Solving Multi-Step Word Problems Given a Part to Part Ratio

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SWBAT solve multi-step problems given part to part ratios.

Big Idea

Using MP 1, 2, 3, 4, and 6 students will grapple through and solve rigorous multi-step real world problems given a part to part ratio.

Pre-Lesson Guided Notes

This lesson affords students the opportunity to grapple through word problems that will assess students over their understanding of part to part relationships.  Students will need to have a strong background over identifying ratios.  For students who have not been fully immersed in the Common Core, many of them may attempt to use a strategy that involves setting up a proportion and solving for the missing value.  This is GREAT to use as a starting point. 

During the bell ringer of this lesson, students will be asked to grapple with the problems on their own for 10 minutes first.  This will allow students to truly exercise MP1.  Learners with strong critical thinking skills will use a variety of strategies.  Some students may recognize how to model the problem, some students may understand part to part relationships and set up and solve equations that will arrive at the final answer.

Students with some understanding will be able to recognize the ratio, recognize that there is a total that is represented with the ratio, however not know what to do to solve for the asking total.  They will be able to set up a strategy, but not know what to do with the strategy.

Students with little to no understanding will not know how to recognize the ratio, and not have a starting point. With these learners you will want to start with identifying the ratio, identifying the numeric value of the order of the ratio, and use the modeling strategy with them.  I have found that using illustrations along with equations help students conceptualize what is happening in the problem.  For those students who use the strategy of setting up a proportion, do not discourage this.  Yes, the common core does ask for us to veer away from this, however this is a great starting point.  Using the proportion, you can move into modeling what each part of the proportion represents.  This will allow students to practice MP4.

Students who are not use to Common Core, will struggle, give up, and shut down.  The majority of my students are having a hard time working through problems, and thinking on their own.  It is frustrating for them.  They perceive me as a teacher who just simply does not want to help them.  I have to consistently refer back to MP 1.  I empower them by motivating them with constant praise.  I use words like:

“You are not giving yourself enough credit, you are so much smarter than what you are showing.”

“You do not need me as much as you think you do, I trust in you, all I need you to do is trust in yourself.”  

Bell RInger

10 minutes

Hand students the Bell Ringer as they enter the room. For this bell ringer, students will work on problems, 1 and 3.  Problems 2 and 4 will be their homework. Students will sit in their Individual Think Time seats and begin right away using MP1, MP2, and MP6 to grapple through two problems. Allow students 10 minutes for I.T.T. Students will need to write their thinking strategies in their interactive notebooks. They will use this to share during pair up time.  Walk the room to check for understanding. 


Student Activity

10 minutes

Once students have worked individually for 10 minutes, have students discuss their work with their pair up partners.  Students should have 10 minutes to discuss their thinking and compare their responses.  Students should be able to guide one another through the process of solving each of these problems. This will put into practice MP3

Whole Group Discussion

10 minutes

During this time, student 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.    This will allow students to practice MP 1 and MP2. Students will need to regroup their thinking and attempt to resolve the problem using the new information.  Students will need a conceptual understanding in order to solve this effectively, or students will need a strong understanding with complex fractions.  I have found that students who illustrate the fractional representation of the ratios will be more successful. 


5 minutes

: It is important for true understanding that students are aware of the correct process in solving problems, as well as the correct answer.  During the closing take time to go over problem 1.  During this time use the modeling method to solve the problem.  Show the students how to solve problem 1 then for the exit ticket have students correctly model problem 3.  Please see below the directions to solve problem 1 using the modeling method. 


Exit Ticket

5 minutes

Have students correctly model problem number 3. 


Have students complete problems number 2 and 4.