Creating a “Comparing Positive and Negative Integers Worksheet” is a fundamental tool for helping students understand the concepts of greater than (>) and less than (<) when dealing with positive and negative numbers. Here’s a detailed description of how to create and use such a worksheet:

Worksheet Title: Comparing Positive and Negative Integers Worksheet

Objective: The goal of this worksheet is to help students practice comparing positive and negative integers. They will learn how to use the greater than (>) and less than (<) symbols to express relationships between these numbers.

Worksheet Structure:

Part 1: Introduction to Integer Comparisons

• Begin with a brief explanation of how positive and negative integers are ordered on the number line. Emphasize that numbers to the right are greater, while numbers to the left are lesser.

Instructions:

1. Comparing Numbers on the Number Line
   • Label a number line with positive and negative integers.
   • Ask students to identify which numbers are greater and which are lesser.
   • Provide examples like -5 < 3 and -3 > -7.

Part 2: Comparing Individual Integers

• In this section, students will compare individual positive and negative integers using the greater than (>) and less than (<) symbols.

Instructions: 2. a. Compare 4 and -2. Explanation: Since 4 is greater than -2, write 4 > -2.

b. Compare -8 and -12. Explanation: Since -8 is greater than -12, write -8 > -12.

c. Compare -1 and 0. Explanation: Since -1 is less than 0, write -1 < 0.

Part 3: Comparing Integer Expressions

• Students will compare algebraic expressions involving positive and negative integers using comparison symbols.

Instructions: 3. a. Compare -3 + 6 and 4 – 1. Calculation: -3 + 6 = 3, 4 – 1 = 3 Explanation: Since -3 + 6 is equal to 4 – 1, write -3 + 6 = 4 – 1.

b. Compare 5 – 7 and -2 + 1. Calculation: 5 – 7 = -2, -2 + 1 = -1 Explanation: Since -2 + 1 is greater than 5 – 7, write -2 + 1 > 5 – 7.

Part 4: Word Problems

• Provide real-world scenarios that involve comparing positive and negative integers. Students will translate these situations into mathematical expressions, evaluate them, and use comparison symbols to express relationships.

Instructions: 4. a. You borrowed $20 from a friend, and you have paid back $12. Write an expression to represent the amount you still owe and compare it to $10. If you owe more, write “Owe > $10”; otherwise, write “Owe < $10.”

Explanation: The expression for the amount you still owe is $20 – $12. If $20 – $12 > $10, it means you owe more, so write “Owe > $10.” If $20 – $12 ≤ $10, it means you owe less or equal to $10, so write “Owe < $10.”

Answer Key:

• Provide answers and explanations for each part of the worksheet, including comparisons and evaluations.

Additional Notes:

• Encourage students to show their work and write out the calculations for each part of the worksheet.
• Review the answers as a class, discuss any misconceptions, and provide additional examples if needed.
• Use this worksheet as a formative assessment to gauge students’ comprehension of comparing positive and negative integers.