Ratio Rules Slides 6th Grade Math
Lesson 1: Ratios
Beginning Math Ratios
Ratio Rules
Let us learn how to compare numbers. We will use words, colons, and fractions.
Subject: Comparing Numbers
Active Learning • Grade 6
STEP 1: LEARNING RATIOS Ratio Rules
What is a Ratio?
A ratio compares two groups. It tells us how much we have of one thing compared to another.
Remember
Order is important! If we compare circles to squares, we must write the number of circles first.
PICTURE MODEL
Comparing Red Circles to Blue Squares
Unit: Ratio Revolution Page 2 of 6
STEP 2: THREE WRITING STYLES Ratio Rules
Three Ways to Write a Ratio!
We can write a ratio in three different ways. All three ways mean the same comparison.
Way 1: Words
3 to 2
Using the word "to"
Way 2: Symbol
3 : 2
Using a colon (:)
Way 3: Fraction
3
2
Using a fraction bar
Unit: Ratio Revolution Page 3 of 6
SPEAKING DRILL Ratio Rules
LET'S PRACTICE SPEAKING
How to Read Ratios
We read all three styles the same way. We always say the word "TO".
Important Rule
When reading a fraction as a ratio, do not say "three halves". Say "three to two".
3 : 2 "Three to two"
3
2
"Three to two"
📢 Pronunciation Tip:
"Three to two"
Unit: Ratio Revolution Page 4 of 6
STEP 3: TWO COMPARING TYPES Ratio Rules
Part-to-Part vs. Part-to-Whole
Ratios can compare one part to another part, or they can compare one part to the whole group.
Part-to-Part
Red to Blue
Comparing one color group to another color group.
Reds : Blues 3 : 2
Part-to-Whole
Red to Total
Comparing one color group to the entire group of shapes.
Reds : Total (3 + 2) 3 : 5
Unit: Ratio Revolution Page 5 of 6
CLASS ACTIVITY Ratio Rules
Color Tile Grab!
Let's practice! In pairs, grab a handful of colored tiles, sort them into two groups, and write their ratios on your mini whiteboards.
1. Grab & Sort
Grab some tiles and separate them by two colors.
2. Write 3 Ways
Write the ratio using words, colons, and fractions.
3. Speak Aloud
Read your ratio out loud to your partner using the word "to".
Unit: Ratio Revolution Page 6 of 6
Ratio Rules Worksheet Math Practice Worksheet
Ratio Rules
GRADE 6 • UNIT 15
Name:
Date:
📢 Help Box:
A ratio compares two groups. We write ratios in three ways: Words (a to b), Colon (a:b), and Fraction (\(\frac{a}{b}\)).
PART 1
Look at the Shapes
Count the shapes below. Then write the ratios in three ways.
Shapes:
|
1. Stars (\(\star\)) to Circles (\(\bigcirc\)):
Words
Colon
Fraction
2. Circles (\(\bigcirc\)) to Stars (\(\star\)):
Words
Colon
Fraction
PART 2
Part-to-Whole Comparisons
Use the shapes above (4 Stars, 3 Circles). Total shapes = 7. Write the ratios in three ways.
3. Stars to Total Shapes :
Words
Colon
Fraction
4. Circles to Total Shapes :
Words
Colon
Fraction
PART 3
Word Problems
Scenario A: Classroom Items
Anna has 5 pencils and 7 pens . What is the ratio of pens to pencils?
Words: ________
Colon: ________
Fraction: ______
Scenario B: Fruits in a Basket
There are 4 red apples and 6 green pears in a basket. What is the ratio of red apples to total fruits?
Words: ________
Colon: ________
Fraction: ______
UNIT 15: RATIO REVOLUTION • LESSON 1 WORKSHEET CLASSROOM COPY
Ratio Rules Answer Key Teacher Answer Key
Ratio Rules (SOLUTIONS)
GRADE 6 • UNIT 15
SOLUTIONS MANUAL FOR TEACHERS ONLY
PART 1 KEYS
Look at the Shapes
Shapes: 4 Stars and 3 Circles. Total shapes = 7.
1. Stars (\(\star\)) to Circles (\(\bigcirc\)):
Words
4 to 3
Colon
4 : 3
Fraction
\(\frac{4}{3}\)
2. Circles (\(\bigcirc\)) to Stars (\(\star\)):
Words
3 to 4
Colon
3 : 4
Fraction
\(\frac{3}{4}\)
PART 2 KEYS
Part-to-Whole Comparisons
3. Stars to Total Shapes :
Words
4 to 7
Colon
4 : 7
Fraction
\(\frac{4}{7}\)
4. Circles to Total Shapes :
Words
3 to 7
Colon
3 : 7
Fraction
\(\frac{3}{7}\)
PART 3 KEYS
Word Problems
Scenario A: Classroom Items
Anna has 5 pencils and 7 pens . What is the ratio of pens to pencils?
Words: 7 to 5
Colon: 7 : 5
Fraction: \(\frac{7}{5}\)
Scenario B: Fruits in a Basket
There are 4 red apples and 6 green pears in a basket. (Total = 10 ). What is the ratio of red apples to total fruits?
Words: 4 to 10
Colon: 4 : 10
Fraction: \(\frac{4}{10}\)
UNIT 15: RATIO REVOLUTION • LESSON 1 ANSWER KEY CONFIDENTIAL
Ratio Rules Task Cards Printable Station Activity
Ratio Practice Task Cards
MATH GRADE 6 • UNIT 15
Instructions: Cut along the dotted lines. Place cards around the classroom. Students can solve in pairs or play Scoot!
Task Card 1
Pencils & Pens
WRITING UTENSILS
A box contains 5 blue pens and 8 red pencils.
Your Task:
Write the ratio of red pencils to blue pens in all three formats.
STATION: CLASSROOM UNIT 15 • L1
Task Card 2
Classroom Library
BOOK COLLECTION
The reading shelf has 4 story books and 9 science books.
Your Task (Part-to-Whole):
Write the ratio of story books to total library books in all three formats.
STATION: READING UNIT 15 • L1
Task Card 3
Format Change
CONVERT THE RATIO
Look at this colon ratio:
7 : 12
Your Task:
Write this ratio in Words form and Fraction form.
STATION: FORMAT UNIT 15 • L1
Task Card 4
Fruit Salad
HEALTHY SNACKS
In a bowl, there are 3 oranges, 2 apples, and 1 banana.
Your Task (Part-to-Whole):
What is the ratio of apples to total pieces of fruit ? Write it in all three formats.
STATION: FRUIT UNIT 15 • L1
UNIT 15: RATIO REVOLUTION • LESSON 1 TASK CARDS CLASSROOM COPY
Scale Masters Slides 6th Grade Math
Lesson 2: Equal Ratios
Equivalent Ratios
Scale Up, Scale Down!
Let us learn how to make equal ratios by multiplying or dividing our numbers.
Subject: Making Equal Ratios
Active Learning • Grade 6
STEP 1: MULTIPLY TO SCALE UP Equivalent Ratios
Scaling Up
To scale up a ratio, we multiply both numbers by the same number .
Example: 2 : 3
Multiply both numbers by 2 :
MATH FLOW
2 : 3
× 2
× 2
4 : 6
The ratios 2 : 3 and 4 : 6 are equivalent (equal)!
Unit: Ratio Revolution Page 2 of 6
STEP 2: DIVIDE TO SCALE DOWN Equivalent Ratios
SIMPLIFYING
6 : 8
÷ 2
÷ 2
3 : 4
The ratios 6 : 8 and 3 : 4 are equivalent (equal)!
Scaling Down
To scale down or simplify a ratio, we divide both numbers by a common factor .
Simplest Form
A ratio is in its simplest form when we cannot divide the numbers any more (except by 1).
Unit: Ratio Revolution Page 3 of 6
SPEAKING CHANT Equivalent Ratios
CHORAL DRILL
"Do the same to the left and right!"
The Equal Rule
"Multiply or divide!
If you multiply the left number, you must multiply the right number by the same count!
Unit: Ratio Revolution Page 4 of 6
STEP 3: RATIO TABLES Equivalent Ratios
The Ratio Table
A ratio table helps us organize equal ratios in rows or columns. It helps us see the multiplication pattern clearly.
Keep applying the rule: Multiply both parts by 2, then by 3, then by 4!
TABLE VIEW
Group Base Scale 2 Scale 3 Scale 4 Apples 3 6
Scale Masters Worksheet Math Practice Worksheet
Equivalent Ratios
MATH GRADE 6 • UNIT 15
Name:
Date:
📢 Help Box:
To make equal ratios, multiply or divide both sides by the same number. Remember: "Do the same to the left and right!"
PART 1
Scale Up (Multiply)
Multiply both numbers of the ratio by the given scale factor to find the equal ratio.
RATIO: 3 : 5 Multiply by 3
\(3 : 5 = \_\_\_ : \_\_\_\)
RATIO: 2 : 7 Multiply by 4
\(2 : 7 = \_\_\_ : \_\_\_\)
RATIO: 1 : 9 Multiply by 6
\(1 : 9 = \_\_\_ : \_\_\_\)
PART 2
Simplify (Divide)
Divide both numbers by a common factor to write each ratio in its simplest form.
RATIO: 6 : 10 Divide by 2
\(6 : 10 = \_\_\_ : \_\_\_\)
RATIO: 15 : 20 Divide by 5
\(15 : 20 = \_\_\_ : \_\_\_\)
RATIO: 18 : 24 Divide by 6
\(18 : 24 = \_\_\_ : \_\_\_\)
PART 3
Complete the Ratio Tables
Complete the ratio tables by filling in the empty boxes.
Table A: Pencils to Erasers
<table class="w-full text-center text-xs border border-slate-200 rounded overflow-hidden"><tbody><tr class="bg-slate-50 font-semibold text-slate-500"><td class="p-2 border-b border-r border-slate-200 text-left">Pencils</td><td class="p-2 border-b border-r border-slate-200 font-bold text-slate-950">2</td><td class="p-2 border-b border-r border-slate-200">4</td><td class="p-2 border-b border-r border-slate-200">______</td><td class="p-2 border-b border-slate-200">8</td></tr><tr class="text-slate-700"><td class="p-2 border-r border-slate-200 text-left font-semibold text-slate-500">Erasers</td><td class="p-2 border-r border-slate-200 font-bold text-slate-950">5</td><td class="p-2 border-r border-slate-200">______</td><td class="p-2 border-r border-slate-200">15</td><td class="p-2">______</td></tr></tbody></table>
Table B: Oranges to Lemons
<table class="w-full text-center text-xs border border-slate-200 rounded overflow-hidden"><tbody><tr class="bg-slate-50 font-semibold text-slate-500"><td class="p-2 border-b border-r border-slate-200 text-left">Oranges</td><td class="p-2 border-b border-r border-slate-200 font-bold text-slate-950">3</td><td class="p-2 border-b border-r border-slate-200">6</td><td class="p-2 border-b border-r border-slate-200">______</td><td class="p-2 border-b border-slate-200">12</td></tr><tr class="text-slate-700"><td class="p-2 border-r border-slate-200 text-left font-semibold text-slate-500">Lemons</td><td class="p-2 border-r border-slate-200 font-bold text-slate-950">7</td><td class="p-2 border-r border-slate-200">______</td><td class="p-2 border-r border-slate-200">21</td><td class="p-2">______</td></tr></tbody></table>
Scale Masters Answer Key Teacher Answer Key
Equivalent Ratios (SOLUTIONS)
MATH GRADE 6 • UNIT 15
SOLUTIONS MANUAL FOR TEACHERS ONLY
PART 1 KEYS
Scale Up (Multiply)
RATIO: 3 : 5 Multiply by 3
\(3 : 5 = \mathbf{9} : \mathbf{15}\)
RATIO: 2 : 7 Multiply by 4
\(2 : 7 = \mathbf{8} : \mathbf{28}\)
RATIO: 1 : 9 Multiply by 6
\(1 : 9 = \mathbf{6} : \mathbf{54}\)
PART 2 KEYS
Simplify (Divide)
RATIO: 6 : 10 Divide by 2
\(6 : 10 = \mathbf{3} : \mathbf{5}\)
RATIO: 15 : 20 Divide by 5
\(15 : 20 = \mathbf{3} : \mathbf{4}\)
RATIO: 18 : 24 Divide by 6
\(18 : 24 = \mathbf{3} : \mathbf{4}\)
PART 3 KEYS
Complete the Ratio Tables
Table A: Pencils to Erasers
<table class="w-full text-center text-xs border border-slate-200 rounded overflow-hidden"><tbody><tr class="bg-slate-50 font-semibold text-slate-500"><td class="p-2 border-b border-r border-slate-200 text-left">Pencils</td><td class="p-2 border-b border-r border-slate-200 font-bold text-slate-950">2</td><td class="p-2 border-b border-r border-slate-200">4</td><td class="p-2 border-b border-r border-slate-200 text-red-600 font-bold bg-red-50/20">6</td><td class="p-2 border-b border-slate-200">8</td></tr><tr class="text-slate-700"><td class="p-2 border-r border-slate-200 text-left font-semibold text-slate-500">Erasers</td><td class="p-2 border-r border-slate-200 font-bold text-slate-950">5</td><td class="p-2 border-r border-slate-200 text-red-600 font-bold bg-red-50/20">10</td><td class="p-2 border-r border-slate-200">15</td><td class="p-2 text-red-600 font-bold bg-red-50/20">20</td></tr></tbody></table>
Table B: Oranges to Lemons
<table class="w-full text-center text-xs border border-slate-200 rounded overflow-hidden"><tbody><tr class="bg-slate-50 font-semibold text-slate-500"><td class="p-2 border-b border-r border-slate-200 text-left">Oranges</td><td class="p-2 border-b border-r border-slate-200 font-bold text-slate-950">3</td><td class="p-2 border-b border-r border-slate-200">6</td><td class="p-2 border-b border-r border-slate-200 text-red-600 font-bold bg-red-50/20">9</td><td class="p-2 border-b border-slate-200">12</td></tr><tr class="text-slate-700"><td class="p-2 border-r border-slate-200 text-left font-semibold text-slate-500">Lemons</td><td class="p-2 border-r border-slate-200 font-bold text-slate-950">7</td><td class="p-2 border-r border-slate-200 text-red-600 font-bold bg-red-50/20">14</td><td class="p-2 border-r border-slate-200">21</td><td class="p-2 text-red-600 font-bold bg-red-50/20">28</td></tr></tbody></table>
PART 4 KEYS
Word Problem
Scenario: Sugar for Cakes
Scale Masters Match Cards Printable Matching Game
Ratio Sorting Match Cards
MATH GRADE 6 • UNIT 15
Instructions: Cut along the dotted lines. In pairs, students sort the 12 cards into 4 distinct groups of equivalent ratios (each group has: a base ratio, a scaled ratio, and a simple scenario card).
RATIO ID: A1 SIMPLEST
1 : 3
Simplest Form
RATIO ID: A2 SCALED
3 : 9
Scaled Up (×3)
RATIO ID: A3 STORY
"For every 1 teacher , there are 3 students ."
Real-World Case
RATIO ID: B1 SIMPLEST
2 : 5
Simplest Form
RATIO ID: B2 SCALED
6 : 15
Scaled Up (×3)
RATIO ID: B3 STORY
"For every 2 dogs , we need 5 bones ."
Real-World Case
RATIO ID: C1 SIMPLEST
3 : 4
Simplest Form
RATIO ID: C2 SCALED
12 : 16
Scaled Up (×4)
RATIO ID: C3 STORY
"For every 3 blue pens , we need 4 red pencils ."
Real-World Case
RATIO ID: D1 SIMPLEST
4 : 7
Simplest Form
RATIO ID: D2 SCALED
8 : 14
Scaled Up (×2)
RATIO ID: D3 STORY
"For every 4 markers , we need 7 notebooks ."
Real-World Case
UNIT 15: RATIO REVOLUTION • LESSON 2 MATCH CARDS CLASSROOM COPY
Rate Raiders Slides 6th Grade Math
Lesson 3: Rates
Rates & Unit Rates
Best Buys!
Let us learn how to find the price for ONE item. We can use division to find the best shopping deal.
Subject: Unit Prices
Active Learning • Grade 6
STEP 1: UNDERSTANDING RATES Rates & Unit Rates
What is a Rate?
A rate compares two groups that have different labels or units (like money and pieces of fruit, or distance and time).
Example Rate:
$12 for 3 apples
Labels compared: Dollars ($) and Apples (items) .
SHOPPING MODEL
🍎
Apple 1
🍎
Apple 2
🍎
Apple 3
TOTAL PRICE = $12
This is a rate comparison!
Unit: Ratio Revolution Page 2 of 6
STEP 2: FINDING THE PRICE FOR 1 Rates & Unit Rates
DIVISION STEPS
$12 ÷ 3 apples
divide to find ONE!
$4 per apple
We write this shorthand as: $4/apple
The Unit Rate
A unit rate tells you the rate for exactly ONE item . The second group count is always 1!
Shopping Rule
Unit Rate = Total Cost ÷ Total Items
Unit: Ratio Revolution Page 3 of 6
SPEAKING CHANT Rates & Unit Rates
CHORAL CHANT
"Unit rate means for ONE item!"
The Division Chant
"Unit rate means for ONE item!
To solve any unit rate problem: Divide the cost by the number of items!
Unit: Ratio Revolution Page 4 of 6
STEP 3: COMPARING PRICES Rates & Unit Rates
Finding the Best Buy
We compare the price for ONE item to find which shopping deal is cheaper.
Option 1: Smaller Box
2 Soda Cans for $6
Find the unit rate:
$6 ÷ 2 cans = $3.00 per can
Option 2: Larger Box
6 Soda Cans for $15
Find the unit rate:
$15 ÷ 6 cans = $2.50 per can ★
Unit: Ratio Revolution Page 5 of 6
CLASS ACTIVITY Rates & Unit Rates
Grocery Store Comparison!
Let us look at some school store and grocery store ads. Find the price for exactly 1 item, and tell your team which option is the "best buy"!
Rate Raiders Worksheet Math Practice Worksheet
Rates & Unit Rates
MATH GRADE 6 • UNIT 15
Name:
Date:
📢 Help Box:
A rate compares things with different labels. A unit rate tells you the price or speed for exactly 1 item (like price for 1 bottle, or miles in 1 hour).
PART 1
Is it a Rate or a Unit Rate?
Look at each phrase and circle the correct word.
A. $15 for 3 soda cans
Rate Unit Rate
B. $4 for 1 notebook
Rate Unit Rate
C. 120 miles in 2 hours
Rate Unit Rate
D. 65 miles in 1 hour
Rate Unit Rate
PART 2
Calculate the Unit Rate
Divide the numbers to find the price or rate for ONE item. Show your work.
1. $24 for 4 t-shirts
Unit Rate: $________/shirt
2. 150 miles on 5 gallons
Unit Rate: ________ miles/gallon
3. 32 math problems in 8 minutes
Unit Rate: ________ problems/minute
PART 3
Find the Best Buy
Find the unit price for each pack. Write down which option is cheaper (the Best Buy ).
🍏 Item 1: Juice Bottles
Pack A: 3 bottles for $18 $________ / bottle
Pack B: 5 bottles for $25 $________ / bottle
Best Buy Option: _____________________
✏️ Item 2: Marker Packs
Pack X: 4 boxes for $12 $________ / box
Pack Y: 10 boxes for $28 $________ / box
Best Buy Option: _____________________
UNIT 15: RATIO REVOLUTION • LESSON 3 WORKSHEET CLASSROOM COPY
Rate Raiders Answer Key Teacher Answer Key
Rates & Unit Rates (SOLUTIONS)
MATH GRADE 6 • UNIT 15
SOLUTIONS MANUAL FOR TEACHERS ONLY
PART 1 KEYS
Is it a Rate or a Unit Rate?
A. $15 for 3 soda cans
Rate Unit Rate
B. $4 for 1 notebook
Rate Unit Rate
C. 120 miles in 2 hours
Rate Unit Rate
D. 65 miles in 1 hour
Rate Unit Rate
PART 2 KEYS
Calculate the Unit Rate
1. $24 for 4 t-shirts
Work: 24 ÷ 4 = 6
Unit Rate: $6 / shirt
2. 150 miles on 5 gallons
Work: 150 ÷ 5 = 30
Unit Rate: 30 mpg
3. 32 math problems in 8 mins
Work: 32 ÷ 8 = 4
Unit Rate: 4 problems/min
PART 3 KEYS
Find the Best Buy
🍏 Item 1: Juice Bottles
Pack A: 3 bottles for $18 $6.00 / bottle
★ Pack B: 5 bottles for $25 $5.00 / bottle
Best Buy: Pack B (Saves $1.00 per bottle)
✏️ Item 2: Marker Packs
★ Pack X: 4 boxes for $12 $3.00 / box
Pack Y: 10 boxes for $28 $2.80 / box
Best Buy: Pack Y (Cheaper: $2.80 < $3.00)
UNIT 15: RATIO REVOLUTION • LESSON 3 ANSWER KEY CONFIDENTIAL
Rate Raiders Match Cards Printable Card Game
Rate Sorting Match Cards
MATH GRADE 6 • UNIT 15
Instructions: Cut out the cards. Students sort and match them into 4 groups of three cards: a Scenario card, a Unit Rate comparison card, and a Best Buy card.
DEAL ID: T1-S STORY
🥤 Orange Juice
Option A: 3 bottles for $12
Card 1 of 3
DEAL ID: T1-R RATES
Option A: $4.00 per bottle
Card 2 of 3
DEAL ID: T1-B BEST BUY
Option B is Best!
Saves $1.00 per bottle compared to Option A.
Card 3 of 3
DEAL ID: T2-S STORY
🥛 Small Milk Packs
Option 1: 4 cartons for $20
Card 1 of 3
DEAL ID: T2-R RATES
Option 1: $5.00 per carton
Card 2 of 3
DEAL ID: T2-B BEST BUY
Option 2 is Best!
Saves $1.00 per carton compared to Option 1.
Card 3 of 3
DEAL ID: T3-S STORY
📓 Notebook Deals
Store X: 2 packs for $14
Card 1 of 3
DEAL ID: T3-R RATES
Store X: $7.00 per pack
Card 2 of 3
DEAL ID: T3-B BEST BUY
Store Y is Best!
Saves $1.00 per pack compared to Store X.
Card 3 of 3
DEAL ID: T4-S STORY
🎟️ Movie Tickets
Group A: 3 tickets for $18
Card 1 of 3
DEAL ID: T4-R RATES
Group A: $6.00 per ticket
Card 2 of 3
DEAL ID: T4-B BEST BUY
Group B is Best!
Saves $1.00 per ticket compared to Group A.
Card 3 of 3
UNIT 15: RATIO REVOLUTION • LESSON 3 MATCH CARDS CLASSROOM COPY
Proportion Patrol Slides 6th Grade Math
Lesson 4: Proportions
Proportions & Missing Values
Finding Missing Numbers
Let us learn how to find missing numbers in equal ratios by using multiplication rules.
Subject: Proportions
Active Learning • Grade 6
STEP 1: WHAT IS A PROPORTION? Proportions
What is a Proportion?
A proportion is an equation (math sentence) that shows two ratios are completely equal to each other.
Proportion Sentence
\(\frac{2}{5} = \frac{6}{15}\)
PROPORTIONAL BALANCE
2
5
=
6
15
They are balanced! Both fractions represent the exact same ratio value.
Unit: Ratio Revolution Page 2 of 6
STEP 2: FIND THE MISSING NUMBER Proportions
MATH CALCULATION
Find the missing number x:
\(\frac{2}{5} = \frac{x}{15}\)
1 Check the bottom numbers: \(5 \times \mathbf{3} = 15\)
2 Do the same to the top: Multiply 2 by \(\mathbf{3}\)
3 Result: \(x = 6\) \(\rightarrow\) \(\frac{2}{5} = \frac{6}{15}\)
Find the Multiplier
Find the multiplication rule between the known numbers. Then, use that exact same rule to find the missing number!
Remember
Whatever you multiply (or divide) the bottom by, you must do the same to the top!
Unit: Ratio Revolution Page 3 of 6
SPEAKING CHANT Proportions
CHORAL DRILL CHANT
"Find the rule! Multiply top and bottom!"
The Scaling Rule
"Find the rule!
Say it together before scaling any recipe or solving math equations!
Unit: Ratio Revolution Page 4 of 6
STEP 3: RECIPE SCALING Proportions
Recipe Scale Up
We often scale cooking recipes. If a recipe is made for 4 people , how do we scale it up to feed 12 people ?
Find the multiplier factor:
12 ÷ 4 = 3
Multiply all ingredients by 3 !
RICE RECIPE DATABASE
Ingredient Base (Feeds 4) Scaled (Feeds 12) Cups of Rice 2 cups
Proportion Patrol Worksheet Math Practice Worksheet
Proportions
MATH GRADE 6 • UNIT 15
Name:
Date:
📢 Help Box:
A proportion statement shows that two ratios are completely equal. Find the multiplication rule (multiplier) to solve for the missing number \(x\)!
PART 1
Solve for the Missing Number
Solve for the missing term \(x\) in each proportion. Write the multiplier rule you used.
QUESTION 1 RULE: _________
\(\frac{2}{5} = \frac{x}{15}\)
\(x = \) ______
QUESTION 2 RULE: _________
\(\frac{3}{4} = \frac{9}{x}\)
\(x = \) ______
QUESTION 3 RULE: _________
\(\frac{1}{6} = \frac{x}{24}\)
\(x = \) ______
PART 2
Scale the Cooking Recipe
A recipe for a delicious soup is designed for 4 people . Scale the ingredients up to feed a group of 12 people .
Multiplier Calculation: \(12 \div 4 = \) _________
Ingredient Original (Feeds 4) Scaled Amount (Feeds 12) Cups of Soup Broth 3 Cups ___________ Cups Bags of Noodles 2 Bags ___________ Bags Spoons of Salt 5 spoons ___________ spoons
UNIT 15: RATIO REVOLUTION • LESSON 4 WORKSHEET CLASSROOM COPY
Proportion Patrol Answer Key Teacher Answer Key
Proportions (SOLUTIONS)
MATH GRADE 6 • UNIT 15
SOLUTIONS MANUAL FOR TEACHERS ONLY
PART 1 KEYS
Solve for the Missing Number
QUESTION 1 RULE: × 3
\(\frac{2}{5} = \frac{x}{15}\)
\(x = \mathbf{6}\)
QUESTION 2 RULE: × 3
\(\frac{3}{4} = \frac{9}{x}\)
\(x = \mathbf{12}\)
QUESTION 3 RULE: × 4
\(\frac{1}{6} = \frac{x}{24}\)
\(x = \mathbf{4}\)
PART 2 KEYS
Scale the Cooking Recipe
Multiplier Calculation: \(12 \div 4 = \mathbf{3}\)
Ingredient Original (Feeds 4) Scaled Amount (Feeds 12) Cups of Soup Broth 3 Cups 9 Cups (3 × 3) Bags of Noodles 2 Bags 6 Bags (2 × 3) Spoons of Salt 5 spoons 15 spoons (5 × 3)
UNIT 15: RATIO REVOLUTION • LESSON 4 ANSWER KEY CONFIDENTIAL
Proportion Patrol Task Cards Printable Station Activity
Proportion Practice Task Cards
MATH GRADE 6 • UNIT 15
Instructions: Cut along the dotted lines. Place cards around the classroom. Students solve in pairs to find the missing numbers!
Task Card 1
Baking Cookies
CHOCOLATE CHIPS
A cookie recipe uses 2 cups of chocolate chips to make 12 cookies .
Your Task:
Set up a proportion: \(\frac{2\text{ cups}}{12\text{ cookies}} = \frac{x\text{ cups}}{24\text{ cookies}}\).
STATION: BAKING UNIT 15 • L4
Task Card 2
Mixing Juice
JUICE POWDER
A juice mix uses 5 spoons of juice powder for every 4 cups of water .
Your Task:
Set up a proportion: \(\frac{5\text{ spoons}}{4\text{ cups}} = \frac{x\text{ spoons}}{8\text{ cups}}\).
STATION: DRINKS UNIT 15 • L4
Task Card 3
Gardening Pots
FLOWER SEEDS
A gardener plants 3 flower seeds in every 4 pots .
Your Task:
Set up a proportion: \(\frac{3\text{ seeds}}{4\text{ pots}} = \frac{x\text{ seeds}}{16\text{ pots}}\).
STATION: GARDEN UNIT 15 • L4
Task Card 4
Mixing Paint
BLUE & WHITE PAINT
To make light blue, a painter mixes 1 cup of blue paint for every 4 cups of white paint .
Your Task:
Set up a proportion: \(\frac{1\text{ blue}}{4\text{ white}} = \frac{x\text{ blue}}{20\text{ white}}\).
STATION: ART UNIT 15 • L4
UNIT 15: RATIO REVOLUTION • LESSON 4 TASK CARDS CLASSROOM COPY
Ratio Revolution Homework Cumulative Homework
Ratio Practice
MATH GRADE 6 • WEEK 15
Name:
Date:
📢 Unit Recap Help Box:
This homework sheet reviews all 4 key lessons: writing ratios, finding equal ratios, calculating unit rates, and setting up proportions. Complete all tasks carefully!
L1
Stage 1: Writing Ratios
A pencil box has 3 blue markers and 5 red pens .
1. Blue markers to Red pens in 3 ways:
Words: _________ | Colon: _________ | Fraction: _________
2. Blue markers to Total writing tools in 3 ways:
Words: _________ | Colon: _________ | Fraction: _________
L2
Stage 2: Equal Ratios
3. Scale Up (Multiply by 5):
\(2 : 9 = \_\_\_ : \_\_\_\)
4. Simplify (Divide by common GCF factor):
\(12 : 20 = \_\_\_ : \_\_\_\)
L3
Stage 3: Unit Rates
5. Find the Unit Rate:
Anna rode her bike 180 km in 3 hours.
Speed: ____________ km per hour
6. Find the Best Buy Deal:
Pack A: 3 notebooks for $12 | Pack B: 5 notebooks for $15
Best Buy Option: _________________________
L4
Stage 4: Proportions
Find the missing number \(x\) by using the multiplier rule.
7. Solve for x:
\(\frac{3}{7} = \frac{x}{28}\) Rule: × ___ \(x = \_\_\_\)
8. Solve for x:
\(\frac{2}{3} = \frac{10}{x}\) Rule: × ___ \(x = \_\_\_\)
UNIT 15: RATIO REVOLUTION • WEEK 15 HOMEWORK CLASSROOM COPY
Ratio Revolution Homework Answer Key Teacher Answer Key
Ratio Practice (SOLUTIONS)
MATH GRADE 6 • WEEK 15
SOLUTIONS MANUAL • WEEK 15 CUMULATIVE HOMEWORK
L1 KEY
Stage 1: Writing Ratios
Pencil box contains: 3 blue markers and 5 red pens. (Total = 8 items).
1. Blue markers to Red pens (Part-to-Part):
Words: 3 to 5 | Colon: 3 : 5 | Fraction: \(\frac{3}{5}\)
2. Blue markers to Total tools (Part-to-Whole):
Words: 3 to 8 | Colon: 3 : 8 | Fraction: \(\frac{3}{8}\)
L2 KEY
Stage 2: Equal Ratios
3. Scale Up (Multiply by 5):
\(2 : 9 = \mathbf{10} : \mathbf{45}\)
4. Simplify (Divide by GCF of 4):
\(12 : 20 = \mathbf{3} : \mathbf{5}\)
L3 KEY
Stage 3: Unit Rates
5. Find the Unit Rate:
Anna rode 180 km in 3 hours. (Work: 180 ÷ 3)
Speed: 60 km per hour
6. Find the Best Buy Deal:
Pack A ($4/notebook) vs Pack B ($3/notebook)
Best Buy: Pack B (Cheaper per single item)
L4 KEY
Stage 4: Proportions
Solve for the missing value \(x\).
7. Solve for x:
\(\frac{3}{7} = \frac{x}{28}\) Rule: × 4 \(x = 12\)
8. Solve for x:
\(\frac{2}{3} = \frac{10}{x}\) Rule: × 5 \(x = 15\)
UNIT 15: RATIO REVOLUTION • WEEK 15 HOMEWORK SOLUTIONS CONFIDENTIAL
