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# Rational Numbers Operations - Final Unit Assessment

Lesson 27 of 27

## Objective: Students take the final unit assessment on rational number operations and concepts.

*45 minutes*

#### Fluency

*20 min*

This section of the assessment is designed to assess a students' fluency with rational number computations. Students should not be allowed to use calculators on this section unless it is required by their IEP or 504 accommodation.

Multiple choice items have been included, though some teachers may prefer to remove these items. I have included them for the convenience of the teacher; grading multiple choice items can save time. The multiple choice item distractors are all designed in a similar way; they are based on common student errors. That being said, the astute student will often be able to eliminate two choices just by reasoning about the quantities (**MP2**). Using problem 2 as an example:

-15 + 5

A) -20 B) -10 C) 10 D) 20

A student may know that the sum will be negative because -15 has a greater absolute value than +5. Therefore the students will eliminate choices C and D. A students may know that adding a positive 5 results in moving to the right of -15 on a number line - it creates a greater value. Now the student can eliminate choice A. This only leaves choice B.

Personally speaking, I like the fact the a student can reason their way through these items, but feel free to remove them if you would prefer.

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#### Concepts and Problems

*25 min*

These items are meant to assess a students' conceptual understanding of rational number operations as well as their problem solving abilities. Originally, these items (except the last) were presented as open response items. I added the multiple choice items after feedback from colleagues. Again, they felt it would take much too long to grade.

If I had more time to give the assessment, I would keep many of these items open response and spread the assessment out over several days by only devoting a small part of class time each day to these items. Problem 2 was originally written so that a student must explain each of their choices. I think this would be a great standalone assessment in itself. But again, to save time students here are only required to select the 3 negative expressions out of the 6 given.

Please forgive me for using fractional yards in problem 9! I do know that fractions of a yard are not recorded in a football player's statistics. Change the context of the problem if this bothers you!

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I have included a rubric with suggestions for how to score this item. It is not necessarily a perfect rubric but I think it is a valid way to score the items.

Let me explain some of my thinking on the rubric.

Part A is worth only 1 point because these represent skills from 6th grade. It is an all or none item.

Part B is worth 2 points. Students can rely on the number line placements in part A to find the various distances. Distances are to be positive. If a student has an incorrect placement - meaning they did not earn points in part A - they can still earn 1 point in part B if they correctly found the distances based on their incorrect placement.

Part C is also worth 2 points. Students are expected to write two valid expressions to represent the given distance. I have included a few samples. Anything equivalent to the samples would be acceptable. I know that some students will want to rewrite a difference as a sum. I will accept that as long as it represents the distance. Also note that a student can earn 1 point for having two correct expressions based on an incorrect placement in part A.

Finally, many students may want to change the values to decimals. This is also acceptable.

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- LESSON 1: Fractions as Quotients - Using Long Division to Convert a Fraction to a Decimal
- LESSON 2: Finding the Distance Between Integers On a Number Line
- LESSON 3: Where Do We Go From Here? Adding Integers on the Number Line
- LESSON 4: What is the Sign of the Sum?
- LESSON 5: Algorithms for Adding Integers
- LESSON 6: How Addition and Subtraction are Related (Part 1 of 3)
- LESSON 7: Subtracting for More or Less. Subtracting Integers on a Number Line
- LESSON 8: How Addition and Subtraction are Related (Part 2 of 3)
- LESSON 9: How Addition and Subtraction are Related (Part 3 of 3)
- LESSON 10: Algorithms for Subtracting Integers
- LESSON 11: Assessment - Fluency and Concepts of Integer Sums and Differences
- LESSON 12: Integer Product Signs - Using Counters to Discover Signs of Products
- LESSON 13: Integer Quotients
- LESSON 14: Expand Expressions Using the Distributive Property
- LESSON 15: Integers Assessment
- LESSON 16: Finding the Distance Between Signed Decimals on a Number Line
- LESSON 17: Adding and Subtracting Positive and Negative Decimals on a Numberline
- LESSON 18: Adding and Subtracting Signed Decimals Using a Procedure
- LESSON 19: Multiplying Signed Decimals
- LESSON 20: Dividing Signed Decimals
- LESSON 21: Finding the Distance Between Signed Fractions on a Number Line
- LESSON 22: Adding and Subtracting Positive and Negative Fractions on a Numberline
- LESSON 23: Adding and Subtracting Positive and Negative Fractions Using Counters
- LESSON 24: Adding and Subtracting Signed Fractions Using a Procedure
- LESSON 25: Multiplying Signed Fractions
- LESSON 26: Dividing Signed Fractions
- LESSON 27: Rational Numbers Operations - Final Unit Assessment