Math: Unit 2 Lesson 7 Part 2

October 27, 2025

Aim: I can look at a table and tell if the numbers show a proportional relationship or not.

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Naruto opens his own ramen shop, and he’s training Boruto and Sarada to take orders. Each day, he tracks how many bowls they serve compared to how many minutes they work. But something’s off — sometimes the data looks proportional, and sometimes it definitely isn’t. 720 you must help Team 7 figure out which tables show proportional relationships!

By SIMMIE HAYES

WARM UP

Multiple Choice

Do Now: What does proportional mean?

• two quantities (amounts) are unrelated.

• a fixed relationship between two quantities (amounts) things.

• a relationship where two quantities(amounts) increase or decrease at the same rate.

Multiple Choice

Do Now: If Naruto makes 4 bowls in 2 minutes, and 8 bowls in 4 minutes, what kind of relationship does that show?”

• Proportional

  (goes up and down at the same rate)

• NOT Proportional

  (does not go up and down at the same rate)

Multiple Choice

Do Now: What is the formula to find Constant?

K = ?

• K = x/y
• K = y + x
• K = y/x

Multiple Choice

Do Now:

If Naruto makes 4 bowls in 8 minutes , and 8 bowls in 16 minutes, how long does it take him to make 1 bowl?”

• 2 minutes
• 3 minutes
• 1 minute

Multiple Choice

Do Now:

If Naruto makes 3 bowls (B) in 15 minutes (M), and 8 bowls in 40 minutes, how long does it take him to make 1 bowl?”

• 5 minutes
• 3 minutes
• 10 minutes

Multiple Choice

If Naruto makes 1 bowls (B) in 2 minutes (M)...how many bowls (B) can he make in 2 minutes

• 2 bowls
• 6 bowls
• 4 bowls

DIRECT INSTRUCTION

• The formula for constant is K=Y/X

• The constant tells us the rate in which something is increasing or decreasing

• If the constant in a table is the same in each row then it's proportional

• If the constant is not the same then it is NOT proportional

​Character	​Minutes	​Bowls	​Constant
​Naruto	1	3	​3
​Boruto	​3	​7	​2.33
​Sarada	2	6	​3

Let's Discuss
✅ If k stays the same, it’s proportional.
❌ If k changes, it’s not.
Pay close attention as I show you how to determine if each table is proportional

​Character	​Minutes	​Bowls	​Constant
​Naruto	10	20	​2
​Boruto	5	10	2
​Sarada	8	16	2

​Character	​Minutes	​Bowls	​Constant
​Naruto	1	20	​20
​Boruto	​4	12	3
​Sarada	2	1	1/2

GUIDED INSTRUCTION

Now we'll try together!
We'll look at some tables and decide if they are proportional or NOT proportional

できるよ

Dekiru yo!
You Can Do It!

Open Ended

Scenario: Sophia helps Naruto in the ramen shop. She can make 3 bowls of ramen every minute. Is this a proportional relationship? Explain

Open Ended

Scenario: Jayden practices basketball shots after school. He makes about 20 baskets every hour he practices. Is this a proportional relationship? Explain.

Open Ended

Scenario: Jalen is gaming on his console. Each round gives him 100 XP points. Is this proportional? Explain

Open Ended

Scenario: Ski orders pizzas for her friends. Each pizza costs $10, but there’s a delivery fee added to every order. Is this proportional? Explain

Open Ended

Scenario: Shannon practices typing. At first she types slowly, but speeds up as she gets comfortable. Is this proportional? Explain

Independent Instruction

Now try on your own. Prove that your ready to learn a new ninjutsu!


できるよ

Dekiru yo!

You Can Do It!

Open Ended

Naruto is practicing how fast he can make ramen bowls each minute.
Check if his rate stays the same.

Question: Is the relationship proportional? Explain how you know.

Open Ended

Boruto delivers ramen around the Hidden Leaf Village.
He tracks how far he travels over time.

Question: Is this data proportional? Why or why not?

Open Ended

Sakura mixes healing herbs. For every spoon of powder, she adds cups of water.
She wants the mixture to stay consistent.

Question: Does Sakura’s mixture show a proportional relationship?

Open Ended

Sasuke records his chakra energy output after different training times.

Question: Is Sasuke’s energy growth proportional to time?

Open Ended

Kakashi times how many pages he reads from Make-Out Paradise. He wants to see if he reads at a constant rate.

Question: Is Kakashi reading at a proportional rate? Explain your reasoning.

Let's
Review

• How can we tell if a table is proportional?

• “One way I can tell if a table is proportional is ___.”

• “I know a relationship is not proportional when the constant is ___.”

Cool
Down

Multiple Choice

Sasuke records his chakra energy output after different training times.

What is the constant?

• 100 chakra points per minute
• 200 chakra points per minute
• 300 chakra points per minute
• 50 chakra points per minute

Multiple Choice

In this table, which is X?

• Chakra Points

• Minutes

Multiple Choice

In this table, which is Y?

• Chakra Points

• Minutes

Multiple Select

In this table, what is K?

• 50

• 50 . 0

• 50/1

Multiple Choice

Is this table proportional?

• No
• Yes

Multiple Choice

Why is this table proportional?

• The table is proportional because the ratio of Minutes to Chakra Points remains constant.
• The table is proportional because the values are random.

Activity 2
Writing Equations
(For Wednesday October 29)

We can write proportions as equations using the following formula
Y=KX

If Naruto can make 5 shadow clones (S) for every 1 ball of chakra (C)
we can represent this using an equation.

S=5(C)

Y=K(X)

# of Shadow Clones = The Constant times (# of Chakra Balls)

Multiple Choice

Naruto uses 3 chakra balls (X) to make 15 shadow clones (Y). Which equation shows this relationship.

• Y= KX

• Y=XK

• K=Y/X

• K=XY

Multiple Choice

Naruto uses 3 chakra balls (C) to make 15 shadow clones (S). Which equation shows this relationship.

• S = 15C

• S=5C

• C=5S

• K=Y/X

Multiple Choice

Naruto uses 6 chakra balls (C) to make 24 shadow clones (S). Which equation shows this relationship.

• 6S = C

• S=6C

• C=6S

• S=4C

Multiple Choice

Naruto uses 6 chakra balls (A) to make 24 shadow clones (G). Which equation shows this relationship.

• 6G = A

• G=6A

• A=6G

• G=4A