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Mathematical Practices Lesson-Planning Tool

 

Name:

Erin Barbieri

Grade Level/School/Mentor: 

5th Grade/Woodrow Wilson/Morgan

Unit: Add and Subtract Decimals                                               

Date:

Nov. 2016

Lesson Title:

Iphone in the mail

Utah Elementary Math Learning Standard [State the strand/standard for the unit addressed by this lesson.]

Strand: NUMBER AND OPERATIONS IN BASE TEN (5.NBT) Standard 5.NBT.7

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. In this standard, dividing decimals is limited to a whole number dividend with a decimal divisor or a decimal dividend with a whole number divisor. Compare the value of the quotient on the basis of the values of the dividend and divisor.

Learning Objective Specific to Lesson: As a result of today’s lesson, students will be able to . . .

Students will add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies.

Overarching Essential Question(s) Specific to Lesson

How accurate (precise) does this solution need to be?

Targeted Mathematical Practices: As a result of today’s lesson, students will have opportunities to . . .   [select the targeted practice standard(s) for this lesson].

Apply number and operation to add and subtract to the hundredths in order to equal whole numbers and an exact total.

1-Make sense of problems and persevere

2-Reason abstractly and quantitatively

3-Construct viable arguments and critique the reasoning of others

4-Model with mathematics

5-Use appropriate tools strategically

6-Attend to precision

7-Look for and make use of structure

8-Look for and express regularity in repeated reasoning

Prerequisite Knowledge This Lesson Draws Upon:   

  • Read, write, and compare decimals to thousandths.

  • Use place value understanding to round decimals to any place

  • Place value understanding and the role that this plays in decimal computation.

Vocabulary Focus

  • Postage

  • Estimation

  • Currency

Materials*/Resources/Technology

  • Math Journals

  • Stickers to represent stamps

  • Pencils

  • Padded envelope

  • Bubble wrap

  • Small box

 

Lesson Purpose (Introduce; Build Understanding/Make Connections; Solidify/Get Precise/Get General/Practice/Reinforce)

Students will demonstrate strategies for solving the problems and be able to determine the efficiency of various strategies for computing decimal numbers.  Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Brief Overview of Lesson

Anticipated Time Frame

Present a real life problem of having to send a package with stamps

60 minutes

Formative Assessment/Evaluation Strategies: How will students be expected to demonstrate their understanding of the learning objective? How will you make student learning visible?

Students will record their work in their math journal and report their strategies to the class.

Access for All: (How will you ensure that all students have access to and are able to engage appropriately in this lesson?  Adaptations--for Gifted/Talented, ELL, and other Special Needs)

  • Organizational strategies including graph paper, T-Charts, etc.

  • Modeling with coins and dollars

  • Cut-outs of the stamps

  • Display Vocabulary with definition on the board or math wall

Probing Questions for Differentiation on Mathematical Tasks

Assessing Questions—to Scaffold

[Create questions to scaffold instruction for students who get stuck during the lesson.]

Advancing Questions—to Elaborate/Extend

[Create questions to move the learning forward for students who are ready to advance beyond the learning objective.]

  • Talk me through the steps you’ve used to this point.

  • What would happen if you tried to use only $.33 stamps or only $.15 stamps?

  • What is the closest postage you can get if you use only $.33 stamps?

  • In what ways could a table or chart help you organize the combinations you’ve tried?

  • Extension 1: I still want to use up my $.33 and $.15 stamps, but I decide to add additional bubble wrap to the padded envelope/package. This added weight increases the total postage to $2.77. Can you make postage equal to $2.77?

  • Extension 2: Since I had to add the extra bubble wrap I am worried that the envelope will open and my iPhone will get lost, so I decide that it will be best to mail a larger package The total postage will now be $4.77.

  • Extension 3: I want my phone back faster so I am going to overnight my package, but this costs more money and now the postage total is $17.76!

 

 

 

INSTRUCTIONAL PROCEDURES/Lesson Sequence

 

Here you will outline the sequence and content of the activities in a step-by-step format to help a reader understand how you see the lesson unfolding.  This is the heart of your lesson plan!

 

TASKS

What will the teacher be doing?

[How will the teacher present and then monitor student response to the task?]

 

What will the students be doing?

[How will students be actively engaged in each part of the lesson?]

Beginning of Class

How does the warm-up/starter activity connect to students’ prior knowledge, or how is it based on analysis of homework?

I enter the class sad and I explain to the class that I was playing Pokemon Go and I fell and broke my phone.  I explain that my phone does not work, but the good thing is that I have insurance, but I have to mail it to T-Mobile.

Students will be sitting in their desks already arranged in teams of 3 and 4 students.

  1. Engage:

How does this part of the lesson engage students in the learning objective?

I am connecting the class to this lesson by giving them a problem that they themselves have had or know someone has had.  The students will also be able to relate playing Pokemon Go or playing a game on a mobile device.

Students will be sitting in their desks already arranged in teams of 3 and 4 students.

  • Students may have questions for my story and I will answer 2 questions before moving on.

  1. Launch:

How will you introduce students to the task so that they are invited to work like a mathematician? How will you check/know that students are ready to work on the task? How will you distribute materials, transition into individual or small-group work, keep students engaged in the lesson . . . signal students back to whole group?

 

I month ago I found a bunch of old stamps and I decided that this would be a great time to use up the rolls of old stamps. What combination of $.33 and $.15 stamps will total the exact postage of $1.77? Record all your work and strategies in your math journal.

Students will work in pairs or groups of 3.  If students are sitting in a group of 4 they will work with the person to their right or left, not across from them. 

  1. Explore:

How will the task develop student sense making and reasoning? How will the task require student communication and development of practice standards?

 

Students will work together in their groups or pairs to solve the problem.  They will be asked to keep notes on their progress and work the problems out in their journals.

  • Students will be encouraged to draw pictures, write out the problem in multiple ways, and use multiple strategies.

Students will work together in their groups or pairs to solve the problem.  They will keep notes on their progress and work the problems out in their journals.

 

  1. Explain, Synthesize, Reinforce:

How will student sharing, questions, and reflections be elicited in this part of the lesson? How will student thinking be brought into the open? What kinds of questions and math talk strategies might support communication and reinforce learning objectives?

 

  • Guess and check – Estimation

  • Money (coins/bills) representation – Picture model

  • Table/Chart of possible combinations

  • Algorithms with repeated addition of decimals amounts

  • Algorithms with multiplication of decimals amounts

 

$1.77 Task Solution: Four 33¢ stamps and three 15¢ stamps equals $1.77 in postage.  [Use as many $.33 stamps as you can so that the remainder can be made with $.15 stamps]

  • Could we have used another operation or property to solve this task? Why or why not?

  • How did you decide in this task that you needed to use...(repeated addition, multiplication)?

Extension 1 $2.77 Solution: There is no way to make the additional dollar ($2.77) of postage from combinations of $.33 and $.15 stamps.

  • Why did this not work? What do we know about multiples in relation to the numbers involved in this task?

Extension 2 $4.77 Solution: You already know how to make $1.77 in postage. Make the additional $3.00

  • By using five $.33 stamps and nine $.15 stamps or twenty $.15 stamps.

  • Either twelve $.15 stamps and nine $.33 stamps, or twenty-three $.15 stamps and four $.33 stamps make $4.77 in postage.

  • What patterns do you find?

  • What ideas that we have learned before were useful in solving this problem?

  • What would be a more efficient strategy?

Extension 3 $17.76 Solution: You already know how to make $1.77 and $3.00 in postage. Use your prior knowledge to make increments of $3.00 using twenty $.15 stamps. Five sets of $3.00 plus the set for $1.77 equals $16.77. Since $17.76 is $.99 more than $16.77, you need three more $.33 stamps. The $17.76 in postage can be made using thirty-two $.33 stamps and forty-eight $.15 stamps, or one hundred three $.15 stamps, and seven $.33 stamps.

  • How did you know your solutions were reasonable?

  • What ideas that we have learned before were useful in solving this problem?

Encourage students to share their strategies and solutions with the class.

  1. Recap and Close:

How will you close the lesson so that students have something to “take away” from the lesson? Learning Residue!

 

Have students return pencils, put away math journals, and clean off desks.

Ask:

  • Does anyone find this problem helpful in a real life situation?

  • How would you use what you learned today in your life?

  • If you do not mail things how do you get things from place to place?

  • Do you have to have the exact amount when mailing a letter or package?

  • What would have been easier?

Students will remain in their assigned desks and participate in an open discussion about today’s problem.

 

Students can go home and try calculating the number of stamps needed at the current rate of $0.49 and/or research FedEX and UPS rates, compare costs, and delivery times.

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