Unit 3 — Building Fractions & Decimal Notation
Description
Unit 3 extends fraction work to addition and subtraction with like denominators and introduces decimal notation. Students add and subtract mixed numbers with like denominators and solve word problems involving fraction addition and subtraction using visual models. Line plots are used to display measurement data in fraction units and to solve problems involving addition and subtraction of fractions. Multiplication of fractions by whole numbers is explored through visual models and applied to word problems. The connection between fractions and decimals is developed as students express fractions with denominators of 10 and 100 as decimals, add fractions with denominators 10 and 100 by converting to common denominators, and compare decimals. Measurement problems incorporating simple fractions and decimals are solved using the four operations.
Essential Questions
- How are fractions used in problem-solving situations?
- How are decimal fractions written using decimal notation?
- How are decimal numbers and decimal fractions related?
- What is a decimal fraction and how can it be represented?
- How do we make a line plot to display a data set?
Learning Objectives
- Add and subtract mixed numbers with like denominators and solve word problems involving fraction addition and subtraction.
- Make a line plot to display measurement data in fractions of a unit and solve problems involving addition and subtraction using the data.
- Multiply a fraction by a whole number using visual models and solve word problems involving this operation.
- Express fractions with denominators 10 and 100 as decimals and recognize the connection between fractions and place value.
- Add fractions with denominators 10 and 100 by expressing them with a common denominator.
- Compare two decimals to hundredths by reasoning about their size and using models.
- Solve word problems involving measurements of fractions or decimals using all four operations.
Supplemental Resources
- Fraction models and decimal place value charts
- Measurement tools for line plot activities
- Printed decimal comparison cards
- Grid paper for line plot construction
- Graphic organizers for fraction and decimal relationships
Digital Literacy
Measurement
Number and Operations in Base Ten
Number and Operations—Fractions
Students use reading comprehension skills to decode words, study vocabulary, and solve word problems. Students identify important information and write explanations of their mathematical thinking using mathematical terms. Students connect everyday vocabulary to strengthen understanding of mathematical terms.
Students represent data, discover patterns, and read information to analyze observations. Students use measuring tools to create models and measure results of experiments. Students analyze data to form conclusions and use data to prove theories across life science, physical science, and earth science modules.
Students understand how to read dates properly and interpret historical information.
Formative Assessments
- Exit tickets on fraction addition and subtraction with like denominators
- Task cards for multiplying fractions by whole numbers
- Line plot construction activities
- Classwork converting between fractions and decimals
- Whiteboards for comparing decimal values
Summative Assessment
Unit benchmark assessing fraction addition/subtraction, fraction multiplication, line plots, decimal notation, and measurement word problems; chapter tests; performance tasks
Benchmark Assessment
— not configured —
Alternative Assessment
Students may demonstrate understanding through manipulatives, drawings, or teacher-guided oral explanations in place of written responses. Visual models such as fraction bars, number lines, or area models may be provided, and responses may be recorded by the teacher or delivered verbally during one-on-one or small group check-ins.
IEP (Individualized Education Program)
Students may benefit from visual fraction models, number lines, and place value charts to support understanding of fraction operations and decimal notation throughout this unit. Providing a reference sheet with fraction-decimal equivalents and step-by-step process guides for adding and subtracting mixed numbers can reduce cognitive load while keeping focus on conceptual understanding. Allow students to demonstrate mastery through oral explanation or use of manipulatives when written output is a barrier, particularly on exit tickets and benchmark tasks. Breaking multi-step measurement word problems into smaller, sequenced parts with visual cues will help students access the problem-solving process more independently.
Section 504
Extended time on unit assessments and classwork involving fraction operations, decimal comparison, and measurement word problems should be provided to ensure students can demonstrate understanding without time as a barrier. Preferential seating that minimizes distraction is especially helpful during instruction on the fraction-decimal connection, where sustained attention to place value reasoning is essential. Providing a printed copy of any board work, including decimal comparison models or line plot examples, reduces the demand of copying while keeping students engaged with the content.
ELL / MLL
Visual models such as fraction bars, decimal grids, and labeled number lines are particularly supportive in this unit, as they make abstract fraction and decimal concepts more concrete and accessible across language levels. Key vocabulary — including terms like numerator, denominator, equivalent, tenths, hundredths, and mixed number — should be introduced with visual support and reviewed consistently throughout instruction. Directions for multi-step tasks such as constructing line plots or solving measurement word problems should be simplified and given in short, clear steps, with opportunities for students to restate the task in their own words before beginning. Where possible, connecting fraction and decimal concepts to real-world measurement contexts familiar to students can help bridge language and content understanding.
At Risk (RTI)
Connecting new fraction and decimal work to students' prior understanding of whole number operations and basic fraction concepts will help build a confident entry point into this unit. Offering a reduced set of problems that targets the core skill — such as adding fractions with like denominators or converting a fraction with a denominator of 10 to a decimal — allows students to build mastery before encountering additional complexity. Visual models and hands-on tools should remain consistently available so students can anchor their reasoning in something concrete, particularly when transitioning between fraction and decimal representations.
Gifted & Talented
Students who demonstrate early mastery of fraction addition, subtraction, and decimal conversion can be challenged to explore the relationship between fractions, decimals, and percentages, or to investigate patterns in equivalent fractions across different denominator families. Posing open-ended measurement and data problems — such as designing their own line plot scenario, analyzing real measurement data, or justifying decimal comparisons in multiple ways — encourages deeper mathematical reasoning beyond procedural fluency. Encouraging students to explain and generalize the connection between place value structure and fraction-decimal equivalence develops the abstract thinking and mathematical argumentation appropriate for advanced learners at this level.