Digital Leadership

Digital Leadership Math Lesson Plan

Teacher: Grade: Math Teacher 6th Grade Lesson Title: Leadership and Problem Solving STRANDS

The Number System

LESSON OVERVIEW Summary of the task, challenge, investigation, career-related scenario, problem, or community link.

A good leader is also a good problem solver. Students will be exploring the Number System through problem solving. First, students will review the Mathematical Practices as problem solving tools. An emphasis will be placed on the similarities of the Mathematical Practices and the Scientific Method. Students will also communicate how they came to their answers through writing.

Next, students will begin their exploration of rational number operations. Students will investigate decimal operations. This will get students ready for the Ship the Chip project. In this project, students will work through the Engineering Design Process to design a package in which to ship a potato chip. Students will be required to calculate the cost of creating and shipping their potato chip package. This requires students to do the operations using rational numbers.

Finally, students will begin their investigation of LCM and GCF. Through this exploration, students will investigate the history of technology. Specifically, they will research how much faster a computer is now than it was during various different periods of time. MOTIVATOR Hook for the week unit or supplemental resources used throughout the week. (PBL scenarios, video clips, websites, literature)

Watch “Are You a Leader?” (See Resource Folder). This video is an inspirational video that illustrates that leaders can come from any walk of life. Students will discuss the character traits of a good leader. Problem Solving is an essential trait of a good leader. Math’s contribution to leadership is problem solving. Students will use their problem solving skills to create their shipping container for “Ship the Chip”.

DAY Objectives Materials & Resources Instructional Procedures Differentiated Assessment (I can….) Instruction

1 I can explain the Differentiated Instruction – Formative Assessments: mathematical practices. Word Problems (See Essential Question: What Remediation: Peer Resource Folder) are the mathematical Tutoring Observations practices? How do they Questioning Mathematical Practice assist me in problem Grouping Ticket Out the Door Poster (See Resource solving? Think-Pair-Share Folder) Mathematical Practices Cubes Rubric for Problem Solving (See Resource Folder) Prompting

Mathematical Practices I Use of Calculators Can Statements (See Resource Folder) Use of an Advanced Organizer Mathematical Practices Four Corners (See Resource Differentiated Instruction – Folder) Enrichment: Use of the more advanced Paper Word Problems.

Pencil

Materials for Differentiated Instruction – Remediation: Advanced Organizer (See Resource Folder)

Mathematical Practices Cubes (See Resource Folder)

Calculators

Materials for Differentiated Instruction – Enrichment: Use some of the more advanced Word Problems (See Resource Folder).

Leadership and Problem Solving

Teaching Strategy:  Explain to the students that we are starting the leadership unit. Ask the students to think about the qualities of a good leader. After giving them some time to think, ask them to turn to their table and share their thoughts with their table. Finally, we’ll discuss this as a whole group.

 If problem solving is not on the list of leader qualities generated by the class, add that onto the list. Problem Solving is the ability to reason through a problem and generate solutions to the problem. It’s not a skill only found in Math. It’s a valuable skill to have in life.  Introduce the Mathematical Practices. Many of the students should already know about the Mathematical Practices, but it’s good to review them. Use the Mathematical Practice I Can Statements to help the students make sense of the standards.

Ask students to compare and contracts the Mathematical Practices with the Scientific Method. Discuss the similarities and the differences.

During this time, introduce the Mathematical Practices Four Corners graphic organizer. This is a tool help them keep their work organized as they are solving problems.  Give each table a complex word problem, such as Jane’s Aquarium. Have them use the Four Corners organizer as they solve the problem. Ask that the students work independently at first. When students have had enough time to process the problem, ask the students to turn to their neighbors and discuss what they have noticed.

Summarizing Strategy: Ticket Out the Door: What are the mathematical practices? How do they assist me with problem solving? 2 I can add, subtract, iPads Essential Question: How Differentiated Instruction – Formative Assessments: multiply, and divide do I add, subtract, multiply Remediation: Think-Pair- decimals. Create a list of at least 30 and decimals? Share Observations expressions that include Ticket Out the Door add, subtracting, Grouping Student responses to the multiplying, and dividing game. decimals. Questioning

Materials for Differentiated Prompting Instruction – Remediation: Expressions with just 1 Use of a Calculator place past the decimal or only whole numbers. Peer Tutoring

Materials for Limit the number of places Differentiated Instruction – after the decimal place to 1 Enrichment: or return to whole number operations. Word Problems involving Decimal Operations Differentiated Instruction – Enrichment: Use word problems during the game instead of expressions. Decimal Operation Tournament

Set: Watch a Review on Operations with Decimals.

Teaching Strategy:

 Give students a multi-digit multiplication problem and a multi-digit division problem. Both problems should include decimals. Have the students work out the problems on their own. Once they have completed the problems, ask the students to compare their results with their table groups. If there is a disagreement, students are to re- work the problem together. Ask for volunteers to AirPlay their work onto the television.  Explain to the students that we are going to be playing a game. The game is called the Decimal Tournament. The game goes as follows:

a. The students will work as a table group. They will decide on the order students will go. They must stay in that order. Only one person per table will be asked to answer the question at a time. They will always go in the pre-determined order.

b. Using your iPad, AirPlay a decimal problem. The students can begin working as soon as the problem is displayed. The first team to raise their hands, will get to AirPlay their work. The only answer that will count will be from the student whose turn it currently is. If the team that raises their hands gets it correct, they get 1 point. If they get it wrong, they get -1 point. c. All students should be working out all of the problems. In the event that all of the groups do not answer the question correctly, the other students will have an opportunity to answer it.

d. Continue the tournament until everyone has had a few turns.

 Discuss any difficult problems as they arise. Ask probing questions to assist students in understanding.

 In order to hold students accountable for the tournament, collect the work for all of the problems that we worked out during the game.

Summarizing Strategy:

Write a set of directions for adding and subtracting decimals, multiplying decimals, and dividing decimals.

3 I can multiply and divide Reasoning about Essential Question : How Differentiated Instruction – Formative Assessments: decimals. Multiplication and Division do I multiply and divide Remediation: Think-Pair- Observations and Place Value decimals? Share Questioning Materials for Differentiated Grouping Ticket Out the Door Instruction – Remediation: Think-Pair-Share Questioning

Calculator Prompting Performance Assessment:

Materials for Differentiated Use of a Calculator Student response to task. Instruction – Enrichment: Peer Tutoring Reasoning about Differentiated Instruction – Multiplication and Division Enrichment: and Place Value Part 2 (See Resource Folder) Reasoning about Multiplication and Division and Place Value Part 2 (See Resource Folder) Reasoning about Multiplication and Division and Place Value

Set: Watch: Solving a Problem, Make a Plan from The Teaching Channel.

Teaching Strategy: 1. Present the students with “Reasoning about Multiplication and Division and Place Value”. Answer any questions the students may have. Allow students to work independently, gathering their ideas on how to solve this problem. After giving students adequate time to work on their own, have them turn to their table and discuss ideas. Ask probing questions in order to stimulate student thinking. 2. Have students work together to fill out the Four Corner graphic organizer (See Resource Folder) for this problem. When they complete the problem, each person in the group will use the rubric (See Resource Folder) and the “I Can Statements” (See Resource Folder) to evaluate the end product. 3. After students have answered the questions on this task as a group, ask each student to recreate this problem on their own with different numbers. Students are to write their new problem out on a piece of paper. (Students are to answer their own questions on another sheet of paper. These will be stapled together at the end of class to be turned in.) 4. Ask students to exchange papers with another student and they will workout the problems of the other student. Summarizing Strategy: Ticket Out the Door: Turn in the problems you made and the answers to your questions. Please explain your reasoning to your questions.

Project Day 1 – refer to Unit Plan

Topic – “Ship the Chip”- Leadership

6 I can find the GCF of two Materials for Differentiated Essential Question: How Differentiated Instruction – Formative Assessments: whole numbers less than or Instruction – Remediation: do I find the GCF of two Remediation: Think-Pair- equal to 100. whole numbers less than or Share Observations equal to 100? Questioning Calculator Grouping Ticket Out the Door Think-Pair-Share Materials for Differentiated Questioning Foldable Instruction – Enrichment: Prompting GCF with Algebraic Expressions Use of a Calculator

Peer Tutoring

Differentiated Instruction – Enrichment:

GCF with Algebraic Expressions Set: Watch this video on Finding GCF Using the Ladder Method.

Teaching Strategy:  Ask students to define the word factor. Let them think about it for a short time. Then let them pair with their tablemates, and then ask for a volunteer to share the definition of factor.  Next asked students what the Greatest Common Factor is. Discuss the definition. Ask them what the Greatest Common Divisor is. This is sort of a trick question because GCF and GCD are actually the same thing.  Pass out paper to do a foldable. We will be doing a shutter fold with 4 flaps. We will only be working with the top two flaps. The bottom two flaps will be filled in a later lesson. Ask the students to label the top left flap as GCF List Method.  Inside the flap, ask the students to copy down an example as you teach them how to do the list method of finding the GCF of two numbers. a. GCF (12, 18). b. List all of the factors of 12. (1,2,3,4,6,12) c. List all of the factors of 18. (1,2,3,6,9,18). d. Find the greatest factor they have in common. In this case, it’s 6.  Continue to give students examples. First model for the students, then guide the students, then allow the students work collaboratively, then ask the students to work independently.  Ask the students to write GCF Ladder Method on the top right flap.  Inside the flap, ask students to copy down an example as you teach them how to do the ladder method of finding the GCF of two numbers. a. GCF (24, 36) b. Write the numbers inside an upside down division box as shown below:

c. Ask the students to identify a number that is a factor of both. For example, let’s say a student identifies the factor of 4 that divides into both evenly. Record the 4 on the outside of the box, and record the quotients below as shown:

d. Ask the students to identify a factor of both 6 & 9. A student might say that 3 is a factor of both 6 & 9. Record the 3 and the quotients as shown. e. Ask the students if there is a common factor for both 2 & 3. Once the class agrees that there is not one (other than 1), inform the class that we have reached the endpoint. The GCF can be found by multiplying the numbers on the left hand side, as shown below: f. By multiplying 4 x 3, we find that the GCF of 24 & 36 is 12. This method works regardless of the numbers chosen by the students. For example, you could have started with a 2 as a common factor rather than 4, and the result would have been the same.  Continue to give students examples. First model for the students, then guide the students, then allow the students work collaboratively, then ask the students to work independently.

Summarizing Strategy: Have the students write a paragraph explaining what a GCF is, and describe a method to find the GCF of a pair of numbers. Provide them with an example as a guide. 7 I can find the LCM of any Materials for Differentiated Essential Question: How do Differentiated Instruction – Formative Assessments: two whole numbers less Instruction – Remediation: I find the LCM of any two Remediation: Think-Pair- than or equal to 12. whole numbers less than or Share Observations equal to 12? Questioning Calculator Grouping Ticket Out the Door Think-Pair-Share Materials for Differentiated Questioning Foldable Instruction – Enrichment: LCM and Algebraic Prompting Expressions Use of a Calculator

Peer Tutoring

Differentiated Instruction – Enrichment:

LCM and Algebraic Expressions Set: Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookie. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need?

Have students collaborate to find the answer. Discuss what students found. This will serve as a review of GCF.

Teaching Strategy: 1. Review with the students the term “Multiple”. How is it different than “Factor” (since the two terms are often confused)? . Let them think about it for a short time. Then let them pair with their tablemates, and then ask for a volunteer to share the definition of factor. 2. Next asked students what the Least Common Multiple is. Discuss the definition. 3. Ask students to pull out their foldables from the previous day. 4. Have students label the bottom left flap as LCM List Method. Inside of the flap, have students copy down an example as you teach them how to find the LCM of two numbers. a. LCM (4, 12) b. List all of the multiples of 4: 4, 8, 12, 16, 20, 24, 28… c. List all of the multiples of 12: 12, 24, 36… d. The least number the two have in common is the least common multiple. 5. Continue to give students examples. First model for the students, then guide the students, then allow the students work collaboratively, then ask the students to work independently. 6. Ask the students to write LCM Ladder Method on the bottom right flap. 7. Inside the flap, ask students to copy down an example as you teach them how to do the ladder method of finding the LCM of two numbers. 8. This is done the same way as listed in GCF, expect when we finish, we multiply all of the numbers listed on the outside of the ladder. For example:

LCM (24, 36) = 9. Continue to give students examples. First model for the students, then guide the students, then allow the students work collaboratively, then ask the students to work independently.

Summarizing Strategy: Have the students write a paragraph explaining what a LCM is, and describe a method to find the LCM of a pair of numbers. Provide them with an example as a guide.

8 I can use GCF and LCM to Bake Sale (See Resource Essential Question: How Think-Pair-Share Formative Assessments: solve a problem. Folder) can I use GCF and LCM to Working with a group. Observations solve problems? Materials for Differentiated Questioning Instruction – Remediation: Questioning Ticket Out the Door Think-Pair-Share Differentiated Instruction – Calculator Remediation: Performance Task: Student Materials for Differentiated Use a calculator response to the task. Instruction – Enrichment:

Ask students to come up with their own LCM and Differentiated Instruction – GCF problems. Enrichment: Ask students to come up with their own LCM and GCF problems. Bake Sale Task

Set: Review GCF and LCM Using the Ladder Method Video (See Resource Folder).

Teaching Strategy: Present the students with “Bake Sale” (See Resource Folder). Give the students some time to read through and understand the question. Answer any questions the students have about the problem. Allow students to work independently. After giving students adequate time to being the problem on their own, ask students to talk with their table groups to see what they have discovered.

Have students work together to fill out the Four Corner graphic organizer (See Resource Folder) for this problem. When they complete the problem, each person in the group will use the rubric (See Resource Folder) and the “I Can Statements” (See Resource Folder) to evaluate the end product.

Summarizing Strategy: Ticket Out the Door: How did your knowledge of GCF and LCM help you solve this problem?

Project Day 4– refer to Unit Plan

Topic – “Glogster Reflection”- Leadership

STANDARDS Identify what you want to teach. Reference State, Common Core, ACT College Readiness Standards and/or State Competencies.

6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).