Step 1
Each box is one ratio part
A tape diagram uses equal boxes to show how the parts of a ratio compare.
👀 Red: ■ ■ | Yellow: ■ ■ ■
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Grade 6 · Maths · Lesson 1.3
Tape Diagrams for Ratio Problems
Use equal parts to solve part-to-part and part-to-total ratio problems.
CCSS.MATH.CONTENT.6.RP.A.1CCSS.MATH.CONTENT.6.RP.A.3
Lesson Mission
How can a tape diagram make a ratio problem easier to solve?
⚖️ MATH-G6-RP01 · Ratios, Unit Rates, and Proportional Relationships
✅ I can represent ratio parts with equal-size boxes.
✅ I can find the value of one box in a tape diagram.
✅ I can solve part-to-total ratio problems using a visual model.
AI Learning Helper
Grade 6 Teacher
Helping with: Tape Diagrams for Ratio Problems
MATH-G6-RP01 · The Ratio Balance Lab
Teacher Welcome
Hi, I am your Grade 6 Math Coach. Today we are working inside MATH-G6-RP01: Ratios, Unit Rates, and Proportional Relationships. I will help you understand Tape Diagrams for Ratio Problems by focusing on using tape diagrams to solve ratio problems.
Teacher Response
Guided Hint
How many total ratio parts are there?
Ask for a Specific Hint
Teacher Tip
Read the problem, identify the quantities, choose a model, and explain each step. This skill matters because Tape diagrams help students model recipes, teams, art designs, app icons, and construction mixes.
Common Mistake Alert
Do not divide by only one part of the ratio when the problem gives a total. Divide by total ratio parts.
Student Question Box
Helper Suggestion
Type a question above. The helper will guide the student toward the first step without giving away the answer immediately.
Challenge Prompt
Create a tape diagram for a 4:5 ratio and a total of 63.
Warm-Up
Think First
A ratio is 2 parts red to 3 parts yellow. How many total equal parts are in the ratio?
Show expected answer
There are 5 total parts because 2 + 3 = 5.
Vocabulary
Key Words
Ratio
A comparison of two quantities by division, written as a:b, a to b, or a/b.
Equivalent ratios
Ratios that compare quantities in the same relationship, even if the numbers are different.
Unit rate
A rate that compares a quantity to exactly 1 unit of another quantity.
Proportional relationship
A relationship where two quantities increase or decrease by the same constant factor.
Tape diagram
A visual model that uses equal-sized parts to show ratio relationships.
Real-World Connection
Why This Matters
Tape diagrams help students model recipes, teams, art designs, app icons, and construction mixes.
Mini Lesson
Learn the Concept
Step 2
Add the parts for the total
If the problem gives a total amount, first count all ratio parts.
👀 2 + 3 = 5 total parts
Step 3
Divide to find one part
Divide the total amount by the number of equal parts.
👀 Total ÷ parts = value of one part
Interactive Practice
Practice, Build, Simulate, Explain
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Activity 1 · tape-diagram
Team Shirt Design
A team orders shirts in the ratio 2 black shirts to 3 gold shirts.
15 ptsNot checked
💡 Use the equal parts in the tape diagram to compare the quantities.
Black Shirts to Gold Shirts
Black Shirts
1
2
Gold Shirts
1
2
3
Question
If the team orders 40 shirts total, how many shirts are gold?
Show answer and explanation
Answer: 24 gold shirts
The ratio has 5 total parts. 40 ÷ 5 = 8 shirts per part. Gold has 3 parts, so 3 × 8 = 24.
Activity 2 · numeric-input
Find One Part
A ratio has 4 parts apple juice to 5 parts water. The mixture has 27 cups total. How many cups are in one part?
10 ptsNot checked
💡 Type the number only unless the question asks for a unit.
Unit: cups
Activity 3 · step-by-step
Model a Fruit Basket
A basket has oranges and apples in a 3:2 ratio. There are 25 fruits total.
15 ptsNot checked
💡 Read each step carefully. Notice how the model connects to the calculation.
Step 1
Add the ratio parts: 3 + 2 = 5 total parts.
Step 2
Find one part: 25 ÷ 5 = 5 fruits per part.
Step 3
Oranges: 3 × 5 = 15. Apples: 2 × 5 = 10.
Final Answer
15 oranges and 10 apples