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Recap: Understanding Integers – Integers: Positive, negative, and zero – Integers are whole numbers without fractions or decimals – Integers on the number line – Visualize integers as points on a line where zero is the center – Examples of integers – 3, -76, and 0 are integers – Non-examples to clarify – 1/2, 3.5, and pi are not integers | This slide is a quick recap of what integers are, aimed at helping students recall the basics before moving on to more complex topics like integer inequalities with absolute values. Integers are the set of whole numbers that include all positive numbers, negative numbers, and zero. They can be visualized on the number line, which helps in understanding their order and the concept of absolute value. Provide clear examples of integers, such as 3, -76, and 0, and contrast them with non-examples like fractions and decimals to reinforce the concept. This foundation is crucial for understanding subsequent lessons on inequalities involving these numbers.

Understanding Absolute Values – Absolute value: distance from zero – Always positive or zero – Example: |3| equals 3 – Absolute value of 3 is 3 units from 0 on the number line – Example: |-5| equals 5 – Absolute value of -5 is 5 units from 0, despite being negative | This slide introduces the concept of absolute values, which is foundational for understanding integer inequalities with absolute values. Emphasize that absolute value is the distance a number is from zero on the number line, which means it is always non-negative. Use a number line diagram if possible to visually demonstrate this concept. Provide clear examples with both positive and negative integers to show that regardless of the direction, the absolute value is positive. Encourage students to think of absolute value as ‘how far, not which direction’. Prepare to explain how this concept applies when comparing integers and solving inequalities in subsequent lessons.

Understanding Integer Inequalities – Inequalities explained – Inequalities show how numbers compare – Inequality symbols and meaning – Symbols: > (greater), < (less), e (greater or equal), d (less or equal) – Plotting integers on a number line – Use a number line to visualize integer positions and compare – Solving inequalities with absolute values – Absolute values affect solutions; |x| < 3 means x is within 3 units of 0 | This slide introduces the concept of inequalities, which are statements about the relative size or order of two numbers. It’s crucial to explain each symbol and what it represents. Use a number line to give a visual representation of inequalities, which can help students understand how integers are positioned relative to each other. When introducing absolute values, ensure to clarify that they represent the distance from zero, which can change how inequalities are solved. Provide examples like |x| < 3 to show that x can be any integer within 3 units of 0 on the number line, such as -2, -1, 0, 1, or 2.

Inequalities with Absolute Values – Combining absolute values & inequalities – Reading & writing absolute inequalities – Example: |x| 2 – x is more than 2 units from 0 on a number line | This slide introduces students to the concept of combining absolute values with inequalities. Absolute value represents the distance of a number from zero on the number line, regardless of direction. When combined with inequalities, it shows the range of numbers that satisfy the condition. For example, |x| 2 means x is any number more than 2 units away from zero, such as -5, -4, 3, or 6. Encourage students to visualize these concepts on a number line and provide additional examples to solidify their understanding.

Class Activity: Inequality Match-Up – Group matching activity – Receive inequality & solution cards – Discuss to find correct matches – Talk about why each solution fits the inequality – Collaborate with team members – Work together to solve problems | This interactive group activity is designed to help students understand integer inequalities with absolute values. Divide the class into small groups and provide each group with a set of cards, some with inequalities and others with possible solutions. Students will discuss within their groups to match each inequality with its correct solution. Encourage them to explain their reasoning for each match to reinforce their understanding. As a teacher, circulate around the room to guide discussions and offer hints if necessary. Possible activities for different groups could include matching inequalities to word problems, real-life scenarios, or graphical representations. This will cater to different learning styles and keep the activity dynamic.

Integer Inequalities with Absolute Values – Solve individual inequalities – Discuss solutions as a class – Teacher-guided problem review – The teacher will explain solutions and methods – Understand absolute value concepts – Absolute values measure distance from zero | This slide is focused on class activity where students will individually work on solving inequalities involving absolute values. After attempting the problems, students will share their solutions with the class to foster collaborative learning. The teacher will then provide a guided explanation for each problem, ensuring that students understand the correct approach and where they might have made mistakes. Emphasize the concept of absolute value as the distance from zero on a number line, which remains positive. Encourage students to ask questions during the review. Possible activities include solving |x – 3| > 7, |2x + 5| <= 10, and interpreting the solutions in the context of real-world scenarios.