From the first look of this 3 step problem, it appears fairly simple. Once students dive into this 3 step problem they will notice that they need to draw upon prior knowledge. You can use this lesson as a formative assessment during a number sense lesson, equation lesson, percent lesson, or a culmination of the three.
I am using this during my percent unit. My students are fairly low. This is an example of a problem that would take us a day or two. I would want my students to exercise MP 1, MP 2, MP4 and MP 6 heavily. I would distribute this problem to my students as they entered my classroom. For my bell ringer section, the students will work in their Individual Think Time seats and work on the problem by themselves for 20 minutes. Students will struggle, they will want you to give them the answers, however, this is a great problem that will excite critical thinking. It is important that during this time you walk the room engaging in student thinking. The open ended questions that you will ask will foster student thinking, help students with starting points, rather than give answers.
An example of this would be for part one of this multi-step problem. Students are asked: will Stephanie meet her goal in the next two weeks and to explain why or why not.
First, you may want to lead them back to the opening text of the problem. Many lower level students will bypass the importance of going back to the text to gather the information needed to solve the problem. Students will see that Stephanie gets paid $6.75 per hour and will work 24.5 hours. Her goal is to make $200.
Students will need to create an equation in order to find out if Stephanie will in fact make $200. Students will need to know which operation to use in order to do so. Of course we will need to multiply. To help those students who will not know to multiply, you may have them set up a (x,y) table. This will draw upon MP 4. Students will model the repetition of adding $6.75 24 times, but must also need to figure out what will .5 of $6.75 represent. This will then allow students to draw upon MP 8. Students will want to add $6.75, 24 times.
Discussion from here could be what would be a more efficient way in solving for this? Students should recognize multiplication is a way to solve for repeated addition. Have students create the equation that would represent the work from the table. This may seem like a lot of work to simply multiply 24.5 hours by $6.75, however CCSS works toward student mastery through conceptual understanding. Using the multiplication equation, does not guarantee that students understand why Stephanie did not make $200.00. Ultimately, yes we want students to be able to know that you must multiply but it is deeper than that.
For part 2 of this task, students must understand which decimal representation will be equivalent to the nearest 15 minutes, and also know which equation will get them to $200.00, this will take some thinking. Part 3 brings in percentage understanding. This in itself is multi-step.
I would highly suggest you work out each part of this task so that you are able to scaffold each question in order to service your students effectively. Identify your learning targets for each part of the question.
For the first 20 minutes have students work through this task on their own. Walk the room engaging in student thinking. Ask those critical open ended questions. Refer to my strategy folder for example questions to ask. The best way to create great questions to enable students to practice MP1, 2, 4, and 6 is to go through the task yourself and understand what the task is asking of your students.
Pair up students for 10 minutes. Have students compare the work that they did on their own with one another. Have students engage in rich mathematical conversation. Use what you observed during the first 20 minutes to drive your engagement with the pairs or the groups. As you pair up students, it will be helpful to pair up students who shared the same thinking. If you found students who were able to easily recognize that multiplying the two numeric values in part 1 was the strategy they chose, It would be helpful to pair these students up to share their thinking. You may also want to pair up students who solved the problems completely different but answered correctly. This will allow students to practice MP 3. If you have a few students who were unable to answer on their own at all, group those students and take time to have a small group discussion with these students. These students will need direct instruction.
If you have software interventions such as Gizmos, Plato, Study Island, Accelerated Math, etc. you can also assign specific assignments that would help with specific objectives that the students are not mastering.
Students will need to be sure that they are attending to precision and answering correctly. Students will need direct instruction in order to validate correct thinking, and correct incorrect thinking. During this closing, go through each part of the task giving the correct way in which to solve each part. Students should correct mistakes and be sure to document the correct way in which to solve each. Students who solved one or all of the parts of the task correctly, but not how you are sharing, allow those students to share what they did to solve the task. It is important for students to know there is not one way to solve problems. You may choose during this closing to have students who effectively solved these problems to share out what they did as a part of your direct instruction. These students should be identified during your walk through and engagement in student thinking.
Example Questions to zone in on the real world aspect of part 3. 9% of Stephanie’s check is being withheld. What is the 9% that is being withheld? If you have a goal amount in mind to save, why would it be important to figure in the 9% being withheld in order to meet the goal amount?