Integers and Operations - Addition and Subtraction Study Notes

Integers and Operations Overview

• Main Topic: Integers – Numbers
• Learning Objective: To determine solutions involving the addition and subtraction of negative integers.

Starter Activity: Ordering Integers

• Given Random Numbers:

  • $10$
  • $6$
  • $-3$
  • $0$
  • $21$
  • $-11$
  • $23$

• Arrangement in Ascending Order:

  • $-11 < -3 < 0 < 6 < 10 < 21 < 23$

Temperature Difference Calculations ("We Do")

• Real-World Context:

  • Ambient temperature in the United Arab Emirates (UAE): $41\,^\circ\text{C}$
  • Comparison destination 1 (Kazakhstan): Cold weather below $0\,^\circ\text{C}$
  • Comparison destination 2 (Georgia): Temperature of $-5\,^\circ\text{C}$

• Mathematical Calculation:

  • Determining the difference in temperature between the UAE and Georgia:     $41\,^\circ\text{C} - (-5\,^\circ\text{C}) = 46\,^\circ\text{C}$

• Conclusion:

  • The temperature difference between the UAE and Georgia is $46\,^\circ\text{C}$.

Financial Applications and Scenario Justification ("You Do")

• Part A Calculations:

  • First step operation: $-60 + 100 = 40\,\text{AED}$
  • Second step operation: $40 - 15 = 25\,\text{AED}$

• Part B Disagreement Statement & Reasoning:

  • Position: Disagree
  • Justification: Depositing $80\,\text{AED}$ and withdrawing $5\,\text{AED}$ yields a net balance of $15\,\text{AED}$, not $2\,\text{AED}$.

• Scenario Generation to Justify Target Balance:

  • Objective: Construct a specific transaction scenario resulting in a final balance of $2\,\text{AED}$.
  • Parameters:
  • Opening Balance: $25\,\text{AED}$
  • Deposit Amount: $80\,\text{AED}$
  • Withdrawal Amount: $103\,\text{AED}$
  • Step-by-Step Calculation:
  1. Calculate total funds after deposit:        $80 + 25 = 105\,\text{AED}$
  2. Subtract total withdrawal amount:        $105 - 103 = 2\,\text{AED}$
  • Narrative Explanation:
  • To obtain a final balance of $2\,\text{AED}$, add the deposit of $80\,\text{AED}$ to the opening balance of $25\,\text{AED}$ (totaling $105\,\text{AED}$), and then withdraw $103\,\text{AED}$.
  • Final Balance Result: $2\,\text{AED}$

Error Analysis: Subtracting Negative Integers ("Spot the Mistake")

• Incorrect Problem Statement:

  • $-12 - (-4) = -16$

• Mathematical Rule:

  • Subtracting a negative integer is equivalent to adding its absolute value (positive counterpart):     $a - (-b) = a + b$

• Corrected Calculation:

  • $-12 - (-4) = -12 + 4 = -8$

• Correct Final Answer:

  • $-8$

Assessment and Administrative Details

• Peer Evaluator: Sarah
• Date of Assessment: $3/9/26$
• Continuation Marker: NP \rightarrow