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Multi-Digit and Fraction Computation
Students extend their understanding of multiplication and division to divide fractions by fractions, and develop fluency with whole number and decimal operations.
Math
Unit 3
6th Grade
Unit Summary
Please Note: In October 2026, this unit and its lesson plans received a round of enhancements. Teachers should pay close attention as they intellectually prepare to account for the updated pacing and content.
In Unit 3, 6th Grade students extend their understanding of the number system by applying multiplication and division concepts to fractions, whole numbers, and decimals. Students begin by developing conceptual understanding of fraction division, using visual models and patterns to make sense of why dividing a fraction is connected to multiplying by its reciprocal. They then extend their understanding of division strategies to develop fluency with whole number and decimal operations, making connections between concrete representations, partial quotients, and efficient algorithms. They also look for and use structure across representations and procedures, recognizing how mathematical relationships can be generalized and applied across fraction division, whole number and decimal operations, and the relationships among factors, Greatest Common Factor (GCF), and Lowest Common Multiple (LCM). MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.
Throughout the unit, students examine the structure behind computation methods to make sense of how the algorithm works. By reasoning about patterns and place value relationships, students develop more efficient strategies for multiplying and dividing decimals and apply these methods to solve and interpret real-world problems, including rate applications from Unit 2.
In 6th Grade math, students develop, practice, and demonstrate fluency with decimal operations. However, practice should be embedded throughout the rest of the year to support fluency. Future units, including units on expressions and equations provide some additional opportunities for students to use these skills in meaningful contexts. See our Procedural Skill and Fluency Guide for additional information and activity suggestions.
Throughout elementary grades, students developed their understanding of the base-ten system. They found sums, products and quotients by using concrete models, place value, properties of operations, and the relationships between operations. Intentionally, students did not learn a standard algorithm until they had the conceptual understanding to back it up. Some of these strategies are revisited in this unit in order to ensure that students firmly understand the reasoning behind an algorithm, rather than using it without understanding.
Once students have completed their study of the positive number system of fractions, decimals, and whole numbers, they will investigate the numbers to the left of 0 on the number line, or negative rational numbers, in Unit 4. In 7th Grade Math, students will learn how to compute with all rational numbers, including negatives, and in 8th Grade Math and high school, students learn about irrational numbers, rounding out their study of the real number system.
Pacing: 22 instructional days (19 lessons, 2 flex days, 1 assessment day)
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Assessment
The following assessments accompany Unit 3.
Pre-Unit
Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Mid-Unit
Have students complete the Mid-Unit Assessment after Lesson 12.
Post-Unit
Use the resources below to assess student understanding of the unit content and action plan for future units.
Use student data to drive instruction with an expanded suite of assessments. Unlock Pre-Unit and Mid-Unit Assessments, and detailed Assessment Analysis Guides to help assess foundational skills, progress with unit content, and help inform your planning.
Unit Prep
Intellectual Prep
Before you teach this unit, unpack the standards, big ideas, and connections to prior and future content through our guided intellectual preparation process. Each Unit Launch includes a series of short videos, targeted readings, and opportunities for action planning to ensure you're prepared to support every student.
Internalization of Standards via the Post-Unit Assessment
- Take Post-Unit Assessment. Annotate for:
- Standards that each question aligns to
- Strategies and representations used in daily lessons
- Relationship to Essential Understandings of unit
- Lesson(s) that Assessment points to
Internalization of Trajectory of Unit
- Read and annotate the Unit Summary.
- Notice the progression of concepts through the unit using the Lesson Map.
- Do all Target Tasks. Annotate the Target Tasks for:
- Essential Understandings
- Connection to Post-Unit Assessment questions
- Identify key opportunities to engage students in academic discourse. Read through our Teacher Tool on Academic Discourse and refer back to it throughout the unit.
Unit-Specific Intellectual Prep
- Read the Progressions for the Common Core State Standards in Mathematics, The Number System, 6-8 for relevant standards in this Number System domain.
Essential Understandings
- Dividing by a fraction is the same as multiplying by the denominator and dividing by the numerator, or equivalently, multiplying by the reciprocal of the fraction.
- The general approach to dividing with fractions can be applied to real-world problems involving division, such as partitioning into equal groups and finding missing factors.
- Standard algorithms for computing with decimals are efficient strategies to add, subtract, multiply, and divide decimals. These algorithms are rooted in the same concepts as previously learned strategies.
- Every number can be decomposed into a product of prime factors. These prime factors can be used to find greatest common factors and least common multiples between pairs of numbers.
Materials
- Markers or crayons (1 set per group)
- Poster paper (1 per group)
- Slicing Scenario Info Gap Handout & Cards (1 per group)
- Ruler (1 per group)
- Graph Paper (16-24 sheets per student)
- Factor Dominoes (1 per small group) – the cards can be printed so the pictures can be cut out and optionally pasted onto a cardstock or a different colored paper background.
- Optional: Colored Pencils (1 set per student pair)
- Optional: Calculators (1 per student) – calculators can be used to check answers
Vocabulary and Models
Unit Vocabulary
composite number
factor
greatest common factor (GCF)
least common multiple (LCM)
long division/ standard algorithm for division
multiple
prime number
prime factorization
reciprocal
relatively prime
Foundational Vocabulary
divisor
dividend
partial product
quotient
To see all the vocabulary for Unit 3, view our 6th Grade Vocabulary Glossary.
Access foundational vocabulary for Unit 3 in the same 6th Grade Vocabulary Glossary.
Models
| Model | Example |
| partial product | Multiply 12.6 and 4.8 using partial products.
|
| partial quotient | Divide 67,764 by 12 using partial quotients.
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| Venn Diagram | Use a Venn diagram to find the GCF of 12 and 18.
|
Unit Practice
Lesson Map
Topic A: Dividing with Fractions
Topic B: Computing with Decimals
Topic C: Applying the Greatest Common Factor and the Least Common Multiple
Common Core Standards
Key
Major Cluster
Supporting Cluster
Additional Cluster
Core Standards
The Number System
Foundational Standards
Number and Operations in Base Ten
Number and Operations—Fractions
Operations and Algebraic Thinking
Future Standards
The Number System
Standards for Mathematical Practice
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CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
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CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
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CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
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CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
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CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
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CCSS.MATH.PRACTICE.MP6 — Attend to precision.
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CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
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CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
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