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.
: As the students enter the room, hand them the Sales tax bell ringer that will focus on the objective of the day. 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. Please see my strategy folder on how students unpack a word problem.
: 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.
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 sales tax. I like to teach this lesson after teaching discount. Sales tax is calculated after all discounts are taken. When you begin to merge each of the objectives into one question, it will be beneficial for students to understand that they will need to calculate the discounts before calculating the sales tax. Students will need to understand subtotals vs. final cost. Subtotal is the amount before sales tax is applied. The subtotal is the amount that they will need to identify in order to calculate the sales tax. This is not always stated in the problem thus students will need to know once calculations are made what the calculations mean. I like to stress to my students that math today is more about comprehension of text then calculations. As we know, calculators are a great tool that is in place that we use in the real world. No, I am not saying to replace meaningful understanding of basic skills with the calculator, but I am saying to teach a student how to calculate is fairly an achievable task, however if we are not teaching our students how to understand what the problem is asking them to do, they will never get to the calculations.
With this lesson, I like to refer back to the prior understanding the students gained from percentage of numbers and discounts. I will refer them back to this so that they may navigate through the word problem effectively using prior knowledge. I always place the students in the real world, as if they were the ones doing the action of the problem. Many of our students get so caught up in the “math” of the question and bypass their real life experiences. The “math” confuses them. I open this questioning with what do you know about taxes? Student responses ranged from “What the government takes out of your check.” To “Money their parents receive in January.” We discussed the difference between income tax and sales tax. There will be more discussion about this in my reflection.
As we go through the notes of this lesson, our discussion leads to if discount is amount we take off, then sales tax is amount we have to pay, so we must add it on. It is important for students to see the coherence of the lessons prior in this progression. Students should recognize the similarities between discount and tax. Once again, if the tax is represented as a percentage, fraction or decimal, they will need to find the dollar amount first. This should trigger their memories and realize just as they did with discounts, they will need to multiply the part by the subtotal to find the amount of tax. Students should then be able to tap into their prior understanding of discounts to understand that this amount is the tax, not the final cost.
It is also important for real world application that students know each state has a set sales tax and within the state local cities may have the authority to increase or decrease this amount. This will bring in cross curricular teachable moments. Students can research their state’s sales tax amount and compare it to other states. Please refer to the reflection for an “aha” moment I had with my class regarding this discussion. Included in the resource section of this lesson will be a link for sales tax list, and steps to solving for sales tax.
During your closing summarize what has been learned in the lesson. For this lesson, students should understand how to translate mathematical text into equations, how to interpret what the text is asking them to do, and how to identify what their computational results mean in reference to the questions.
Assign students the Monica problem for homework that is included in this lesson or create a question on your own. I would give the students one rich question that allows them to show how they unpack a word problem and use the steps to solve.