How do you differentiate Fifth grade equations with proficiency scales? 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. Pre-testing and post-testing is the easy part; but how do you TEACH differently with Standards based grading? This video will walk you through one way to get your students understanding a scale.  In this fifth grade standard for operations and Algebraic thinking, fifth grade students are asked to use parentheses, brackets and braces in numerical expressions and be able to evaluate the expressions with symbols, which means being able to tell what it equals. They have to know the order of operations. Let’s see how to visually build on last year’s content for student’s to make lasting connections that facilitate progress in the standard.

Level 1

They have to understand the order of the different brackets embraces what to do first, second or third. So there are a lot of sub skills involved in this standard. I have the scale posted in my classroom and I start from the bottom up. When I introduce this standard, the first thing I want to do is access the background knowledge of my students from fourth grade, third grade, any levels where they understand grouping objects because that is what the braces, the brackets and the parentheses are all about. I want to help them to know that they already know what the standard is about.

They’re just going to apply it in a new way. So a level one question, students know how to represent groups of objects in different ways. We’re going to start very simple with pictures. So I would ask them to draw a picture to represent six groups of four, three groups of seven. If you want to give them a challenge, you could say also do four groups of six and seven groups of three. Make sure that they know, uh, they can flexibly use groups and understand how they might be different or the same. Very basic. Make a picture on their paper, something they would probably have done in second or third grade.

Level 2

At the second level, I would ask students to apply the grouping to a problem or have a little adjustment to the problem. In fourth grade they were asked to solve word problems involving groups in numbers, this is setting them up to understand what steps come first and second. A group of 37 was divided evenly into three groups. The extras were subtracted. If you think about how students will set this up in a number sentence, you want to make sure that the division is first and the subtraction is second. That seems really obvious now. But as soon as you move up to level three where students are adding, subtracting, multiplying, and dividing within brackets and braces, they’re going to very quickly get confused about what to do first, second, and third. You want to remind them how to pay attention to the order of operations, when it comes to multistep problems. This is an example how many were in each group and how many were subtracted. The two questions below helped students to remember that there is an order of operations in word problems. Then you’re going to help them make the connection from word to number sentences with symbols.

Level 3

Let’s take a look at a level three example, which is the grade level expectation for fifth grade. Eight divided by two in parentheses, (that’s one group), times two and a half minus 75 hundredths in parentheses, that’s another group, inside brackets. Now what do they do with that, plus 37. How many operations are in this problem? Your students would identify that there’s four different operations, all four operations, and then they’d have to think about what to do first, second, third, and fourth.

You could use this activity as a pretest for your students to see who’s mastered this or has a good idea of how to do this and who is going to need a lot more instruction. Have them copy the problem on a piece of paper and find a solution.

If you have time, you can go through the problem with students and experiment with the order of operations. You want to make sure they understand that doing it different ways, we’ll get them different answers, hence the importance of knowing the right order. At this point you may have already taught students the order of operations or you might use this problem as an introduction. Let’s explore the different ways to do this problem. How are we going to come up with all the same answer and know that it’s the right answer? Well, that’s what the order of operations our for. I usually have this on a separate poster in my classroom somewhere. As you practice this standard, you’re going to want to take down all the extra hints and make sure students are memorizing the process on their own.

Level 4

Once your students have mastered the grade level standard and not everyone will, I have an extension in level four where I asked students to explain situations where the parentheses are needed in any equation, and this is where they can adapt it to real life problems, make their own story problems. You can do a lot of different things in level four. It’s a little fun to be flexible and if you have gifted or advanced students, they may even enjoy coming up with their own problems to give to each other. Here’s an example. Create a story problem that requires parentheses to solve. There must be at least three steps, meaning three operations, show the solution for your gifted or advanced students who’ve already shown mastery of level three. You could easily extend this to doing four or five operations. You could extend it to real world situations and problems. It’s fun to be creative at this level.

Hopefully this has given you a lot of great ideas about how to introduce the scales to your students and how to differentiate your standards for different levels of difficulty. If you’d like an assessment that’s already done for you, you could assess your students on their current level of mastery and use it to plan before you even get started. I find this really helpful so I can cut out things that I don’t need to do and spend more time on the lessons that they really need. Visit my website I have a freebies tab where you can find copies of the scale, these posters and copies of assessments with problems already done for you at all four levels.

Thanks so much for your time and I hope you’ve gotten some great ideas. I’d love to hear your comments, criticisms, or how you use scales in your classroom. Feel free to leave a comment 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 Cain’s Collections for your feedback!

“This is amazing. Plus, you giving the portfolio pages for free is wonderful. I know this will help me out so much next year. We don’t use Marzano’s, but I am interested in seeing how it helps the students take ownership of their learning and how it will help me differentiate. Thanks for your hard work!” – May 2017

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