Operations Mastery

Unit: Bridging Fractions & Decimals

Lesson 4 of 6: Operations with Mixed Forms

Duration: 45 minutes
Class size: 2 students (online via Zoom and Google Classroom)

---

Common Core State Standards Addressed

CCSS.MATH.CONTENT.6.NS.C.6
Fluently divide multi-digit numbers using the standard algorithm.

CCSS.MATH.CONTENT.6.NS.B.3
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

CCSS.MATH.CONTENT.6.NS.A.1
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.

CCSS.MATH.CONTENT.6.NS.C.5
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values.

(Focus for this lesson mainly on addition and subtraction of decimals and fractions in mixed forms.)

---

Learning Objectives

By the end of this lesson, students will be able to:

• Accurately add and subtract fractions and decimals presented in mixed forms (i.e., expressions containing both fractions and decimals).
• Use visual aids (number line, pie charts) to represent operations with mixed forms for better conceptual understanding.
• Apply addition and subtraction skills in real-world contexts involving budgeting scenarios.
• Collaboratively solve problems using a mini-game format to foster engagement and teamwork.
• Independently create a simple budget that includes both fractions and decimals, demonstrating understanding of operations across formats.

---

Success Criteria

• I can add and subtract fractions and decimals correctly.
• I can explain my method for solving mixed operations problems.
• I can use visuals like number lines or models to show my work.
• I can apply these operations in a realistic budgeting situation.
• I feel confident creating a budget using fractions and decimals.

---

Materials & Technology Needed

• Virtual whiteboard (Zoom feature)
• Google Classroom shared folder with:
  • Fraction and decimal budget worksheet (dyslexia-friendly formatting)
  • Mini-game question cards (digital slides)
• Visual aids: number line templates, pie chart segment templates (digital and printable)
• Calculator (optional for checking work)
• Pen/pencil and scratch paper for note-taking

---

Lesson Outline

1. Hook (5 minutes) – Real-World Budgeting Scenario

• Teacher introduces a story: “Imagine you’re planning a party with a budget of $50. You’ve spent 12.5 dollars on decorations and 3/4 of $10 on food.”
• Ask students: “How much money have you spent in total? How much is left?”
• Write the problem on the whiteboard, highlighting the mixture of decimal and fraction amounts.
• Purpose: Immediately relate math to a practical application to capture attention.

---

2. Direct Instruction (12 minutes) – Adding and Subtracting Mixed Forms

• Explain step-by-step how to add and subtract decimals and fractions when they appear together:
  • Convert fractions to decimals OR decimals to fractions (choose one method depending on comfort).
  • Align decimal points when adding/subtracting decimals.
  • Use visual aids: Show a number line with fractional and decimal points plotted.
  • Use pie chart segments to visually represent parts of a whole.
• Model a few example problems:
  1. 0.6 + 3/10
  2. 5 1/4 - 2.75
• Encourage students to verbalize each step as they watch.
• Dyslexia-friendly strategy: Use color-coded numbers and highlight important operation signs.

---

3. Interactive Practice Mini-Game (12 minutes) – "Mix & Match Math"

• Each student/team receives 4 digital "problem cards" mixing fractions and decimals (examples below).
• Students solve problems out loud or in the chat, showing work on digital whiteboard.
• Teacher provides immediate feedback, highlighting strategies.
• Examples:
  • Add 1.5 + 2 2/5
  • Subtract 3.7 − 1 3/8
• Game format fosters multisensory engagement: speaking, visual modelling, clicking answers.

---

4. Independent Work (10 minutes) – Create Your Budget

• Worksheet prompt: “Using a budget of $30, plan your supply shopping list. Include at least 3 items priced as decimals and 2 as fractions.”
• Students add up their costs, showing addition/subtraction work in mixed forms.
• Submit work via Google Classroom.
• Differentiation:
  • Support: Provide partially completed templates for numbers or visual budget charts.
  • Extension: Challenge to include subtraction (returns/refunds) and decimal-fraction conversions in their budget.
• Dyslexia-friendly formatting: clear font, spacing, and color-coded sections.

---

5. Exit Reflection (6 minutes) – Sharing Favorite Strategies

• Each student shares in Zoom or chat: “What was your favorite strategy for solving these mixed operations problems?”
• Prompt scaffolding: “Did you prefer converting everything to decimals, using visual aids, or something else?”
• Teacher affirms all strategies and ties back to success criteria.
• Quick review of any misconceptions.

---

Differentiation Strategies

Learner Type	Strategy
Struggling with fraction-decimal conversions	Use fraction-to-decimal chart and one-to-one conversion flashcards; provide extra step-by-step guides.
Dyslexic learners	Use dyslexia-friendly fonts (e.g., OpenDyslexic), color-coded numbers/signs, audio recordings of instructions, and break instructions into smaller chunks.
Advanced learners	Challenge with multiplication/division of mixed forms; explore real-life applications like currency exchange rates using fractions and decimals.
ELL students	Use visual aids extensively; pair vocabulary terms with images; allow oral explanations in addition to writing.

---

Assessment & Feedback

• Informal assessment through observation during mini-game and class discussions.
• Review of independent budget worksheet for accuracy and method.
• Teacher provides personalized, constructive feedback on Google Classroom.
• Exit reflection captures students’ confidence and understanding.

---

Notes for Virtual Teaching

• Use Zoom breakout rooms if needed for teamwork during mini-game (even with 2 students, pair or individual approach).
• Share Google Slides for interactive "problem cards."
• Encourage use of chat and audio for student participation — some may prefer typing responses.
• Record the lesson or key instruction parts for later review.

---

Thank you for embracing this multisensory, real-world grounded lesson that bridges fractions and decimals — empowering students to confidently operate with mixed numbers in practical contexts.