Tape Diagram Mastery Slides
Grade 6 Mathematics • Ratios & Proportions
CCSS 6.RP.A.3
Tape Diagram Tactics
Mastering real-world ratio problems by drawing equal units, unlocking values, and seeing the math clearly.
1 unit
1 unit
1 unit
:
1 unit
1 unit
Visual problem solving made simple
Interactive Lesson Deck Unit 2: Proportional Reasoning
01
What is a Tape Diagram?
Concept Foundation
A Visual Math Tool
A tape diagram (also known as a strip diagram or bar model) is a drawing of connected rectangles used to illustrate ratios and number relationships.
It turns complicated word problems into an easy-to-read visual puzzle.
The Golden Rule
Every single block in the diagram represents the exact same amount!
Once you discover the value of one single block, you can instantly solve for any unknown quantity.
Think of each rectangle as an identical container holding the exact same number of items.
02
Anatomy of a Tape Diagram
Model Breakdown
Example: The ratio of Cats to Dogs at a rescue shelter is 2 : 3
Cats (2):
Unit ?
Unit ?
← 2 equal units
Dogs (3):
Unit ?
Unit ?
Unit ?
← 3 equal units
1. Category Labels
Name each bar clearly so you never mix up quantities.
2. Equal Unit Boxes
Drawn identically in size to remind you they hold equal amounts.
3. Total / Bracket
Represents total parts (5 total equal units in this ratio).
Always draw equal rectangles aligned on the left edge for clean comparison.
03
Real-World Problem: The Smoothie Shack
Word Problem
Scenario: Maya's Tropical Blast Smoothie
At the Sunshine Smoothie Shack, Maya makes a large batch of fruit smoothies. Her recipe requires mango chunks and strawberries in a ratio of 3 : 5.
Maya uses a total of 72 ounces of fruit altogether.
TARGET QUESTION How many ounces of mango and strawberries does she need?
Given Ratio Mango 3 : Strawberries 5
Total Fruit 72 Ounces Total
Unknown Ounces of each fruit
How can a tape diagram make this easy to solve without guessing? Let's solve it step-by-step →
04
Step 1 & 2: Draw Bars & Count Total Units
Solving Maya's Recipe
Step 1: Draw the bars for the 3 : 5 ratio Total Weight = 72 oz
Mango:
Unit
Unit
Unit
(3 equal units)
Strawberry:
Unit
Unit
Unit
Unit
Unit
(5 equal units)
Step 2: Add up all equal units
3 units + 5 units = 8 total equal units
All 8 units together equal the entire 72 ounces of smoothie fruit!
Next: How do we determine the exact ounce value of just ONE unit block?
05
Step 3 & 4: Unlock the Unit Value & Solve
Solving Maya's Recipe
Step 3: Divide to find 1 unit
Total Ounces ÷ Total Units = 1 Unit Value
72 ÷ 8 = 9 oz
Each rectangle holds 9 ounces!
Mango:
9
9
9
Strawb.:
9
9
9
9
9
Step 4: Multiply for each quantity
Mango Chunks:
3 units × 9 oz = 27 ounces
Strawberries:
5 units × 9 oz = 45 ounces
Check Your Work:
27 oz + 45 oz = 72 total oz
✓ Matches
Maya needs 27 ounces of mango chunks and 45 ounces of strawberries.
06
Challenge Type: "Difference" Problems
When you are NOT given the total
School Spirit Shirt Fundraiser
The 6th grade class is selling Blue and Gold shirts in a ratio of 4 : 2. They sold 30 more blue shirts than gold shirts. How many total shirts did they sell?
Blue (4):
15
15
15
15
← 2 EXTRA boxes = 30 shirts!
Gold (2):
15
15
(Pairs match up)
Find 1 Unit:
30 shirts ÷ 2 extra units = 15
Total Sold (6 units):
6 units × 15 = 90 total shirts
Tape diagrams let you clearly see the difference as the extra blocks!
07
The 4-Step Tape Diagram Playbook
Problem-Solving Strategy
1
Draw & Label
Draw rectangles for each part of the given ratio. Align them neatly and write names beside each bar.
Ratio 2:3 → Draw 2 boxes and 3 boxes.
2
Identify Given
What does the number in the problem represent? The total, just one part, or the difference?
Bracket the right boxes!
3
Find 1 Unit
Divide the given number by the count of corresponding boxes to find the value of exactly one block.
Value = Amount ÷ Units
4
Multiply & Answer
Multiply the 1-unit value by the number of boxes requested in the question, then check your answer!
Boxes × Unit Value = Target
Follow these 4 steps every single time for 100% accuracy on ratio word problems!
08
Your Turn: Wildlife Center Rescue
Whiteboard Challenge
CHALLENGE PROBLEM
A wildlife sanctuary cares for Rabbits and Turtles in a ratio of 4 : 3.
The sanctuary currently has 28 rabbits.
How many turtles are at the sanctuary? What is the total number of animals?
Hint 1: Draw Bars
Draw 4 boxes for rabbits and 3 boxes for turtles.
Hint 2: Match 28
Does 28 represent the total, or just the rabbits' 4 boxes?
Hint 3: Find 1 Box
Divide 28 by 4 to get the value of one box.
Work with your partner or sketch on your paper now! Solution reveal on next slide →
09
Solution Reveal & Key Takeaway
Check Your Answer
The Completed Tape Diagram:
Rabbits (4 units = 28): 28 ÷ 4 = 7 per unit
7
7
7
7
Turtles (3 units): 3 × 7 = 21 Turtles
7
7
7
Total Animals: 28 + 21 = 49 animals
Remember This Rule:
One Unit Unlocks Everything: Find 1 box first, and every other question becomes simple multiplication.
Match the Number Carefully: Never divide by the total number of boxes unless the problem gives the total!
When in doubt, tape it out: A 10-second sketch avoids 90% of ratio mistakes!
Great Job! You have mastered 6th Grade Tape Diagrams! Ready for Independent Practice
