Printing Presses: Solving more difficult Linear Equations

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SWBAT attend to persevering in problem solving by working through a complex problem.

Big Idea

Mathematically proficient students are able to try various approaches to solving a problem and monitor those that work from those that do not.

Warm UP

5 minutes

This is one of those lessons that will make the student's head's hurt (it might make your head hurt a little, too).  The emphasis of this lesson is all about students tackling a challenging problem and persevering in the process (MP1).  

Throughout this lesson, students should be able to solve the problems in any way they choose.  The lesson starts with a short Warm Up question just to get students thinking:


This question can be solved fairly simply by setting up a proportion or similar type of equation such as:


However, other students may try to solve the problem by drawing a diagram such as a bar model or tape diagram.  

I will let my students work on the problem with their partners and after about 5 minutes have one or two students share out their solutions.  If any pairs of students have great difficulty with the warm up question, I may pull them into a small group to go through the problem solving portion of the lesson in a more guided way.

Problem Solving

30 minutes

Before students begin to work on the Printing Press Problem, I will ask everyone in the class to read the question silently to themselves.  After this quiet time, I usually ask my students to read the question a second time and underline the important information that they see.  I explain to students that they may need to read the question a 3rd, 4th or even 5th time. I encourage them to read slowly and carefully. This is all part of the problem solving process.  

After the students seem to be on top of the task, I will ask students to do a quick brainstorming activity with their partners.  When brainstorming, I encourage students to record all ideas, without rendering a judgement of which ideas are good and bad.  The goal is to get down as many important pieces of information as possible.

I will typically lead the brainstorming sessions as a Think-Pair-Share. I will ask students to write for at least one-minute on their own. Then, they can take another minute to combine lists with their partners. Lastly, we can make a list as a class.

The question is far from trivial, so all of this reading, writing and sharing is worth the effort.  Some students will not come to a solution, but all will do some valuable thinking.  I encourage students to recognize that I am "grading" them on is effort and problem solving. "Don't give up on the problem," I'll say over and over, "If they try 10 things that don't work, try an 11th." At the same time, I will encourage creativity and finding different ways to solve the problem.  

I try to leave 5-10 minutes in the end of this portion of the lesson to let pairs of students share their approach with the rest of the class.  If enough time is available, I will call on pairs who did not arrive at a solution first. I want to reinforce the norm that working on solving the problem is an important mathematical habit of mind (MP1).


Note: I have included an algebraic solution for this question:

Printing Press Problem Solution

I may share this solution with my students (if none of them happened to solve it this way).  The algebraic solution formalizes the thinking that most students will demonstrate in whatever method they choose.




5 minutes

This closure is an extension to the question posed in the problem solving portion of the lesson:

If each of the 8 printing presses can print 5,000 pages per hour and runs constantly for 6 hours per day, how many pages will be printed in the scenario that you studied in class today.

Bonus: If the novel has 250 pages and the cookbook has 125 pages how many of each will be printed?

This closure does not require as much algebraic thinking but the students will need to reason quantitatively about how to solve this problem.




Answers: 540,000 pages total, 1440 novels and cookbooks.