Objectives - Tennessee STEM Innovation Web viewStudents will use their problem solving skills to create their shipping container for “Ship the ... word problem, such as ... help

Leadership 2 Weeks

MathLesson Plan

Teacher: Math Teacher Grade: STEM Math IALesson 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. First, they will research the properties. Next, they investigate the algorithms of adding and subtracting integers. Both of these 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 Multiplying and Dividing Integers. 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?” . 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 DifferentiatedInstruction

Assessment

(I can….)

1 I can explain the mathematical practices.

I can use the mathematical practices to help me solve problems.

See Resource Folder for the following:

Word Problems

Mathematical Practice Poster

Rubric for Problem Solving

Mathematical Practices I Can Statements

Mathematical Practices Four Corners

Paper

Pencil

Materials for Differentiated Instruction – Remediation:Advanced Organizer

Mathematical Practices Cubes

Calculators

Essential Question:1. What are the mathematical practices?2. How do I use them to help me solve problems?

Differentiated Instruction – Remediation:

Peer Tutoring

Grouping

Mathematical Practices Cubes

Prompting during group work

Use of Calculators

Use of an Advanced Organizer

Differentiated Instruction – Enrichment:Use of the more advanced word problems.

Formative Assessments:

ObservationsQuestioningTicket Out the DoorThink-Pair-ShareStudent response to word problem.

Leadership and Problem Solving

Set: 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.

Teaching Strategy:1. 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.

2. 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.

3. Give each table a complex word problem, such as The Checker Board Problem (see Word Problems in resource folders). 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.

Materials for Differentiated Instruction – Enrichment:Use some of the more advanced word problems.

Summarizing Strategy: Ticket Out the Door: What are the mathematical practices? How do they assist me with problem solving?

2 I can simplify expressions using the properties.

iPad

"Math Properties”

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

Calculators

Materials for Differentiated Instruction – Enrichment:Simplifying Algebraic Expressions with the Distributive Property.

Essential Question: How to do simplify expressions using the properties? Differentiated Instruction – Remediation: Peer Tutoring

Grouping

Prompting

Use of Calculators

Use of a foldable

Differentiated Instruction – Enrichment:Simplifying Algebraic Expressions with the Distributive Property.

Formative Assessments:

Observations

Questioning

Ticket Out the Door

Think-Pair-Share

Foldable

Math Properties

Set: Have students watch this video titled “"Math Properties" on TeacherTube.

Teaching Strategy:

Ask students if they have heard of the properties we have in Math. Assign table groups to research and teach the class about one of the following properties: Commutative Property of Addition, Commutative Property of Multiplication, Associative Property of Addition, Associative Property of Multiplication, Identify Property of Addition, and the Identity Property of Multiplication. Give groups 5 minutes to research and 5 minutes to come up with their presentation. Their presentation must include an example of their property.

Students will present. While students are not presenting, they are to take notes. A foldable is available for students who need extra support. Ask probing questions to enrich the students’ presentations.

Show students examples of properties. Ask them to identify the property.

After the presentations are over, ask students to multiply 12x24 in their head. Use these student answers to describe the distributive property. This problem can be done two ways.

12×24=12 (20+4 )=12 (20 )+12 (4 )=240+48=288

or

12×24=(10+2 )24=24 (10 )+24 (2 )=240+48=288

After giving these two examples to the students, ask them what they notice about the two methods. Ask them if they can describe the distributive property.

Give the students some more examples of the distributive property. Ask the students to simplify the expression using the distributive property. Model a few examples for the students. Guide the students through some examples. Allow the students to work collaboratively through some examples. Finally, ask students to work independently through some examples. The examples can include:

a. 15×34

b. 112×14

c. 125×28

d. Katelyn’s ballet class is performing a spring recital for which they need

butterfly costumes. Each fairy costume is made from 6 34 yards of fabric. Use the

Distributive Property to find the number of yards of fabric needed for 7 costumes. (Hint: a mixed number can be written as the sum of an integer and a fraction.)

e. During a math facts speed contest, Jacob calculated the following expression faster than anyone else in his class.

196×9

When classmates asked him how he was able to answer so quickly, he told them he used the Distributive Property to think of the problem differently. Write and evaluate an expression using the Distributive Property that would help Jacob perform the calculation quickly.

Summarizing Strategy:

Ask students to create their own multiplication problem and to use the distributive property to simplify the expression

3 I can add integers.

Two Color Counters

Essential Question: How do I add integers? Differentiated Instruction –

Formative Assessment:

Paper for Foldable

Rulers

Khan Academy video

Materials for Differentiated Instruction – Remediation:

Calculators

Materials for Differentiated Instruction – Enrichment:Adding positive and negative Decimals.

Remediation: Peer Tutoring

Grouping

Prompting

Use of Calculators

Differentiated Instruction – Enrichment:Adding positive and negative Decimals.

Observations

Questioning

Ticket Out the Door

Foldable

Student created examples

Adding Integers

Set: Watch the Khan Academy video on Absolute Value.

Teaching Strategy: Pass out the paper to make a foldable. The students will be making a shutter

fold with four flaps. (For directions, please visit this website.) This foldable will be used for a few days. The first flap is labeled with “Addition with Like Signs”. The second is labeled with “Additional with Unlike Signs”. The third is Subtraction. The last is for multiplication and division. Have students put the foldable to the side.

Review with the students the concept of a zero pair. A zero pair is 1 positive and 1 negative combined creates zero. Make any clarifications that need to be made. Next, explain to the students how to use the colored tiles (yellow is positive and red is negative).

Model adding with like signs for the students. Start out by modeling positive addition, because this is something familiar for the students. Next, move on to negative numbers. Have the students model problems for each other and for the class. The examples can include -1+-5, -2+-7, -4+-6. When students have discovered the algorithm, have them write it in their own words in the foldable. Also have students draw a picture to explain the algorithm.

After everyone understands the algorithm for adding like signs, move on to unlike signs. Model problems for the students. These examples can include -2+5, -7+3, 8+(-3), and 6+(-4). Have table groups create problems for each other. Encourage conversations about what they are observing at the tables. When students have discovered the algorithm, have them write it in their own words in the foldable. Also have students draw a picture to explain the algorithm.

Summarizing Strategy:Students will write a Dear Teacher letter (See Resource Folder). This note will include what they already know about integers, what they liked/disliked, and what they are unclear about integers.

4

Project Day 1– refer to Unit Plan

Topic – “Ship the Chip”- Leadership

5

Project Day 2 – refer to Unit Plan

Topic – “Ship the Chip”- Leadership

6 I can subtract integers.

Subtracting Integers

Two Color Counters

Paper for Foldable

Rulers

Materials for Differentiated Instruction – Remediation:

CalculatorsMind MapFlow Chart

Materials for Differentiated Instruction – Enrichment:Adding positive and negative Decimals.

Essential Question: How do I subtract integers? Differentiated Instruction – Remediation: Peer Tutoring

Grouping

Prompting

Use of Calculators

Mind Map

Flow Chart

Differentiated Instruction – Enrichment:Adding positive and negative Decimals.

Formative Assessment:

Observations

Questioning

Ticket Out the Door

Foldable

Subtracting Integers

Set: Watch this video on Subtracting Integers video.

Teaching Strategy: Review with the students how to add using the two-color counters. Model subtraction with the students using the two color counters. Start out

by subtracting with like signs, because this is familiar to the students. These examples can include 5-2, 7-3, 3-5.

Next move on to negative numbers. Have students model problems for each other and for the class. When students have discovered the algorithm, have them write it in their own words in their own words in their foldable. Also have students draw a picture to explain the algorithm.

If needed, model subtraction on a number line for the students as well. Continue doing examples until all students can explain how to subtract with integers. Have students work with their table groups.

Summarizing Strategy: Write the directions to subtracting integers. Please include examples in your explanation.

7 I can add and subtract integers.

Problem-Solving Rubric

Positive or Negative

Materials for

Essential Question: How do I add and subtract integers? Differentiated Instruction – Remediation: Peer TutoringGroupingPromptingUse of Calculators

Formative Assessment:ObservationsQuestioningTicket Out the DoorThink-Pair-Share

Positive or Negative Task

Set: Watch this video on Adding and Subtracting Integers.

Teaching Strategy: Present the students with the “Positive or Negative” task. Work

Differentiated Instruction – Remediation:

CalculatorsMind MapFlow Chart

Materials for Differentiated Instruction – Enrichment:Adding and

through the task on his/her own. Encourage students to show as much detail in their problem solving. They may use the Four Corner organizer used on Day 1 of this unit.

As student finish, pair the students up and ask them to critique each others’ work using the problem-solving rubric. In addition, students should tell each other at least two things they liked about how the other students did the problem. When they are done, they should thank each other.

Summarizing Strategy: Give the students an exit ticket that includes addition and subtraction of integer problems.

Mind MapFlow Chart

Differentiated Instruction – Enrichment:

Adding and Subtracting positive and negative fractions.

Summative Assessment:Student Answers to the Task.

8 I can multiply and divide integers.

VCR or DVD player

Video

Foldable

Instruction – Remediation:

CalculatorsMind MapFlow Chart

Materials for Differentiated Instruction – Enrichment:Multiplying Decimals

Multiplying and Dividing Fractions

Essential Question: How do I multiply and divide integers?Differentiated Instruction – Remediation: Peer TutoringGroupingPromptingUse of CalculatorsMind MapFlow Chart

Differentiated Instruction – Enrichment:

Adding and Subtracting positive and negative fractions.

Formative Assessment:ObservationsQuestioningTicket Out the DoorThink-Pair-Share

Multiplying and Dividing Integers

Set: Play a fun and appropriate movie clip. Fast forward the clip and rewind the clip at different speeds for comedic effect.

Teaching Strategy: Have students take out their foldable from last week. Review with them

what they learned last week. Ask students to imagine a person who was walking (forward) at 2 steps per

second was videotaped. Have a student demonstrate this by walking across the front of the classroom for all students to see. We are now pretending that we are watching the videotape.

If we pressed the forward button on the VCR and suppose that the forward button speeds up the tape 3 times as fast as normal playing, how fast would the person be walking/running now? (You can have someone demonstrate this, too.) The students will answer 6 steps per second. Write down the multiplication example used to solve this problem: 2 x 3 = 6.

If we pressed the rewind button on the VCR and suppose that the rewind button speeds up the tape twice as fast as normal playing as it runs backwards, how fast would the person be walking/running now? The students will answer 4 steps per second. Next, ask the students if the person is running in the same direction? The answer is no; the person is running backwards now so we must use a negative sign in our answer to indicate that the direction has changed. So the answer is –4. Write down the multiplication example used to solve this problem: 2 x (-2) = -4.

Suppose that the person who was videotaped was originally walking backwards at 2 steps per second. Have a student demonstrate this by walking backwards across the front of the classroom.

If we pressed the forward button on the VCR and suppose that the forward button speeds up the tape 3 times as fast as normal playing, how fast would the person be walking/running now and in what direction would they be walking/running? The students will answer 6 steps per second backwards.

Write down the multiplication example used to solve this problem reminding the students that backwards must be indicated by writing a negative sign with the number: -2 x 3 = (-6).

If we pressed the rewind button on the VCR and suppose that the rewind button speeds up the tape twice as fast as normal playing as it runs backwards, how fast would the person be walking/running now? The students will answer 4 steps per second. Next, ask the students if the person is running in the same direction? The answer is no; the person who was running backwards has reversed and is now running forward. So the answer is 4. Write down the multiplication example used to solve this problem: -2 x (-2) = 4.

Have students turn to their table and discuss what this means. Have students construct meaning of multiplying and dividing integers through this. If there are students that need extra examples, use patterns in function tables to show them the pattern. Once students have discovered the algorithm, have them write it in their own word in their foldable and draw a picture to explain the algorithm.

Summarizing Strategy: Ticket Out the Door: How do you, in your own words, multiply and divide integers?

9

Project Day 3– refer to Unit Plan

Topic – “Ship the Chip”- Leadership

10

Project Day 4– refer to Unit Plan

Topic – “Glogster Reflection”- Leadership

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

1. 7.NS.1.d. Apply properties of operations as strategies to add and subtract rational numbers.

2. 7.NS.2.c. Apply properties of operations as strategies to multiply and divide rational numbers.

3. 7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers.