Pretesting and post-testing your students is the easiest way to practice standards based grading. The hardest part for me was figuring out how to 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 eighth grade equations and expressions standard, students must know and apply the properties of integer exponents to generate equivalent numerical expressions. That can be a mouthful for adults as well as eighth graders. Some students at the middle school level start to get lost in the details, especially if they haven’t mastered previous concepts. A well-designed scale is like holding your students’ hands through memory lane; by aligning the current grade level standard with content from previous grade levels. Let’s see how to differentiate eighth grade equations with proficiency scales.
You’ll see level one I can write the evaluate expressions with exponential notation. Then I’m going to give students an example to remind them of things they’ve already seen that are going to help them this year. At level two I can apply properties of operations to expand expressions and then level three I can use properties of exponent to create equivalent expressions. As we go through each level with some example problems, I make sure that students understand the language and the vocabulary as well.
You can decide if you’re going to use these problems as an introduction to your new standard for the year or if you want to use these problems as a pretest. You can have your students write them on a piece of paper, one at a time, to see how much they can do with the problems and turn them into you at the end so you have an idea of how to plan the rest of your instruction for this standard. At level one, I would give problem students a problem like this, something they would have seen in sixth grade. They have to evaluate the expression. They’re probably going to know what that is. With exponential notation. They’re going to see, five to the power of three and two to the power of four. The use of parentheses, brackets or braces will also tell you if the students remember some of the order of operations skills from fifth and sixth grade and if they can apply them correctly to this problem. Make sure that they’ve identified that there’s four different operations here and that the order matters. You can see if they come up with the right answer. In the description for this youtube video, I have all the answers listed for you, so don’t stress out about that. Just make sure your students don’t see them first. After they have a few minutes to try that problem, you can show them level two.
Properties of operations to expand or simplify expressions means that students know how to combine or simplify the coefficients for each exponent. Three to the third power times three to the second, power, x to the seventh power divided by x to the fourth power. Give this as a sample problem to your students and see who remembers what to do. This is a little simpler than what they’ll be asked to do this year because at the level three students will show that they’ve mastered every combination of exponents and expressions.
In this example, students are going to see variables with positive and negative exponents in expressions where they have to multiply and divide. Now I don’t have an example here of dividing with a negative exponent, but that is something else you could throw in the mix. See if your students have mastered this level. If they’re able to do every combination of problems with positive and negative exponents, then your students have really mastered the grade level standard and you can be confident that they’re ready to move on to a challenge.
Now, level four is not something I give every student. I might give it to my gifted or advanced students, but only after they prove that they’ve mastered grade level skills. As an extension, I might have them use the properties of exponents to create equivalent expressions, maybe coming up with a variety of expressions, maybe applying the expressions to real world problems or coming up with their own problems. There’s a lot of creative and fun things you can do at level four. Here’s an example of a level four problem. Write a paragraph or create a poster that explains how to quickly simplify expressions with exponents. This means students would have identified the rules for multiplying and dividing.
Multiplying with negative exponents and dividing with negative exponents. Basically you’re looking to see if they can minimize the instruction to one sentence, adding positive integers and multiplication, subtracting positive integers in division or figuring out what combination of operations they need for negative exponents. This is a good exercise to extend the thinking of your higher-level students and make sure they can apply this standard at a different level.
Hopefully this has given you some really good ideas about how to use a scale in your classroom and how to introduce a new standard to students so that you can access their background knowledge and help them build some confidence for the expectations of a new year. I would love to hear your ideas, your comments, your questions, or how you use scales in your classroom. If you would like to see more standards, you can go to MrsLsleveledlearning.com I have a freebies tab or you can find links and downloads for free samples of posters and assessments with questions already created for you. My assessments include multiple questions for each level of the scale so that you have documentation that your students have mastered each level. I hope you found this helpful and I would love to hear from you. Thanks so much for your time.
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 Jodi F. for your feedback!
“Starting SBG grading this year, so happy to have a place to start!” – August 2018
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