Conversion Facilitation Guide Facilitation Guide
Lesson 1: The Conversion Build
30 Minutes
Tier 2 Small Group Intervention
Learning Objective
Students will conceptually understand and fluently convert between mixed numbers and improper fractions using area models and the "Multiply & Add" algorithm.
Prep Checklist
Print Conversion Construction Worksheet (1 per student)
Ready the Conversion Build Slides
Gather sets of pattern blocks or fraction circles (optional)
Instructional Roadmap
1
Warm Up: Blueprint Basics (5 Mins)
Concept Check
Script: "Before we build, we need to know our materials. What does the denominator tell us? What does the numerator tell us?"
Quickly sketch \( \frac{3}{4} \) and \( \frac{5}{4} \) on a whiteboard.
Ask: "How many parts make one whole in these drawings?"
2
Direct Instruction: The Build Dance (10 Mins)
Modeling
Step 1: Mixed to Improper (The Wheel)
Demonstrate \( 2 \frac{1}{3} \). Show 2 full circles and 1 third. Count them: "One third, two, three (that's one), four, five, six (that's two), seven thirds."
Algorithm: (Whole \(\times\) Denom) + Numerator
Step 2: Improper to Mixed (The Remainder)
Demonstrate \( \frac{11}{4} \). Draw 11 fourths. "How many groups of 4 can we make?"
Strategy: Division with Remainders (Numerator \(\div\) Denom)
3
Guided Practice: Construction Site (10 Mins)
Intervention
Distribute the Conversion Construction Worksheet. Complete the first two "Drafting" problems together. Watch for students who forget to keep the same denominator.
4
Wrap Up: Final Inspection (5 Mins)
Assessment
"If you have \( 3 \frac{1}{2} \) pizzas, how many half-slices do you have in total?"
Scaffolding Tip
If students struggle with multiplication facts during conversion, provide a multiplication table or use repeated addition of the denominator.
Conversion Build Slides Conversion Blueprints
Level 1: Building Wholes and Parts
The Two Designs
Mixed Numbers
Whole numbers combined with a proper fraction.
2
1 3
Improper Fractions
The numerator is greater than or equal to the denominator.
7 3
Building Improper Fractions
The "Multiply & Add" Method
Multiply the Whole by the Denominator.
Add the Numerator.
Keep the same denominator!
"Think of it as counting all the small pieces in every whole brick."
Solve: \( 3 \frac{2}{5} \)
1 \( 3 \times 5 = 15 \)
2 \( 15 + 2 = 17 \)
3 \( \frac{17}{5} \)
Building Mixed Numbers
Solve: \( \frac{13}{4} \)
Division
\( 13 \div 4 = ? \)
Wholes
3
Leftover
1
\( 3 \frac{1}{4} \)
The "Divide & Remainder" Strategy
Divide the Numerator by the Denominator.
The answer is your Whole Number.
The Remainder is your new numerator.
"How many full boxes can we pack? What's left on the shelf?"
On-Site Inspection
Time to test the blueprints! Let's practice converting these as a team.
A
\( 4 \frac{2}{3} \)
B
\( \frac{19}{5} \)
Conversion Construction Worksheet Conversion Construction
Fraction Blueprints: Lesson 1 Worksheet
Name:
Date:
Phase 1: Visual Drafting
Shade the models to represent the mixed number, then count the total pieces to find the improper fraction.
\( 2 \frac{3}{4} \)
\( 1 \frac{2}{3} \)
Phase 2: Building Improper
Use the Multiply & Add method to convert these mixed numbers.
\( 5 \frac{1}{2} \)
\( 3 \frac{4}{5} \)
\( 8 \frac{2}{3} \)
Phase 3: Remodeling Wholes
Use Division to find how many wholes and remainders are in these improper fractions.
\( \frac{17}{3} \)
\( \frac{25}{4} \)
Phase 4: Site Challenge
An architect needs \( \frac{11}{2} \) feet of copper wire for a circuit. The supply store only sells wire in mixed number labels (like 5 and 1/2). Which label should the architect look for? Show your work.
Conversion Key Answer Key
Conversion Construction: Lesson 1
Teacher Resource
Phase 1: Visual Drafting
Problem 1: \( 2 \frac{3}{4} \)
\( \frac{11}{4} \)
(Count 11 shaded fourths total)
Problem 2: \( 1 \frac{2}{3} \)
\( \frac{5}{3} \)
(Count 5 shaded thirds total)
Phase 2: Building Improper
\( 5 \frac{1}{2} \)
\( \frac{11}{2} \)
\( (5 \times 2) + 1 = 11 \)
\( 3 \frac{4}{5} \)
\( \frac{19}{5} \)
\( (3 \times 5) + 4 = 19 \)
\( 8 \frac{2}{3} \)
\( \frac{26}{3} \)
\( (8 \times 3) + 2 = 26 \)
Phase 3: Remodeling Wholes
\( \frac{17}{3} \)
\( 5 \frac{2}{3} \)
\( 17 \div 3 = 5 \) with remainder \( 2 \)
\( \frac{25}{4} \)
\( 6 \frac{1}{4} \)
\( 25 \div 4 = 6 \) with remainder \( 1 \)
Phase 4: Site Challenge
Correct Answer: \( 5 \frac{1}{2} \) feet
Work: \( 11 \div 2 = 5 \) R \( 1 \).
Operations Assembly Facilitation Guide Facilitation Guide
Lesson 2: Operations Assembly
30 Minutes
Tier 2 Small Group Intervention
Learning Objective
Students will accurately add and subtract mixed numbers with like denominators, focusing on the regrouping process when sums exceed a whole or differences require borrowing.
Prep Checklist
Print Assembly Line Worksheet (1 per student)
Ready the Operations Assembly Slides
Ensure students have red pens for "Final Inspections" (checking work)
Instructional Roadmap
1
Warm Up: Inventory Check (5 Mins)
Concept Recall
Script: "Last time we built improper fractions. Today we’re assembling them together. What happens if I have 4 fourths? What does that equal?"
Quickly review \( \frac{4}{4} = 1 \) and \( \frac{8}{4} = 2 \).
Practice a simple addition: \( 1 \frac{1}{4} + 1 \frac{1}{4} \).
2
Direct Instruction: The Assembly Line (10 Mins)
Modeling
Assembly Strategy: Wholes then Parts
Model \( 2 \frac{2}{5} + 1 \frac{4}{5} \). Add wholes: \( 2 + 1 = 3 \). Add parts: \( 2/5 + 4/5 = 6/5 \).
Regrouping: \( 3 + 1 \frac{1}{5} = 4 \frac{1}{5} \)
Deconstruction Strategy: Borrowing
Model \( 3 \frac{1}{4} - 1 \frac{3}{4} \). We can't do \( 1/4 - 3/4 \).
The Fix: \( 3 \frac{1}{4} = 2 \frac{5}{4} \). Now subtract.
3
Guided Practice: Team Build (10 Mins)
Coaching
Students work on the first 3 problems of the Assembly Line Worksheet. Use the "Convert First" strategy as an alternative for students struggling with borrowing.
4
Wrap Up: Inspection Pass (5 Mins)
Debrief
"What's one thing you have to remember when your fraction answer is improper (like 8/5)?"
Common Misconception
Students may try to add the denominators (e.g., \( 1/4 + 2/4 = 3/8 \)). Remind them that the denominator is the "size of the brick" and doesn't change during assembly.
Operations Assembly Slides Operations Assembly
Level 2: Adding and Subtracting Mixed Numbers
The Assembly Strategy
Add the Wholes First
"Gather all the full bricks together."
Add the Fractions
"Assemble the smaller pieces."
Wait! If the fraction is > 1...
REGROUP!
On the Workbench
\( 2 \frac{2}{3} + 1 \frac{2}{3} \)
\( 3 \frac{4}{3} \)
4 thirds = 1 whole and 1 third
\( 4 \frac{1}{3} \)
Deconstruction (Borrowing)
The Problem
\( 5 \frac{1}{4} - 2 \frac{3}{4} \)
Wait! We can't do \( 1/4 - 3/4 \)!
Borrow 1 Whole
\( 4 \frac{5}{4} \)
\( 2 \frac{2}{4} \)
How to Borrow:
Take 1 whole away from the whole number.
Add that whole (as a fraction) to the numerator.
Example: 1 whole = \( 4/4 \)
New fraction: \( 1/4 + 4/4 = 5/4 \)
The "Cheat Code" Strategy
Don't want to borrow? Do this instead:
1
Convert Both
Change to Improper Fractions first.
2
Operate
Just add or subtract the numerators.
3
Convert Back
Turn it back into a Mixed Number.
Quality Control: Practice
Addition Job
\( 4 \frac{5}{8} + 1 \frac{7}{8} \)
Subtraction Job
\( 6 \frac{1}{5} - 3 \frac{3}{5} \)
Assembly Line Worksheet Assembly Line
Fraction Blueprints: Lesson 2 Worksheet
Name:
Date:
Phase 1: Addition Assembly
Add the whole numbers, then the fractions. Remember to simplify if your answer is improper!
JOB #01
\( 2 \frac{1}{4} + 3 \frac{2}{4} = \)
JOB #02
\( 1 \frac{4}{5} + 2 \frac{3}{5} = \)
Phase 2: Subtraction Deconstruction
Borrow from the whole number if the first fraction is smaller than the second.
JOB #03
\( 4 \frac{3}{8} - 1 \frac{1}{8} \)
JOB #04 (BORROW!)
\( 5 \frac{1}{6} - 2 \frac{5}{6} \)
Phase 3: Final Inspection
Flawed Blueprint
\( 3 \frac{1}{3} + 1 \frac{2}{3} \)
\( 4 \frac{3}{6} \)
What error did the junior architect make? Fix the blueprint below.
CORRECTED ANSWER:
Operations Assembly Key Answer Key
Assembly Line: Lesson 2
Teacher Resource
Phase 1: Addition Assembly
Job #01
\( 5 \frac{3}{4} \)
Steps: \( (2+3) = 5 \); \( (1/4+2/4) = 3/4 \)
Job #02 (Regrouping)
\( 4 \frac{2}{5} \)
Steps: \( 3 \frac{7}{5} \rightarrow 3 + 1 \frac{2}{5} = 4 \frac{2}{5} \)
Phase 2: Subtraction Deconstruction
Job #03
\( 3 \frac{2}{8} \)
Steps: \( (4-1) = 3 \); \( (3/8-1/8) = 2/8 \)
Job #04 (Borrowing)
\( 2 \frac{2}{6} \)
Steps: \( 5 \frac{1}{6} = 4 \frac{7}{6} \); \( (4-2) = 2 \); \( (7/6-5/6) = 2/6 \)
Phase 3: Final Inspection
The Error:
The architect added the denominators (\( 3+3=6 \)). The denominator represents the size of the pieces and should stay the same.
Correct Answer: \( 5 \)
Steps: \( 3+1 = 4 \); \( 1/3+2/3 = 3/3 \); \( 4 + 1 = 5 \)
Blueprint Breakdown Facilitation Guide Facilitation Guide
Lesson 3: Blueprint Breakdown
30 Minutes
Tier 2 Small Group Intervention
Learning Objective
Students will apply their knowledge of fraction conversions and operations to solve multi-step word problems within real-world construction and measurement contexts.
Prep Checklist
Print Project Manager Tasks (1 per student)
Ready the Blueprint Breakdown Slides
Optional: Physical measuring tapes or yardsticks for concrete modeling.
Instructional Roadmap
1
Warm Up: Site Survey (5 Mins)
Readiness
Script: "We've learned to build and assemble. Now we’re the Project Managers. What words in a problem tell us to add? What words tell us to subtract?"
Create a quick T-chart: Add (sum, total, combined) vs Subtract (difference, left over, how much more).
2
Direct Instruction: Analyzing the Blueprint (10 Mins)
Strategy
Step 1: Identify the Units
Are we talking about feet, pounds, or gallons? Ensure we’re working with the same denominators before doing anything else.
Step 2: The Multi-Step Map
Sometimes we have to add first, THEN subtract. Model a problem like: "We have 10 feet of wood. We use \( 2 \frac{1}{2} \) ft and \( 3 \frac{1}{2} \) ft. How much is left?"
3
Guided Practice: Construction Site (10 Mins)
Application
Work through Task #1 on the Project Manager Tasks Worksheet. Focus on drawing a tape measure model for the word problems to help visualize the lengths.
4
Wrap Up: Project Completion (5 Mins)
Summary
"Why is it important to convert our final answer to a mixed number in a real construction job?" (e.g., tape measures don't show 15/4, they show 3 3/4).
Mastery Check
By the end of this lesson, students should be able to:
Extract mixed numbers from text accurately.
Select addition or subtraction based on context.
Perform operations with regrouping/borrowing.
Explain their steps using architectural terms.
Blueprint Breakdown Slides Blueprint Breakdown
Level 3: Application & Problem Solving
Project Manager's Glossary
Addition Clues
Total amount
Combined length
Altogether
Subtraction Clues
How much more?
Remaining length
Trimmed off
Task #1: The Support Beam
"A carpenter needs to glue two boards together. One is \( 3 \frac{2}{5} \) feet long, and the other is \( 2 \frac{4}{5} \) feet long. What is the total length of the beam?"
Operation
ADDITION
Denominator
5
Calculation
\( 3 \frac{2}{5} + 2 \frac{4}{5} \)
\( 5 \frac{6}{5} \)
\( 6 \frac{1}{5} \text{ ft} \)
Task #2: The Electrician's Cut
Calculation
\( 8 \frac{1}{4} - 3 \frac{3}{4} \)
"We must borrow!"
\( 7 \frac{5}{4} - 3 \frac{3}{4} \)
\( 4 \frac{2}{4} \text{ ft} \)
"An electrician starts with \( 8 \frac{1}{4} \) feet of wire. They cut off a piece that is \( 3 \frac{3}{4} \) feet long. How much wire is remaining?"
Strategy
BORROWING
Multi-Step Job
"A painter mixes \( 1 \frac{3}{8} \) gallons of blue paint and \( 2 \frac{7}{8} \) gallons of white paint. They use \( 1 \frac{5}{8} \) gallons for the first room. How much paint is left?"
Step A
Add the paints to find the TOTAL.
Step B
Subtract the USED amount.
Project Manager Tasks Worksheet Project Manager Tasks
Fraction Blueprints: Lesson 3 Word Problems
Name:
Date:
Standard Operating Procedure:
Read each task carefully. Highlight or underline the key numbers. Show all steps of your assembly (calculation). Convert final answers to mixed numbers.
1
Task #1: Flooring Installation
A flooring installer needs to combine two pieces of molding. The first piece is \( 4 \frac{5}{8} \) feet long and the second piece is \( 3 \frac{7}{8} \) feet long. What is the total length of the molding needed?
Workspace (Draft)
Final Blueprint (Answer)
2
Task #2: Plumbing Adjustment
A plumber has a copper pipe that is \( 6 \frac{1}{4} \) inches long. They need to trim off \( 2 \frac{3}{4} \) inches to make it fit. How long will the pipe be after it is trimmed?
Workspace (Draft)
Final Blueprint (Answer)
3
Task #3: Multi-Step Site Cargo
A supply truck is carrying two bags of cement. One bag weighs \( 12 \frac{1}{2} \) pounds and the other weighs \( 8 \frac{1}{2} \) pounds. If the driver delivers \( 5 \frac{1}{2} \) pounds of cement to the first job site, how much weight remains on the truck?
Step-by-Step Build
REMAINING WEIGHT:
Inspection Challenge
"An architect says that \( 3 \frac{1}{4} \) and \( 2 \frac{1}{4} \) is the same as \( 5 \frac{2}{8} \). Explain why this architect is NOT ready for the job site."
Project Manager Key Answer Key
Project Manager Tasks: Lesson 3
Teacher Resource
1
Flooring Installation
Result: \( 8 \frac{1}{2} \) feet
Solution Path:
1. Add wholes: \( 4 + 3 = 7 \)
2
Plumbing Adjustment
Result: \( 3 \frac{1}{2} \) inches
Solution Path:
1. Borrow: \( 6 \frac{1}{4} = 5 \frac{5}{4} \)
3
Multi-Step Site Cargo
Result: \( 15 \frac{1}{2} \) pounds
Step A (Total Weight):
\( 12 \frac{1}{2} + 8 \frac{1}{2} = 20 \frac{2}{2} = 21 \) lbs
Step B (Remaining):
\( 21 - 5 \frac{1}{2} = 20 \frac{2}{2} - 5 \frac{1}{2} = 15 \frac{1}{2} \) lbs
Inspection Challenge
Expert Commentary:
The architect added the denominators (\( 4+4=8 \)). When adding fractions with like denominators, the denominator should remain unchanged because it describes the size of the pieces. The correct answer is \( 5 \frac{2}{4} \) (or \( 5 \frac{1}{2} \)).
