Solving Real World Problems Involving Decimals

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Objective

Students iwll be able to solve problems involving adding, subtracting, multiplying, and dividing multi-digit decimal quantities.

Big Idea

Decimals Involved in Problems to Solve: Problem solving with decimals

Curriculum Reinforcer

5 minutes
My students will complete the following problems for Warm Up. This warm up contains simple word problems that are simply for the purpose of getting the students brains working so that they are ready to learn. This warm up will also let me know if there are any students that still struggle with basic word problems. Also, In each of these problems the students will be required to regroup in order to subtract. Often times, students have issues with regrouping, especially regrouping over zeros. This exercise, will help me to see which of my students have that issue.

1. James has 21 pieces of candy. He gives his friend 8 pieces. How many does James have left?  (Answer: 13)
2. Laura and Jill both collect stickers. Jill has 2,010 stickers and Laura has 1,789 stickers. How many more stickers does Jill have than Laura? (Answer 221)
3. Paul goes to the store and purchases a shirt for \$19.99. He gives the sales clerk a \$50 bill. How much change will Paul receive? (Answer: \$30.01)

Engagement

5 minutes

For the opening exercise, I will provide students with time to review the algorithms to calculating with decimals. I will divide the students in groups. I will do this by creating one group of 4 or 5 that contains all of my high academic achievers. The rest of the groups will consist of students with mixed abilities and will also contain 4 or 5 members. I group students in this manner so that the higher achievers get an opportunity to compete and push each other to the next level. It also keeps those particular students from being the "go to" in the group as well as keeping the high achievers from always taking over the group. Grouping my classroom in this manner will create 8 groups.

Each group will be given chart paper and each group will be assigned one of the four operations. As a group, students will write a detailed algorithm as to how to calculate a problem involving a decimal, based upon the operation that was assigned to their group. They will only address the operation assigned to their group. Each group will also provide an example to illustrate their steps.

Instruction & Teacher Modeling

10 minutes

Each group will give a presentation of what they have written on their chart paper. The groups with the same operation will come up together and present side by side one after the other so that their approaches to the assignment can be compared. I will help students to clarify any misconceptions that arise during their presentation by using strategic questioning. To make sure that I am able to do this successfully, I will make sure to have written my own algorithms for each operations so that they too can be compared to what the groups have written. However, my chart with the different algorithms will not be presented until after each pair of groups present their chart. In other words, after the groups who created a chart about addition present then I will present my chart and ask questions to see if anything that I have should be added their chart or if there is anything that needs to be added to my chart.

The presentations made by each group of students will serve as instruction along with the discussions surrounding the presentations.

Try It Out

10 minutes

Students will receive Guided Practice while creating their presentations of the four operations. At that time, teacher will provide feedback concerning their presentation clarifying any misconceptions and driving home conceptions that students need to master. Students will also receive Guided Practice while working on the activities at the stations. There will be four stations total, two of which will be teacher led for those students who are struggling with calculating and understanding the concepts taught in this unit.

Independent Exploration

20 minutes

Students will work on activities in four stations.

Station 1: Vacation Budget – Students will randomly choose a budget for a vacation. Using this budget as a guide, students will plan a vacation to do one of the following; cruise to Jamaica, fly to Hawaii, or travel to spend time in a cabin in the mountains. This center requires students to use the addition algorithm while calculating decimal quantities to ensure that they do not go over budget.

Station 2: Balance That Checkbook – In this station, students will be given a starting balance in their account. This starting balance will be recorded on their check register. Students will then randomly choose 5 expense cards. The students will record their expenses and complete their check register according to the expenses that they chose. Students will show their work at the bottom of their paper. This center requires students to use the subtraction algorithm to balance their “checkbook.”

Station 3: Multiplication Skill Development – Students will have to complete two skill practice problems involving multiplying decimal quantities. Then, students will solve a word problem that requires them to use the multiplication algorithm. Students will highlight keywords and important elements of the word problem before solving.

Station 4: Division Skill Development – Students will have to complete two skill practice problems involving dividing decimal quantities. Then, students will solve a word problem that requires them to use the division algorithm. Students will highlight keywords and important elements of the word problem before solving.

Upon finishing the stations, Students will place their work in the folder designated to their group.

Closing Summary

20 minutes

I will select a group to present their solutions to each of the 4 stations. I may choose 1 group per station or more than one group. The way I choose will depend upon what I see. If I see a common approach to the problem presented in the center as well as an approach that is unique, then I will choose a group to present the common approach as well as the group with the unique approach so that the students can see that there is more than one way to arrive at the same solution.

While presenting, the students will give a detailed description as to their solution process. They will answer my questions as well as questions coming from their peers. Each station will be given a total time of 3 minutes for presentation.

TOTD:

Students will be given four problems to work out to show that they have mastered all four operation algorithms. Students will solve these problems, then provide three keywords that they may see in a word problem that would indicate that they would have to perform the indicated operation.

 PROBLEM KEYWORDS 1)      2,348 + 3.768 = 2)      7,000.984 – 975.1 = 3)      4.671 x 0.21 = 4)      1.36 ÷ 0.4 =