Solving Multi-Step Real World Problems Involving Percent of Increase (progression lesson six)
Lesson 8 of 16
Objective: SWBAT solve real world, multi-step problems involving sales tax and percent of increase.
This lesson affords the students the opportunity to practice several mathematical practices including MP 1, 2, 3, 4, and 6. Students may use strategies within their own thinking that may bring out other mathematical practices not listed, or not use some that may be listed. Students will complete a scaffold problem during the bell ringer section. The scaffold questions are included directly on the bell ringer. Once students complete the bell ringer, they will discuss the problem with their identified partner or group. They will practice MP 3 during this time, checking for understanding, and using their peers to critique their work. This is a crucial time within this lesson. Students learn so much more from mathematical discussions between themselves. You will see a major difference in their understanding as they perfect how to use this practice. The training of this practice will take a lot of guided questioning. The questions within the scaffold bell ringer are prime examples of questions to ask to help students begin the process of breaking down word problems on their own to help deepen understanding. Once students have concluded their peer to peer discussions over the bell ringer, they will be given a word problem that has the same objective. This word problem is a formative assessment to see if they can transfer knowledge. You will be able to assess if students are able to use the scaffold bell ringer to break a problem down on their own to calculate the final answer. Students will work as individuals to start and then go back into their peer to peer groups to discuss. Once the student activity has concluded there will be a whole group discussion, then a closing.
Hand the students the bell ringer as they enter the door. Students are to sit in the I.T.T seats. You may want to do a quick vocal review of what students were able to accomplish thus far with this unit. This is a progression unit. Students should be able to see the connections between each lesson. Students will work as individuals through the bell ringer for 10 minutes. After students answer each question in the bell ringer, allow them time to discuss their work with a peer or a peer group. Afford students 10 minutes to have the mathematical discussions. This again is a great time for students to practice MP 3. Students will check their work, correct mistakes, ask questions, and discuss personal strategies used to solve the problem. In the bell ringer, students are given two strategies to use to help find the dollar amount of the percent of increase. They will be able to use proportional reasoning, or an equation. It will be important for students to know they are not limited to these strategies. They may want to use modeling as a strategy which is perfectly ok. (MP 4)
Once students have gone through their mathematical discussions, place them back into I.T.T time. Hand out the student activity. You may allow your students to use their bell ringer to help them solve the student activity word problem. Students should work through the problem using (MP 1, 2, and possibly 4.) The bell ringer is a modeled problem that scaffolds down a similar task. This will help students understand what to identify within the word problem, and the questions to ask to solve the problem. Allow students 5 minutes to solve the problem. Have students discuss their work with a peer. Students will check for understanding and accuracy. (MP 3, and 6) Allow students 5 minutes to discuss.
Whole Group Discussion
: During this point in the lesson students are encouraged to share their mathematical discussions, discuss mistakes that were made, how mistakes were corrected, misconceptions, and final answers. This is the time in which direct instruction can take place. During this time, go through the bell ringer, be sure to give correct answers for each of the scaffold questions. This may be done through validation of student responses, or you going through each question and having the students check for correct responses. Be sure to go through the thinking process of each. Once you have the correct responses for each of these, go through the student activity word problem.
Important emphasis here: (Real World Discussion)
What does it mean to buy wholesale? What does markup mean? Mathematically, what is this telling you to do? (Calculate percent of increase) Be sure to make that connection. Why would a store owner do this? What is profit?
When calculating the problem, break it down step by step with them.
If you are using proportional reasoning, it is important for students to understand the connection of the amounts. I do allow my students to set up a proportion, however, it is imperative they are able to articulate the connection of the amounts. We usually use our percent model proportion. I discuss this with my students early on in the unit. The “percent model proportion” is set up with the left side being the percent side. This will always have a constant denominator of 100. Why, because percentages are always out of 100. The right side being the original amount compared to the new amount side. Students know that the original amount is always represented by the denominator, why because this is the amount being changed. Now, I tell my students to navigate through the text to find out what the text is telling us about the proportional relationship. Is it asking us to find the percentage? If so, the numerator of the percent side will be the variable. Is it asking for the amount of the percentage of change? If so the numerator of the right side will be the variable. This process will afford the students the opportunity to navigate the text and use the text for understanding.
Students may also use an equation, if given the percent of change, the students will simply take the percent of change and multiply it by the original amount. With this students will need to understand contextual information to know what the equation is calculating. In this case, the word markup is crucial in understanding this is finding percent of increase.
Now let’s break this down. This is a six step problem! Wow!
Step 1: Identify the original amount (context understanding)
$55.00 is the wholesale price (original amount)
Step 2. Multiply the original amount by the percentage of change
$55.00 (.29) = $15.95 (the markup amount)
Step 3. Add the markup to the original amount/ this will take contextual understanding to know whether to add or subtract
$55.00 + $15.95= $70.95 (the markup total cost)
Step 4. Multiply the markup amount by the tax percentage to calculate the tax amount
$70.95(9.5%) = $6.74025
Step 5. Estimate
$6.74 (estimated tax amount)
Step 6. Add the tax to the markup amount to calculate the final cost
$70.95 + $6.74 = $77.69 (final cost)
Reiterate that being able to answer a multi-step word problem will take using the prior knowledge gained from previous lessons. This is the importance of consistent review of what has been previously taught. Students need to see the connections from one objective to the next. I have found, breaking a problem down into steps will allow students to make connections.
Give the exit ticket as a formative assessment five to ten minutes before dismissal. Collect as the students depart.