Scaffold Lesson to Increase Deeper Understanding in Solving Problems Involving Discount, Tax, and Tip
Lesson 9 of 16
Objective: SWBAT understand terminology needed to solve problems involving discount, tax, and tip. SWBAT apply the deeper understanding to solve real world problems.
Pre-Lesson Teacher Guided Notes:
Students must know the terminology needed to deepen their understanding in solving discount, tax, and tip. More important they must know what to do when the terminology is within a word problem. For example, if the problem states: Malissa wants to purchase a pair of jeans for $10.00. There is a 10% discount on the jeans she wants to buy, how much will she spend purchasing the jeans after the discount. Students will need to know that the original cost is $10.00. Students must understand discount means that they will subtract, however they must also understand they must find an amount to discount, in order to do so they must multiply the percentage by the original cost. If students are using a scientific calculator they may have the option to use a function key on the calculator to multiply the percentage by the original cost. If students are not using a calculator, or the option of the percent key is not there, students will also need to know how to convert a percent to a decimal then multiply. If the decimal that is found to subtract is more than the hundredths place, students will also need to estimate to solve. Once students solve for the amount to discount they then will be able to subtract to find the discounted cost.
For high level learners, SWBAT understand terminology from real world experiences and discover strategies to use to solve for the discount. If students have had previous CCSS implementation they will have had prior understanding in finding a percent of a quantity as a rate per 100. In 6.RP.A.3c students multiplied the quantity by the ratio of the quantity of the percent out of 100. For example, 30% of 25 would be solved by 30/100(25). Struggling learners will show little to no understanding of what to do with the terminology in order to apply it in solving for discounts, tax or tip. I would allow students to grapple with an example question to assess the level of student understanding. For those students that you identify as low level learners, give them the list of vocabulary words that they will need to know in order to be successful in solving for discount, tax, and tip. Have students write the terms in their interactive notebooks, as well as an example of how they will see it in a word problem, and the process in using the term to solve the problem. For example:
Original Cost: The original cost is the cost of the item before discounts, taxes, or tips are subtracted or added to the item. This is the starting amount that will be increased or decreased.
Discount: A discount is amount that will be subtracted by the original cost. The discount can be represented as a fraction, decimal, or percent. The discount must be found by multiplying the fraction, decimal, or percent by the original cost.
Hand students the Bell Ringer as soon as they enter the room. Students will sit in their Individual Think Time seats to grapple with the problem on their own for 10 minutes. Students will practice MP1, 2, 4 and 6 during this time. The initial problem that students will be solving is a multi-step word problem. Choosing this problem will allow you to assess what students already know how to solve. Some students may already know how to solve for discount, but may not know how solve for the tax, and/or tip. This will allow you to differentiate your future assignments with segregated lessons over discount, tax, and tip. If students show understanding in one standard, you will have the opportunity to tailor instruction to the needs of your students within this unit. Students who you identify with little understanding will benefit from the lessons as written in this unit. Other groups with more understanding will benefit from problems that are like the bell ringer. You may use the bell ringer problem from this lesson to research like problems to use or create other problems on your own.
Once students have had the opportunity to grapple through the problem on their own, have the students pair up with a partner or group to discuss their mathematical thinking, compare responses, and debate their work. This will engage students in MP3. During this time students should learn from their peers different strategies used to solve the problem, relate their thinking to the thinking of their peers, and change any work that is incorrect resulting from the discussions that the students have with one another. Students should attend to precision at this time MP6. Through their conversation, students should work toward finding the correct response to the problem and be able to defend their answer.
As you walk the room you will check for understanding. Students should be able to show that they are able to identify the original cost, the cost after taxes, the cost after the discount has been applied, and finally the cost after the tip has been applied. Students should be able to know the order in which to apply the specific operations to end up with the final cost.
If students have no starting point, one guided question you may want to ask is:
“How is the amount of the meal changing first?”
“Are you adding money to the bill?”
“How do you know?”
Student thinking should be guided toward what should be the first step.
Whole Group Discussion
Allow selected students to discuss the processes they took to solve this problem. During the whole group discussion allow students to defend their responses through explaining what strategies they used to solve the problem. Some students may opt to estimate. If students estimate will they still need to know the process in solving for tax, tip, and discount? Yes, however the operations may be easier to solve rounding to the nearest dollar. This may be a part of the whole group discussion. This is a great strategy to use, we all use this strategy in the real world, especially when grocery shopping. If you want to challenge your students have them also find the exact dollar amount and compare it to the estimated dollar amount. Discuss if the estimated amounts make sense. Does estimating help you answer the question? How do you know if your estimated amount is too far off and what mistakes did you make? A few common mistakes that students may make are, not using the appropriate decimal value for 7%. Students may convert 7% to .7 instead of .07. This will be a great time to talk about converting decimals to a percent. When finding the discounted price, students may use the amount found when multiplying the percent to find the amount of the discount as the discounted price. This is a great time to talk about what makes sense.
In the closing be sure students are leaving with the correct process in solving the problem. Address misconceptions that arise and be sure students know where they made a mistake. Have students correct all mistakes and have a clear understanding in solving the problem. Take it step by step. Be sure students know how to find the sales tax and apply it to the initial cost, how to take the new cost with the tax added and find the discount, and finally applying the tip to compute the final cost. Isolating each will allow them to understand what to expect from the future lessons. Tell your students that the upcoming lessons will focus on finding discounts, tax, and tips. This problem is a problem they are expected to solve at the end of the unit.