# puzzle it out!Writing a Math Argument

### Practice explaining clear math reasoning so youcan show other people how you found your solution.

#### Why is this important? Many people use math intheir jobs. For example, an actuary uses complicatedmath to help businesses make decisions, so theyhave to be able to clearly explain their calculationsto people who aren’t math experts.

Carlita’s Cafe

You’ve just been hired to help Carlita, a hot new chef
known for her bold, creative food. You’re in charge of the
calculations for her recipes. Congrats!

Just so you know, Carlita was unhappy with her last assistant because they were a
bit sloppy and didn’t clearly explain their calculations. So you’ll need
to choose the most precise language when you explain your math reasoning!

Ready to help Carlita figure out the exact amounts she
needs for the perfect dish?

A Tasty Problem!

Carlita has gotten her first celebrity birthday party reservation for tomorrow night, so she needs you to act fast! She wants to make her signature dish, Turkey Surprise, but it must be 225% of the original recipe to feed the large crowd.

Q: How many ounces of chocolate chips will
Carlita need for tomorrow’s dinner?

HINT 1 pound (lb) = 16 ounces (oz)

How can you tackle this math problem?

Drag the pieces below into the order that best explains how you plan to solve the problem.

Q: To feed the big crowd and increase the original recipe by 225%, how many ounces of chocolate chips will Carlita need for tomorrow’s dinner?

I’ll finish by multiplying the original quantity of chocolate chips by 225% (converting
the percentage to the decimal 2.25 for easy multiplying) for the new recipe.

At that point, I’ll have the information I need in order to figure out how many ounces
of chocolate chips were used in the original recipe.

The question asks me to determine how many ounces of chocolate chips are needed.
Since the recipe lists the chocolate chips as a proportion of the cherries, I must figure
out the amount of cherries first.

But because the cherries are given as a proportion of the pounds of turkey, I’ll need
to start by converting the 2½ pounds of turkey to ounces. That conversion will allow
me to figure out how many ounces of cherries are needed.

Great! You have a plan for solving the problem and

From: You
To: Chocolate Chips Order
Subject: Chocolate Chips Order

SEND

1. Choose the strongest introductory sentence for your math argument. Assume that your audience—in this case, the food supplier—doesn’t know the details of the problem, so describe it clearly for them.

a

I love chocolate. Do you? I think cherries are just OK. How about you? Turkey is kind of gross. What do you think? Carlita likes these ingredients, so she's going to use 225% of them.

b

I have a lot of ideas for how to solve this problem! To find the ounces, I start with the turkey.

c

To figure out the problem of Carlita's restaurant ingredients, I have to look at how many chocolate chips were needed for the original Turkey Surprise. Carlita is increasing that recipe.

d

To solve the problem of how many ounces of chocolate chips Carlita needs for her larger batch of the Turkey Surprise recipe, I first need to determine the quantities of ingredients in the original recipe.

HINT You could still be clearer! Find a balance between precise (accurate and clear) and concise (avoid unnecessary detail).

2. Now choose the option to explain your next steps in the most
precise way.

Looking at the original recipe, I see that the ingredients are

each other. The quantities are ultimately determined by the amount of turkey.
a

fractions of

b

proportional to

c

part of

HINT You could still be clearer! Find a balance between precise (accurate and clear) and concise (avoid unnecessary detail).

3. Now choose the option to explain your next steps in the most
precise way.

The turkey amount is given in pounds, but I need to find the increased amount of chocolate chips in ounces. So I’ll start by

the turkey’s units from pounds to ounces.
a

converting

b

changing

c

modifying

d

re-weighing

HINT You could still be clearer! Find a balance between precise (accurate and clear) and concise (avoid unnecessary detail).

4. Now choose the option to explain your next steps in the most
precise way.

a

First, I’ll convert the 2½ pounds of turkey to its decimal equivalent of 2.5 to make multiplying easier. I will multiply 2.5 by 16, which is 40 oz.

b

Multiplying the conversion by 2.5 gives me 2.5 x 1 = 2.5 x 16, so 40 oz of turkey.

c

First, I’ll convert the 2½ pounds of turkey to its decimal equivalent of 2.5 to make multiplying easier. Then, since 1 pound = 16 oz, I’ll set up this equation: 2.5 lbs of turkey x 16 oz per pound = 40 oz of turkey.

HINT You could still be clearer! Find a balance between precise (accurate and clear) and concise (avoid unnecessary detail).

5. Now choose the option to explain your next steps in the most
precise way.

a

Cherries are listed as ¼ of the turkey. So I’ll multiply the turkey by 0.25 to find that the recipe needs 10 oz of cherries.

b

The amount of the next ingredient, cherries, is listed as ¼ (which I can convert to 0.25) of the amount of the turkey. So I’ll set up this equation: 40 oz of turkey x 0.25 = 10 oz of cherries.

c

¼ = 0.25, 0.25 x 40 oz = 10 oz

HINT You could still be clearer! Find a balance between precise (accurate and clear) and concise (avoid unnecessary detail).

6. Now choose the option to explain your next steps in the most
precise way.

Since the amount of chocolate chips is 0.35 of the 10 oz of cherries, I’ll set up this equation:
0.35

10 oz of cherries = 3.5 oz of chocolate chips in the original recipe. I feel confident I chose the right

and put the decimal point in the correct place because I checked it with mental math. I know 0.35

, and if I were to

10 oz into three equal parts, the parts would be about 3 oz each. So 3.5 oz of chocolate chips sounds right. And 35 oz would definitely be too much—it’s more than the amount of cherries!
a

+

b

c

x

d

÷

HINT You could still be clearer! Find a balance between precise (accurate and clear) and concise (avoid unnecessary detail).

6. Now choose the option to explain your next steps in the most
precise way.

Since the amount of chocolate chips is 0.35 of the 10 oz of cherries, I’ll set up this equation:
0.35

10 oz of cherries = 3.5 oz of chocolate chips in the original recipe. I feel confident I chose the right

and put the decimal point in the correct place because I checked it with mental math. I know 0.35

, and if I were to

10 oz into three equal parts, the parts would be about 3 oz each. So 3.5 oz of chocolate chips sounds right. And 35 oz would definitely be too much—it’s more than the amount of cherries!
a

sign

b

operation

HINT You could still be clearer! Find a balance between precise (accurate and clear) and concise (avoid unnecessary detail).

6. Now choose the option to explain your next steps in the most
precise way.

Since the amount of chocolate chips is 0.35 of the 10 oz of cherries, I’ll set up this equation:
0.35

10 oz of cherries = 3.5 oz of chocolate chips in the original recipe. I feel confident I chose the right

and put the decimal point in the correct place because I checked it with mental math. I know 0.35

, and if I were to

10 oz into three equal parts, the parts would be about 3 oz each. So 3.5 oz of chocolate chips sounds right. And 35 oz would definitely be too much—it’s more than the amount of cherries!
a

b

is equal to ⅓

c

reminds me of ⅓

HINT You could still be clearer! Find a balance between precise (accurate and clear) and concise (avoid unnecessary detail).

6. Now choose the option to explain your next steps in the most
precise way.

Since the amount of chocolate chips is 0.35 of the 10 oz of cherries, I’ll set up this equation:
0.35

10 oz of cherries = 3.5 oz of chocolate chips in the original recipe. I feel confident I chose the right

and put the decimal point in the correct place because I checked it with mental math. I know 0.35

, and if I were to

10 oz into three equal parts, the parts would be about 3 oz each. So 3.5 oz of chocolate chips sounds right. And 35 oz would definitely be too much—it’s more than the amount of cherries!
a

divide

b

multiply

HINT You could still be clearer! Find a balance between precise (accurate and clear) and concise (avoid unnecessary detail).

7. Now choose the option that concludes the argument in the most
precise way.

I’m keeping in mind that Carlita needs to adjust the recipe for a large crowd by making it 225% bigger. I’ll first convert 225% to its equivalent decimal of 2.25. Then I set up this equation: 2.25 x 3.5 oz of chocolate chips in the original recipe = 7.875 oz.

a

Therefore, both the original recipe and the expanded recipe use 7.875 oz of chocolate chips.

b

That’s why I converted the percentage to a decimal.

c

Therefore, Carlita will need 7.875 oz of chocolate chips for the bigger batch of her recipe.

HINT You could still be clearer! Find a balance between precise (accurate and clear) and concise (avoid unnecessary detail).

From: Carlita’s Food Supplier
To: You
Subject: Re: Re: Chocolate Chips Order

Thanks for explaining your reasoning. That was very clear and precise!

You completed the math argument!

From: Carlita’s Food Supplier
To: You
Subject: Re: Re: Chocolate Chips Order

I’m still a little confused. Please find a clearer, more precise way to state some of your claims. For example, check that you included units and an explanation of how the numbers and steps relate to one another!

Let's go back and look at the steps where your argument could be stronger!
You'll be able to pick a different answer to write a really precise math argument.