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Introduction to Inequalities – Understanding inequalities – An inequality shows how values differ, like ‘x > 5’ means ‘x is more than 5’. – Inequalities vs. equations – Unlike equations, inequalities don’t show equality but a range of possible solutions. – Real-life inequality examples – Budgeting allowance, or minimum height for a ride show real-life inequalities. – Graphing on a number line | Begin with a basic definition of inequalities, emphasizing how they represent a range of possible solutions rather than a single answer like equations. Draw parallels and contrasts between equations and inequalities to solidify understanding. Use relatable examples such as budgeting a weekly allowance or requirements for riding a roller coaster to illustrate how inequalities are present in everyday life. Introduce the concept of graphing inequalities on a number line, which will be a visual aid for students to understand the solutions to inequalities. Encourage students to think of other real-life scenarios where inequalities apply.

Inequality Symbols in Word Problems – Understanding ‘>’ and ” means more than, ‘<' means less than – Meaning of 'e' and 'd' – 'e' includes the number, 'd' means up to and including – Significance of '`' – '`' shows that things are not the same – Applying inequalities in problems – Use symbols to represent real-world situations | This slide introduces students to the basic inequality symbols and their meanings, which are essential for solving and graphing inequalities in word problems. Begin by explaining the symbols for greater than (>) and less than (<), and then move on to greater than or equal to (e) and less than or equal to (d), emphasizing that the 'equal to' part includes the number itself. Discuss the not equal to (`) symbol and its importance in representing situations where quantities are not the same. Finally, illustrate how these symbols can be used to represent real-world situations, such as comparing amounts of money, weights, or distances. Encourage students to think of examples where they might use these symbols in their daily lives.

Writing Inequalities from Word Problems – Identify keywords in problems – Look for ‘at least’, ‘maximum’, ‘greater than’ – Translate words to inequalities – Convert phrases into symbols like >, <, e, d – Practice with 'At least' – 'At least' means a minimum, so use e – Practice with 'No more than' – 'No more than' implies a maximum, so use d | This slide introduces students to the concept of writing inequalities from word problems. Start by explaining how to identify keywords that indicate inequality, such as ‘at least’ for a minimum value or ‘no more than’ for a maximum value. Teach students how to translate these phrases into mathematical symbols. Provide practice examples using common phrases like ‘at least’ and ‘no more than’, and guide students through the process of converting them into inequalities. Encourage students to solve these inequalities and graph them on a number line. This will help solidify their understanding of how inequalities represent ranges of possible values in real-world situations.

Graphing Inequalities on a Number Line – Plotting with open/closed circles – Open circle for ‘>’, closed for ‘d’ or ‘e’ – Shading the solution set – Shade right for ‘>’, left for ‘d’ – Graphing x > 5 – Open circle at 5, shade to the right – Graphing x d 3 – Closed circle at 3, shade to the left | This slide introduces students to graphing inequalities on a number line, a key concept in understanding one-variable inequalities. Start by explaining the difference between open and closed circles: open circles represent ‘greater than’ (>) or ‘less than’ ( 5 and x d 3 as concrete examples. For x > 5, place an open circle at 5 and shade to the right to show all numbers greater than 5. For x d 3, place a closed circle at 3 and shade to the left to include 3 and all numbers less than 3. Encourage students to practice with additional examples.

Solving Inequality Word Problems – Understand the problem’s question – What is the problem asking us to find? – Translate words into an inequality – Convert the problem’s words into a mathematical inequality – Solve the inequality step-by-step – Use inverse operations to find the variable’s value – Check solution with substitution – Replace the variable with your solution to verify it works | This slide is aimed at guiding students through the process of solving word problems that involve inequalities. Start by ensuring students understand the question being asked in the problem. Next, teach them to translate the words of the problem into a mathematical inequality, identifying keywords that indicate inequality (e.g., ‘at least’, ‘no more than’). Show them how to solve the inequality using step-by-step inverse operations. Finally, demonstrate how to check their solution by substituting the variable with the value they found back into the original inequality to see if it makes a true statement. During class practice, provide a word problem for the students to solve, and walk around the classroom to assist and ensure understanding. Encourage students to discuss their thought process and how they arrived at their solutions.

Inequality Word Problem Challenge – Pair up and create word problems – Solve your own inequality problems – Use variables and inequality signs correctly – Share with the class for review – Graph solutions on the board – Show solutions on a number line | This class activity is designed to encourage collaborative learning and peer feedback. Students will pair up to create their own word problems involving inequalities, which will help them understand how inequalities are used in real-life situations. They will then solve these problems, ensuring they understand how to manipulate inequalities and express their solutions. After solving, each pair will present their problem to the class for peer review, fostering a collaborative learning environment. Finally, students will graph their solutions on the board, which will help them visualize the solution set of the inequality. For the teacher: Prepare to guide students in creating realistic word problems, solving inequalities, and graphing. Have extra examples ready for students who finish early or need additional help. Encourage students to think critically about the solutions their peers present and to provide constructive feedback.

Review and Reflection: Inequalities – Recap: Inequalities & graphs – Revisit how to write, solve, and graph inequalities – Discuss today’s learnings – Reflect on real-world problems and solutions – Address any questions – Open floor for student queries and misconceptions – Clarify doubts interactively – Engage with examples for better understanding | This slide aims to consolidate the students’ understanding of one-variable inequalities and their graphical representations. Begin with a brief recap of the key concepts taught, including how to write and graph inequalities. Encourage students to discuss and reflect on the real-world applications of inequalities they learned today, such as budgeting their allowance or comparing scores. Open the floor for any questions the students might have, providing a safe space for them to seek clarification on any part of the lesson they found challenging. Use this opportunity to address common misconceptions and reinforce learning with interactive examples. The goal is to ensure that students leave the class with a clear understanding of the topic.

Homework: Mastering Inequalities – Complete Inequality Problems Worksheet – Graph Inequality Solutions – Use a number line for each problem’s solution – Review for Inequalities Quiz – Quiz covers word problems and graphing – Aim for understanding, not just completion | This homework assignment is designed to reinforce the concepts taught in class about writing and graphing inequalities. Students are expected to complete a worksheet that provides practice on word problems involving inequalities. They should focus on understanding how to translate word problems into inequality statements and then graph the solutions on a number line. Additionally, students should begin reviewing the material in preparation for a quiz on inequalities during the next class. Teachers should provide guidance on how to approach studying for the quiz and encourage students to seek help if they are struggling with any concepts. The goal is for students to have a solid grasp of one-variable inequalities and be able to apply this knowledge to solve problems.