Lesson 15

Integers Assessment

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SWBAT take an assessment on integer operations.

Big Idea

Students take a test that assesses computation of integers, integer concepts, and problem solving. A rubric and answer guide is included.

Computational Fluency

15 minutes

This part of the assessment contains 20 multiple choice items involving adding, subtracting, multiplying, dividing, and powers of integers.   As with all multiple choice tests, the wrong answers are distractors that are designed based on common student errors.  Before giving this to students, I will remind them to be very careful and to check their work.  With multiple choice items, it is very easy for a student to think they are doing well because of the distractor items.  Over the years I have heard students say "that test was easy".  Then upon grading their assessment I would find they were no where near mastery.  So, I now warn my students that it it is easy to find the WRONG answer.  I explain how the wrong answer choices are created.  

It may be preferable to not have multiple choice items for a fluency test.  I created this knowing that it is quicker for me to grade multiple choice items.  It may be more desirable to remove the multiple choice items from this part of the test.  It will just take more time to grade, especially if you plan to dig into student work to analyze mistakes. 


The last 4 items of this section require students to apply the properties of operations in order to solve.  For these I have added the multiple choice item "E) NH".  This means the answer is not given.  None of the 4 items have this has a correct answer.  Sometimes this type of answer choice is a way to assess perseverance in solving a problem.  A student who is tired at this point may quickly solve a problem, not check their work, and quickly choose E for their answer.



Open Response

40 minutes

These items mirror the items on the final unit assessment.  The only difference is that these items only use integers and the final uses any rational number.

Open Response 1 "OR1"

This item comes from the formative assessment lesson titled "Temperature Changes".



This item is intended to assess the basic concepts of integer operations in a more abstract manner.  Values are given only as variables on a number line.  This pushes students to reason abstractly and quantitatively (MP2).  Many students may choose to substitute a value for A and this is fine.  Many will choose 6 for A because it is 6 units to the right of 0.



I borrowed this item from here.  This is meant to assess the idea that distance is the absolute value of the difference between two points (7.NS.1.C).  Parts A and B are the "entry level" steps for this problem.  Part C then asks students to be able to represent these distances using a sum or difference.   


This is a "simple" application problem where students apply integer operations to a real-world situation - yards gain by a football player.  It requires students to write an expression, find a total, and average based on data in a table.


Open Response Scoring Rubric

I have provided an answer key and suggested points for the items.  

It is not a perfect rubric or the only way to score items, but it represents my thinking. 

For example, open response 1 "OR1" is worth a total of 3 points.  In part A, students are only able to earn 1 point if they correctly circle the 3 correct values.  You may want to make this worth a total of 3 points, but then the question arises as to what to do if a student circles 4 choices - 1 being incorrect.  Do you take away a point and award only 2 points?  Or is this a sign that the student doesn't understand the problem at all so it is worth 0 points.  My thinking is with the latter.

OR2 is straight forward and perhaps a less controversial rubric than OR1. Notice that some items are worth 2 points: 1 point for correct placement on the number line and 1 point for a valid explanation.  Notice that partial credit can be earned if a student makes a correct answer based on an incorrect placement.  For example, if a student mistakenly places point C as a positive value in part B, they can still earn a point by saying that C / B is negative which is true based on their incorrect placement.

The rubric for OR3 treats each part of the task equally for a total of 16 points.  It may be preferable to restructure the points to make part C worth the most since this is the most difficult task.  I sometimes will scale this item to 4 points, based on how Louisiana scores the open response items.

OR4's rubric is straight forward.  I may want to give partial credit (1 point) for part C if a student correctly finds an average based on an incorrect total in part B.