State Standards

Learning Objectives

1. The student will be able to apply procedures for adding integers.
2. The student will be able to recognize that the sum of two negative integers is a negative integer.
3. The student will be able to recognize that the sum of two positive integers is a positive integer.
4. The student will be able to perform the addition of integers with unlike signs.
5. The student will be able to apply procedures for subtracting integers.
6. The student will be able to perform subtraction of integers using a number line.
7. The student will be able to describe how to convert an integer subtraction problem into an addition problem.
8. The student will be able to apply procedures for integer multiplication.
9. The student will be able to restate that the product of two integers with unlike signs is a negative integer.
10. The student will be able to restate that the product of two integers with like signs is a positive integer.
11. The student will be able to apply procedures for dividing integers.

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• The student will be able to recognize that positive and negative numbers have opposite directional values on a number line.
• The student will be able to write a short essay on real-life encounters with integers.

Formative Assessment 1

[Objective: 1-5]

Students will take out their whiteboards, and as a class, will practice problems on the main topic of integers applying the use of procedures and number lines to find solutions. Eight problems, in total, we will practice (two questions per subtopic-adding, subtracting, multiplying, and dividing). Students can take this time to clarify questions.

Formative Assessment 2

[Objective: 1-5]

Students will form small groups of four to participate in an online jeopardy game. This will be used as a review before the test.

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Summative Assessment 1

______________________________________________________________________________

For questions 1-3, write the letter from Column B next to the correct description in Column A. There are two choices in Column B that do NOT correspond to a description in Column A.

[Objective: 1a and 1b – Taxonomy Level: Remembering]

(2.5 points each)

Column A:

1. ___ A whole number that can be positive, negative, or zero.
2. ___ The sum of two positive integers is a
3. ___ The sum of two negative integers is a

Column B:

1. Negative Integer
2. An Integer
3. Unlike Signs
4. A Number Line
5. Positive Integer

For questions 4-7, fill in the blank with the correct answer.

[Objective: 3a  – Taxonomy Level: Remembering]

(2.5 points)

• When multiplying 2 numbers with different signs, you get a ___________ sign.

[Objective: 3b  – Taxonomy Level: Remembering]

(2.5 points)

• When multiplying a negative number and another negative number your result will be a ________.

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[Objective: 5  – Taxonomy Level: Remembering]

(2.5 points)

• On a number line, the numbers to the left are always _________.

[Objective: 5  – Taxonomy Level: Remembering]

(2.5 points)

• On a number line, the numbers to the right are always _________.

For questions 8-13, circle the letter corresponding to the best answer choice.

[Objective: 2b, 3b, and 4 – Taxonomy Level: Remembering/Understanding/Applying]

(2.5 points)

• -3(-2)
• 12/-2
• -6 – (-2)
• 5-9

[Objective: 2  – Taxonomy Level: Remembering/Understanding/Applying]

(2.5 points)

• What is the difference between a fish swimming 10 feet underwater and a bird flying 20 feet above the water?
• -10 feet
• 10 feet
• 30 feet
• -30 feet

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[Objective: 1c  – Taxonomy Level: Remembering/Understanding/Applying]

(2.5 points)

1. -4 + 4 =
2. 1
3. 0
4. 2
5. 3

[Objective: 4  – Taxonomy Level: Remembering/Understanding/Applying]

(2.5 points)

1. -20/-4 =
2. 3
3. -5
4. 5
5. 12

[Objective: 3 and 3a  – Taxonomy Level: Remembering/Understanding/Applying]

(2.5 points)

1.  -6(12) =
2. -50
3. 50
4. 72
5. -72

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[Objective: 5 – Taxonomy Level: Remembering/Understanding/Applying]

(2.5 points)

1. What is the distance between -4 and 5?
2. 5
3. 4
4. 9
5. -5

For questions 14-18, circle the word “True” if the statement is true or “False” if the statement is false.

[Objective: 1a – Taxonomy Level: Remembering/Understanding/Applying]

(2.5 points)

1. -8 + (-2) = -10                                                                         True                False

[Objective: 2b  – Taxonomy Level: Remembering/Understanding/Applying]

(2.5 points)

1. -10 – 32 = 42                                                                          True                False

[Objective: 1b  – Taxonomy Level: Remembering/Understanding/Applying]

(2.5 points)

1. Jim has \$250 in his savings account. He makes a deposit of \$75. Jim has \$325 in his savings account now.                                                    True                False

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[Objective: 1c  – Taxonomy Level: Remembering/Understanding/Applying]

(2.5 points)

1. Your checking account is overdrawn by \$25. You write a check for \$10. Your new balance is \$35.                                                                            True                False

[Objective: 1c  – Taxonomy Level: Remembering/Understanding/Applying]

(2.5 points)

1. It was positioned 800 feet below sea level. If it ascends 350 feet, the new position will be 450 feet below sea level.                                                   True                False

For question 19, in the space provided, solve the problem by drawing a number line to show your answer.

[Objective: 2a  – Taxonomy Level: Remembering/Understanding/Applying]

(2.5 points)

1. While hiking, Sarah went down 120 meters. If Sarah started at 800 above sea level, what is her elevation now?

For question 20, in the space provided, solve the problem and show your work.

[Objective: 1c  – Taxonomy Level: Remembering/Understanding/Applying]

(2.5 points)

• Write the sum of the integers to find the overall change in field position for a football team that gained 9 yards on one play and lost 22 yards on the next.

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Summative Assessment 2

Essay

[Objective: 6 – Taxonomy Level: Remembering/Understanding/Applying/Analyzing/Evaluating/Creating]

(30 points)

Essay Reminders:

1. Font: Times New Roman
2. Size of font: 12 pts
3. Indentations: 0.5 pts
4. At least 4 paragraphs

Instructions: Write an essay that responds to the given prompt.

Prompt: Write about 3 real-life instances where you might encounter having to add, subtract, multiply, and/or divide integers.

Summative Assessment 3

Performance-Based Assessment

[Objective: 1a, 1b, 1c, 2b, 3b – Taxonomy Level: Remembering/Understanding/Applying/Analyzing/Evaluating]

(20 points)

Demonstrate your knowledge of integers by completing the tasks below. Use the Check Register provided to record your results.

• Note: For 1/31, answer the question at the bottom of your Check Register

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For a month, you will be responsible for managing your family’s checkbook. During this time, you will make deposits, make withdrawals, and write checks to pay various bills.

You will begin with a balance of \$100.00. Your task is the following:

1. 1)  Record the transactions in date order in your checkbook register.
2. 2)  Choose the necessary operation in order in your checkbook register.
3. 3)  Solve correctly to have an accurate balance at the end of the month.

The following deposits were made this month:

1/5 It rained all week, and there was a leak on the roof. The rate for the leak to be repaired was \$100.00, so you hired a repairman to come in and fix it.

1/9 The rain made the grass grow in your entire neighborhood. Mom and dad own a lawn mowing business, and you are in charge of mowing your neighbors’ lawns. The rate you charge is \$50 per lawn, and you mowed 6 lawns.

1/15 The next day, you received the electricity bill. The bill is \$125.00. You wrote a check to Edison.

1/18 That night, you went to see a movie. The tickets cost \$22.50 each, and you paid for you and your friend to get them. You also went to the concession stand, purchased some food, and charged \$17 to your ATM debit card.

1/24 When you got home, you received a notice that the check your mom and dad wrote last week for your tutoring cleared. The amount withdrawn from your account was \$123.

1/25 An overdraft fee of \$25 was withdrawn to your account for insufficient funds.

1/27 You count up all the spare change in your family’s piggy bank because of the overdraft fee. You found \$43.87, which you deposited into your family’s account.

1/29 You also deposited the money you received from babysitting your little cousin. You babysat for 4 hours and received \$9 an hour.

1/31 What is your account balance? Do you have enough money to buy your friend a birthday present? The gift you want to buy costs \$35. How much more do you need if you do not have enough? How much extra money do you have, if you have any?

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Check Register

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1. B
2. E
3. A
4. Negative
5. Positive
6. Negative
7. Positive
8. A
9. C
10. B
11. C
12. D
13. C
14. True
15. False
16. True
17. False
18. True
19. Written Response Number line with 680
20. 9 + (-22) = -13

Rubric for the Essay

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Point Values

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The student’s learning gains will be evaluated by criterion-referenced grading, meaning that when assessing a student’s performance, it will be “against a fixed set of predetermined criteria” (Criterion-Referenced Test, 2014, p. 1). On criterion-referenced grading of assessments, all of the students have the ability to pass with a perfect score. Opposite to norm-referenced grading, where students are graded on a bell curve, with the average scores being the largest percentage. I have also chosen the total points method to determine the grade letter that will correspond to the number of points. In advance, I will determine the total point grade boundaries. The total amount of points that the students could receive on the assessments I created is one hundred points. An example of how I will grade performance is included below:

Furthermore, modifications can be made to accommodate my diverse learners. Lengths of assignments could be reduced to meet their needs, as well as time allotted could be increased. For those who are visually impaired, the font size will be enlarged to the preferred size. For my English Language Learners, the assessments could be modified by giving those students a list of translation words. Some words included in the assessments have a higher vocabulary, so giving them a translation list beforehand will benefit them. Individualized Education Plans will be followed to meet the needs that pertain to that individual student. These can include anything from the setting of where they are taking the assessments to how they are giving their responses

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to the assessments. Learning standards and objectives for students with significant cognitive disabilities will be lessened to fit their specific levels. All assessments are distributed in a way where no questions or answers are separated across different pages. All instructions are presented on the first page, which is easy to understand and read to maximize clarity of what is expected from each student.

Student and colleague feedback will influence my future instruction, tools, and assessments. If the student is not responding well to the assessments, there is a problem with the instruction. Thus, actions will be taken to improve instruction. If a particular question or instruction is hard to understand for multiple students, it will be changed to one that is universally understood. Students will also be open to leaving their suggestions to me in an anonymous box, or they could tell me. I have an open mind and want to make the class a positive environment where they are not afraid to voice their thoughts. If colleagues suggest other ideas of assessments or tools to grade assessments, I will consider implementing them into my classroom. Other teachers might suggest a different way of grading, for instance, norm-referenced grading. I will give it a try, and if I like it, I will keep using it. If the students are not gaining anything, I will switch back to criterion-based grading. I am open to all suggestions, whether from teachers or students.

Assessment data will be shared with the stakeholder by the school-provided grade book. The grade book that is used by most schools is Canvas. Canvas is an online tool that offers multiple resources, one of them being grades. Parents and students can access uploaded grades from their computers or smartphones. Interim reports and report cards, when sent home, will need to be signed by a parent and returned. This is ensuring that the parents are receiving those reports and have an idea of where their child is doing academically. Students will have all their graded assessments handed back to them with feedback that they could use for improvement.

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References

Criterion-Referenced Test. The Glossary of Education Reform. (2014, April 30). Retrieved from https://www.edglossary.org/criterion-referenced-test/

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