Anyway, we've all heard that a goal of 10,000 steps a day is a great way to increase movement and to stay healthy. How far is that? How many calories does that burn? Is that consistent?
As you know, I do a lot of thinking about "how much I have left" when I'm working out. This is similar to my treadmill post, but slightly different.
Grade Level: 6-7Course: Pre-Algebra, 6th and 7th grade math
Standards: 6.RP.1, 6.RP.2, 6.RP.3, 7.RP.1, 7.RP.2, 7.RP.3
SMP: SMP1, SMP2, SMP3, SMP4
Skills: Ratios, Proportions, Unit Rates, Problem solving, Real world problems
How to use this as a mad minute:
You have 60 seconds. Estimate the number of steps someone takes in one mile.
How to use this as a warm up:
You could ask the students to consider one of the following:
1. What is the relationship between steps and distance?
2. What is the relationship between steps and calories?
3. What is the relationship between calories and distance?
4. Estimate the number of steps you would take in 10 miles.
5. Estimate how far you would have to walk (either in steps or in distance) to burn off a large McDonald's French Fries. (500 calories.)
How to use this as a mini-lesson:
0:00--I'd like you to take 60 seconds to brainstorm everything you know about ratios or proportions.
1:00--Partner up and share your ideas with a partner. Make sure to add anything you forgot to your list!
2:00--Can we make a list of properties of ratios and proportions and define them?
4:00--I'm going to show you three photos. (Link here.) When you look at them, don't talk to your friends, but take a minute to write down your immediate "math wonders" about the photos.
5:00--Take a second to reflect. Are your questions mathematical? Are you focused on applications of math and not off-topic? If so, please share them with your partner. When both have shared, select two questions you feel are your "best" and write them on the board.
7:00--Here you will want to zoom in on the most relevant and appropriate questions. I suspect that several will be able to be answered through solving proportions. Feel free to "prime" groups as you observe to encourage them to think proportionally. I will post "pretend" questions for the remainder of the lesson based on what I would expect kids to "wonder" about. It looks like we have a lot of questions about the distance and the steps! Do you know what a "unit rate" is? Think about this, if you can buy 4 candy bars for $1, how much is each candy bar? (Allow time.) Finding the cost for one candy bar is the UNIT rate, how much for 1 of that thing. I think we are wondering how many steps for 1 mile. Can you set up a proportion that shows steps compared to distance?
9:00--How could you change that to find out how many steps are in 1 mile? (This assumes previous knowledge of solving proportions. If I were introducing the skill for the first time, I would have spent at least a class period on setting up equivalent fractions and observing/discovering the property of cross products being equal. Kids should know how to set up a proportion with a missing value.)
10:00--Please solve your proportion and determine how many decimal places you need. When are done, discuss with a partner and come to an agreement.
12:00--(Discuss the answers as a class. The exact answer, rounded to the nearest hundredth is 2148.22. I rounded here because the next two places are zeros. However, I would round to the nearest whole step, or even to the nearest ten.) How did you solve? Why? How can you be sure that makes sense? How did you round? Why? How can you be sure that is reasonable? (Choose two students who rounded differently and ask them to explain. I hope someone would note that 2150 is much easier to use in long term estimating than 2148 or 2149.22, I also hope someone would note that 2148 is easier than 2148.22 and there is no such thing as .22 of a step. Finally, I hope someone would note that 2148.22 is the exact value and that the extra decimals are negligible.)
14:00--Can you repeat this magic? Can you tell me how many calories I'll burn in an hour? Or how many steps it takes to burn 100 calories?
16:00--Are both of the questions I asked Unit Rates? Why or why not? Be prepared to back up your answer!
17:00--Who thinks they are? Who thinks they are not? (Hold a mini debate, or allow students to change sides of the room. Revisit the definitions you established if there is still a question at the end of your "debate".)
19:00--Can anyone, after looking at these examples, think of a time when they might solve a proportion to answer a real life question?
How to use this as a full lesson?
I always recommend extending the mini-lesson into a full lesson with further exploration. First, I wondered if the FitBit readings and unit rates would differ for a different person. I had to enter my height and weight in the online program when I registered, so I asked another user to share a few screen shots of HER FitBit. Adding this second set of data opens another opportunity for exploration and extension. For example, are the unit rates the same? If not, what can you tell about each person's rates? Can you graph the data? Can you compare the two sets on a single graph? Will one person "go farther" with the same number of steps or burn more calories with the same distance? This is a great introduction to slope! Slope is a rate of change, or a relationship between two numbers, just like a proportion! Even if you don't calculate the unit rates for the second FitBit, you could definitely have students graph the data (assuming both started at 0,0,0) and talk about what the slope represents. What does a steeper line mean in this real life situation?
I included both sets of FitBit data on FitBit Worksheet 2.
How to use this as an assessment?
If your students are proficient with unit rates, it would be perfectly reasonable to provide the FitBitMath1 or FitBitMath2 worksheets and ask them to calculate unit rates and explain the meaning of their answers. Short, simple, effective.
Please feel free to use any of these ideas and modify them to meet your needs. However, please acknowledge the original source of the items and my own lesson outlines. ©NatalieRSprigg 2013
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