice jump-start in fraction thinking. You will need 8-10 unfolded fraction strips per student. Students should have the following fraction strips in their kits: whole (white), pink (halves), purple (fourths), salmon (eighths), blue (thirds), green (sixths), yellow (fifths), dark pink (tenths).
- Remember to cut extra especially for thirds and fifths. You may wish to pre-fold some thirds and fifths.
- Model and encourage the use of “unit fraction language” as the students fold their fraction strips. e.g., 5/5 is 5 pieces of size 1/5.
- Do NOT label the fraction strips
Keep in mind:
Students worked with many visual models including number lines, bar models (vertical and horizontal), circle models, set models, and area models in Grades 3-5. Model, support, and ask for students to work with a variety of models when the opportunity is available.
Throughout this unit:
(1)Students are to engage regularly with Lesson Openers and Lesson Closers by drawing out models on whiteboards or modeling problems using fraction strips.
(2)Actively encourage mathematical discourse through the use of the Talk Moves as they referenced in Lesson Openers and Lesson Closers.
(3)Model and encourage the use of “unit fraction language” during Lesson Openers, Lesson Closers, and one-on-one teaching conversations as you monitor the Guided Practice.
(4)Reminder: Skills Checks are to be done independently.
(5)CCSSM Standard 5.NF.1 is developed throughout this work, especially in Big Idea 7.
(6)5.NF.2 will be addressed in the homework for this unit. Though, as regularly as possible during Lesson Openers or Lesson Closers, ask students to give contextual situations for the various addition and subtraction equations they are working on within lessons.
Use equivalent fractions as a strategy to add and subtract fractions.
5.NF.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
Lesson / Instruction Format / CCSSM / Implementation Suggestion (when applicable) and/or instructional focus for each lessonsSept 4-Sept 6 Big Idea 3 Topic 1: Adding to 1 Whole Review ***No individual computers needed.
3-1-1 Add Unit Fractions
3-1-3 Add Proper Fractions
3-2-3 Subtract Proper Fractions
**”Shift, Command & Click on ” to advance a screen.
***”Shift, Caps Lock & Click on ” to reverse a screen. / Whole Group Review / 4.NF.3 / Day #1
3-1-1 Add unit fractions using only visual models.
Conduct 3-1-1 Opener. Engage students in selected tasks from the Guided Practice. Students should draw models on white boards or use fraction strips to model the recommended tasks. Conduct 3-1-1 Closer
Recommended Guided Practices Tasks:
#2, #6 draw on whiteboards, #11, #12, #13, #16 using all visual models, #22-30 (your pick!) students solve, draw a visual model, and develop a realistic context.
Day #2
3-1-3 Add like fractions using visual models, visual models with numbers, numbers only.
Conduct 3-1-3 Opener. Engage students in selected tasks from the Guided Practice. Students should draw models on white boards or use fraction strips to model the recommended tasks. Conduct 3-1-3 Closer
Recommended Guided Practices Tasks:
Do a few examples from #1-#10 which use visual models only, Do a few examples from #11-#15 which shows equations and models. All should do #15 on their whiteboards and show 2 different models, #21-#30 do any and be sure to ask for a few to be done with visual models. Students should practice developing a realistic context for selected problems.
Day #3
3-2-3 Subtract proper fractions using visual models, visual models with numbers, numbers only.
Conduct 3-2-3 Opener. Engage students in selected tasks from the Guided Practice. Students should draw models on white boards or use fraction strips to model the recommended tasks. Conduct 3-2-3 Closer
Recommended Guided Practices Tasks:
You may select from the following categories to go through with the students: #1-#10 Includes only visual models. Take this opportunity to reinforce precise unit fraction language, e.g., 5 pieces of size ⅙, remove 2 pieces of size ⅙, how many pieces of size ⅙ remain? Create a context. “I have 5/6 yard of fabric. I used 2/6 yard to make a pencil pouch. How much fabric is left?” #11-#20 includes visual models & equations, #21-#25 are equations only. Continue to model and ask students to produce realistic and correct contextual situations throughout.
BI 5: Learning Equivalent Fractions Topic 3: Learn the Procedure for Finding Equivalent Fractions (Review)
**Assign Big Idea 5 Topic 3 to your class.
5-3-1 Use Words and
Models to Find Equivalence / Opener, Guided Practice, Skills Check, Closer / 4.NF.1
4.NF.2 / Day #4 5-3-1 Find equivalent fractions using a sentence frame and models.
5-3-2 Use Multiplication
by 1 for Equivalence / Opener, Guided Practice, Skills Check, Closer / Day #5 5-3-2 Use the “one” fraction procedure and models to create fraction equivalence
5-3-3 Find Equivalence
with Procedures / Opener, Guided Practice, Skills Check, Closer / Day #6 5-3-3 Use the “one” fraction procedure with or without models to create fraction equivalence
CCSSM Standards reviewed in this first section:
Extend understanding of fraction equivalence and ordering.
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
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.
Topic 1: Find Common Denominators to Add and Subtract Common Fractions
***Assign Big Idea 6 Topic 2 to your class.
6-1-1 Model Common
Denominators for Related
Fractions / Opener, Guided Practice, Closer / 5.NF.1 / Day #7
1st Facilitate Opener for 6-1-1
6-1-1 has students finding common denominators for related fractions using bar model only.
2nd Facilitate Opener for 6-1-2
6-1-2 has students finding common denominators for related fractions using visual models and then adding or subtracting those fractions. All sums and differences are less than 1.
3rd Students login and complete Guided Practice for 6-1-1 and 6-1-2
4th Close with 6-1-2 Closer.
6-1-2 Add/Subtract Related
Fractions Using Models / Opener, Guided Practice, Skills Check, Closer
6-1-3 Model/Write Common
Denominators–Related Fractions / Opener, Guided Practice, Skills Check, Closer / Day #8 – Day #9 1st Facilitate Opener for 6-1-3
6-1-3 has students changing one fraction so it has the same denominator as the other fraction shown.
2nd Facilitate Opener for 6-1-4
6-1-4 has students changing one fraction so it has the same denominator as the other fraction shown.
3rd Students login and complete Guided Practice for 6-1-3 and 6-1-4
4th Close with 6-1-4 Closer.
6-1-4 Add/Subtract
Related Fractions
Using a “One” Fraction / Opener, Guided Practice, Skills Check, Closer
Topic 2: Add and Subtract Related Fractions (Lessons 6-2-1 & 6-2-2) ***Assign Big Idea 6 Topic 2 to your class.
6-2-1 Find Common
Denominators for Related
Fractions / Opener, Guided Practice, Skills Check, Closer / 5.NF.1 / Day #10
1st Facilitate Opener for 6-2-1
6-2-1has students use the “one” fraction procedure to find common denominators for related fractions with and without models.
2nd Facilitate Opener for 6-2-2
6-2-2 has students use the “one” fraction procedure to solve + and – with related fractions without using models.
3rd Students login and complete Guided Practice for 6-2-1 and 6-2-2
4th Close with 6-2-2 Closer.
6-2-2 Add/Subtract Related
Fractions Using Equations / Opener, Guided Practice, Skills Check, Closer
Day #11
Suggestion: Administer Progress Monitoring Probe from easyCBM
Big Idea 7 will be taught using the standard Conceptua Lesson Plan format of Opener, Guided Lesson, and Closer. One lesson per day.
Big Idea 7 Topic 1: Add and Subtract Related Improper Fractions ***Assign Big Idea 7 Topic 1 to your class.7-1-1 Find Common
Denominators for
Improper Fractions / Opener, Guided Practice, Skills Check, Closer / 5.NF.1 / Use the “one” fraction procedure to find a common denominator for two related improper fractions.
Fractions will be greater than 1 and less than 1. This work is one with models and without models. No adding/subtracting yet.
7-1-2 Add/Subtract
Related Improper Fractions / Opener, Guided Practice, Skills Check, Closer / Use models and the “one” fraction procedure to find a common denominator for two related improper fractions in order to complete addition or subtraction equations.
This work is done with models and the “1” fraction procedure. Sums will be greater than 1 and will be displayed as improper fractions (not mixed numbers). Subtraction will start with the subtrahend as an improper fraction.
7-1-3 Review How to
Convert Improper Fractions / Opener, Guided Practice, Skills Check, Closer / Convert improper fractions to mixed numbers with and without models.
7-1-4 Add Related Improper
Fractions: Convert Sum / Opener, Guided Practice, Skills Check, Closer / Add and subtract related improper fractions and convert the sum to a mixed number. Moving from computing with models and computing without models.
Topic 2: Add and Subtract Related Mixed Numbers ***Assign Big Idea 7 Topic 2 to your class.
7-2-1 Find Common
Denominators for Related
Mixed Numbers / Opener, Guided Practice, Skills Check, Closer / 5.NF.1 / Use the “1” fraction procedure to find a common denominator for two mixed numbers with and without models.
7-2-2 Add/Subtract Related
Mixed Numbers / Opener, Guided Practice, Skills Check, Closer / Use models and the “one” fraction procedure to find a common denominator for two related mixed numbers in order to complete addition or subtraction equations.
7-2-3 Convert to Add
Related Mixed Numbers / Opener, Guided Practice, Skills Check, Closer / Add related mixed numbers and convert the sum to a mixed number with the help of models.
7-2-4 Convert to Subtract
Related Mixed Numbers / Opener, Guided Practice, Skills Check, Closer / Convert mixed number minuends of related mixed numbers to improper fractions in order to complete subtraction equations.
Suggestion: Administer Progress Monitoring Probe from easyCBM after Topic 2 has been completed.
Topic 3: Add/Subtract Unlike Improper Fractions/Mixed Numbers ***Assign Big Idea 7 Topic 3 to your class.
7-3-1 Model/Write Common
Denominators–Unlike Fractions / Opener, Guided Practice, Skills Check, Closer / 5.NF.1 / Use the “1” fraction procedure to find a common denominator for two unlike fractions or mixed numbers with and without models.
7-3-2 Add/Subtract Unlike
Fractions / Opener, Guided Practice, Skills Check, Closer / Use the “one” fraction procedure to find a common denominator for two unlike fractions or mixed numbers with and without models.
7-3-3 Add Unlike Improper
Fractions–Convert Sum / Opener, Guided Practice, Skills Check, Closer / Add related mixed numbers and convert the sum to a mixed number with and without the use of models.
7-3-4 Convert to
Subtract Unlike Mixed Numbers / Opener, Guided Practice, Skills Check, Closer / Convert mixed number minuends of unlike mixed numbers to improper fractions in order to complete subtraction equations.
Topic 4: Apply Your Knowledge of Related/Unlike Improper and Mixed Numbers
***Assign Big Idea 7 Topic 4 to your class.
7-4-1 Compare Equations
of Uncommon Fractions / Opener, Guided Practice, Skills Check, Closer / 5.NF.1 / Use 2 strategies to compare fractions and fraction expressions with uncommon denominators.
7-4-2 Add/Subtract Uncommon Fractions with
Unknowns / Opener, Guided Practice, Skills Check, Closer / Solve for an unknown in an addition or subtraction equation of unlike fractions with and without the use of models.
Suggestion: Administer Progress Monitoring Probe from easyCBM