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Multiplying by a Negative Integer – Integers in daily life – Integers represent gains/losses, temperatures, etc. – Recap: What are integers? – Integers include positive, negative numbers, and zero – Focus: Multiplying by a negative – Understand the rules for multiplication with negatives – Using a number line – Visualize how negative multiplication works step by step | This slide introduces the concept of multiplying by a negative integer, which is a key part of understanding operations with integers. Start by discussing how integers are used in everyday life, such as in financial transactions (gains and losses) or measuring temperatures (above/below zero). Recap the definition of integers as a set that includes positive numbers, negative numbers, and zero. The main focus of today’s lesson is to understand the rule that multiplying by a negative integer inverts the sign of the product. Use a number line to visually demonstrate this concept, showing how each step of multiplication by a negative moves in the opposite direction. Encourage students to think of real-life scenarios where this might apply, and prepare them for practice problems where they will apply this rule.

Multiplying with Negative Integers – Multiplication: Repeated addition – Positive vs. Negative numbers – Positive numbers increase value; negative numbers decrease value. – Multiplying with a number line – Use a number line to visualize adding a negative number repeatedly. – Examples of negative multiplication – E.g., 3 x -2: Start at 0, move left 2 steps, repeat 3 times. | This slide introduces the concept of multiplication as repeated addition and how it applies to negative numbers. Emphasize that while positive numbers increase the value when multiplied, negative numbers will decrease the value. Demonstrate using a number line to show that multiplying by a negative number means moving to the left on the number line for each multiplication step. Provide clear examples, such as multiplying 3 by -2, and show the steps on a number line. Encourage students to visualize the process and practice with different examples to solidify their understanding.

Multiplying with a Number Line – Using a number line for multiplication – A number line can represent multiplication as repeated addition – Positive & negative direction on number line – Right for positive, left for negative direction – Multiplying positive numbers visually – Example: 3 x 2 is 3 steps to the right, starting from 0 – Practice with negative integers – How does multiplying by a negative integer differ? | This slide introduces the concept of using a number line to visualize multiplication, especially focusing on the multiplication of integers. Start by explaining how a number line can be used to represent multiplication as repeated addition. Clarify the directionality of the number line, with right representing positive and left representing negative. Show how to multiply positive numbers by taking steps to the right. Then, pose the question of how this process changes when multiplying by a negative integer, setting the stage for the next lesson where this will be explored in detail. Encourage students to think about the rules they’ve learned for adding and subtracting on the number line and how these might apply to multiplication.

Multiplying by a Negative Integer – Rules for negative multiplication – Multiplying by a negative flips the number’s sign – Visualize on a number line – A number line helps us see the flip in direction – Example: -1 x 3 – Starting at 0, move left 3 spaces for -1 x 3 – Practice with different numbers | This slide introduces the concept of multiplying by a negative integer. Begin by explaining the rules: when we multiply a positive number by a negative, the result is negative, and vice versa. Use a number line to visually demonstrate this concept, showing how multiplication by a negative integer results in a ‘flip’ in direction. For the concrete example, illustrate -1 x 3 by starting at zero and moving left on the number line three spaces to show the result of -3. Encourage students to practice with different numbers to solidify their understanding. Provide additional examples and encourage students to try creating their own number line examples.

Multiplying Negative Integers on a Number Line – Example 1: Multiplying -2 by 4 – Starting at 0, move left 4 steps, 2 times – Example 2: Multiplying 5 by -3 – Starting at 0, move left 3 steps, 5 times – Group Practice: Let’s solve together – Work in groups to practice multiplying – Guided Questions for Understanding – Why do we move left for negative numbers? | This slide is designed for a collaborative classroom activity to practice multiplying by a negative integer using a number line. Begin with two examples, illustrating the process on a number line. For -2 x 4, show that you start at zero and move left (the negative direction) 4 steps, two times, ending at -8. For 5 x -3, start at zero and move left 3 steps, five times, ending at -15. Then, have students form groups to practice similar problems, guiding them with questions to ensure they understand why the direction of movement on the number line changes with negative numbers. The goal is to reinforce the concept that multiplying by a negative number reverses the direction of the number line steps.

Multiplying by a Negative Integer – Why negative times positive is negative – Multiplying by a negative flips the number’s sign. – Inverse operations explained – Inverse operations undo each other, like addition and subtraction. – Negative multiplication in real life – Examples: debts or temperature drops. – Practice with number lines | This slide introduces the concept of multiplying by a negative integer. Start by explaining that when we multiply a positive number by a negative, the result is negative, which can be thought of as a ‘direction change’ on the number line. Then, discuss inverse operations, such as how multiplication and division are opposites and can reverse effects. Provide real-world scenarios, like accumulating debt (owing money) or temperature changes, to illustrate negative multiplication. Finally, encourage students to use number lines to visualize these concepts and solidify their understanding through practice.

Class Activity: Exploring Multiplication on a Number Line – Create your own number line – Solve multiplication problems – Multiply negative integers using your number line – Reflect on the patterns observed – Notice how multiplying by a negative affects direction on the line – Share solutions with the class | This activity is designed to help students visualize the process of multiplying by a negative integer using a number line. Students will create their own number lines with both positive and negative integers. They will then practice multiplying negative integers by positive and negative numbers and observe the patterns that emerge, such as the ‘sign flip’ rule. After individual work, students will be encouraged to share their solutions and discuss their observations with the class. This will reinforce their understanding and allow them to learn from each other’s insights. Possible activities include multiplying different pairs of integers, observing the effects of multiplying by -1, and predicting the product of two negative integers.

Homework and Previewing Next Steps – Complete the worksheet on number line multiplication – Preview the concept of dividing integers – Understand how division of integers extends our knowledge of multiplication – Review today’s key points – Summarize the process of multiplying by a negative integer – Bring any questions to the next class | For homework, students are expected to complete a worksheet that provides practice on multiplying integers using a number line, reinforcing today’s lesson. Looking ahead, students will begin exploring the division of integers, which builds on their understanding of multiplication. During the next class, we will review the key concepts covered today, ensuring that students are comfortable with the material before moving on. Encourage students to bring any questions they have to the next class for clarification. This approach helps to solidify their learning and prepares them for the upcoming topic.