Assessment - Fluency and Concepts of Integer Sums and Differences
Lesson 11 of 27
Objective: Students will take an assessment on integer sums and differences.
This task is a variation on a problem that I found here. This task, however, focuses on integers only.
Part A of the task requires students to place the locations of the houses on a number line. Houses to the west are represented by negative numbers; houses to the east are represented by positive numbers. This is the most basic part of the task. It recalls what students have learned already in 6th grade. If a student has difficulty with this part of the task, this is evidence for serious intervention!
Part B is finding the distances. If a student has a well graphed number line in part A, this should be relatively simple. Students may mistakenly use negative numbers to represent distance. Distances should be represented by positive numbers only. When explaining this to kids I will ask them if they have ever heard someone answer a question about how far something is by saying "It's about negative three blocks down the road".
Part C & D assess the 7th grade standard on distance between points on a number line (7.NS. 1.c). An example with the distance expressed as the absolute value of the difference of two points is given. That is to encourage students to follow that model. Any equivalent answer will be acceptable.
Part E introduces a new house based on the location of a known house. It may be of more value to rewrite this question so that students are to write an expression that represents where this new house is. The house is 16 blocks to the east of Rogan's house, so an expression like -9 + 16 would be appropriate. As it is written, an acceptable answer would be that the house is 7 blocks to the east of the zoo.
This task will be worth a total of 4 points. Scoring goes as follows:
Part A) 4 points total for correct placement of houses on the number line
Part B) 6 points for correct positive values. I will award 3 points if negative numbers are used that have the same absolute value as the correct positive choice. I will award half a point for a correctly calculated distance based on a wrong placement in part A.
Part C) 2 points for 2 correct expressions. The expressions must evaluate to a positive.
Part D) 2 points for 2 correct expressions. The expressions must evaluate to a positive.
Part E) 2 points. 1 point for a correct distance and 1 point for a correct direction.
This is a total of 15 points. To calculate the total number of points earned I will multiply total points/15 * 4.
This section of the assessment is presented in a multiple choice format to allow for quick grading. I have included typical distractor choices that allow for item analysis. In other word, the wrong answer choices represent the typical mistakes a student will make.
I'll use problem 2 as an example. Students are to find the sum of -21 + 8.
A) -29 <-- Students incorrectly added the absolute values and assigned a negative sum
B) -13 <-- CORRECT
C) 13 <-- Students subtracted the absolute values but assigned a positive sum
D) 29 <-- Students added the absolute values and assigned a positive sum
E) NH <-- Students were not able to find the correct sum
I also added a multiple choice item stating that the correct answer is not given. There may be only one problem where this is the case.
It is my hope that some students realize they can reason their way through many of the answers without doing a single computation. They might rely on answering essential questions. Using example 2 again. We know the sum should be negative because the absolute value of -21 is greater than that of 8 - zero pairs are created so what is left? This should lead students to eliminate choices C and D. Then, we know that when adding a positive we end up with a greater value. We should eliminate choice A because it is a lesser value than -21.
If there is no evidence of students solving the problems in this manner, this will definitely be a topic for discussion when we review the assessment.
Students will earn 1 point for each correct answer on this section.
This section assesses how well students understand concepts of integer sums and differences. These speak to two essential questions from the unit: 1) When does adding to a number result in a lesser amount? greater amount?; 2) How can you determine if a sum will be positive or negative?
A number line with variables placed in positive and negative positions is to be used for all but one of these problems. The use of variables makes this more abstract and forces students to grapple with the quantities (MP2).
I have used a bold font and capitalization to focus on key words in questions such as NOT, TRUE, FALSE, NEGATIVE in the hopes that this helps students make sure they are properly answering the questions given. Often students will ignore words such as "not".
Students will earn 1 point for each correct answer on this page.