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Here is a 15-minute lesson for the Math-Aids Understanding Integers Worksheets that includes integer representation, absolute value, opposites, comparing and ordering integers, and addition, subtraction, multiplication, and division.

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15-Minute Math Lesson Plan: Understanding and Working with Integers

Understanding and Working with Integers

Grade Level: Grades 6–7
Time: 15 minutes
Topic: Integer Operations

Learning Objective

Students will understand positive and negative integers and apply the correct rules when adding, subtracting, multiplying, and dividing integers.

Materials

1. Warm-Up (3 minutes)

Explain that integers include positive numbers, negative numbers, and zero.

Write these numbers on the board:

  • +5

  • -3

  • 0

  • -8

  • +2

Ask students to arrange them from least to greatest.

Answer: -8, -3, 0, +2, +5

Explain:

  • Positive numbers are greater than zero.

  • Negative numbers are less than zero.

  • The farther a negative number is from zero, the smaller its value.

Introduce absolute value, which represents a number's distance from zero.

Examples:

  • |-5| = 5

  • |+7| = 7

  • |0| = 0

2. Teacher Modeling (4 minutes)

Review the rules for adding, subtracting, multiplying, and dividing integers.

A. Adding Integers

When the signs are the same, add the numbers and keep the sign.

Example:

(-4) + (-3) = -7

When the signs are different, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the greater absolute value.

Example:

(-8) + (+5) = -3

B. Subtracting Integers

Change subtraction to adding the opposite.

Example:

7 - (-3)

Change to:

7 + 3 = 10

Another example:

(-5) - (+2)

Change to:

(-5) + (-2) = -7

C. Multiplying and Dividing Integers

Use these sign rules:

  • Positive × Positive = Positive

  • Negative × Negative = Positive

  • Positive × Negative = Negative

  • Negative × Positive = Negative

The same sign rules apply to division.

Examples:

(-4) × (+3) = -12

(-20) ÷ (-5) = +4

Explain that multiplying or dividing two numbers with the same sign produces a positive answer. Different signs produce a negative answer.

3. Guided Practice (3 minutes)

Work through these problems together.

Problem 1:

(-6) + (+9) = ?

Different signs: subtract 9 - 6 = 3.

Keep the positive sign.

Answer: +3

Problem 2:

(-8) - (-3) = ?

Change subtraction to adding the opposite:

(-8) + (+3) = -5

Answer: -5

Problem 3:

(-5) × (-4) = ?

Same signs produce a positive answer.

5 × 4 = 20

Answer: +20

Problem 4:

(+24) ÷ (-6) = ?

Different signs produce a negative answer.

24 ÷ 6 = 4

Answer: -4

Ask students to explain which rule they used for each problem.

4. Independent Worksheet Practice (3 minutes)

Have students complete several problems from the Math-Aids Integers worksheets.

Choose the worksheet that matches the skill being practiced:

  • Representation of Integers: Translate written situations into positive or negative numbers.

  • Absolute Value: Find the distance of an integer from zero.

  • Opposite Value: Identify the opposite of a given integer.

  • Comparing Integers: Use greater-than and less-than symbols to compare numbers.

  • Greatest / Smallest Integers: Identify the largest or smallest number in a group.

  • Arranging Orders of Integers: Put integers in increasing or decreasing order.

  • Addition Integers: Practice adding two, three, or four integers.

  • Subtraction Integers: Practice subtracting positive and negative numbers.

  • Multiplication and Division Integers: Apply the sign rules.

  • Mixed Problems: Practice all four operations.

Encourage students to write down the rule they used before solving each problem.

5. Exit Ticket (2 minutes)

Ask students to solve these three problems independently.

  1. (-7) + (+4) = -3

  2. 6 - (-5) = 11

  3. (-3) × (+6) = -18

Ask students to explain why the answer to the third problem is negative.

Differentiation

Support: Provide a number line and an integer rules reference sheet. Begin with positive and negative numbers within 10. Practice addition and subtraction before introducing multiplication and division.

Extension: Give students mixed integer problems involving multiple operations. Ask them to explain each step and apply the order of operations.

Common Misconceptions

  • Thinking negative numbers are always smaller based on their digits: Remind students that -9 is smaller than -3.

  • Confusing subtraction with adding a negative: Teach students to change subtraction into addition of the opposite.

  • Forgetting the sign rules: Have students identify whether the signs are the same or different before multiplying or dividing.

  • Confusing absolute value with the opposite: Absolute value is distance from zero; the opposite is the same distance on the other side of zero.

Assessment

Review student responses during guided practice and check their independent worksheet work and exit ticket.

Success Criteria: Students can identify positive and negative integers, compare and order integers, and correctly apply integer rules when solving basic operations.

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Posted 11/14/26

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