Ratio Road Intervention Guide Ratio Road
Teacher Facilitation Guide • Tier 2 Intervention
Standard
CO 6.RP.A.3a
Objective
Students will complete tables of equivalent ratios using multiplication and plot the pairs on a coordinate plane.
Group Size
Small group (3-5 students) requiring additional scaffolding with proportional reasoning.
Duration
30-40 Minutes
1
Concrete Modeling (10 min)
Start with a "Secret Recipe" (e.g., 2 blue beads for every 3 yellow beads). Use physical manipulatives if possible.
Prompt: "If I want to double the recipe, what do I do to the blue beads? What about the yellow? Can we have 4 blue and 3 yellow? Why not?"
Key Concept: Ratios are like a 'locked' relationship. If one side grows by 2x, the other must grow by 2x to stay equivalent.
2
The Table Bridge (15 min)
Transition to the Ratio Road Worksheet . Guide students to see the table as a shortcut for repeated addition or multiplication.
Scaffold: Have students draw arrows from the first row to the next, labeling them with "\(\times 2\)", "\(\times 3\)", etc.Check: "If I multiply the top by 5, what MUST I do to the bottom?"
3
Mapping the Road (10 min)
Convert table pairs to \((x, y)\) coordinates. Emphasize that \(x\) is always the first column and \(y\) is the second.
Look For:
Are they plotting (0,0) first?
Do the points form a straight line through the origin?
Observation Checklist
Lesson: Ratio Road
Date: ___________
Student Name Identifies Base Ratio Uses Multi. Patterns Correct (x, y) Pairs Accurate Plotting Notes / Next Steps ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐
Common Misconceptions
• Adding the same number to both sides instead of multiplying.
• Reversing x and y when plotting.
• Missing (0,0) as the starting point of the ratio relationship.
Refining Questions
• "If we had zero blue beads, how many yellow would we have?"
• "Does your line point directly at the corner (0,0)?"
• "What does the point (2, 3) tell us about our recipe?"
Ratio Road Slides Tier 2 Intervention
Ratio
Road
Building equivalent tables and mapping them to the coordinate plane.
01
The Ratio Rule
A ratio is a locked relationship between two quantities.
Recipe: 2 Blue, 3 Yellow
To make a bigger batch, we must multiply BOTH by the same number.
Double the Batch (\(\times 2\))
02
The Scaling Table
Blue (\(x\)) Yellow (\(y\)) Scaling 2 3 Base Ratio 4 6 \(\times 2\) 6 ? \(\times 3\) ? 12 \(\times 4\)
03
Plotting the Path
Each row in our table is a Coordinate Pair.
1
(2, 3) → Go right 2, up 3
2
(4, 6) → Go right 4, up 6
3
(0, 0) → Always start here!
"If you plot them correctly, they will form a straight line."
Ratio Road Worksheet Ratio Road
Practice Sheet: Equivalent Tables & Plotting
Name
Date
Case #1: The Perfect Lemonade
The ratio of lemons to cups of water is 1 to 2.
x2 →
x3 →
x4 →
x5 →
Cups of Water (y)
Number of Lemons (x)
0
2
4
6
8
10
2
4
6
8
10
"Plot your points and draw a line through them."
Case #2: The Gear Racer
A toy car travels 3 meters for every 1 second.
Tip: Multiply the base ratio (1, 3) by the same number to find the missing values!
Distance in Meters (y)
Time in Seconds (x)
0
1
2
3
4
3
6
9
12
Ratio Racers Activity Ratio Racers
Partner Activity Guide
Team Challenge
How to Play
Pick a secret ratio from the card deck below.
Partner A: Fills out the first 3 rows of the table.Partner B: Plots those 3 points on the graph.Switch: Partner B completes the next 2 rows, Partner A plots.Check: Does your path make a perfect straight line to (0,0)?
The Golden Rule
"Whatever you do to the top, you MUST do to the bottom. Multiply to grow, never add!"
Challenge Cards
The Snail
1 cm : 4 min
The Baker
3 Eggs : 1 Cake
The Gamer
5 Wins : 2 Gems
Table of Truth
Quantity 1 (x) Quantity 2 (y)
Plot the Path
Quantity 1 (x)
Quantity 2 (y)
__
__
__
__
__
__
__
__
Check Your Work!
Did you start at (0,0)? Is your line straight? If it looks like a zigzag, re-check your multiplication!
Ratio Road Answer Key Ratio Road
Answer Key • Teacher Resource
Case #1: Perfect Lemonade (1 to 2)
Lemons (x) Water (y) 1 2 2 4 3 6 4 8 5 10
Points to Plot:
(1,2), (2,4), (3,6), (4,8), (5,10)
Teacher Note: Ensure students start their line at (0,0) even if it's not in the table. The line should be perfectly straight.
Case #2: Gear Racer (3m per 1s)
Time (x) Meters (y) 1 3 2 6 3 9 4 12
Points to Plot:
(1,3), (2,6), (3,9), (4,12)
Check for scale: The y-axis in Case #2 must be scaled to at least 12. Most students will use intervals of 3.
Challenge Cards (Base Ratios)
Snail (1:4)
(2,8), (3,12), (4,16)
Baker (3:1)
(6,2), (9,3), (12,4)
Gamer (5:2)
(10,4), (15,6), (20,8)
