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Welcome to Integers! – Understanding Integers – Integers include whole numbers and their negatives – Defining Integers – Integers are like… -3, -2, -1, 0, 1, 2, 3 – Real-life Integer Examples – Elevator floors below ground, temperatures below zero – Graphing on Number Lines – Plotting integers on lines shows their order and value | Introduce the concept of integers as a broader category of numbers that includes all whole numbers and their negatives, not just the positive numbers students are familiar with. Emphasize that zero is also an integer. Provide relatable examples such as temperatures, especially when they fall below zero, or floors in a building that are below ground level to illustrate negative integers. Explain how graphing integers on a horizontal or vertical number line can help visualize their order and relative value. Encourage students to think of other examples where they encounter integers in their daily lives. This will set the foundation for understanding how to work with integers in various mathematical operations.

Exploring Number Lines with Integers – Define a number line – A visual representation of numbers in order – Identify components of a number line – Consists of a straight line with tick marks and numbers – Plot positive numbers – Positive numbers are to the right of zero – Plot negative numbers – Negative numbers are to the left of zero | A number line is a fundamental concept in mathematics that visually represents numbers as points on a straight line. Each point corresponds to a number, and the distance between the points is always equal, representing the numerical difference. The components of a number line include the line itself, tick marks, and numbers, with zero typically in the center. Positive numbers are located to the right of zero, while negative numbers are to the left. When plotting integers on a number line, it’s crucial to understand the direction and relative position of numbers. This slide will help students grasp the basics of number lines and how to represent positive and negative integers graphically. Encourage students to practice by plotting various integers on both horizontal and vertical number lines to solidify their understanding.

Graphing Integers on a Horizontal Line – Graphing integers step-by-step – Start at zero, move left for negatives, right for positives – Plotting points: a hands-on approach – Use a ruler for accuracy, mark points clearly – Practice Example: -3, 0, and 4 – Let’s plot -3, 0, and 4 on the line and discuss | This slide introduces students to the concept of graphing integers on a horizontal number line. Begin by explaining the number line, with zero in the center, positive numbers to the right, and negative numbers to the left. Demonstrate how to plot integers by starting at zero and moving to the appropriate location. Use a practice example with -3, 0, and 4 to show students how to graph integers in a sequence. Encourage students to use a ruler for precision when drawing their own number lines. After plotting, discuss how the distance from zero represents the absolute value of the integer. This activity will help solidify their understanding of integers in a visual and interactive way.

Graphing Integers on a Vertical Line – Plotting integers vertically – Place integers on a vertical number line with positive numbers up and negative numbers down – Vertical vs. Horizontal lines – Horizontal lines run left-right; vertical lines run up-down – Practice: Graph 2, -5, 1 – Let’s locate 2, -5, and 1 on a vertical line and discuss their positions | This slide introduces students to the concept of graphing integers on a vertical number line. Begin by explaining that on a vertical line, numbers increase as we move up and decrease as we move down. Contrast this with a horizontal number line where numbers increase from left to right. Provide a practice example with the integers 2, -5, and 1, and guide students through plotting these on a vertical number line. Emphasize the difference in directionality between horizontal and vertical lines and ensure students understand that the position of the number corresponds to its value. Encourage students to think about real-life examples such as elevators or thermometers that use vertical number lines.

Understanding Coordinates on the Plane – Explore the coordinate plane – A flat surface with two number lines: horizontal (X-axis) and vertical (Y-axis) – Learn about the X-axis and Y-axis – X-axis is horizontal, Y-axis is vertical. Together, they divide the plane into four quadrants – How to plot points with coordinates – Each point is defined by an (x, y) pair showing its position on the plane – Practice plotting integers – Use integer pairs to mark points on the grid and see their locations | This slide introduces students to the basics of the coordinate plane, which is an essential concept in graphing integers. Start by explaining the two perpendicular lines, the X-axis (horizontal) and the Y-axis (vertical), and how their intersection creates a reference point called the origin. Emphasize that every point on the plane is determined by an (x, y) coordinate pair, where ‘x’ represents the position along the X-axis and ‘y’ represents the position along the Y-axis. Provide examples of plotting points with positive and negative integers, and encourage students to practice by plotting given integer pairs to reinforce their understanding. This foundational knowledge will be crucial for their future studies in algebra and geometry.

Class Activity: Number Line Challenge – Create your own number lines – Engage in Graphing Integers Race – A fun race to plot integers accurately and quickly – Pair up and plot integers – Use horizontal or vertical lines to graph given numbers – Discuss findings with the class | This interactive class activity is designed to help students understand the concept of graphing integers on number lines. Provide each student with a blank number line template or have them draw their own on graph paper. Organize a ‘Graphing Integers Race’ where pairs of students compete to accurately plot given integers on their number lines the fastest. After the activity, facilitate a discussion where students can share their number lines and reflect on the experience. This will reinforce their understanding of positive and negative integers in a visual and engaging way. Possible variations of the activity could include plotting integers in ascending or descending order, or finding the distance between integers on the number line.

Wrapping Up: Integers on Number Lines – Review of graphing integers – Significance of integer concepts – Homework: Graph integers on a line – Plot -10, -3, 0, 7, 12 on a number line – Be prepared to discuss your work – Think about the distance between points | As we conclude today’s lesson, it’s important to recap the process of graphing integers on both horizontal and vertical number lines. Understanding integers and their placement is crucial for future math concepts. For homework, students are to graph the integers -10, -3, 0, 7, and 12 on a number line, which will reinforce their learning from today. Encourage them to consider the relative distance between each integer and zero. In the next class, we will discuss their findings, which will help solidify their understanding and provide an opportunity for addressing any misconceptions.