Standards based grading means that you can pre-assess and post-assess your students to document their progress; but how do you TEACH differently? Proficiency Scales are all about helping students show growth in small steps instead of being overwhelmed by a year-end goal that seems way over their head. This video will walk you through one way to get your students understanding a scale. In this seventh grade standard for ratios and proportions, students are expected to compute unit rates associated with ratios of fractions including lengths and areas with different measurements. I like to introduce students to my scale starting with level one and then work up to level three which is the grade level expectation. Sometimes up to four, sometimes not depending if they’re ready. In the middle school math grades, there’s a lot of vocabulary that draws on previous knowledge from earlier grade levels. I like to review that with my students or give them a little pretest and see who remembers the vocabulary and the kinds of problems they did before that will help them on this year standard. Let’s see how to differentiate seventh grade ratios with proficiency scales.
Here’s an example of a level one problem that I would ask my students to see who’s mastered using rates. Your family’s driving to their summer home on a lake, for the first 45 minutes you drive at 60 miles per hour, how far do you travel? For the next hour you drive 47 miles per hour. How far do you travel? For the final two and a half hours, you drive 50 miles per hour. How far do you travel? Calculate the distance of the entire trip.
I’m asking students to solve three different problems using a rate and then to combine their answers. Your students could probably solve this problem without knowing they’re using a rate. One thing you’d want to discuss or ask them is what a rate is. How is this a rate? Which number is the rate? Is it the 45 minutes? Is it 60 miles per hour? Is that the total hours that they’re going to calculate? or the total distance that they’re going to calculate? See if your students remember what our rate is, because in the second level they’ll have to use a unit rate and your want to make sure that they know what that difference is as well. This is a really basic problem that will probably build their confidence to understand what they need to do this year.
At the second level, we’re still doing problems that are related to mastery, but they’re a little easier than the grade level problems. Again, this is going to build your students confidence and give you a little information about who has the background knowledge to move on and how much reteaching you need to do. At level two students should understand unit rates and solve for them. Again, you want to make sure they know what a unit rate is. What is the key word, the clue and the story problems that tell them they’re working with a unit rate. An example would be, Nadia bikes three kilometers in 45 minutes. What is the unit rate of kilometers per hour? We know that per hour is that clue that their unit rate, the denominator will be in one unit, per hour means one hour.
Make sure your students are going to be able to identify the difference between rates and unit rates because three kilometers in 45 minutes is also a rate, but it’s not a unit rate because the denominator is not one minute or one hour. Doing these kind of problems will help you identify if you need to reteach some of those specific language terms.
Problem B: At this rate, how long will it take her to bike 20 kilometers? The students will use the unit rate for a different distance. If she bikes for three hours, how far will she go? Now the students have to use the same unit rate in a different way to find distance, instead of time. Giving this problem to your students as a pretest, will give you a lot of information about what kind of problems they can do and what kind of problems you’ll need to reteach so they can master level three.
Level three is the seventh grade expectation. I can compute unit rates with ratios of fractions. What does that mean? If you’re breaking this down and introducing it to your students for the first time, you want to make sure they remember what fractions are about. The tricky thing is fractions are also ratios part to whole ratios, but in this case the fraction is a part, being compared to another part, which makes the total ratio. They want to make, you want to make sure that they remember what unit rates are meaning what ever two quantities they compare, they need to have one in the denominator. Anna babysits for five and a half hours and is paid $33 at the end of the night. How much does she make per hour? You want to make sure that your students understand that per hour is their clue, and connect that language with unit rate. It’s a unit rate because they’re comparing it to a denominator of one unit of time. Also, make sure that your students can work with the fractions and compare it to dollars. You might find them drawing pictures on their paper using different strategies. Converting the five and a half to a decimal in order to multiply it or divide it. Ask your students to do this problem on a piece of paper and turn it in to see who has already mastered this level and who hasn’t. This one way to do a quick pre-assessment.
I like to extend this problem for my students who are advanced or I know they’re going to need a challenge. Not everybody gets this far, but if students do pass level three, I usually make them try level four. Here’s an example of a level four problem for seventh grade standard. I understand this so well. I can explain how I found my solution. This language is very general because you can have a lot of fun in this level and ask your students to apply it in different ways. Here I created another story problem that’s a little more challenging because I’m asking students to compare a fraction with another fraction or a decimal of dollars. Anna babysits for four and three quarters of an hour and is paid $33 and 25 cents at the end of the night. How much does she make per hour? So again, students are still working with unit rates, but you can see how we made the problem a little more complicated. You could ask your students to come up with a ratio table, that shows how they figured out per hour, to come out with the amount for one hour, two hours, three hours, four hours, five hours. Or You could just ask them to find the exact answer to this problem in fractions of an hour. But either way, you could keep your advanced kids busy for longer while you work with the lower students who really need your attention.
I hope you found some good ideas in this example of a scale. If you would like more examples of math scales or assessments already done for you, please visit my website, misseslleveledlearning.com. I have a freebies tab where you can download samples of posters already made and assessments with problems already done for you at all four levels of the scale.
I would love to hear your comments, questions, or ideas. I hope you found this helpful and have a great year.
You can find this resource in my TpT store. Follow the links to download a FREE Leveled Assessment and FREE Scales for this math standard and more!
Thank you to Juli F. for your feedback!
“This really helped me to effectively explain how students should assess their mastery.” – June 2019
and Sonia H. said,
“The questions were accurate and rigorous. It works very well for standards-based grading.” – January 2019
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