Solving Real World Problems Involving Tips (Lesson five in lesson progression)
Lesson 7 of 16
Objective: SWBAT solve real world problems involving tips through translating mathematical text into computational equations.
This lesson will be taught with 5 other lessons that will allow you to culminate the percentage unit with a performance task. Each of these lessons will allow students to focus on one objective within the percentage unit in order for students to build mastery. The objective of doing each of these lessons consecutive is students being able to answer a multi-step, complex, rigorous, word problem that will combine each objective in one problem. Lower level learners will struggle with solving a multi-objective problem if they do not have mastery with each objective. Students will appreciate being able to scaffold the complex problems using their understanding of each objective and feel empowered in doing so. You may choose to teach each of these lessons in any order you feel is best suited for your class. The lessons are Percentages of Numbers, Discount, Sales Tax, Additional Discounts, and Tip. There will be two separate lessons included in this unit of Percentage of Increase and Percentage of Decrease that you may opt to teach in conjunction with these lessons. I culminate the lessons over Percentage of Numbers, Discount, Sales Tax, Additional Discounts, and Tip with a performance task that is used as a summative assessment. It is refreshing to get away from the traditional summative assessments and use a performance task to assess mastery of several objectives taught.
When teaching this lesson as well as the accompanying lesson over percentages, you will have a consistent routine that will give students an opportunity to understand when the mathematical practices are being used, how to use them, and appreciate the power these practices have in gaining a deeper understanding of complex questions. Students will appreciate having a routine built into the lessons taught. They will be able to get started right away with the lesson, and begin to work independently. This will allow you to be a facilitator when necessary and give direct instruction when necessary.
In these lessons, you will focus on content area vocabulary, word problem strategies, scaffolding questions, unpacking the question, and critical thinking in real world scenarios. The computation will be done with the calculator. We will focus more on understanding what the problem is asking the students to do and how to create the equations to answer the questions accurately. Each of these lessons will have the same routines. You will have a large emphasis on MP 1, 2, 3, 4, and 6. Each lesson will have a bell ringer that will focus on MP 1, 4, and 2, a student activity that will focus on MP 3 and 6, a whole group discussion that will be driven by direct instruction, that will focus on MP 6, and a closing. Not all will have an assigned homework task. Each task will focus on one rich word problem that will be scaffold down according to the needs of the class. With each of these lessons, my students are grouped homogenously. I’ve grouped these students in groups of 4. I identified who should be paired up using their Star Math assessments, data gathered using teacher made assessments, understanding how my students think, and ability level as a whole. I have two groups that are considered high level learners, a bubble group, and two lower level groups who tend to need more attention from me. Grouping students this way allows the students to utilize one another on the same level. Not one student will take over the conversations. This allows students to feel comfortable because they are paired up with their peers that are like thinkers and are typically on the same level. Students are not intimidated by one another. This is an amazing strategy that will afford you the opportunity to differentiate your instruction effectively.
In each of these lessons, I give my students guided notes that are already printed. I have my students cut out the notes, and the example problems (problems used for their bell ringer) and glue them into their Interactive Math Journals. In my reflection I will add student examples that will give you an idea of how this is done. This will cut down on time needed for students to copy notes, and afford an opportunity for students to write down their own thinking to accompany the given notes which will deepen student understanding.
Students will use the homework assignment from lesson 4's progression as the bell ringer. Students were asked to create their own rigorous word problem to assess understaning of additional discounts, and sales tax. Have students exchange their created word problems. Students will work independently for 10 minutes. During this time students should practice MP 1, 2, 4, and 5. Walking the room gauging student understanding will benefit the type of open ended questioning you will want to ask during the student activity. This will also drive your whole group instruction. Start students with unpacking the problem. This will allow students to identify important information from the problem to help give them a starting point. Have the students who exchanged with one another group up, and discuss their work. They are each an expert at their own question. This should be fun. What a great way for students to be immersed in the thinking process of writing a problem and scaffolding the answer!
After students have had an opportunity to grapple through the problem on their own for 10 minutes, have them discuss their work with one another in their designated groups. In the above pre lesson guided notes I discuss how I group my students to maximize this time. Mathematical practice 3 comes into play heavily during this time. Students should also focus on solving the problem with their peers accurately during this time. This places heavy emphasis on MP 6. As you teach each of these lessons, students will be able to practice MP 5 as they use the notes given to help with each upcoming objective that is being taught. Students will be given 15 minutes to discuss their findings together. During this time you will want to visit each group to listen to their mathematical discussions, asked guided questions that will help them navigate through the problem, and gather data that will help you guide your whole group discussion. With your lower level learners you may want to take this opportunity to give small group direct instruction so that they may offer rich discussion during the whole group instruction and to pin point what the scaffolding questions you need to ask during the whole group instruction. My reflection will give you specific questions I came up with to help student mastery.
Whole Group Discussion
During this time, your goal is for students to share out what was discussed during the student activity. This is the time in which all students are able to learn from one another at one time. Students will share what process they used to solve the problem, what difficulties they are having with the problem, what successes they had while solving the problem, and which strategies were used to accomplish the task. As you walked the room you were able to gauge what questions you will ask during this time. For this specific lesson students are asked to calculate tip with sales tax. This problem is a rigorous 10 step word problem. Please see the breakdown teacher resource that will guide you through the steps of this problem. Use this resource to help scaffold the problem during the whole group discussion.
During your closing summarize what has been learned in the lesson. For this lesson, students should understand how to translate mathematical text into equations, and how to interpret what the text is asking them to do, how to identify what their computational results mean in reference to answering the questions of the problem accurately.