Unit 2 — Modeling Multiplication, Division and Fractions
Description
Unit 2 deepens understanding of multiplication and division by applying properties of operations (commutative, associative, distributive) as strategies. Students explore how area models and tiling represent the distributive property and connect this to finding areas of rectangles with different dimensions. The unit introduces fractions by having students partition shapes into equal parts and recognize unit fractions. Students understand that a fraction a/b is composed of a parts of size 1/b. They fluently multiply and divide within 100 using strategies based on number relationships. Two-step word problems using all four operations are solved using equations with unknowns, and students assess reasonableness using estimation. Addition and subtraction within 1000 build computational fluency.
Essential Questions
- How can area be determined without counting each square?
- How can the knowledge of area be used to solve real world problems?
- How can the same area measure produce rectangles with different dimensions?
- How does understanding the distributive property help us multiply large numbers?
- How are multiplication and division related?
- How can you write a mathematical sentence to represent a multiplication or division model we have made?
Learning Objectives
- Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide.
- Use tiling and area models to represent the distributive property.
- Solve real-world problems involving areas of rectilinear figures by decomposing into non-overlapping rectangles.
- Fluently multiply and divide within 100 using strategies based on properties and relationships.
- Solve two-step word problems using all four operations and represent with equations containing unknowns.
- Identify arithmetic patterns in addition and multiplication tables and explain them using properties of operations.
- Fluently add and subtract within 1000 using strategies and algorithms based on place value and properties.
- Partition shapes into parts with equal areas and express each part as a unit fraction.
- Interpret unit fraction 1/b as the quantity formed by 1 of b equal parts of a whole.
Supplemental Resources
- Fraction bars and visual fraction models for partitioning shapes
- Grid paper and unit squares for tiling and area representation
- Multiplication and addition/subtraction charts for pattern identification
- Sticky notes for organizing and explaining arithmetic patterns
- Plastic page protectors for dry-erase activities with properties of operations
Geometry
Measurement
Number and Operations in Base Ten
Number and Operations—Fractions
Operations and Algebraic Thinking
Students use reading comprehension skills to problem solve and explain mathematical thinking in written form using mathematical terms. Students connect everyday vocabulary to strengthen their understanding of mathematical concepts.
Formative Assessments
- Exit tickets checking understanding of properties of operations and fraction concepts
- Classwork using area models and tiles to show distributive property
- Individual work solving two-step word problems and writing equations with unknowns
- Math journals showing student thinking about fractions and equal partitions
- Group activities identifying and explaining arithmetic patterns
Summative Assessment
Chapter tests on properties of operations, area of rectilinear figures, and fractions; performance tasks requiring application of properties to solve multiplication problems; extended projects creating shapes partitioned into unit fractions.
Benchmark Assessment
Benchmark assessments within Go Math, Eureka Math, and iReady programs; PARCC practice tests; state testing results.
Alternative Assessment
Students may demonstrate understanding of properties of operations and area models through manipulatives (tiles, base-ten blocks, or fraction strips) combined with oral explanation or teacher-guided questioning in place of written work. Visual supports such as labeled area model diagrams or pre-drawn partition templates may be provided to support fraction identification and representation.
IEP (Individualized Education Program)
Students may benefit from visual and concrete supports such as manipulatives, grid paper, and fraction models when working with area representations and equal partitions. Providing a reference card with multiplication and division fact strategies, labeled area model templates, and fraction strips can reduce cognitive load while keeping focus on conceptual understanding. For two-step word problems, breaking the problem into clearly numbered steps with space to show each part of the equation supports processing and organization. Output options such as oral explanation, pointing to models, or dictating responses to a scribe should be made available, particularly during assessments involving written equations or math journals.
Section 504
Students should be provided extended time on chapter tests and performance tasks, particularly those involving multi-step problem solving and fraction work. A distraction-reduced environment and preferential seating near instruction supports focus during modeling of properties and area concepts. Allowing the use of a multiplication reference chart during non-fact-fluency assessments ensures that access to the broader unit content is not blocked by recall difficulties.
ELL / MLL
Teachers should use visual representations consistently throughout this unit — labeled area models, fraction bar diagrams, and illustrated word problem supports help make abstract concepts accessible across language levels. Key vocabulary such as 'partition,' 'equal parts,' 'unit fraction,' 'area,' and operation property terms should be introduced with visual anchors and reinforced through repeated, contextualized use. Directions for multi-step tasks should be simplified and delivered in short segments, and students should be encouraged to demonstrate understanding through models or gestures before transitioning to written equations. When possible, connecting fraction concepts to real-world contexts familiar to students' home cultures and allowing students to discuss reasoning in their home language before expressing it in English supports both comprehension and confidence.
At Risk (RTI)
Instruction should begin by connecting multiplication and division concepts to familiar grouping and sharing situations before introducing symbolic notation and properties. Students who need additional entry points can start with smaller, friendly numbers in area models and fact practice before extending to the full range within 100. Fraction work should be grounded in concrete partitioning of physical or drawn shapes into equal parts, allowing students to build the concept of a unit fraction from direct experience rather than abstract definition. Frequent brief check-ins and structured practice with immediate corrective feedback help students build confidence and close gaps before moving to two-step problem solving.
Gifted & Talented
Students who have demonstrated fluency with multiplication, division, and basic fraction concepts can be challenged to investigate how the distributive property generalizes across larger numbers and connect it to mental math efficiency. Extending the fraction work to explore relationships between unit fractions — such as how the size of the part changes as the denominator grows — and beginning to reason about non-unit fractions builds readiness for future fraction content. Posing open-ended problems that require students to create and justify their own rectilinear figures with specified area, or to design shapes that can be partitioned in multiple ways into equal parts, encourages deeper mathematical reasoning. Encouraging students to explain arithmetic patterns they notice in multiplication tables using the properties of operations, in writing or verbal argument form, develops both mathematical communication and abstract thinking.