Pre-testing and post-testing is the easy part; but how do you TEACH differently with Standards based grading? 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 sixth grade standard, students are going to be asked to show that they understand the concept of a ratio and ratio language to describe ratios, which are relationships between two quantities. We’re going to visually build on last year’s content for student’s to make lasting connections that facilitate progress in the standard. Let’s see how to differentiate sixth grade ratios with proficiency scales!

Level 1

Now when you introduce new vocabulary to students, sometimes they can really get thrown off guard. If you work with a lot of lower level students, title one students, students who don’t feel confident in math, it’s really helpful to identify the things that they’ve already learned. Fifth Grade, fourth grade previously that’s going to help them to understand and master this standard. One thing I like to do is compare ratios to multiplication and division or fractions because what students don’t know is all the time they spent in fourth and fifth grade studying fractions parts to wholes groups of objects in different arrangements is a form of ratios. Once they understand that they already know something about ratios and they’re a little more open to learning something new. I started level one and two, to help students access their background knowledge from fourth and fifth grades.

Level three describes the grade level expectation, which explains that students will be able to use ratio language to describe ratio relationships. They’ll have to understand how to identify the ratio and then put that into a sentence. Level four is a challenge for students who have already mastered grade level skills. Not all of your students will need to go this far, but we’ll get to that later.

At level one I asked students to think about multiplication and division and how to compare amounts in that way. They were asked to do this in fourth grade, so hopefully they’ll feel like this is something pretty manageable. Here’s a story problem to help them demonstrate what they already know.

Pool admission costs a $1.50 per day. A pool pass costs $13.50. How many times more expensive is the pass?

First students have to remember what’s important for them to know. They’re going to have to remember how they worked with money and decimals in the past. They’re going to use multiplication or division and they can make the decision of how to compare these two quantities, $1.50 to $13.50. If you notice they’re struggling, you can tell them how to do it. Say use multiplication, use division, whatever they think is easier. You might find students scribbling pictures on their paper trying to add $1.50 multiple times, whatever they need to do to get through the problem. Seeing how they work out the problem is a great part of the assessment because you can use this as a pre test to determine how much instruction you’ll need to do for them to understand ratios and what kind of background knowledge they may be missing.

Level 2

A level two problem might look like this, I asked students to convert measurements using rates. This was something they were also asked to do in fifth grade. I’m using a similar problem so they can build on what they just did and I can see if they can take the problem one step further. In this problem, pool admission costs a $1.50 a day, a pool pass worth five days cost $6.50.

The students have two questions. They may already be comparing the amounts using multiplication division, which is what we just asked them to do at level one. But now I’m going to ask them to do a little more with it. If you buy a pool pass, how much are you paying per day? We know they’d want to use division to find that out, but they might work backwards and use multiplication. Which option is cheaper? So now they’re comparing amounts and making an evaluation to answer a question with the information.

Why is this a rate? You’re going to want to make sure that your students know the difference between ratios, which is comparing two quantities and rates. See if your students know what the key word is in the problem that identifies that they’re finding a rate. There is a special secret word, a key word, that will tip them off that they’re finding a rate. That word is PER,  “Per Day”.

In fifth grade, students were introduced to the concept of rates, that they’re comparing two quantities, but that the denominator’s always one thing. A $1.50 for every one day, and $6.50 for every one pass. So if the denominators, one item that’s a rate they may or may not remember that. So again, this could be a great pretest to see exactly what vocabulary and details you will have to reteach to make sure that your students can describe a ratio and ratio language accurately at the sixth grade level.

Level 3

Here’s some example of a problem that they would have to do in sixth grade to show mastery of the standard. There’s three different kinds of chocolates in a box, milk chocolate, mint chocolate, and dark chocolate. There’s different quantities of each one in one box. Boxes of chocolate candy come with the three flavors.

Write one sentence describing the ratio of milk to dark chocolate, Write One sentence describing the ratio of mint to dark chocolate. Now this is also a great pre-assessment to see if your students remember how to reduce fractions and ratios. You’re going want to make sure that they have done that in order to get a completely correct answer. If they don’t, you’ll know something else that you want to include in your instruction. Have them do this on a piece of paper. They can do it alone or with a partner, depending how much information you want for your planning and have them turn it in. It’ll be a quick way for you to assess how many students need some background instruction before they’re ready to master this standard.

Level 4

Now if you have students doing really well, there’s a lot of fun ways that you can extend this standard. Have them create their own problems, have them create their own ratios, have them do more complicated ratios in this problem. I’m using the same setup, but I’m going to ask my level four students to create a ratio table listing all of the possibilities.

This is going to be a lot more thinking for them and they’re going to have to make sure that they’re very thorough at finding all the possible combinations of comparison between the three kinds of chocolate and the total amount in each box. Because we can’t have a real ratio without including parts and wholes. Now create three more box sizes with different total amounts using the same ratios. Once your students reduced the ratios, all possible ratios in their table, they can use the same ratios to expand again and make different amounts. They can’t use 1812 and nine again in the same combination, but they might think of a different combination with bigger boxes of chocolates. This could keep your gifted kids busy for a little while in a small group or on their own while you attend to the students who really need your attention in class.

I love planning this way. I love having my scale ready so that if I need to make a quick modification or double check a concept or vocab with a student, I have it right in front of me on a paper on the wall posted in my room and it makes a great pretest post test or a quick reference for me to modify classroom assignments and help my students who really need to fill in some holes.

I hope you found this example helpful. If you would like to see more math scales for sixth grade, please visit my website, I have a freebies tab where you can download examples of math and ELA Scales and assessments that are already done for you. The assessments have problems attached to each level of this scale. Just like our examples here, except many more so that you can assess whether or not your students have mastered the grade level standard and which ones need some extra work. I hope you found this example helpful. I’d love to hear any comments or ideas you have. Questions or suggestions. Criticisms are welcome too, and have a great year. Thank you for your time. Yeah.

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 Jasmine F. for your feedback!

“One of the best purchases. It has every standard and scaffolds all the standards as far as 4th grade. I use them as quizzes, test, and even pretest or a game. Totally worth it.” – September 2019

Tricia W. said;

“This resource has taught my students more about themselves as learners.” – JANUARY 2016

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