Multiplying Decimal Quantities: Real World Application

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Objective

Students will be able to fluently calculate decimal quantities while making sense of real world situations.

Big Idea

Connection to Decimal Perfection: Using decimal quantities in real world contexts.

Curriculum Reinforcer

5 minutes

I will have my students complete a word problem involving subtotal, tax, and grand total.

Kelli went shopping she bought deodorant for $3.69, lip gloss for $2.09, a candy bar that was $0.65, hair gel that was $5.29, and a magazine for $3.50. If she had to pay a tax of 8%, how much did Kelli pay in all for the items she bought?

I created this Warm Up problem for students to complete to help me determine student retention of concepts taught during the previous lesson. I am looking for students to show that they know how to do the following:

  1. Add decimal quantities
  2. Recognize when they need to add 
  3. Multiply decimal quantities
  4. Recognize when they need to multiply
 

Engagement

5 minutes

For the opening exercise, I will provide my students with an organizer for the purpose of listing keywords and phrases that help you know when to add, subtract, multiply, and divide. The organizer will have four columns. I will pass out the organizer to my students face down. I will then explain that they will be participating in a race. I will provide the students with the rules to the race which are that they will have 2 minutes to write down as many keywords and phrases that tell you when to add, subtract, multiply, and divide. I will let them know that they will have to write that keyword or phrase under the correct operation on their organizer. 

Once the students have completed the two minute race, I will ask who has at least a total of 10 keywords and phrases. Then, I will increase or decrease the amount when asking the same question based upon my students' responses. Once I figure out who has the most keywords and phrases written on their organizer, I will have that student present their organizer under the document camera. If everything that he/she listed is correct, he/she will win a prize. If their organizer has errors, I will then go to the student with the next highest number of keywords and phrases.

Instruction & Teacher Modeling

10 minutes

Today, I will teach my students a Four Step Problem Solving Process:

Step 1: Understand - In this step, students are taking the time to figure out what information is important to finding the solution to the problem presented. It is in this step that students are to find keywords and/or phrases that will help them to make sense out of the problem.

Step 2: Plan - It is in this step that students create a plan of action. The plan should begin with an entry point into the problem and the steps that must follow to pursue a solution to the problem.

Step 3: Solve - In this step the students execute their plan. 

Step 4: Check - In this step students should be checking their answer to make sure that it makes sense as far as what the problem is asking. If it does, then students should provide a complete answer to that solution. If their answer does NOT make sense, then the student should return to Step 1 and try again.

This process is designed to help a student slow down and take the time to make sense out of a word problem. After teaching this process, I will transition into the Guided Practice where this process will be illustrated.

Try It Out

10 minutes

I will have my students complete the first 2 of 6 problems that will allow students to explore patterns with numbers while using a problem solving strategy. The strategy is a process where the students will complete the following 4 steps:

1. Understand - Students are to figure out what are the facts presented in the problem. They should be able to pull out keywords and important information that will allow them to gain entry into the solving of the problem.

2. Plan - Once the students understand the problem and what it is asking them to do, then they need to figure out the manner in which they will solve this problem.

3. Solve - After planning a strategy to solving the problem, then the students need to try their strategy to see if it works.

4. Check - Once arriving at an answer to the problem, students need to check to see if their strategy lead to an answer that makes sense. If not, student need to start this process over to see what they may have missed.

The first two problems provide step by step assistance to the solution. These cases will serve as an example as to how to approach and solve the other 4 problems that will be completed during the independent practice.

Independent Exploration Jigsaw

20 minutes

Students will continue to work on the six problems presented in the Guided Practice. These problems allow students to learn about strategic problem solving. The first two of the six problems should have been completed during the guided practice for the purpose of providing a step by step example as to the breakdown of the problem solving strategy. The remaining four problems require students to breakdown the problems on their own. Students will complete the remaining four problems during the independent practice.

Prior to completing this assignment, students should be placed in groups of 4. Each group member will be assigned one of the remaining 4 problems. They will be given approximately 5 minutes to solve their problem.

After the 5 minutes have expired, students will then have 10 seconds to regroup themselves according to the problem that they solved. In their new groups, students will compare and discuss their solutions and their method of problem solving. While in their new groups, the students should be talking about why they chose their strategy and how they came to their conclusions. The students will be given 7 minutes for discussion. Then, the students will go back to their original groups and they will discuss all 4 of the problems.

Each students will be given 2 minutes to present their problem and its solution to their other group members. Students will “teach” their peers how to solve their particular problem. By the time all group members have presented, every student should have a step by step solution to every problem in the exploration activity.

Closing Summary

20 minutes

To prepare for the closing, I will ensure that each problem is presented on a PowerPoint slide. I will display each problem one by one giving each problem approximately 4 minutes to be on the table for discussion. While a case is being displayed, each group will be given an opportunity to give commentary on that problem. After 4 minutes of discussion concerning a problem, then we will move on to the next problem and repeat the process. As a teacher, I will ensure to facilitate this discussion so that the understanding that I want students to gain during the conversation does present itself before the 4 minutes of discussion time is up. I will do this by guiding the discussion using strategic questioning.

Some questions that I might ask are as follows:

  • So why did you choose that method?
  • What lead you to choose that method?
  • So what did you think was important in this problem? Why? What did that (keyword, phrase..etc.) tell you?
  • How did you know that your answer was correct?
  • Did your solution provide a correct answer to the problem? How do you know?
  • What did you do to check your answer?

 

The elements that I want students to understand before leaving this lesson are as follows:

  • How to determine what is important in a problem
  • How to understand what a problem is telling you to do
  • How to create a strategy to solving a problem 
  • How to gain entry to a solution to a problem
  • How to determine whether your answer makes sense