Question
Multiply Factions & Decimals Discussion
in your journal, you explained the Associative and Commutative Properties of Multiplication to a friend. you told them that they would get the same answer every time they multiplied the numbers in the problem.
imagine that your neighbor is scrolling through social media. your cousin is considering making and in-app purchase.your neighbor shows you advertisements for products that make bold claims:
"get rich quick! do you want to work fewer hours for the same amount of money per hour, and get even richer? click here to see how you can relax and earn. you'll work 10 fewer hours at the same wage, and you'll still make more money!"
"get hydrated now! do you hate drinking water? click here to see how drinking less water is actually the secret to having more water in your body. it's the study the government doesn't want you to see!
select one of the advertisements and advise your cousin:
represent the advertisement's claim with a sample mathematical statement.
using the Associative and Commutative Properties of Multiplication, evaluate whether the claim is reasonable.
explain your reasoning in your post.
then read your peers' advice. respond to two of your peers:
for each post, evaluate your peer's sample mathematical statement and determine whether it is accurate.
tell your peers what you agree with and disagree with in their advice.
post a detailed response to the Multiply Fractions and Decimals Discussion prompt. then respond to two classmates' post.
participate in the discussion to learn more about using multiplication to check reasonability. write it as a 6th grader
in your journal, you explained the Associative and Commutative Properties of Multiplication to a friend. you told them that they would get the same answer every time they multiplied the numbers in the problem.
imagine that your neighbor is scrolling through social media. your cousin is considering making and in-app purchase.your neighbor shows you advertisements for products that make bold claims:
"get rich quick! do you want to work fewer hours for the same amount of money per hour, and get even richer? click here to see how you can relax and earn. you'll work 10 fewer hours at the same wage, and you'll still make more money!"
"get hydrated now! do you hate drinking water? click here to see how drinking less water is actually the secret to having more water in your body. it's the study the government doesn't want you to see!
select one of the advertisements and advise your cousin:
represent the advertisement's claim with a sample mathematical statement.
using the Associative and Commutative Properties of Multiplication, evaluate whether the claim is reasonable.
explain your reasoning in your post.
then read your peers' advice. respond to two of your peers:
for each post, evaluate your peer's sample mathematical statement and determine whether it is accurate.
tell your peers what you agree with and disagree with in their advice.
post a detailed response to the Multiply Fractions and Decimals Discussion prompt. then respond to two classmates' post.
participate in the discussion to learn more about using multiplication to check reasonability. write it as a 6th grader
Answers
GPT-4o mini
**My Response:**
Hey everyone! I want to talk about the first advertisement: "get rich quick!" It says you can work 10 fewer hours at the same pay and still earn more money. Let’s break this down with some basic math.
Let’s say your cousin earns $20 per hour. If they normally work 40 hours a week, they make:
**Normal pay = 20 dollars/hour × 40 hours = 800 dollars/week.**
Now, if they work 10 fewer hours, they will only work 30 hours at the same pay:
**New pay = 20 dollars/hour × 30 hours = 600 dollars/week.**
So, according to the ad, they would be making less money, not more! This shows that the advertisement's claim is not reasonable.
Using the **Commutative Property of Multiplication**, we know that it doesn't matter in which order we multiply numbers. It will always give us the same result. So whether I say
**20 × 30 or 30 × 20**, I still get 600.
Using the **Associative Property of Multiplication**, we could also group these numbers differently, but since we can see how many total hours they were working before and after in a straight math problem, we see that they can’t make more money by working fewer hours at the same rate.
In this case, both properties of multiplication help me understand that the claim that working less allows you to earn more is not true!
---
**Responses to Classmates:**
**Response to Classmate 1:**
Hey! I read your post about the "get hydrated now!" advertisement. Your mathematical statement comparing water intake is really important. I think you showed that drinking less water wouldn’t actually increase hydration, just like you explained.
But I wonder if you could also show how many liters of water you would need per day. Let's say you normally drink 2 liters a day. If you drink 1 liter instead, you’ll end up dehydrated! It would be great if you added that to give more clarity.
I agree with your reasoning that the claim isn’t reasonable. It’s great that you argued using multiplication to show how hydration works!
**Response to Classmate 2:**
Hi there! I loved your analysis of the "get rich quick!" ad. Your math example with $15/hr and the number of hours worked definitely illustrated how unrealistic the claim is. When you showed how much less money you make working fewer hours, it made total sense!
I think it would be really cool if you also mentioned how the properties of multiplication helped you figure this out as well, like how swapping the hours and pay around won’t change the outcome, just like you did.
I agree that the ad is misleading and your math was solid. Thanks for sharing your thoughts!
Hey everyone! I want to talk about the first advertisement: "get rich quick!" It says you can work 10 fewer hours at the same pay and still earn more money. Let’s break this down with some basic math.
Let’s say your cousin earns $20 per hour. If they normally work 40 hours a week, they make:
**Normal pay = 20 dollars/hour × 40 hours = 800 dollars/week.**
Now, if they work 10 fewer hours, they will only work 30 hours at the same pay:
**New pay = 20 dollars/hour × 30 hours = 600 dollars/week.**
So, according to the ad, they would be making less money, not more! This shows that the advertisement's claim is not reasonable.
Using the **Commutative Property of Multiplication**, we know that it doesn't matter in which order we multiply numbers. It will always give us the same result. So whether I say
**20 × 30 or 30 × 20**, I still get 600.
Using the **Associative Property of Multiplication**, we could also group these numbers differently, but since we can see how many total hours they were working before and after in a straight math problem, we see that they can’t make more money by working fewer hours at the same rate.
In this case, both properties of multiplication help me understand that the claim that working less allows you to earn more is not true!
---
**Responses to Classmates:**
**Response to Classmate 1:**
Hey! I read your post about the "get hydrated now!" advertisement. Your mathematical statement comparing water intake is really important. I think you showed that drinking less water wouldn’t actually increase hydration, just like you explained.
But I wonder if you could also show how many liters of water you would need per day. Let's say you normally drink 2 liters a day. If you drink 1 liter instead, you’ll end up dehydrated! It would be great if you added that to give more clarity.
I agree with your reasoning that the claim isn’t reasonable. It’s great that you argued using multiplication to show how hydration works!
**Response to Classmate 2:**
Hi there! I loved your analysis of the "get rich quick!" ad. Your math example with $15/hr and the number of hours worked definitely illustrated how unrealistic the claim is. When you showed how much less money you make working fewer hours, it made total sense!
I think it would be really cool if you also mentioned how the properties of multiplication helped you figure this out as well, like how swapping the hours and pay around won’t change the outcome, just like you did.
I agree that the ad is misleading and your math was solid. Thanks for sharing your thoughts!