If you have lower level learners please see my lesson on calculating discounts with the graphic organizer and use that lesson before using this lesson. You may also opt to use this lesson when introducing finding discounts, just be sure students understand that calculating additional discounts involve a few steps that are not inclusive in calculating one percentage off. This may need to be left unsaid to you as an educator, however I have found that lower level students tend to be confused when asked to find additional discounts as opposed to one singular discount. One main misconception that students have when finding discounts is that once they multiply the percentage by the original cost, they think that amount is the discount. The lesson using the graphic organizer will really help students organize their thinking and itemize the steps in solving for discounts. In this lesson students will practice MP 1, 2, 3, and 6.
As always, my students line up at my door before entering into the classroom. Students form a single file line, and I greet each student as they enter the room. If my bell ringer is a task that I want them to begin as soon as they enter the room, I hand each student a bell ringer upon them entering the classroom. This practice helps students not to have any idol time. Idol time will create student misbehavior. Students will sit in their designated Individual Think Time seats.
Students are aware that they are to get started on the bell ringer right away. Students will have 10 minutes to persevere through the problem on their own calling upon MP 1, 2, and possibly 4. If students find a way to use bar diagrams, tables, charts, or graphs in any way, please be sure to allow them to do so. Students being able to draw upon MP 4 are showing a true conceptual understanding and this is awesome!
It is important to walk the room and check for understanding. If you have a class that is comprised of multi-level learners you will definitely want to personally check in on the strategies being used. Your lower level learners will need help with starting points.
Things you want to look for:
Are students aware of the original price?
Do students know what to do with the first discount percentage?
How are students calculating the discount?
Are students calculating the discount amount and finding the sale price, or just calculating the discount?
Are students using the sale price to calculate the additional discount?
BIG MISCONCEPTION: Be sure when finding additional discounts that students are using the sale price, and not going back to the original cost amount. Notoriously I find many of my students going back to the original cost and not using the sale price to calculate the additional discount.
Once students have grappled through the task, pair up the students into pairs or groups. Give the students the opportunity to practice MP 3. On a daily basis you will find my students using MP 1, 2, 3, and 6. I believe these mathematical practices will give you the biggest bang for your buck. Students who are engaging in MP 1, and 2 daily will build their stamina, learn how to draw upon prior knowledge, understand how to use mistakes as their guide toward understanding, learn how to organize their thoughts without being spoon fed, learn how to lean toward their peers and formulate conversations that are fostering true understanding, and truly appreciating the process in which it takes to persevere toward the correct response. The self-gratification the students will feel the first time in engaging in the practices and using them to move toward true understanding is priceless. Students will take 10 minutes in their groups to discuss the strategies used, their responses, and discuss mistakes made. In this time, you are listening for rich mathematical discussion among the groups. Allow students to talk through misconceptions, mistakes, and proper processes used. Allow students to compare strategies and discuss the similarities and differences in the ways in which they arrived at their final answers.
During this time, students groups should have the opportunity to share out their pair up time discussions, and reveal each of their responses. You may not have time to have each student share. As you filter through the room during pair up time, attempt to identify a group who has understanding, some understanding and little understanding. During the whole group discussion have students debate their responses and defend their thinking. This again will practice MP 3.
As the facilitator of the discussion, you can head the discussion with open ended questions that will evoke students to defend. For example:
A student may state that the final sale cost with the additional discount is $72.17, if a student responds this way, this means that they used the 20% discount amount as the sale price and found the additional discount off of this amount. A great way to curve this is to take students back through the process they used in the earlier lesson using the graphic organizer to help them through the process in solving for discounts. Some questions you may find yourself asking are:
“What is the difference between the discount amount and the sale price?”
“What did you do to find the additional discount?”
“Did you use the sale price or the original cost to find the additional discount?”
After having a rich discussion with the whole group, allowing the students to defend their thinking, identify their mistakes, and critique others, close the lesson with the correct answers. Validate correct thinking as you go through the correct responses.
Go through each part of the task. Validate those who shared correct thinking at this time. Be sure students are correcting their mistakes. Ask students to leave their original work on their sheets. Have students explain what they did wrong and how they corrected their mistake.