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Ratio Relationships

Comprehensive study guides and practice resources for Grade 6 Module 1 ratio concepts, representations, tables, tape diagrams, and coordinate graphs.

JSjerell saint phar

Ratio Relationships

Comprehensive study guides and practice resources for Grade 6 Module 1 ratio concepts, representations, tables, tape diagrams, and coordinate graphs.

JSjerell saint phar

Ratio Mastery Study Guide

Grade 6 Math • Module 1 Topic A

Ratio Concepts Study Guide

Review definitions, key models, and practice strategies before taking the quiz.

Name:

Date:

Class:

1. Essential Vocabulary

Ratio Core Term

A comparison of two quantities or values. Can be written in three forms: $a : b$, $a \text{ to } b$, or $\frac{a}{b}$.

Part-to-Part Ratio Type 1

Compares one specific group to another group. Example: 6 bananas to 8 apples $\rightarrow 6 : 8$ (or $3 : 4$).

Part-to-Whole Ratio Type 2

Compares one specific group to the total of all groups combined. Example: 5 oranges to 20 total fruits $\rightarrow 5 : 20$.

Equivalent Ratios Key Skill

Ratios that express the same proportional relationship. Formed by multiplying or dividing each term by the same nonzero number.

2. Three Golden Rules for the Quiz

Rule 1: Order Matters!

The order of numbers must match the order in words. "Ratio of lemons to bananas" means Lemons : Bananas (1 : 6), NOT 6 : 1.

Rule 2: Read the Whole!

Always find the total sum first:
Total = Part A + Part B + Part C Check whether a question compares to the whole or just another part!

Rule 3: Combined Parts

If asked for "apples to total apples and oranges", add only those two specific categories ($8 + 5 = 13$).

3. Visual Tool: Tape Diagrams & Unit Value Method

How Tape Diagrams Work:

In a ratio of 7 : 4 (Pasta to Rice), draw 7 equal units for pasta and 4 equal units for rice. Every single box represents the exact same number.

Pasta:

5 5 5 5 5 5 5

= 35

Rice:

5 5 5 5

= 20

The 2 Big Problem Types:

Type A: Given One Quantity

If Pasta is 35: divide by its 7 boxes $\rightarrow 35 \div 7 = \mathbf{5}$ per box.
Then Rice = $4 \times 5 = \mathbf{20}$ boxes.

Type B: Given the Total Sum

If Total is 88: add the parts ($7 + 4 = 11$ total boxes).
Divide total by all boxes: $88 \div 11 = \mathbf{8}$ per box.
Then Rice = $4 \times 8 = \mathbf{32}$ boxes.

4. Quick Warm-Up Checks

A. Fruit Bowl Quick Check:

There are 4 plums and 6 peaches. What is the ratio of plums to the total fruit?

Answer:

B. Recipe Scaling Quick Check:

1 batch of sauce takes 2 cups tomato and 3 tsp basil. For 3 batches, how much basil?

Answer:

Topic A: Understanding & Applying Ratios Turn page for Quiz Preparation Problems → Page 1 of 2

Targeted Practice

Quiz Preparation Practice

Complete each problem showing full steps.

1 Sports Equipment Bag (Writing & Matching Ratios)

Part-to-Part & Part-to-Whole

A gym storage bin has 5 soccer balls, 7 basketballs, 4 volleyballs, and 2 footballs. Write the correct ratio next to each description using the answer choices below.

Soccer balls to basketballs

Total balls to volleyballs

Footballs to soccer balls

Basketballs to (volleyballs + footballs)

Answer Bank: 5 : 7 7 : 5 18 : 4 2 : 5 7 : 6 18 : 7

2 Communication Log & Tape Diagram Analysis

Select All That Apply

Marcus receives 12 text messages, 4 voicemails, and 8 emails throughout the day.

Part A: Select ALL correct statements:

The ratio of texts to emails is 3 : 2. The ratio of voicemails to total messages is 4 : 24. The ratio of emails to texts is 12 : 8. The ratio of voicemails to (texts and emails) is 4 : 20.

Part B: Interpreting Statements

Fill in the blank with the correct description:

The ratio 8 : 4 represents the ratio of

The ratio 8 : 16 represents the ratio of emails to

3 Recipe & Batch Scaling

Multiplication / Scaling

A bakery makes 1 batch of artisan bread using 4 cups of whole wheat flour and 3 cups of warm water. The baker makes 3 full batches of the bread. How many cups of water does the baker use?

A 6 cups

B 9 cups

C 12 cups

D 15 cups

Show reasoning or calculation:

4 Equivalent Ratios & Tape Diagrams

2-Part Multi-Step

The ratio of the number of blue pens to the number of red pens in the school store is 5 : 3.

Part A: Given One Part

The school store has 40 blue pens. How many red pens are in the store?

Answer: red pens

Part B: Given the Total

In a new shipment, there are 56 total pens (blue and red). The ratio is still 5 : 3. How many red pens are in this shipment?

Answer: red pens

Test Tip: Always find the value of 1 box ($\text{Total} \div \text{Total Boxes}$ or $\text{Part} \div \text{Part Boxes}$).

Page 2 of 2

Ratio Representations Study Guide

Grade 6 Math • Eureka Math² Module 1 Topic B

Topic B Quiz Mastery Study Guide

Tape Diagrams, Ratio Tables, Coordinate Graphs & Unit Rates

Name:

Date:

Period:

★

+10 POINTS BONUS

Monday Quiz Reward Opportunity!

Complete every section of this study guide with full work shown and turn it in on Monday before your quiz to receive 10 BONUS POINTS on your Topic B Quiz!

Teacher Stamp +10 PTS

1. Four Core Topic B Strategies

1. Total Given: Find 1 Unit Tape Diagram

When given a ratio $a : b$ and a total:
• Add total parts: $a + b = \text{total units}$
• Divide: $\text{Value of 1 box} = \text{Total} \div \text{Total Units}$
• Multiply: $\text{Desired Part} = \text{Boxes} \times \text{Value of 1 box}$

2. Tape Redistribution (Moving Units) Fractions

When moving a fraction of units from Jar A to Jar B:
• $\frac{1}{4}$ of 4 boxes = 1 box moved.
• Jar A: loses 1 box $(4 - 1 = 3 \text{ boxes})$.
• Jar B: gains 1 box $(3 + 1 = 4 \text{ boxes})$.
• New ratio becomes $3 : 4$ (Jar A now has fewer).

3. Multiple Representations Check All

• Ratio Tables: Must have constant multiplier $(\times k)$, never constant addition $+k$!
• Statements: Compute rate per 1 item to verify claims.
• Graphs: Ensure points follow straight line through $(0,0)$.

4. Rates & Coordinate Plane Graphing

• Unit Rate: $\frac{\text{Total Dollars}}{\text{Total Hours}} = \text{Earnings per 1 hour}$.
• Coordinates: Write pairs as $(x, y) = (\text{Hours}, \text{Dollars})$.
• Trap Alert: Do NOT flip coordinates! $x$ is horizontal, $y$ is vertical.

2. Visual Model Walkthroughs

Model A: Moving Units Between Ratios

Original Ratio: Jar A (4 units) to Jar B (3 units) $\rightarrow 4 : 3$

Jar A:

u u u 1/4

← Move 1 box

Jar B:

u u u

(3 units)

After Transferring 1 Box:

Jar A:

8 8 8

= 24

Jar B:

8 8 8 8

= 32

Notice: 1 box = $24 \div 3 = 8$. Then Jar B = $4 \times 8 = 32$.

Model B: Rate Tables & Ordered Pairs

Ratio Representations Answer Key

Teacher Resource • Answer Key Eureka Math² Grade 6 • Module 1 Topic B

Topic B Study Guide Answer Key & Scoring Guide

Complete solutions, model tape diagrams, rubric criteria, and common misconceptions

Grading Target +10 Bonus Pts Full work required

Page 1: Quick Self-Check Warm-Up Solutions

1 pt each

A. Unit Value Check Ans: 6

Total = 30 markers, ratio 3 : 2 (blue to red).

$3 + 2 = 5\text{ units}$
$30 \div 5 = \mathbf{6\text{ markers/unit}}$

Key misconception: Dividing 30 by 3 or 2 instead of total parts.

B. Coordinate Check Ans: (12, 4)

Plastic beads = $x$, metal beads = $y$.

$x = 12, \; y = 4$
$(x, y) = \mathbf{(12, 4)}$

Trap: Inverting coordinates to (4, 12). Remind: $(x, y)$ is alphabetical!

C. Rate Prediction Ans: 12 hrs

Rate = $8/hr. Earn $96 total.

$\text{Hours} = 96 \div 8 = \mathbf{12\text{ hours}}$

Verification: $12 \times 8 = 96$. Rate multiplier is constant.

1

Problem 1: Ratios with a Given Total (Bin of Markers)

Correct Choice: C (20 markers) 2 pts

Given: Total = 36 markers. Ratio of Blue to Red = 5 : 4. Find Blue markers.

Step 1: Find total unit boxes: $5 + 4 = \mathbf{9\text{ total units}}$.

Step 2: Determine value of 1 box: $\text{Value} = 36 \div 9 = \mathbf{4\text{ markers per box}}$.

Step 3: Calculate Blue markers: $5 \text{ units} \times 4 = \mathbf{20\text{ blue markers}}$.

Check: Red markers = $4 \times 4 = 16$. Total = $20 + 16 = 36$ markers. Matches!

Model Tape Diagram:

Blue (5):

4 4 4 4 4

= 20

Red (4):

4 4 4 4

= 16

Distractor Analysis:
• A (9): Total units, not number of markers.
• B (16): Red markers calculated instead of Blue.
• D (24): Arithmetic miscalculation or guessing.

2

Problem 2: Tape Diagram Redistribution (Counters in Cups)

3 pts total (1 pt Part A, 2 pts Part B)

Part A: New Tape Diagram 1 pt

Original: Cup A = 4 boxes, Cup B = 3 boxes.
$\frac{1}{4}$ of 4 boxes = 1 box moved from Cup A to Cup B.

Cup A:

6 6 6

(3 units)

Cup B:

6 6 6 6*

Ratio Comparison Study Guide

Grade 6 Math • Module 1 Topic C

Comparing Ratio Relationships Study Guide

Master ratio tables, unit rates, and visual models to compare which ratio is greater.

Name:

Date:

Class:

1. Three Ways to Compare Ratios

Strategy 1: Unit Rate Best

Calculate the amount of one quantity for 1 unit of the other quantity ($\frac{a}{b}$).

Punch A: $6 \div 4 = \mathbf{1.5}$ cups/orange
Punch B: $10 \div 5 = \mathbf{2.0}$ cups/orange
$\rightarrow$ Punch B has more pineapple per cup!

Strategy 2: Common Quantity Scale

Scale both ratios to find equivalent pairs that have the exact same amount for one item.

Recipe A: 4 cups OJ $\rightarrow$ 6 pine
Recipe B: 4 cups OJ $\rightarrow$ 8 pine
$\rightarrow$ Compare directly with equal OJ!

Strategy 3: Line Steepness Visual

Plot both ratios on the same coordinate plane. The steeper line has a greater unit rate of $y$ to $x$.

Higher point at same $x$
$=$ Higher rate $(y \div x)$
$\rightarrow$ Steeper = stronger $y$-quantity!

2. Three Golden Rules for the Topic C Quiz

Rule 1: Avoid the Additive Trap!

Ratios compare quantities multiplicatively. Adding 1 cup of juice to a batch changes the ratio and flavor! Ratios are NOT preserved by simple addition.

Rule 2: Keep the Order Straight

"Cups of syrup per cup of yogurt" means $\frac{\text{syrup}}{\text{yogurt}}$. "Cups of yogurt per cup of syrup" means $\frac{\text{yogurt}}{\text{syrup}}$. Always verify which quantity is the denominator ($1\text{ unit}$).

Rule 3: Flavor Strength Logic

Stronger flavor $=$ more flavor ingredient per 1 unit of base, OR less base ingredient per 1 unit of flavor ingredient.

3. Comparing with Double Number Lines & Coordinate Graphs

Double Number Line Check:

Two double number lines represent the same ratio relationship only if every pair scales by the exact same multiplier:

• Line 1: $4 : 2 = \mathbf{2 : 1}$ • $8 : 4 = \mathbf{2 : 1}$

• Line 2: $2 : 1 = \mathbf{2 : 1}$ • $6 : 3 = \mathbf{2 : 1}$

✓ Both have unit rate of 2 pretzels per 1 peanut (Equivalent!)

Coordinate Graph Check:

Points from equivalent ratios lie on a straight line through $(0, 0)$:

• If points form a steeper ray, that mixture has a larger $y$-to-$x$ ratio.

Ratio Comparison Answer Key

Teacher Resource • Answer Key Eureka Math² Grade 6 • Module 1 Topic C

Topic C Study Guide Answer Key & Scoring Guide

Complete solutions, reasoning strategies, common student traps, and scoring criteria

Quiz Target Topic C Mastery Comparing Ratios

Page 1: Quick Warm-Up Solutions & Concepts

Self-Check Verification

A. Unit Rate Calculation Ans: 8 oz/gal

24 oz of tint for every 3 gallons of base paint.

$\text{Unit Rate} = \frac{24\text{ oz}}{3\text{ gallons}} = \mathbf{8\text{ oz per gallon}}$

Teaching Note: Verify students put the base quantity (gallons) in the denominator to get tint per 1 gallon.

B. Flavor Strength Comparison Ans: Batch X

Batch X: 3 tsp / 2 cups (1.5). Batch Y: 5 tsp / 4 cups (1.25).

$\text{Batch X} = 1.50\text{ tsp/cup} > \text{Batch Y} = 1.25\text{ tsp/cup}$

Teaching Note: Higher cocoa-to-milk unit rate means more flavor per cup of milk. Batch X is stronger.

Pedagogical Framework: Comparing Ratios in Topic C

1. Unit Rate Method

Compute $\frac{a}{b}$. Best for comparing prices, speeds, and ingredient concentrations per 1 single unit.

2. Common Quantity Method

Scale both pairs to match either $x$ or $y$. Ideal when fractions are awkward or tables share a common multiple.

3. Graphical Steepness Method

Compare rays on a coordinate grid starting at $(0,0)$. The steeper line indicates a greater $y$ per $x$ unit rate.

1

Part 1 Solution: Completing Ratio Tables & Finding Unit Rates

Total: 3 Points

Context: Maya uses 24 centimeters of decorative tape for every 3 greeting cards created.
Base ratio: 24 cm : 3 cards. Simplified base unit rate: $\frac{24}{3} = \mathbf{8\text{ cm per card}}$.

A. Completed Ratio Table 2 pts (all 5 correct)

Centimeters of Tape	Number of Cards	Work / Scaling
24	3	Given ratio pair
32	4	$4 \times 8 = 32$
48	6	$48 \div 8 = 6$
64	8	$8 \times 8 = 64$
96	12	$96 \div 8 = 12$

B. Unit Rate Statement 1 pt

Rates Mastery Study Guide

Grade 6 Math • Module 1 Topic D

Rates and Unit Rates Study Guide

Master rates, unit rates, the “per” order rule, rate tables, and multi-unit conversions.

Name:

Date:

Class:

1. Rates vs. Unit Rates & The Order Rule

Rate vs. Unit Rate Key Idea

A rate compares two quantities with different units (e.g., 16 meters per second). A unit rate is the numerical value associated with the rate (e.g., 16).

Rate: $16\text{ m/s}$
Unit Rate: $\mathbf{16}$

Watch the Order! Quiz Trap

The unit after “per” is always the denominator ($1\text{ unit}$). Pay close attention to what is asked!

• hours per puzzle: $\frac{\text{hours}}{\text{puzzles}} = \frac{2}{4} = \mathbf{0.5}$
• puzzles per hour: $\frac{\text{puzzles}}{\text{hours}} = \frac{4}{2} = \mathbf{2}$

Rate Tables Equivalent

In a rate table, multiply or divide both rows/columns by the same factor, or multiply the input by the unit rate.

$1\text{ s} \times 16 = 16\text{ m}$
$7\text{ s} \times 16 = 112\text{ m}$

2. Three Master Strategies for Quiz D

Strategy 1: Flavor Strength

Find the unit rate for each shop: $\frac{\text{flavor ingredient}}{\text{item}}$. The shop with the larger unit rate has the stronger flavor (more flavor per single item).

Strategy 2: Scaling Prices

To find how many items for a target cost, first find the unit price: $\text{Cost} \div \text{Items}$. Then divide: $\text{Target Cost} \div \text{Unit Price} = \text{Total Items}$.

Strategy 3: Multi-Unit Rates

Break rate conversions into two clean steps: 1. Convert distance (feet to yards: divide by $3$). 2. Convert time (per min to per hour: multiply by $60$).

3. Measurement Conversion Toolkit

Length Units

• $1\text{ yard} = 3\text{ feet}$
• Feet to yards: $\text{feet} \div 3$
• Yards to feet: $\text{yards} \times 3$

Time Units

• $1\text{ minute} = 60\text{ seconds}$
• $1\text{ hour} = 60\text{ minutes}$
• $4\text{ minutes} = 4 \times 60 = 240\text{ seconds}$

Rate Conversion Example

$240\text{ ft/min} \div 3 = 80\text{ yd/min}$
$80\text{ yd/min} \times 60 = \mathbf{4,800\text{ yd/hr}}$

Rates Mastery Answer Key

Teacher Resource • Answer Key Eureka Math² Grade 6 • Module 1 Topic D

Topic D Study Guide Answer Key & Scoring Guide

Complete solutions, unit rate analyses, conversion steps, and rubric criteria.

Quiz Target Topic D Mastery Rates & Unit Rates

Page 1: Quick Warm-Up Solutions & Concepts

Self-Check Verification

A. Unit Rate Order Check Ans: 0.5 (or 1/2)

10 juices in 5 minutes. Rate in minutes per juice.

$\frac{\text{minutes}}{\text{juices}} = \frac{5}{10} = \mathbf{0.5}\text{ min/juice}$

Common Pitfall: Students invert to $10 \div 5 = 2$. Emphasize that “per juice” makes juice the denominator.

B. Length Conversion Check Ans: 120 yards

360 feet in 2 minutes. Expressed in yards in 2 minutes.

$1\text{ yd} = 3\text{ ft} \implies 360\text{ ft} \div 3 = \mathbf{120\text{ yards}}$

Teaching Note: The time period (2 minutes) stays unchanged here; only distance units convert.

1

Problem 1 Solution: Unit Rate with Order Awareness

1 Point

Context: Elena decorates 4 ceramic bowls in 2 hours. Express rate in hours per bowl.

Correct Answer:

$\frac{2}{4} = \frac{1}{2} = \mathbf{0.5}$ (or $\mathbf{\frac{1}{2}}$)

Either $\frac{1}{2}$ or $0.5$ is fully acceptable.

Distractor & Trap Alert:

An answer of 2 indicates the student answered “bowls per hour” ($4 \div 2$) rather than “hours per bowl” ($2 \div 4$).

2

Problem 2 Solution: Rate Table & Equivalence Statements

Total: 3 Points (1 pt Part A, 2 pts Part B)

Context: Cyclist travels 15 meters per second ($1\text{ s} : 15\text{ m}$).

Part A: Completed Table

Seconds	Meters	Method
1	15	Unit rate
4	60	$4 \times 15$
7	105	$105 \div 15$
10	150	$10 \times 15$

Part B: Select True Statements Correct: A, C, E

A is TRUE: Directly states unit rate ($1\text{ s} \rightarrow 15\text{ m}$).

B is FALSE: Reverses units! It is 105 meters in 7 seconds, not 7 meters in 105 seconds.

Babysitting rate: 4 hours for $24 $\rightarrow \$24 \div 4 = \mathbf{\$6/\text{hr}}$

Hours $(x)$	Earnings $(y)$
1	$6
4	$24
8	$48
12	$72

Ordered Pairs:

(1, 6)

(4, 24)

(8, 48)

(12, 72)

Rule: $y = 6x$. Earnings is 6 times the hours!

3. Quick Self-Check Warm-Up

A. Unit Value Check

A box has 30 markers with ratio 3 : 2 (blue to red). What is the value of 1 unit box?

1 unit =

B. Coordinate Point Check

If plastic beads are $x$ and metal beads are $y$, what ordered pair represents 12 plastic and 4 metal?

$(x, y) =$

C. Rate Prediction Check

If a student earns $8 per hour, how many hours must they work to earn $96?

Hours =

Eureka Math² Grade 6 • Module 1 Topic B Turn page to complete Quiz Preparation Practice (+10 Bonus Points!) → Page 1 of 2

Targeted Quiz B-1 Practice

Topic B Practice Exam (+10 Quiz Points on Monday!)

Show full work for credit

1 Ratios with a Given Total

Part-to-Part & Total

There are a total of 36 blue markers and red markers in a classroom bin. The ratio of the number of blue markers to the number of red markers is 5 : 4. How many blue markers are in the bin?

A 9 markers

B 16 markers

C 20 markers

D 24 markers

Show tape diagram or calculation:

Correct Choice:

2 Tape Diagram Redistribution

Fraction Movement

The tape diagram represents the ratio of the number of counters in Cup A to Cup B:

Cup A:

(4 units)

Cup B:

(3 units)

Part A: Draw New Diagram

Aaliyah moves $\frac{1}{4}$ of counters from Cup A to Cup B. Draw the new diagram:

Part B: Circle the correct answer for each statement:

New ratio Cup A to Cup B:

4 : 3 4 : 7 3 : 4 3 : 7

Now, Cup A has:

fewer than more than the same as

Cup B.

If Cup A now has 18 counters, Cup B has:

18 24 32 42

3 Multiple Representations (Select ALL That Apply)

Tables, Statements & Graphs

Liam makes keychains. For each keychain, he uses 15 plastic beads and 5 metal beads. Which representations show the relationship between the number of plastic beads and metal beads? Choose ALL that apply.

A Table Option A

Plastic	Metal
15	5
30	20
45	35

B Table Option B

Plastic	Metal
15	5
30	10
60	20

C For every 4 keychains, Liam uses 20 metal beads.

D For every 6 keychains, Liam uses 90 metal beads.

E A graph with points at (15, 5), (30, 10), and (45, 15) where $x$ = Plastic.

4 Unit Rates, Rate Tables & Coordinate Graphing

3-Part Extended Response

Marcus walks dogs after school. He earns a total of $32 for 4 hours of dog walking.

Part A: Complete the Table

Hours $(x)$	Total Earned ($) $(y)$
1
4	$32
6
10

Part C: Complete Each Statement

Walks for hours to earn $160.

For 8 hours, he earns $ .

Part B: Plot Four Points on Grid (Hours, $)

0 16 32 48 64 80 0 2 4 6 8 10 12 Hours (x) Total Earned ($) (y)

Plot each ordered pair $(x, y)$ and label coordinates.

Monday Reminder: Turn in completed study guide before quiz to claim your +10 points!

Page 2 of 2

(4 units)

*Student diagram must clearly show Cup A with 3 equal boxes and Cup B with 4 equal boxes.

Part B: Answer Statements & Calculations 2 pts

1. New ratio Cup A to Cup B: 3 : 4

Explanation: Cup A decreased from 4 to 3; Cup B increased from 3 to 4.

2. Now, Cup A has: fewer than

Explanation: Cup A has 3 units, while Cup B has 4 units ($3 < 4$).

3. If Cup A now has 18 counters, Cup B has: 24

$\text{Unit box} = 18 \div 3 = 6 \text{ counters}$ • $\text{Cup B} = 4 \times 6 = \mathbf{24\text{ counters}}$

Common error: Dividing 18 by 4 (forgetting Cup A now has 3 boxes, not 4).

Teacher Resource • Eureka Math² Module 1 Topic B Answer Key Turn page for Problems 3 & 4 + Bonus Rubric → Page 1 of 2

Teacher Scoring Key Topic B Quiz Practice Exam Solutions

Multiple Representations, Rate Tables & Coordinate Graphing

Total Exam Value: 10 Points

3

Problem 3: Multiple Representations (Liam's Keychains)

Select Choices: B, C, and E 2 pts

Context: 15 plastic beads and 5 metal beads per keychain. Base ratio is 15 : 5, which simplifies to 3 : 1. Ratio rule: $\text{Plastic} = 3 \times \text{Metal}$ or $\text{Metal} = \frac{1}{3} \times \text{Plastic}$.

Choice A Incorrect

Additive error trap!
Plastic: $15 \rightarrow 30 \rightarrow 45$ $(+15)$.
Metal: $5 \rightarrow 20 \rightarrow 35$ $(+15)$.
Ratio $30 : 20 = 3 : 2 \neq 3 : 1$. Ratios require multiplication, not constant addition!

Choice B Correct ✓

Valid ratio table.
$15 \div 5 = 3$
$30 \div 10 = 3$
$60 \div 20 = 3$
Every row has identical multiplicative unit rate of 3 to 1.

Choice C Correct ✓

Valid statement.
Each keychain uses 5 metal beads.
$4 \text{ keychains} \times 5 = \mathbf{20\text{ metal beads}}$.
Matches the problem description perfectly.

Choice D Incorrect

Category swap trap!
$6 \times 15 = 90$ plastic beads, NOT metal beads.
Metal would be $6 \times 5 = 30$. Students who misread the category label pick this.

Choice E Correct ✓

Valid coordinate graph.
$(15, 5) \rightarrow 15 \div 5 = 3$
$(30, 10) \rightarrow 30 \div 10 = 3$
$(45, 15) \rightarrow 45 \div 15 = 3$
Passes through $(0,0)$ with straight linear slope.

Scoring Note: Award 2 full points for selecting B, C, and E with no incorrect options chosen. Award 1 point if 2 out of 3 correct options are chosen with 0 incorrect options.

4

Problem 4: Unit Rates, Rate Tables & Coordinate Graphing (Dog Walking)

Unit Rate: $8 per 1 Hour 3 pts total (1 pt per part)

Part A: Completed Table Rule: $\times 8$

Hours $(x)$	Total Earned ($) $(y)$	Ordered Pair
1	$8	(1, 8)
4	$32 (Given)	(4, 32)
6	$48	(6, 48)
10	$80	(10, 80)

Calculation: $\$32 \div 4 = \$8/\text{hr}$. Then $1 \times 8 = 8$, $6 \times 8 = 48$, $10 \times 8 = 80$.

Part C: Statement Solutions

• Marcus walks for 20 hours to earn $160. Work: $\$160 \div \$8/\text{hr} = \mathbf{20\text{ hours}}$.

• For 8 hours of walking, he earns $64. Work: $8 \text{ hours} \times \$8 = \mathbf{\$64}$.

Part B: Plotted Coordinate Plane Solution All 4 Points Plotted

0 16 32 48 64 80 0 2 4 6 8 10 12 Hours (x) Total Earned ($) (y) (1, 8) (4, 32) (6, 48) (10, 80)

Criteria: Points must align linearly at $(1, 8), (4, 32), (6, 48), (10, 80)$. Points should NOT be flipped (e.g., plotting $(8, 1)$ instead of $(1, 8)$).

MONDAY QUIZ BONUS How to Award the +10 Study Guide Points:

• Full +10 Points: Every question attempted with complete mathematical work (tape diagram on Q1 & Q2, work shown on Q3 & Q4).
• Partial +5 Points: All answers circled/written, but partial or incomplete scratch work shown.
• 0 Points: Incomplete study guide or submitted after Monday quiz administration.

Quiz Bonus Stamp VERIFIED Teacher Initials

Teacher Notes: Aligned directly to Eureka Math² Grade 6 Module 1 Topic B Quiz standards.

Page 2 of 2

• If two lines have different slopes, they are different ratio relationships.

Compare: Find $y$ when $x = 1$ (the unit rate)!

4. Quick Warm-Up Checks

A. Unit Rate Calculation:

A painter uses 24 oz of tint for every 3 gallons of base paint. What is the unit rate of tint per gallon?

Answer: oz per gallon

B. Greater Flavor Comparison:

Batch X has 3 tsp cocoa for 2 cups milk $(1.5)$. Batch Y has 5 tsp cocoa for 4 cups milk $(1.25)$. Which batch has a stronger chocolate flavor?

Answer:

Eureka Math² Module 1 Topic C: Comparing Ratio Relationships Turn page for 3-Part Targeted Practice → Page 1 of 2

Targeted Practice

Topic C Quiz Preparation Practice

3 Core Practice Problems

1

Part 1: Completing Ratio Tables & Finding Unit Rates

Mirrors Quiz Q1

Maya decorates greeting cards. She uses 24 centimeters of decorative tape for every 3 cards she creates.

A. Complete the ratio table:

Centimeters of Tape	Number of Cards
24
	4
48
	8
96

B. Fill in the blank:

For every 1 card Maya creates, she uses centimeters of decorative tape.

Show calculation or scaling:

2

Part 2: Comparing Ratio Tables & Flavor Strength

Mirrors Quiz Q2 • Select All

A smoothie stand makes two types of lemon-lime freeze. The tables show the cups of lemon juice and cups of lime juice used:

Freeze A

Cups Lemon Juice	Cups Lime Juice
3	6
6	12
9	18

Freeze B

Cups Lemon Juice	Cups Lime Juice
4	12
6	18
8	24

Based on the tables, which statements are true? Choose ALL that apply:

A. The ratio of cups of lemon juice to lime juice in Freeze A is 1 : 2. B. Freeze B has a stronger lime flavor than Freeze A because Freeze B has 3 cups of lime juice per 1 cup lemon juice, while Freeze A has 2 cups. C. Freeze A has a stronger lemon flavor than Freeze B because Freeze A has $\frac{1}{2}$ cup lemon per cup lime, while Freeze B has $\frac{1}{3}$ cup. D. If a worker adds 1 cup of lemon juice and 1 cup of lime juice to Freeze A, they make Freeze B.

3

Part 3: Value of the Ratio & Stronger Recipe Challenge

Mirrors Quiz Q3 & Q4

Ava and Noah each mix blueberry glaze. Ava uses 3 tbsp blueberry syrup for every 2 cups sugar. Noah uses 5 tbsp blueberry syrup for every 4 cups sugar.

A. Circle the correct terms to complete the statements:

• In Ava's glaze, there are $\frac{3}{2}$ / $\frac{2}{3}$ tbsp syrup per 1 cup sugar.

• In Noah's glaze, there are $\frac{5}{4}$ / $\frac{4}{5}$ tbsp syrup per 1 cup sugar.

• Ava's glaze should have a stronger / weaker blueberry flavor than Noah's because $\frac{3}{2}$ is greater than / less than $\frac{5}{4}$.

Scratch work: $\frac{3}{2} = 1.50\quad\text{vs}\quad\frac{5}{4} = 1.25$

B. Stronger Glaze Challenge:

Zoe wants to create a glaze that has a stronger blueberry flavor than both Ava's and Noah's recipes. Which ratio of tbsp syrup to cups sugar could represent Zoe's glaze?

A 4 : 3 ($\frac{4}{3} \approx 1.33$ tbsp/cup)

B 5 : 4 ($\frac{5}{4} = 1.25$ tbsp/cup)

C 2 : 1 ($\frac{2}{1} = 2.00$ tbsp/cup)

D 7 : 5 ($\frac{7}{5} = 1.40$ tbsp/cup)

Quiz Strategy: To compare flavors or rates, always divide to find the unit rate ($\text{Ingredient} \div \text{Base}$). Greater unit rate = stronger flavor!

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For every 1 card Maya creates, she uses 8 centimeters of decorative tape.

Calculation: $24 \div 3 = 8\text{ cm/card}$ • Value of the ratio = $8$

Common Misconceptions to Watch For:

Inverting the rate: Calculating $3 \div 24 = \frac{1}{8}$ card per cm instead of cm per card.
Additive table error: Adding $+1$ to cards and incorrectly adding $+1$ or $+3$ to tape.
Multiplication confusion: Multiplying 48 by 8 instead of dividing by 8 to find cards.

Teacher Resource • Eureka Math² Module 1 Topic C Answer Key Turn page for Part 2 & Part 3 Solutions + Rubric → Page 1 of 2

Teacher Scoring Key Topic C Quiz Preparation Solutions

Comparing Ratio Tables, Flavor Strength & Value of Ratios

Total Points: 10

2

Part 2 Solution: Comparing Ratio Tables & Flavor Strength

Select Choices: A, B, and C 3 pts

Mathematical Analysis of Both Freezes:
• Freeze A: $\text{Lemon} : \text{Lime} = 3 : 6 = \mathbf{1 : 2}$. Unit rates: $2\text{ cups lime / 1 cup lemon}$ OR $\frac{1}{2}\text{ cup lemon / 1 cup lime}$.
• Freeze B: $\text{Lemon} : \text{Lime} = 4 : 12 = \mathbf{1 : 3}$. Unit rates: $3\text{ cups lime / 1 cup lemon}$ OR $\frac{1}{3}\text{ cup lemon / 1 cup lime}$.

Statement A TRUE ✓

Correct ratio.
In Freeze A, $3 : 6$ simplifies directly to $1 : 2$ by dividing both terms by 3.

Statement B TRUE ✓

Stronger lime.
Freeze B has 3 cups lime per cup lemon vs Freeze A's 2 cups lime. More lime ingredient $=$ stronger lime flavor!

Statement C TRUE ✓

Stronger lemon.
Per 1 cup lime, Freeze A has $\frac{1}{2}$ cup lemon vs Freeze B's $\frac{1}{3}$ cup. Since $\frac{1}{2} > \frac{1}{3}$, Freeze A is more lemony.

Statement D FALSE ✗

Additive Trap!
Adding 1 to both quantities in $(3, 6)$ yields $(4, 7)$, NOT $(4, 12)$. Ratios are multiplicative, not additive!

Scoring Note: Award 3 pts for selecting A, B, and C with D left blank. Award 2 pts if 2 correct are selected with 0 incorrect. Award 0 if D is selected.

3

Part 3 Solution: Value of the Ratio & Stronger Recipe Challenge

Total: 4 Points (2 pts A, 2 pts B)

Context: Ava uses 3 tbsp blueberry syrup for 2 cups sugar. Noah uses 5 tbsp blueberry syrup for 4 cups sugar.

A. Completed Statements Solution 2 pts

• In Ava's glaze, there are $\frac{3}{2}$ tbsp syrup per 1 cup sugar. ($3 \div 2 = 1.5$; trap is circling reciprocal $\frac{2}{3}$)

• In Noah's glaze, there are $\frac{5}{4}$ tbsp syrup per 1 cup sugar. ($5 \div 4 = 1.25$; trap is circling reciprocal $\frac{4}{5}$)

• Ava's glaze should have a stronger blueberry flavor than Noah's because $\frac{3}{2}$ is greater than $\frac{5}{4}$.

Common Denominator Verification: $\frac{3}{2} = \frac{6}{4} > \frac{5}{4}\quad(1.50 > 1.25)$

B. Challenge Choice Solution 2 pts

Correct Answer: Choice C (2 : 1)

Zoe's recipe must have a unit rate greater than $1.50$ (Ava's rate) and $1.25$ (Noah's rate):

A. 4 : 3 $= \frac{4}{3} \approx 1.33$ Too weak $(< 1.5)$

B. 5 : 4 $= \frac{5}{4} = 1.25$ Equal to Noah

C. 2 : 1 $= \frac{2}{1} = 2.00$ ✓ Strongest! $(> 1.5)$

D. 7 : 5 $= \frac{7}{5} = 1.40$ Too weak $(< 1.5)$

TOPIC C RUBRIC Quiz Readiness Scoring Criteria (10 Points Total):

• 9–10 Pts (Exceeding / Ready): Accurately calculates unit rates, scales tables multiplicatively, and justifies flavor comparisons.
• 7–8 Pts (Proficient): Understands unit rates but makes minor arithmetic slips or inverts reciprocal unit rate terms.
• < 7 Pts (Needs Intervention): Fell for additive trap (Statement 2D) or struggles to determine denominator base units.

Topic C Score _____ / 10 Mastery Stamp

Teacher Notes: Directly aligned to Eureka Math² Grade 6 Module 1 Topic C assessment standards.

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4. Quick Warm-Up Checks

A. Unit Rate Order Check:

A machine bottles 10 juices in 5 minutes. When the rate is expressed in minutes per juice, what is the unit rate?

Answer: minutes per juice

B. Length Conversion Check:

A runner covers 360 feet in 2 minutes. At this rate, how many yards does the runner cover in 2 minutes?

Answer: yards

Eureka Math² Module 1 Topic D: Rates and Unit Rates Turn page for Targeted Practice (mirrors Quiz D) → Page 1 of 2

Targeted Practice

Topic D Quiz Preparation Practice

5 Parallel Quiz Problems

1

Unit Rate with Order Awareness

Mirrors Quiz Q1

Elena decorates 4 ceramic bowls in 2 hours. When the rate is expressed in hours per bowl, what is the unit rate?

Fill in the blank:

2

Rate Table & Equivalence Statements

Mirrors Quiz Q2

A cyclist rides at a constant speed of 15 meters per second.

Part A: Complete the ratio table:

Number of Seconds	Number of Meters
	15
4
	105
10

Part B: Which statements are true? Choose ALL that apply:

A. The cyclist travels 15 meters in 1 second. B. The cyclist travels 7 meters in 105 seconds. C. The pairs of numbers in the table form equivalent ratios. D. The cyclist travels 175 meters in 11 seconds. E. The cyclist travels 2,700 meters in 3 minutes.

3

Comparing Flavor Strength Between Two Shops

Mirrors Quiz Q3

The tables show tablespoons of cocoa powder used to make milkshakes at Shop X and Shop Y:

Shop X

Tbsp of Cocoa	Number of Milkshakes
18	6
24	8

Shop Y

Tbsp of Cocoa	Number of Milkshakes
25	5
30	6

Shop X uses (A) tablespoons of cocoa for every milkshake. Shop Y uses (B) tablespoons of cocoa for every milkshake.

Mateo wants a milkshake with a stronger chocolate flavor. Mateo should buy from (C) because it uses more cocoa for every milkshake than (D).

A: 1 • 2 • 3 • 4 • 5

B: 1 • 2 • 3 • 4 • 5

C: Shop X • Shop Y

D: Shop X • Shop Y

4

Finding Quantity from Total Cost

Mirrors Quiz Q4

An art teacher buys 60 sketchbooks for $780. Each sketchbook has the same price.

How many sketchbooks can the art teacher buy for $1,170?

Fill in the blank: sketchbooks

Hint: Find unit price ($\$ \div 60$) or scale by half-batches!

5

Multi-Unit Conversion & Matching Rates

Mirrors Quiz Q5

Leo walks 540 feet in 2 minutes.

Part A:

At this rate, how many yards does Leo walk in 2 minutes? ($3\text{ ft} = 1\text{ yd}$)

Answer: yards

Part B: Match each rate with its numerical value:

feet per minute

yards per hour

Answer Choices (write one value in each box):

9 90 270 540 2,700 5,400

Quiz Strategy: Always verify the denominator in “per” units, check table ratios by multiplying/dividing, and convert units step-by-step.

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C is TRUE: Every row simplifies to the same ratio of $1 : 15$.

D is FALSE: $11\text{ s} \times 15 = 165\text{ m}$, not 175 m.

E is TRUE: $3\text{ min} = 180\text{ s}$. $180 \times 15 = \mathbf{2,700\text{ m}}$.

Teacher Resource • Eureka Math² Module 1 Topic D Answer Key Turn page for Problems 3, 4, 5 Solutions + Rubric → Page 1 of 2

Teacher Scoring Key Topic D Quiz Preparation Solutions

Flavor Comparisons, Price Scaling & Multi-Unit Conversions

Total Points: 10

3

Problem 3 Solution: Comparing Flavor Strength

Answers: A=3, B=5, C=Shop Y, D=Shop X 2 pts

Unit Rate Calculations:

• Shop X: $\frac{18\text{ tbsp}}{6\text{ shakes}} = \mathbf{3}$ tbsp/shake (Blank A = 3).
• Shop Y: $\frac{25\text{ tbsp}}{5\text{ shakes}} = \mathbf{5}$ tbsp/shake (Blank B = 5).

Flavor Comparison Conclusion:

Shop Y uses 5 tbsp per shake, which is greater than Shop X's 3 tbsp per shake.
Therefore, buy from Shop Y (C) because it uses more cocoa per smoothie than Shop X (D).

4

Problem 4 Solution: Finding Quantity from Total Cost

Answer: 90 sketchbooks 2 pts

Context: 60 sketchbooks cost $780. How many can be bought for $1,170?

Method 1: Unit Price

$\text{Unit price} = \frac{\$780}{60} = \mathbf{\$13\text{ per book}}$
$\text{Quantity} = \frac{\$1,170}{\$13} = \mathbf{90\text{ sketchbooks}}$

Method 2: Proportional Chunking

$30\text{ books} = \$780 \div 2 = \$390$.
Notice: $\$780 + \$390 = \$1,170$.
Therefore: $60 + 30 = \mathbf{90\text{ sketchbooks}}$.

5

Problem 5 Solution: Multi-Unit Conversion & Matching

Total: 2 Points (1 pt Part A, 1 pt Part B)

Context: Leo walks 540 feet in 2 minutes.

Part A: Yards in 2 Minutes Ans: 180

$540\text{ feet} \div 3\text{ ft/yd} = \mathbf{180\text{ yards}}$

Keep time at 2 minutes. Only convert the distance unit.

Part B: Matching Rates 240 & 4,800

feet per minute: $\frac{540\text{ ft}}{2\text{ min}} = \mathbf{270}$

yards per hour: $\frac{180\text{ yd}}{2\text{ min}} = 90\text{ yd/min}$
$90\text{ yd/min} \times 60\text{ min/hr} = \mathbf{5,400}$

TOPIC D RUBRIC Quiz Readiness Scoring Criteria (10 Points Total):

• 9–10 Pts (Exceeding / Ready): Mastered unit rate directions (“per” unit), rate table scaling, price division, and two-step unit conversions.
• 7–8 Pts (Proficient): Strong conceptual mastery; may have made an arithmetic slip on 3-digit division or omitted 1 statement in Question 2B.
• < 7 Pts (Needs Intervention): Inverts unit rates (e.g., $4 \div 2 = 2$ on Q1) or struggles with compound rate conversion ($\text{ft/min} \rightarrow \text{yd/hr}$).

Topic D Score _____ / 10 Mastery Stamp

Teacher Notes: Directly aligned to Eureka Math² Grade 6 Module 1 Topic D assessment standards.

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