Fraction Steps Progression Chart
CCSS Math • 5.NF.A.1 & 5.NF.A.2
Fraction Steps Progression Chart
Learning Target Roadmap: Adding Fractions with Unlike Denominators (Prerequisite to Mastery)
Student:
Current Level: 1 2 3 4 5
1. Prerequisites
2. Visual Models
3. Common Denominators
4. Standard Algorithm
5. Mastery & Transfer
LEVEL 1
Foundation: Like Denominators & Equivalence
Prerequisite (4.NF.A.1, 4.NF.B.3)
I Can: Add fractions with matching denominators by combining equal parts, and generate equivalent fractions using multiplication.
Success Criteria: I know the denominator tells the total size of equal slices, so only numerators add.
Sample Model
\(\frac{1}{4} \times \frac{2}{2} = \frac{2}{8}\) | \(\frac{2}{8} + \frac{3}{8} = \frac{5}{8}\)
LEVEL 2
Conceptual: Visual Area Models & Estimation
Conceptual Bridge (5.NF.A.2)
I Can: Represent unlike fractions on partitioned grids or number lines and estimate benchmark sums (0, \(\frac{1}{2}\), 1).
Success Criteria: I can prove why \(\frac{1}{2} + \frac{1}{4} \neq \frac{2}{6}\) by slicing wholes into equal overlapping units.
Area Grid Partition
\(\frac{1}{2}\) [horizontal] + \(\frac{1}{3}\) [vertical] = \(\frac{3}{6} + \frac{2}{6} = \frac{5}{6}\)
LEVEL 3
Strategy: Finding Common Denominators
Method Transition (5.NF.A.1)
I Can: List multiples of unlike denominators to find a shared multiple (LCM) and rewrite both fractions with matching units.
Success Criteria: I multiply the numerator and denominator by the exact same scale factor so the fraction value remains equal.
LCM Strategy for 4 & 6
M(4): 4, 8, 12... | M(6): 6, 12...
Common Denominator = 12
LEVEL 4
Procedural Fluency: Adding Unlike Fractions
Target Standard (5.NF.A.1)
I Can: Convert unlike fractions into equivalent forms with like denominators, add numerators, and simplify or express improper sums.
Success Criteria: I rename both fractions correctly: \(\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}\) and check if the sum can be reduced.
Standard Computation
\(\frac{3}{4} + \frac{1}{6} = \frac{9}{12} + \frac{2}{12} = \frac{11}{12}\)
LEVEL 5
Mastery & Application: Mixed Numbers & Word Problems
Full Mastery (5.NF.A.1, 5.NF.A.2)
I Can: Add mixed numbers with unlike denominators, regroup improper fraction sums into whole numbers, and solve complex multi-step word problems.
Success Criteria: I check answers for reasonableness using benchmark estimation and write clear mathematical explanations.
Mixed Number & Regrouping
\(2\frac{2}{3} + 1\frac{3}{4} = 2\frac{8}{12} + 1\frac{9}{12}\)
\(= 3\frac{17}{12} = 4\frac{5}{12}\)
Instructional Pathway: Ensure students develop conceptual fluency with visual models before practicing the standard algorithm.
Page 1 of 2 • Progression Anchor
Formative Assessment & Goal Setting
Target Evidence & Diagnostic Guide
Domain: 5.NF (Number & Operations)
Teacher Formative & Student Self-Check
Formative Look-Fors & Common Misconceptions
Observe during independent work & math talks
| Level | Demonstrated Look-Fors | Frequent Misconception | Instructional Pivot |
|---|
| L1: Prereq | Multiplies top & bottom by identical factor (\(\times \frac{n}{n}\)). | Adds denominators: \(\frac{2}{5} + \frac{1}{5} = \frac{3}{10}\). | Use fraction strips: "The denominator names unit size; units don't add." |
| L2: Models | Partitions area grids; estimates benchmark sums (\(0, \frac{1}{2}, 1\)). | Treats unequal pieces as equal: \(\frac{1}{2} + \frac{1}{4} = \frac{2}{6}\). | Shade \(\frac{1}{2}\) and \(\frac{1}{4}\); ask: "Can the sum be smaller than \(\frac{1}{2}\)?" |
| L3: Common | Lists multiples systematically to identify the least common multiple. | Scales denominator without scaling numerator proportionally. | Identity Property: Multiplying by \(\frac{3}{3}\) equals multiplying by 1. |
| L4: Fluency | Converts both fractions, adds numerators, and simplifies accurately. | Cross-multiplies mechanically without conceptual understanding. | Require writing full conversion step (\(\frac{1}{3} \times \frac{4}{4} = \frac{4}{12}\)) first. |
| L5: Mastery | Adds whole numbers, renames fraction parts, and regroups sums \(> 1\). | Leaves improper fraction inside mixed number (e.g., \(3\frac{14}{12}\)). | Decompose improper fraction: \(\frac{14}{12} = 1\frac{2}{12}\); add 1 to whole: \(4\frac{2}{12}\). |
Student Self-Reflection & Mastery Evidence Log
1 = Developing | 2 = Approaching | 3 = Proficient | 4 = Mastered
| Level | Learning Target (I Can Statement) | Self-Rating | Date Check | Evidence / Artifact |
|---|
| Level 1 | I can create equivalent fractions and add with like denominators. | 1 2 3 4 | | |
| Level 2 | I can draw area models and estimate sums using benchmark fractions. | 1 2 3 4 | | |
| Level 3 | I can list multiples to find the LCM and rewrite both fractions. | 1 2 3 4 | | |
| Level 4 | I can add unlike fractions with the standard algorithm and simplify. | 1 2 3 4 | | |
| Level 5 | I can add mixed numbers with unlike denominators and solve word problems. | 1 2 3 4 | | |
Student Action Plan & Conference Check-In
My Target Goal:
Current Level: ___ | Target: ___
Strategy or model I will practice this week:
Teacher Feedback & Look-For:
Verified: [ ]
Teacher Signature: __________________ Date: __________
Grade 5 Common Core Standard: CCSS.MATH.CONTENT.5.NF.A.1 & 5.NF.A.2 Page 2 of 2 • Mastery Tracking
