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.
Equations Proficiency Scale Level 1
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.
Equations Proficiency Scale Level 2
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.
Equations Proficiency Scale Level 3
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.
Equations Proficiency Scale Level 4
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! I bought this when I had 4 preps and was required to post a specialized scale for every standard. You saved my sanity! I love that the progression is based on standards in previous grades. I also appreciate how responsive you were in changing the order of the levels. That was not a small change!”
Thank you to Jodi F. – August 2018
“This set of assessments are fantastic! I’ve been able to use them with whole class – as well as individuals to gauge learning and problem areas. Such a relief to find something like this pre-made and not have to spend my own hours creating. Your hours are well worth my money. This is a product that I will continue to use in the years to come – so happy with my purchase!!!”
