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Welcome to Integers! – Understanding Integers Integers include whole numbers, zero, and negatives – Defining Integers Integers are like counting numbers, but they also include negative numbers and zero – Real-life Integer Examples Elevation, temperatures below zero, bank debts – Graphing on Number Lines Use horizontal and vertical lines to plot integers | This slide introduces the concept of integers to seventh-grade students. Begin by explaining that integers are not just the counting numbers they are familiar with, but also include their opposites (negative numbers) and zero. Provide relatable examples such as elevation (above and below sea level), temperatures (especially those below zero), and financial concepts like debts (owing money) to illustrate integers in real life. Then, demonstrate how to graph these integers on both horizontal and vertical number lines, emphasizing the placement of positive and negative numbers relative to zero. Encourage students to think of other examples where they encounter integers in their daily lives.

Exploring Number Lines – Define a number line – A visual representation of numbers in order – Key components of a number line – Includes origin, scale, positive and negative direction – Plot points on a horizontal line – Locate and mark integers on the line – Practice with examples – Use real-life values for hands-on learning | A number line is a straight line with numbers placed at equal intervals along its length. It’s an essential tool in mathematics for representing numbers and understanding their relationships. Key components include the origin (zero point), scale (distance between numbers), and direction indicators for positive and negative values. When plotting points, students should identify the value’s position relative to the origin. Encourage students to practice by plotting real-life values, such as temperatures or elevations, to reinforce the concept. This slide will help students visualize and comprehend the placement of integers on a number line, a foundational skill in math.

Positive and Negative Numbers on Graphs – Understanding Positive Numbers – Positive numbers are to the right of zero on a number line – Exploring Negative Numbers – Negative numbers are to the left of zero on a number line – Graphing on a Number Line – Plot points on horizontal and vertical lines to represent integers – Real-world Examples – Temperatures, elevations, and bank balances use positive and negative numbers | This slide introduces students to the concept of positive and negative numbers and their representation on number lines. Positive numbers, located to the right of zero, represent quantities greater than zero. Negative numbers, found to the left of zero, represent quantities less than zero. Students will learn to graph these numbers on both horizontal and vertical number lines, which is a fundamental skill in mathematics. Real-world examples, such as temperatures above and below freezing, elevations above and below sea level, and positive and negative bank balances, will help students understand the practical applications of these concepts. Encourage students to think of additional examples and to practice plotting integers on number lines.

Graphing Integers on a Horizontal Line – Plotting integers on a number line – Each point on the line represents an integer, with 0 at the center – Example: Graph +3, -2, 0 – Place +3 to the right of 0, -2 to the left, and 0 remains at the center – Class activity: Graph integers – Students will choose their own integers and plot them on a number line | This slide introduces students to the concept of graphing integers on a horizontal number line. Start by explaining that the number line is a visual representation of numbers in order, with positive numbers to the right of zero and negative numbers to the left. Use the example of +3, -2, and 0 to show how integers are plotted. For the class activity, provide each student with a number line and ask them to select a set of integers to graph. This will help them understand the relative position of integers. Possible activities include graphing their age, the temperature from different days, or points scored in a game.

Exploring Vertical Number Lines – Introduction to vertical number lines – A vertical number line goes up and down, with positive numbers up and negative numbers down. – Horizontal vs. vertical lines – Horizontal lines stretch left to right; vertical lines are perpendicular to them. – Appropriate use of vertical lines – Use vertical lines for data that changes over time, like temperature. – Practice plotting on vertical lines – Let’s plot points like 5, -3, and 0 on a vertical number line. | This slide introduces students to vertical number lines, a key concept for understanding how integers can be represented graphically. Start by explaining the orientation of vertical number lines and how they differ from horizontal ones. Emphasize that vertical lines are particularly useful for displaying data that changes over time, such as temperature throughout the day. Encourage students to practice plotting integers on vertical number lines to solidify their understanding. Provide examples and guide them through plotting positive, negative, and zero. This will prepare them for interpreting more complex data representations in future lessons.

Graphing Integers on a Vertical Number Line – Steps to graph integers vertically – Locate zero, plot positive numbers up, negatives down – Example: Graph +5, -4, 0 on vertical line – Start at zero, move up for +5, down for -4, stay for 0 – Class activity: Graph a set of integers – Choose different integers, graph them, and explain your work | This slide introduces students to the concept of graphing integers on a vertical number line. Begin by explaining the steps: starting at zero, moving upwards for positive integers, and downwards for negative integers. Use the example of +5, -4, and 0 to demonstrate how to plot these points on the vertical line. For the class activity, instruct students to select their own set of integers and graph them on a vertical number line. They should be prepared to explain their graphing choices. Provide guidance on how to determine the direction and distance from zero for each integer. This activity will help solidify their understanding of positive and negative values in a visual and interactive way.

Comparing and Ordering Integers – Compare integers on a number line – Use the number line to determine which integers are larger or smaller – Order integers from least to greatest – List integers in ascending order – Class activity: arrange integers – Students will arrange a mixed set of integers on a number line | This slide introduces the concept of comparing and ordering integers using a number line, which is a visual tool that helps students understand the relative position of numbers. Start by explaining how to compare integers by looking at their placement on the number line; numbers to the right are greater, and to the left are smaller. Then, guide students on how to order a list of integers from the smallest to the largest. For the class activity, provide a mixed set of integers and have students place them on a number line they draw. This hands-on activity will reinforce their understanding of the concepts. Possible variations of the activity could include using positive and negative integers, using larger numbers, or timing the activity for a fun challenge.

Class Activity: Number Line Race – Pair up for a graphing challenge – Receive a list of integers to graph – Graph integers on number lines – Use horizontal or vertical number lines – Compete to finish first with accuracy – Check each other’s work for correctness | This activity is designed to be a fun and interactive way for students to practice graphing integers on both horizontal and vertical number lines. Students will work in pairs to encourage collaboration. Each pair will receive a list of integers that they must graph correctly on a number line. The first pair to finish graphing all integers accurately will be declared the winners. As a teacher, ensure that each pair has a number line template and a set of integers. Monitor the class to ensure fair play and correct graphing techniques. Possible variations of the activity could include using different sets of integers for each pair, timing the activity for added challenge, or having a tournament-style competition with multiple rounds.

Review and Reflection: Number Lines – Recap of today’s lesson – We learned to plot integers on number lines. – Significance of number lines – Number lines help visualize numerical relationships. – Real-life application of number lines – Use in navigation, temperature reading, and finances. | Today’s class focused on understanding how to graph integers on both horizontal and vertical number lines. We discussed the importance of number lines in mathematics as a fundamental tool to visualize and understand the relationship between numbers. Number lines are crucial in many real-life situations, such as navigating using a map, reading temperatures on a thermometer, or managing finances by understanding debts and credits. Encourage students to reflect on how the lesson can be applied outside the classroom and to come up with their own examples of number lines in daily life. This reflection will help solidify their understanding and see the practical value of the concepts learned.

Homework: Graphing Integers & Real-Life Application – Graph integers on number lines – Plot -10, -5, 0, 5, 10 on both horizontal and vertical lines – Reflect on integers in daily life – Consider how you use positive and negative numbers every day – Write a paragraph on integer usage – Share examples like temperature changes or bank transactions – Study for a quiz on number lines | This homework assignment is designed to reinforce students’ understanding of graphing integers on number lines and to help them recognize the practical applications of integers in everyday life. Students should graph the given integers on both horizontal and vertical number lines to visualize positive and negative values. Encourage them to think critically about how integers appear in daily activities, such as reading temperatures or managing allowances. The paragraph writing will help them articulate their understanding. Lastly, remind students to review the concepts of number lines to prepare for the upcoming quiz. Provide examples and practice problems in class to ensure they are well-prepared.