Comparing positive and negative integers worksheet

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.”

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

• 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.

Comparing Positive and Negative Integers Worksheet

Objective: The objective of this worksheet is to help students understand and practice comparing positive and negative integers. They will learn to use comparison symbols (>, <, and =) to express the relationships between these numbers.

Worksheet Structure:

Part 1: Comparing Positive Integers

• In this section, students will compare positive integers with other positive integers.

Instructions:

1. a. Compare 5 and 3. Use the “>” symbol if the first number is greater, “<” if the second number is greater, and “=” if they are equal. Explanation: 5 > 3, so write “5 > 3.”b. Compare 8 and 8. Explanation: 8 and 8 are equal, so write “8 = 8.”c. Compare 12 and 15. Explanation: 12 < 15, so write “12 < 15.”

Part 2: Comparing Negative Integers

• In this section, students will compare negative integers with other negative integers.

Instructions: 2. a. Compare -4 and -6. Explanation: -4 > -6, so write “-4 > -6.”

b. Compare -9 and -9. Explanation: -9 and -9 are equal, so write “-9 = -9.”

c. Compare -2 and -1. Explanation: -2 < -1, so write “-2 < -1.”

Part 3: Comparing Positive and Negative Integers

• In this section, students will compare positive integers with negative integers.

Instructions: 3. a. Compare 7 and -5. Explanation: 7 > -5, so write “7 > -5.”

b. Compare -3 and 2. Explanation: -3 < 2, so write “-3 < 2.”

c. Compare -8 and 8. Explanation: -8 < 8, so write “-8 < 8.”

Instructions: 4. a. The temperature today is -3 degrees Celsius, and yesterday it was 5 degrees Celsius. Write an expression to compare today’s temperature to yesterday’s temperature. Use the appropriate comparison symbol. Explanation: Today’s temperature (-3) is less than yesterday’s temperature (5), so write “-3 < 5.”

b. A car gained 15 meters in altitude, and then it lost 20 meters. Write an expression to compare the car’s final altitude after gaining and losing altitude. Use the appropriate comparison symbol. Explanation: The final altitude (-5 meters) is less than the initial altitude (0 meters), so write “-5 < 0.”