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Multiplying by a Negative Integer – Understanding integers – Integers include whole numbers, zero, and negatives – Positive vs. negative numbers – Positive numbers are above zero, negatives are below – Multiplying integers on a number line – Use a number line to visualize multiplication steps – Rules for multiplication with negatives – Multiplying a positive by a negative gives a negative | This slide introduces students to the concept of integers and their operations, focusing on multiplication. Begin by explaining what integers are, including the distinction between positive and negative numbers. Emphasize that zero is neutral. Then, demonstrate how to multiply integers using a number line, which helps visualize the process as a series of ‘hops’ in the positive or negative direction. Highlight the rule that multiplying a positive number by a negative results in a negative product. Use examples like temperature changes or financial transactions to illustrate these concepts. Encourage students to practice with simple examples to build confidence.

Multiplying with a Number Line – What is a number line? – A straight line with numbers placed at equal intervals. – Visualizing numbers in order – It helps us see how numbers compare to each other. – Understanding integer operations – A way to visualize adding, subtracting, multiplying, and dividing. – Practice with negative integers – Let’s multiply -2 by 3 using a number line step by step. | Introduce the concept of a number line as a foundational tool in mathematics for visualizing and understanding the order and spacing of numbers. Emphasize its usefulness in performing operations with integers, particularly multiplication with negative numbers. Demonstrate how to use a number line to multiply a negative integer by a positive one, showing the movement in the opposite direction and the resulting product. Provide examples and encourage students to draw their own number lines for practice. This visual approach will help solidify their understanding of negative number multiplication.

Multiplying Integers on a Number Line – Multiplication with positives – Positive factors increase value – Multiplication with negatives – Negative factors decrease value – Effects of negative factors – Negative x Positive = Negative – Observing product changes – Negative x Negative = Positive | This slide introduces students to the concept of multiplication with integers, emphasizing the difference between multiplying with positive and negative numbers. Begin by explaining that multiplying with positive numbers is an additive increase, which they are familiar with. Then, introduce multiplying with negative numbers, highlighting that this is a concept of directional change on the number line, not just ‘making things bigger.’ Discuss how the product changes when we introduce negative factors, ensuring to illustrate with examples on the number line. For instance, multiplying a positive by a negative results in a negative product, while a negative times a negative gives a positive product. Use number line exercises to reinforce these concepts, allowing students to visualize the ‘jumps’ and direction changes that occur during multiplication.

Multiplying by a Negative Integer – Rules for negative multiplication – When multiplying, two negatives make a positive, a negative and a positive make a negative. – Example: 4 x (-3) using a number line – Starting at 0, move left 3 steps, 4 times. The product is -12. – The flip in direction explained – Multiplying by a negative flips the direction on the number line. – Practice with different examples – Try multiplying 5 x (-2) or -6 x (-3) on a number line. | This slide introduces the concept of multiplying by a negative integer. Begin by explaining the rules: a negative times a positive results in a negative, and a negative times a negative gives a positive. Use the number line to visually demonstrate 4 x (-3), showing that each multiplication step moves to the left instead of right, resulting in -12. Emphasize the ‘flip’ in direction when crossing zero. Encourage students to practice with different examples to solidify their understanding. Provide guidance on how to use the number line for these exercises and ensure they grasp the concept of direction change when dealing with negative numbers.

Let’s Practice Together: Multiplying Integers – Activity: Multiply integers on a number line – Example 1: Multiply (-2) by 3 – Starting at 0, move left 2 steps, repeat 3 times – Example 2: Multiply (-5) by (-4) – Starting at 0, move left 5 steps, repeat 4 times in the opposite direction – Discuss results with the class | This class activity is designed to help students visualize multiplication with negative integers using a number line. For the first example, students will see that multiplying a negative by a positive moves us left on the number line. For the second example, they’ll learn that multiplying two negatives results in a positive, as they’ll move in the opposite direction. Encourage students to draw their own number lines and mark the movements as they perform the multiplication. After completing the examples, have a discussion about the patterns they noticed and how the direction on the number line changes with different signs. Possible activities include pairing up students to create more examples, using manipulatives to represent the integers, or creating a human number line in the classroom.

Multiplying by Negative Integers: Real-Life Applications – Understanding temperature changes – Subtracting degrees can be seen as multiplying by a negative number – Financial gains and losses – Earning money is positive, while spending is like multiplying by a negative – Elevation: Above and below sea level – Sea level as the starting point, going up (positive) or down (negative) – How negatives affect daily life | This slide aims to show students how multiplying by negative integers is relevant in everyday life. For temperature, illustrate how dropping 10 degrees each hour can be represented on a number line. In finances, explain that gaining money moves you one direction on the number line, while losing money moves you in the opposite direction, akin to multiplying by a negative. For elevation, use a number line to show how going above sea level is positive, while going below is negative. Emphasize that understanding these concepts is crucial for interpreting real-world situations involving negative numbers.

Class Activity: Number Line Hopscotch – Create a floor number line – Mark integers with paper or tape – Play Hopscotch Multiplication – Hop on the number line to multiply – Understand negative integer multiplication – Use the game to visualize negative integer multiplication | This interactive class activity is designed to help students visualize and understand the concept of multiplying by a negative integer using a number line. Start by creating a large number line on the classroom floor using paper or tape. Mark the integers clearly. Students will then play a game of hopscotch where they hop along the number line to simulate the multiplication of integers. For example, to multiply -2 by 3, a student will start at zero, hop two spaces to the left three times, and land on -6. This physical activity helps students grasp the concept of negative direction on the number line and the rules of multiplication with negative numbers. Prepare to guide students through several examples and ensure they can explain the process during the activity.

Review and Questions: Multiplying on a Number Line – Recap of multiplying by negatives – Ask your questions now What did you find interesting or difficult today? – Share any confusions Let’s clarify any part of the lesson that was tricky. – Discuss challenges faced We’ll tackle any problems together. | This slide is meant to conclude the lesson on multiplying by a negative integer using a number line. Begin by summarizing the key points of the lesson, ensuring that students understand the concept of direction change on the number line when multiplying by a negative number. Open the floor to students, encouraging them to ask questions about any aspect of the lesson they found challenging or intriguing. Address any misconceptions or difficulties students may have encountered during the lesson. This is also an opportunity to assess understanding and to provide additional support where needed. Encourage students to think critically about the steps involved in multiplying by a negative integer and to articulate their thought process.

Homework: Multiplying Integers on a Number Line – Complete the practice worksheet – Use a number line for 10 problems – Visualize how numbers move left when multiplied by a negative – Understand negative integer multiplication – Negative times a positive equals a negative number – Get ready for a quiz next class | This homework assignment is designed to reinforce the concept of multiplying by a negative integer using a number line. Students are expected to complete a worksheet that provides practice problems, ensuring they understand how to visualize multiplication with negative numbers. Emphasize the importance of using a number line to see the direction and distance numbers move with each multiplication. This will help solidify their understanding that when a positive number is multiplied by a negative, the result is negative. Remind students to prepare for a quick quiz during the next class to assess their grasp of the concept. Provide examples and encourage students to ask questions if they encounter difficulties while completing the worksheet.