Anchor Chart · Ratios & Rates
Roots of Reason
What Is a Ratio?
A ratio compares two quantities.
BBB
YY
3 cups of blue paint, 2 cups of yellow paint
for every 3 blues, there are 2 yellows.
three ways to write it
3 : 2
with a colon
3 to 2
in words
32
as a fraction
PPart to part
blue to yellow = 3 : 2
compares one part with another part
WPart to whole
blue to all paint = 3 : 5
compares one part with the total
Order matters. Blue to yellow is 3 : 2. Yellow to blue is 2 : 3.
Anchor Chart · Ratios & Rates
Roots of Reason
Tape Diagrams
Fiction to nonfiction books is 3 : 2. There are 20 books. How many are fiction?
fiction
444
nonfiction
44
5 boxes share 20 books, so each box holds 4.
1Draw one box per part
3 : 2 means 3 boxes for fiction, 2 boxes for nonfiction. All boxes are the same size.
2Find one box's value
20 ÷ 5 boxes = 4 each
3Count your boxes
3 × 4 = 12 fiction
Every box holds the same amount. That is the whole trick.
Anchor Chart · Ratios & Rates
Roots of Reason
Double Number Lines
Mia swims 4 laps every 10 minutes. How many laps in 30 minutes?
the pair 4 and 10 repeats: +4 laps for every +10 minutes.
1Zeros line up
Both lines start at 0. Each tick above sits exactly over its partner below.
2Move together
Whatever you do to one line, do to the other. Doubling 10 minutes doubles 4 laps.
3Read the answer
30 min sits under 12 laps
A double number line keeps two quantities locked in step.
Anchor Chart · Ratios & Rates
Roots of Reason
Ratio Tables
A recipe uses 2 cups of flour for every 3 cups of milk.
| flour | 2 | 4 | 6 | 20 |
| milk | 3 | 6 | 9 | 30 |
× 2× 3× 10
multiply BOTH rows by the same number. always both.
✓Same ratio, new numbers
2 : 3, 4 : 6, and 20 : 30 all describe the same recipe. Bigger batch, same taste.
✗Never add across
Adding 1 to both sides gives 3 : 4. That is a different recipe. Ratios grow by multiplying.
A ratio table is a list of equivalent ratios. Every column tells the same story.
Anchor Chart · Ratios & Rates
Roots of Reason
Unit Rate
A unit rate is a ratio scaled down until one side is 1.
$12
for
4 pounds
÷ 4÷ 4
$3
for
1 pound
"per" means for each 1. apples cost $3 per pound.
$Unit price
$12 for 4 lb → $3 per lb
$10 for 5 lb → $2 per lb
now you can compare deals
→Speed
120 miles in 2 hours
120 ÷ 2 = 60 miles per hour
a rate of distance for each 1 hour
Divide both sides by the same number until one side reads 1. What remains is the rate.