Grade 7 | Unit 4, Lesson 14 Intellectual Preparation Cover Sheet Directions: Complete the IPP Cover Sheet for every lesson due for submission. Step 1) Understand the concept and/or big ideas at play in the lesson and be able to articulate them clearly and crisply. 2) Do the core tasks of the lesson to develop/refine exemplar work and clear CFS for anticipated strategies. 3) Anticipate misconceptions and create questions/supports to address these misconceptions. 4) Optional/As needed: Adjust the plan for any individualized AOTY or intellectual preparation goals. Action: - Read the entire Lesson Plan and identify the key concepts/big ideas students need to understand. Create a lesson summary annotation that describes, in your own words, the purpose of the lesson (why), the key concepts students need to understand (big ideas/what), and how they will come to understand these within the lesson. - Print the classwork and complete this step directly in the student packet for the TAI, INM/TTC problem (include exemplar annotations), and all GP/IP problems. - For each core task, annotate to describe expected errors on the tasks and back pocket questions to respond to these errors Identify the questions in the TAI debrief and INM/TTC that elicit the most important understandings and annotate with the following: o The exemplar student responses o 1-2 misconceptions or errors that could surface in response to these questions o BPQs and/or the instructional strategy to address these misconceptions. - As determined with coach, you might: o Script MVP directions into lesson plans o Script in additional planned investment moves o Create rapid & batched feedback forms to capture data o Determine additional points for differentiation (especially for very high and very low performance during the lesson) - If you will meet in person to scrimmage this lesson, your coach may also ask you to submit a proposed practice objective and identify the lesson segment to practice. Submit annotated plans and any additional work as per IPP expectations in soft copy of LPs to your coach weekly (and at least 48 hours in advance of the IPP meeting). Implement any feedback from coach prior to the phase 2 meeting. 5) Rehearse and Refine: a. Meet with coach to further internalize and practice executing the plan. Refine plan as needed. b. Refine plan as needed based on practice and/or student exit ticket data. c. If possible, prior to teaching the day of, analyze student work from TAI administered at end of CR block; select S work to show call to drive TAI debrief discussion to land Fence Posts and key point. Copyright: Achievement First. Unless otherwise noted, all of the content in this resource is licensed under a Creative Commons Attribution International 4.0 (CC BY) license. LESSON TYPE: EXERCISE BASED LESSON AIM SWBAT represent one-step real-world problems using an inequality in the form of x + q > r, solve the inequality and represent the solution set on a number line; KEY POINT Mathematicians represent and solve real-world problems using inequalities. STANDARDS 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. SMP1 Make sense of problems and persevere in solving them SMP6 Attend to precision STATE TEST ALIGNMENT Taken from EngageNY Released Items 20161 ASSESSMENT Exit Ticket: 1. Write an inequality statement to represent each phrase below. a. The sum of y and 42 is at least 150 b. The difference of x and (-5) is no more than (-9) 2. For the following situation, Write and solve an inequality Graph the solution set on a number line Choose 2 possible values and use substitution to prove that one of the value is in fact a solution Brothers Raymond and Eduardo are saving up money to send their parents on an anniversary vacation. They have calculated that the trip will cost at least $500. If they’ve already saved $270, how much more do they need to save in order to make enough for the trip? Student Work: 1. a. y + 42 ≥ 150 b. x – (-5) ≤ -9 2. n + 270 ≥ 500 n ≥ 230 230 n=231 231 + 270 ≥ 500 501 ≥ 500 n=229 229 + 270 ≥ 500 499 ≥ 500 CONNECTION TO LEARNING How does this lesson connect to previous lessons? o In the previous three lessons, students have been solving inequalities using the methods and strategies for solving equations with the caveat of multiplying or dividing by a negative rational number which changes the direction of the inequality symbol. In this lesson, students interact with contextual situations that can be represented with one- step inequalities and have to utilize the language of the problem to determine the inequality symbol. This is easy for phrases like “greater than” but becomes more complex with phrases like “no more than” or “at least”. What do we want every student to take away or do as a result of this lesson? How will a teacher know if students have met this goal? o Understand: We write and solve inequalities to represent real-world problems. o Do: Students annotate problems for meaning when they encounter an inequality statement. Students write, solve, and graph inequalities given a contextual situation and test their solution using two values (one that satisfies and one that does not) and checks the answer against the context of the problem. HOW - Key Strategy o Annotate the problem for meaning including inequality symbol o Write an inequality o Solve and check with two solutions o Check final solution with the context of the problem CFS for top quality work o Problem is annotated for meaning o Inequality statement is written o Inequality is solved with inverse operations o Two checks are performed ANTICIPATED MISCONCEPTIONS AND ERRORS Students might not use the correct inequality symbol (especially for phrases like “at least/most” and “no more/less than”) Students might not use the correct operation when writing the inequality Students might not solve correctly using inverse operations Students might check one solution or two solutions that are too far from the actual solution to be a useful check. KEY VOCABULARY Reciprocal/multiplicative inverse: One of a pair of numbers that, when multiplied together, equal 1 Variable: a letter used to take the place of an unknown value Inequality: a statement saying that two expressions are unequal; includes an inequality symbol (<, >, ≤, or ≥) Substitution: the process of replacing a variable with a numerical value Solution: the value that makes an equation true MATERIALS - Handout - Opening – Prompt for work time, Circulate, Debrief, Synthesis, & Frame – 12-15 min THINK ABOUT IT! Write an inequality that represents the situation “Mark has less than 20 dollars to spend on the cost of dinner” Write an inequality that represents the situation “Cindy’s age plus 4 years is no more than 25” and determine all possible ages that Cindy could be. Explain how you knew which inequality symbol to use. Prompt for Work Time (<30 sec) - T sets timing for work and sets work expectations. Circulate (≤ 5 min) - While circulating, collect data on the following: Scholar thinking (correct and erroneous) S writes M<20 for the first inequality and circles S writes C + 4 ≤ 25 for the second inequality S incorrectly writes C + 4 < 25 for the second inequality S explanation includes the phrases “less than” and “no more than” Scholar Initials - Work to show call Debrief (≤ 10 min) - FENCEPOST #1: Specific phrases indicate inequality symbols o Show Call: S work writes m<20 for the first inequality o Do you agree with this inequality? Vote. CC. SMS: I agree because the problem uses the phrase “less than” so we have to use an inequality symbol to show that m is less than 20. o Show Call: Two pieces of work; one with the “less than or equal to” symbol and one with the “less than” symbol. o Which scholar wrote a correct inequality? Vote. TT. CC. SMS: The scholar with the less than or equal to symbol wrote the correct inequality because the problem says that her age plus four can be no more than 25. No more than means that it can’t be more than but it can be 25 so we have to use the less than or equal to symbol. BPQ – Can her age plus 4 equal 25? How do you know? o Name the fencepost: What can we say about determining the inequality symbol from context? SMS: Specific phrases indicate inequality symbols. - KEYPOINT: Mathematicians represent and solve real-world problems using inequalities o Show Call: S work solves the inequality to show c ≤ 21 o Do you agree with how this scholar solved for Cindy’s age? Vote. CC. SMS: I agree because the scholar used inverse operations to solve the inequality they wrote from the problem. o How could we check that our inequality is correct given the context? CC. SMS: We know that her age plus four can’t be more than 25 or that her age has to be less than or equal to 21 so we could substitute 21 and 20 to see if they satisfy the solution. Because 21 + 4 =25 and her age can be no more than 25, this solution satisfies the solution set. o What did our inequality allow us to do? CC. SMS: Our inequality allowed us to solve the problem and find the values that make the inequality true. Key Learning Synthesis (≤ 2 min) - Key Point: Mathematicians represent and solve real-world problems using inequalities. - Let’s form our key point for today. With your partner, come up with a key point about inequalities in context. Frame (≤ 30 sec) - You all have just formed our key point for today about solving inequalities in context. Today’s lesson is only going to include one-step inequalities because the focus of our lesson is on the language used in inequalities. Tomorrow, we will apply this to more complex inequalities. Interaction with New Material – 10 min Post the Key Point in visible place for student reference: Mathematicians represent and solve real-world problems using inequalities. Let’s use our key point from the TAI and apply it to solve two more problems. Ex. 1) 3 times a number is at least 18.6. What are all the possible values of the number? - T directs all Ss to read the prompt and annotate the problem for meaning What is the problem asking us to do? SMS: The problem is asking us for all of the possible values for the number. How should we annotate our problem? SMS: We should circle “at least” because it indicates that the product is greater than but could be 18.6 so we should use a greater than or equal to symbol. How can we represent the problem? SMS: We can write an inequality that says three times a number as 3n and then “at least” which indicates greater than or equal to 18.6 What do we do next? SMS: We solve the problem using inverse operations Independently solve the inequality. Show Call: Do you agree with this work? TT. CC. What do we do next? SMS: We check the solution by substituting in two different numbers. Independently check your solution set. Show Call: Do you agree with this work? TT. CC. Ex. 2) Mr. Cooke is on diet. He has set a goal of weighing a maximum of 175 pounds at the end of the month. If he weighs 200 pounds now, write an inequality statement that represents at least how much he has to lose to meet his goal. - T directs all Ss to read the prompt and annotate the problem for meaning What information is known? SMS: We know that Mr. Cooke weighs 200 pounds and wants to lose weight to weigh 175 at a maximum. What information is unknown? SMS: We don’t know the minimum amount that Mr. Cooke can lose to meet his goal. How should we annotate the problem? SMS: “Weighing a maximum of 175” indicates that he can weigh 175 pounds and meet his goal so we should use the less than or equal to symbol. How can we represent the problem? SMS: Since he currently weighs 200 pounds, we start with 200 and subtract a certain amount that we can represent as n. That amount has to be less than or equal to 175 so our inequality is 200 – n ≤ 175. What do we do next? SMS: Solve the inequality using inverse operations. Independently solve the inequality. Teacher should anticipate that some S might get n ≤ 25 by looking at the problem and not solving it correctly by dividing by a -1 to flip the direction of the inequality symbol. Show Call: Do you agree with this work? TT. CC. What do we always do when we finish solving? We check the solution by substituting in two different numbers. Independently check your solution set. Show Call: Do you agree with this work? TT. CC. What does 25 represent? SMS: 25 represents the minimum amount of weight he lose and meet his goal. Key Learning Synthesis - How did we apply our key point for today to solve this example problem? TT. CC. Frame for PP/IP You will have 5 minutes to work with a partner on PP. Today during PP and IP, make sure your work meets each of the following CFS o Problem is annotated for meaning o Inequality statement is written o Inequality is solved with inverse operations o Two checks are performed Name: ___________________________ Date: ____________________________ UNIT 4 LESSON 14 AIM: SWBAT write and solve one-step inequalities in context. THINK ABOUT IT! Write an inequality that represents the situation “Mark has less than 20 dollars to spend on the cost of dinner” Write an inequality that represents the situation “Cindy’s age plus 4 years is no more than 25” and determine all possible ages that Cindy could be. Explain how you knew which inequality symbol to use. __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ __________________________________________________________________________________________________ Key Point Interaction with New Material Ex. 1) 3 times a number is at least 18.6. What are all the possible values of the number? Ex. 2) Mr. Cooke is on diet. He has set a goal of weighing a maximum of 175 pounds at the end of the month. If he weighs 200 pounds now, what is the smallest amount of weight he can lose and still meet his goal? PARTNER PRACTICE Bachelor Level 1. Write each verbal statement as an inequality statement. a. 5 more than a number is less than or equal to 10 _____________________ b. The sum of 15 and a number is less than (-1) _____________________ c. 45 is greater than the product of a number and 9 _____________________ d. The quotient of 4 and a number is at most 32 _____________________ 2. Penelope set a goal of running at least 100 miles in the month of October. If she has already run 55 miles so far, what is the least amount of miles she can run and still meet her goal? Write, solve, check, and graph the solution. Master Level 3. Ms. Olsen says that each top-quality paragraph will consist of at least 7 sentences. If Damien has already written 4 ½ sentences, what is the least number of sentences he can add and meet Ms. Olsen’s goal? INDEPENDENT PRACTICE2 Bachelor Level 1. Write an inequality statement to match each verbal statement. a. The sum of a number and 10 is less than 22 _______________________ b. The product of a number and 7 is greater than or equal to ½ _______________ c. One-third of a number is no more than 17.5 _______________________ d. 8.2 is greater than or equal to the sum of a number and 11 ________________ e. 9 less than a number is at least 15 _______________________ 2. Rachel has saved $350 towards a trip to visit colleges in New England. If she needs more than $500 to pay for the trip, how much more money does she need to save? Write, solve, check, and graph the inequality. Master Level 3. Tiago entered a snowman building contest in which the person who builds the tallest snowman wins. Currently, the record is 11.2 feet high. If Tiago’s snowman is currently 8 feet high, how many more feet does he need to build on, in order to win the competition? 4. Cindy Scholar says that Tiago needs to add on 3.2 feet in order to win. Do you agree with Cindy? Would Tiago win if he adds this amount of feet? Explain why you agree or disagree. If Cindy has made an error, explain her misconception. ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ 5. A truck can carry no more than 1,500.89 pounds. If it has 949.24 pounds already packed in, how much more weight can be added? 6. To carry your suitcase on the plane, it must weigh no more than 50 ¾ pounds. If Laila’s suitcase weighs 9 ½ pounds when it’s empty, what weight of luggage can she pack into it? Select all the possible weights below. a) 42 pounds b) 41.3 pounds c) 41.25 pounds d) 41 pounds e) 39.5 pounds PhD Level 7. At Skate-a-thon, you can have your birthday party and pay a discounted price. The party base fee is $50, plus $4.50 for each guest that you invite. If Kayla has $100 to spend in total on the party, what is the greatest number of friends that she can invite? 8. Charlie can carry no more than y pounds. He already has n pounds in his hands. Write and solve an inequality to represent how many more pounds he can carry. Name: ______________________________ Date: _______________________ EXIT TICKET Selfassessment Teacher feedback I mastered the learning objective today. You mastered the learning objective today. I am almost there. You are almost there. Need more practice and feedback. You need more practice and feedback. 1. Write an inequality statement to represent each phrase below. a. The sum of y and 42 is at least 150 b. The difference of x and (-5) is no more than (-9) 2. For the following situation, a. Write and solve an inequality b. Graph the solution set on a number line c. Choose 2 possible values and use substitution to prove that one of the value is in fact a solution Brothers Raymond and Eduardo are saving up money to send their parents on an anniversary vacation. They have calculated that the trip will cost at least $500. If they’ve already saved $270, how much more do they need to save in order to make enough for the trip? 1 “Released 2016 3-8 ELA and Mathematics State Test Questions” by EngageNy is licensed under Creative Commons Attribution International 4.0 (CC BY-NC-SA). 2 Author and Source Unknown. Achievement First does not own the copyright in “Independent Practice” and claims no copyright in this material. The material is being used exclusively for non-profit educational purposes under fair use principles in U.S. Copyright laws. 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