Decimals, Fractions, and Percents

SOLS/VESOLS 5.NS.1.aUse concrete and pictorial models to represent fractions with denominators that are thirds, eighths, and factors of 100 in their equivalent decimal form. 5.NS.1.bUse concrete and pictorial models to represent decimals in their equivalent fraction form (thirds, eighths, and factors of 100). 5.NS.1.cIdentify equivalent relationships between decimals and fractions with denominators that are thirds, eighths, and factors of 100 in their equivalent decimal form, with and without models. 5.NS.1.dCompare (using symbols <, >, =) and order (least to greatest and greatest to least) a set of no more than four decimals and fractions (proper, improper) and/or mixed numbers using multiple strategies (e.g., benchmarks, place value, number lines). Justify solutions orally, in writing, or with a model. 6.NS.1.aEstimate and determine the percent represented by a given model (e.g., number line, picture, verbal description), including percents greater than 100% and less than 1%. 6.NS.1.bRepresent and determine equivalencies among decimals (through the thousandths place) and percents incorporating the use of number lines, and concrete and pictorial models. 6.NS.1.cRepresent and determine equivalencies among fractions (proper or improper) and mixed numbers that have denominators that are 12 or less or factors of 100 and percents incorporating the use of number lines, and concrete and pictorial models. 6.NS.1.dRepresent and determine equivalencies among decimals, percents, fractions (proper or improper), and mixed numbers that have denominators that are 12 or less or factors of 100 incorporating the use of number lines, and concrete and pictorial models. 6.NS.1.eUse multiple strategies (e.g., benchmarks, number line, equivalency) to compare and order no more than four positive rational numbers expressed as fractions (proper or improper), mixed numbers, decimals, and percents (decimals through thousandths, fractions with denominators of 12 or less or factors of 100) with and without models. Justify solutions orally, in writing or with a model. Ordering may be in ascending or descending order.

Grade Level

5th and 6th Grade
Class Size: 8 students
Duration: 50 minutes

Learning Objectives

Students will be able to:

5.NS.1a-d & 6.NS.1a-e (Common Core-aligned skills)
Use concrete and pictorial models to represent and convert between fractions, decimals, and percents (including denominators of 3, 8, 12, and factors of 100).
Identify and justify equivalent relationships between decimals, fractions, and percents.
Compare and order fractions, decimals, and percents using multiple strategies including number lines and benchmarks.
Estimate percents, including those greater than 100% and less than 1%.

I Can Statements

I can represent fractions, decimals, and percents using concrete and pictorial models.
I can find equivalent forms of fractions, decimals, and percents.
I can compare and order decimals, fractions, and percents using models and symbols (<, >, =).
I can explain my thinking using numbers, pictures, and words.

Success Criteria

Correctly convert between fractions (especially thirds, eighths, twelfths, and factors of 100), decimals, and percents using models.
Accurately estimate the value of percents on number lines.
Compare and order up to four numbers expressed as fractions, decimals, or percents with justification.
Engage actively in oral and written explanations of reasoning.

Materials Needed

Fraction circles and bars (concrete)
Decimal grids (10x10), number lines
Percent models (e.g., 100 grids, shaded diagrams)
Whiteboards and markers
Worksheets with fraction-decimal-percent conversion exercises
Comparison and ordering task cards
Visual aids for benchmarks (e.g., 0%, 50%, 100%, 150%)
Exit tickets for quick formative assessment

Lesson Breakdown

1. Introduction & Activate Prior Knowledge (5 minutes)

Teacher displays fraction circles: specifically thirds and eighths, and decimal grids (hundredths).
Ask students: “Who can share what they know about fractions and decimals?”
Briefly review fraction to decimal conversions for halves and quarters as warm-up.
Highlight today’s focus on thirds, eighths, twelfths, and factors of 100, plus percents >100% and <1%.

Teaching Tip: Use “I can” statements to frame the lesson goals for students.

2. Guided Exploration: Representations & Equivalencies (10 minutes)

Use fraction circles and decimal grids to show fractions 1/3, 3/8, 7/12, and explain how these relate to decimals and percents.
Model conversions verbally: e.g., “One third is approximately 0.333. How can we show this with our grids?”
Introduce pictorial percent models using 100 grids and number lines. Demonstrate 150% (greater than 100%) and 0.5% (less than 1%).
Students work in pairs: given model cards, they discuss and record equivalent forms for fractions, decimals, and percents.

Differentiation: Provide extra visual supports and guided notes for learners needing scaffolding. Use manipulatives for tactile learners.

3. Independent Practice: Comparing and Ordering (15 minutes)

Task cards with sets of 4 numbers in mixed formats (some fractions, some decimals, some percents) are distributed. Example set: 7/8, 0.75, 85%, 2/3.
Students use number lines, benchmarks, and equivalency strategies to compare and order the numbers least to greatest or greatest to least.
Encourage use of fraction-decimal-percent conversion for justification.
Students write short explanations (on whiteboards or journals) about their ordering choices, using symbols <, >, or =.

Differentiation:

For students needing support, limit to comparing two numbers and provide partially completed number lines.
For advanced learners, challenge them to compare improper fractions, mixed numbers, and decimals through thousandths and justify with multiple strategies.

4. Extension Activity: Percent Estimation Challenge (10 minutes)

Present real-world contexts — such as sales discounts over 100% (e.g., “Buy one get one free plus 25% off” ~ 125%) or very small percents like 0.4%.
Students create their own percent models with number lines or pictorial grids estimating these scenarios.
Volunteers share their thinking strategies and compare models.

Advanced learners: Create their own real-life percent problems, estimating and converting between forms.

5. Wrap-Up and Reflect (5 minutes)

Recap “I can” statements with students aloud.
Quick formative assessment: Exit ticket with 2 questions:
1. Convert 3/8 into a decimal and percent.
2. Order these numbers: 0.9, 7/8, 90%, 85%. Explain your reasoning.
Collect exit tickets for teacher review.

Assessment

Formative checks during guided practice and independent tasks (observations, oral questioning).
Exit tickets to measure achievement of lesson objectives.
Review written justifications from independent practice to assess depth of understanding.

Differentiation Strategies

For learners with difficulties: Use more concrete manipulatives and pictorial models, simplified sets of numbers, and one-on-one or small group support during activities.
For English Language Learners: Pair visuals with clear, simple language; use sentence frames for explanations (e.g., “I know ___ is greater than ___ because ____.”)
For advanced learners: Incorporate decimals through the thousandths place, improper fractions, mixed numbers, and complex percent problems (>100%, <1%) with higher-order justification tasks.

Reflection Prompts for Teachers

How did students use models to deepen their understanding?
Were students able to justify their comparisons effectively?
Which differentiation strategies worked best to engage all learners?
What adjustments could be made for a longer or a shorter lesson?

This lesson plan brings to life the abstract concepts of fraction-decimal-percent relationships through engaging models, peer collaboration, and real-world applications—empowering 5th and 6th graders to confidently compare and convert these important numerical forms.