In this portion of the lesson I want my students to focus on understanding how different strategies can help them solve word problems. My students need to explore multiplicative comparison to determine what amount would be added to one quantity in order to result in the other. In a multiplicative comparison, the underlying question is what factor would multiply one quantity in order to result in the other. To get them thinking and responding to word problems the correct way I model the first problem.
To begin this process, I post a word problem. I ask students to read it with me. I remind students of the BUCKS solving system that we use to help us solve questions more effectively.
B- Box in your question.
U-Underline key words.
C-Circle your numbers.
K- Knock out unimportant words.
Sandra raised $15 for the PTA and Nita raised $45. How many times as much money did Nita raise compared to Sandra?
What do we need to do?
Find out how many times as much money did Nita raise compared to Sandra.
What information does the problem give us?
It tells us that Sandra raised 15 dollars and Nita raised 45 dollars.
Are their any key words that can help us solve the problem ?
How many times as much did Nita raise compared to Sandra?
I display this strategy on the board to remind students later on in the lesson how to explain their reasoning for each step in the problem solving stage. To ensure all students are listening, I ask each student to take a couple of minutes to think of what number operation can be used to solve this problem. I suggest that students turn and talk to their neighbors as well if they need support. As students are busy determining the best method to solve this problem, I circle the room to see what students are thinking. I carefully take down notes to address and model how to do throughout the lesson. I notice that several students solve their problems differently,however, they were able to explain how and why they got their answer.
For struggling students, I use a refer to card to help them remember the problem solving steps as they are working.UNDERSTAND THE PROBLEM.docx
We will work with Mathematical Practices:
MP.1. Make sense of problems and persevere in solving them.
MP.2. Reason abstractly and quantitatively.
MP. 8. Look for and express regularity in repeated reasoning.
Material:Work Group 1.docx
I want to start this section of the lesson off by inviting students to share the strategies they used to solve their problem. As students are sharing I make clarifying statements about the strategy they used. For instance, one students explains how to use repeated addition to solve problems. I ask her to illustrate her findings on the board. Because this is a contextual problem it is good to allow them to explain how they solve using illustrations and symbols.
Why did you choose to solve this way?
Because the first person raised 15 dollars. The problem asked what is three times 15 dollars. So, I added 15 + 15 + 15 to get a total of 45 dollars.
Can you think of another way to solve?
How do you know?
Great Job! I invite a couple of more students to share their strategies with the class. Students eagerly ask questions. Then, I direct students to the next task. I tell them that this strategy is quite simple. Several students raise their hands to get started. I say, well you guys it is really simple! All you have to do is solve the same problem using a different strategy. Guess what? A lot of cool strategies have already been shared. This works because it encourages students to use a strategy already explained by their classmates. On the other hand, it allows students to choose from a variety of problem solving methods. I give students about ten minutes or so to solve their problem. As students are working, I circle the room to reinforce how and why to problem solve. Several students wanted to share out their work with the class. As students shared their learning experience, I ask students to think a bout their favorite strategy from this portion of the lesson and write a two to three sentences in their math journal explaining why they like, or turn and talk to their partner. This takes about five minutes or so, but the students really enjoy sharing their work with others.
Now that students have explored multiple ways of solving word problems. I want them to share the experience of solving problems in a smaller group setting. I invite students to move quickly into their assigned groups. I tell students that the will be implementing the 3 R's. Of course students begin to ask all sorts of questions, but I write the 3 R's on the board. To be sure that all students fully understand what their task will be, I go over the directions. I write Request, Response, and Result on the board.
Ellen went to a garage sale to buy chairs. Each chair cost 15 dollars. How much money did Ellen spend for the 12 chairs she bought?
Step 1: Identify the request.
What does the problem ask for?
How much money did Ellen spend for the 12 chairs she bought?
Step 2: Respond to the request.
How will I find out?
If each chair cost 15 dollars, then I need to find out how much for 12 chairs. I can multiply 15 x 12.
Step 3: Generate the result.
What does the result tell me?
It tells me that one chair cost 15 dollars, and Ellen bought 12 chairs at 15 dollars each.
Therefore, I will multiply the cost of each chair times how many chairs Ellen bought.
15 x 12= 180 So, Ellen spent a total of $180.00 on 12 chairs.
Students seem to be responding well to the given method. I ask students are they ready to group work! Several students shout Yes! Ok! I am going to set the timer guys. You all will have about 20 minutes or so to solve and explain the given set of questions. As students are working, I circle the room to reinforce how to problem solve.
What does the problem ask for?
How will you find out?
What does the result tell you?
How can you prove your answer?
Is there another way to solve the problem? How?
I invite all groups to sit on the carpet. I call on 1 or 2 groups to share out what they learned.
I use their explanations to determine if this activity was successful, or if additional practice should be administered.
Material: note taking paper.pdf
I ask students to move back into their assigned seats. I say guys we will be writing in our math journals today. A couple of students inquire about the task. I tell students that they will be making a journal entry about the math lesson today. You all will write at least one different strategy you learned about today, and explain it in detail. You will have about ten minutes or so to write, so go ahead and think about what you are going to say. This keep the students focused on their work. As students begin to write in their journal, I circle the room to check for understanding.
I carefully ask guided questions, so that I can detect the level of understanding. I use students responses to determine if students need additional support to master this particular skill.