Ratios...
Hello all!
Choosing ratios this week because I think one of the problem set questions is about ratios and it is giving me a little trouble. Turns out this is a common core in 6th grade. I haven't really checked out much of the 6th grade common cores because I think I will end up teaching younger grades, but I guess this is something I need to know! So...ratios, here we go!
What is a ratio?
Simply put, a ratio is a way to compare two values. Ratios are often expressed in a fraction.
Common Core:
CCSS.MATH.CONTENT.6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
CCSS.MATH.CONTENT.6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship
CCSS.MATH.CONTENT.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
Baking comes up a lot when we talk about ratios
Must learn to cook for the correct number of guests! Don't bring in a pie for 8 people to your class when you have 20 people...
People will be so sad :
Ratios are used in so many real world problems! Baking/cooking is a very common place we come across rations, also with exchanging money and also when shopping. I found a lesson plan on shopping, "Are you a good consumer?"
This is also really relevant for 6th grade students. They probably have some cash and shop on their own. I certainly want them to get the best deal and not waste money!
PLEASE LEARN OUR MATH SO YOU DONT THROW YOUR MONEY IN THE GARBAGE!
Before getting into the lesson plan, I wanted to talk about ratio tables. There are a lot of worksheets on this, but a ratio table is a structured list of equal value ratios that help understand the relationship between the ratios and the numbers. These are good as the students start to learn about equivalent rations, Below is an example:
It is good to give some examples here that if you add 1 to the top or bottom of the ratio it is no longer equivalent.
This lesson plan is 4 steps of increasing difficulty. The first step the teacher gives a problem to solve:
Michael is shopping for baseball cards. He finds a deal on cards that is on sale for a special rate of 5 packs for 7.50. At this rate, what is the cost of one pack of cards? The students can re-work this problem to make sure they understand how to find the unit rate. Then I’m going to say, that another store is selling these same cards for $.99 each. Where should Michael purchase baseball cards to get the best deal?
Listen to the students strategies.
In the common core the student must understand both the "per product rate"as well as the "per dollar rate"
So the second step is to find both the unit rates requires the student to use the reciprocal and to simplify. The student has to find the 1 for both the bottom and top measurement.
For me this is easiest to think about in terms of mileage (I am a runner so I think about it running, but we can use it driving also).
A car drives 30 miles an hour
or
A car drives a mile in 2 minutes
Think of different examples to look at both rate units, another one on shopping, cold cuts at a grocery store?
Turkey costs $5 a pound
or
Turkey is 2 pounds for $10
The third step is a more complicated question:
Choosing ratios this week because I think one of the problem set questions is about ratios and it is giving me a little trouble. Turns out this is a common core in 6th grade. I haven't really checked out much of the 6th grade common cores because I think I will end up teaching younger grades, but I guess this is something I need to know! So...ratios, here we go!
What is a ratio?
Simply put, a ratio is a way to compare two values. Ratios are often expressed in a fraction.
Common Core:
CCSS.MATH.CONTENT.6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
CCSS.MATH.CONTENT.6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship
CCSS.MATH.CONTENT.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
Baking comes up a lot when we talk about ratios
Must learn to cook for the correct number of guests! Don't bring in a pie for 8 people to your class when you have 20 people...
People will be so sad :
Ratios are used in so many real world problems! Baking/cooking is a very common place we come across rations, also with exchanging money and also when shopping. I found a lesson plan on shopping, "Are you a good consumer?"
This is also really relevant for 6th grade students. They probably have some cash and shop on their own. I certainly want them to get the best deal and not waste money!
PLEASE LEARN OUR MATH SO YOU DONT THROW YOUR MONEY IN THE GARBAGE!
Before getting into the lesson plan, I wanted to talk about ratio tables. There are a lot of worksheets on this, but a ratio table is a structured list of equal value ratios that help understand the relationship between the ratios and the numbers. These are good as the students start to learn about equivalent rations, Below is an example:
It is good to give some examples here that if you add 1 to the top or bottom of the ratio it is no longer equivalent.
This lesson plan is 4 steps of increasing difficulty. The first step the teacher gives a problem to solve:
Michael is shopping for baseball cards. He finds a deal on cards that is on sale for a special rate of 5 packs for 7.50. At this rate, what is the cost of one pack of cards? The students can re-work this problem to make sure they understand how to find the unit rate. Then I’m going to say, that another store is selling these same cards for $.99 each. Where should Michael purchase baseball cards to get the best deal?
Listen to the students strategies.
In the common core the student must understand both the "per product rate"as well as the "per dollar rate"
So the second step is to find both the unit rates requires the student to use the reciprocal and to simplify. The student has to find the 1 for both the bottom and top measurement.
For me this is easiest to think about in terms of mileage (I am a runner so I think about it running, but we can use it driving also).
A car drives 30 miles an hour
or
A car drives a mile in 2 minutes
Think of different examples to look at both rate units, another one on shopping, cold cuts at a grocery store?
Turkey costs $5 a pound
or
Turkey is 2 pounds for $10
The third step is a more complicated question:
Jen earns $36.00 for 6 hours of babysitting. Ally earns $24 for 3 hours. Who has the better hourly rate. In this problem, the students need to know that when we are looking at earning money, the better deal is to earn more money.
The quetions is how much money do they earn per hour?
You can flip the question around and ask:
How many hours do they work to make $10?
And, who makes more money?
Talk about when the different rates are important. In the turkey example it might be important to know how much turkey you can get for $5 if you only have $5 in you pocket, but it might be important to know how much it is per unit if you know you have to buy 3 pounds of turkey for lunches for the week.
The final challenge in this lesson is the store flyer challenge!
The teacher gathers flyers from a bunch of grocery stores over the course of a few weeks. Students break out into groups and each gets a bunch of flyers. The students have to find similar items (toilet paper, soda, paper towels, etc) and compare which store they should buy it. They will have to look at how many units come in each package and how much each package is to determine the better deal.
Bonnie Jeanne - what great ideas to bring the real world into lessons on ratios! I think that these ideas would be relevant to the students and would be really engaging to incorporate into the lessons. I especially love the idea of comparing prices in grocery store flyers. This is definitely something that would come in handy in everyday life. They might even help their parents save money, which would lead to an even greater sense of pride! I will definitely use these ideas if I end up teaching 6th grade. Thanks for sharing.
ReplyDeleteHi Bonnie, I agree that ratios can definitely get a little bit tricky. I also struggled with that one problem on our problem set assignment. I think that ratios definitely are something that we come across in our daily lives - even if we don't realize that they are math related. I like that you brought up how students are meant to understand problems about ratios in the common core standards. Also, seeing as how I cook daily I definitely am always using ratios to deduce what to add and what not to add to my recipes.
ReplyDeleteBonnie Jeanne,
ReplyDeleteGreat lesson plan for making ratios relevant to students' life experiences. This lesson on newspaper clippings for grocery shopping was assigned to three of my middle schoolers. My husband and I actually kept at it -as a means for "drilling" the kids on their ratio values and comparison readings--by having them do Saturday coupon cut outs. It was our way of being efficient with coupon hunting (which I really dislike to do). I will say for the most part it taught them how to be bargain seekers. I believe it is so important to make if possible, every lesson relevant to students' interests and for life skills, if they are going to retain the information and even be able to effectively apply their understanding on state exams. Thanks for sharing!
Thanks for the peer feedback everyone.
ReplyDelete