TransportationTwo Week

/ Math
Lesson Plan
Teacher:6th Grade Teacher / Grade: STEM Math IA
Lesson Title: Geometry and Boats
STRANDS
Geometry and the Number System
LESSON OVERVIEW / Summary of the task, challenge, investigation, career-related scenario, problem, or community link.
The 6th grade team will be exploring transportation through our maritime modes of transportation. In Math class, students will be investigating volume, integers, and the coordinate plane. Students will investigate volume using manipulatives and tasks. The lessons will tie into Science through discussion of buoyancy, to Social Studies through calculating the square kilometers of different countries, and English Language Arts through reflections of learning.
MOTIVATOR / Hook for the week unit or supplemental resources used throughout the week. (PBL scenarios, video clips, websites, literature)
Students will watch the video titled Dagger Kayaking (See Resource Folder). This video mentions how the volume of a boat will define both the way that a boat travels through a rapid and the maneuvers the boater will be able to do with the boat. Discuss with the students why this happens.
DAY /
Objectives
(I can….) /

Materials & Resources

/

Instructional Procedures

/ Differentiated
Instruction /

Assessment

1 / I can determine the area of a composite figure. / Guided Notes on Area of Composite Figures (See Resource Folder)
Composite Figure Exit Ticket (See Resource Folder)
Materials for Differentiated Instruction – Remediation:
Calculators
Materials for Differentiated Instruction – Enrichment:
Composite Figure Extension (See Resource Folder) / Essential Question:How do I determine the area of a composite figure? / Differentiated Instruction –
Remediation:
Peer Tutoring
Questioning
Calculators
Differentiated Instruction –
Enrichment:
Questioning
Peer Tutoring
Area of Composite Figures Extension / Formative Assessment:Class discussion
Informal Observations
Exit Ticket
Summative Assessment:
Homework
Lesson Title: Area
Set: Watch the Virtual Nerd video on Finding Area of a Triangle.
Teaching Strategy:
  1. Discuss with students the meaning of area. Area is the number of square units it takes to cover a two-dimensional figure. Ask students what they already know about finding area of polygons. Keep a list of what students already know and review with the students how to use some of the formulas.
  2. Ask students to open Guided Notes Composite Figures. This document is for students to take notes and workout examples. Go through this document. Be sure to balance examples that are modeled, guided examples, and independent practice.
Summarizing Strategy: Area of Composite Figures Exit Ticket (See Resource Folder)
Practice problems will be assigned for homework.
2 / I can calculate the area of circles. / The Paper Plate Activity (See Resource Folder)
Area or Circumference(See Resource Folder)
Gallery Walk (See Resource Folder)
Materials for Differentiated Instruction – Remediation:
Calculators
Materials for Differentiated Instruction – Enrichment:
iPads / Essential Question: How do I calculate the area of a circle? / Differentiated Instruction –
Remediation:
Use of calculators
Peer tutoring
Differentiated Instruction –
Enrichment:
Students can research real examples of circles and calculate the area. / Formative Assessment:
Informal observations
Ticket Out the Door
Performance Assessment:
The Paper Plate Task
Summative Assessment:
Homework
Lesson Title: Area of Circles
Set: Show the video on Area of Circles from the Khan Academy. After the video, discuss the formula for finding the area of a circle.
Teaching Strategy:
  1. Explain to the students that we are going to discover on our own how the formula for area was created. We know that the formula for area is A=πr² but we want to know why.
  2. Have students open the Paper Plate Task (See Resource Folder).
  3. Hand out different sized paper plates to each group. Using the paper plate, have students answer questions 1-3. Walk around to make sure that the groups have the correct answers before moving on.
  4. Have each group find the center of their paper plate. Then have them cut the paper plate into 8-10 equal parts (like a pizza).
  5. Groups will then glue their pieces on a piece of construction paper in the shape of a parallelogram.
  6. Ask the groups to complete questions 4-5 on their activity sheet.
  7. Discuss questions 6-7 as a class. When asking how the parallelogram and circle are related, students should mention how the height of the parallelogram is equal to the radius of the circle.
  8. Have groups answer questions 8-11.
  9. Have the groups do a “Gallery Walk” clockwise around the room to look at the other groups finished products.
  10. During the “Gallery Walk” have the groups calculate the area of the circles with the given information. Each member of the group will show their calculations on the “Area Gallery Walk” (See Resource Folder)hand out.
  11. Have each group present their final product. Each group will share their calculations and the area. The other students will check their work during the presentations.
Summarizing Strategy: As a Ticket Out the Door, students will complete Area or Circumference? (See Resource Folder). They will read a problem and decide whether or not they need to find area or circumference to solve the problem.
Practice problems will be assigned for homework.
3 / I can use area and circumference to solve problems. / The Pizza Crust Task (See Resource Folder)
Circumference and Area of a Circle Formulas Video (See Resource Folder)
Materials for Differentiated Instruction – Remediation:
Calculators
Materials for Differentiated Instruction – Enrichment:
Card Stock / Essential Question:How do I use area and circumference to solve problems? / Differentiated Instruction –
Remediation:
Peer Tutoring
Questioning
Calculators
Differentiated Instruction –
Enrichment:
Questioning
Peer Tutoring
Have students design a box for one of the pizzas. Have students calculate the area of the pizza box. / Formative Assessment: Class discussion
Informal Observations
Ticket Out the Door
Performance Assessment:
The Pizza Crust Task sheet
Summative Assessment:
Homework
Lesson Title: The Pizza Crust Task
Set: Watch the Circumference and Area of a Circle Formulas video (See Resource Folder).
Teaching Strategy: Introduce The Pizza Crust Task to the students (See Resource Folder). This task allows students to work with real-life situations dealing with circumference and area.
Have students complete Part A of the task. When they have finished, have students check with their table groups to make sure everyone has the correct formulas listed.
Have students complete Part B. Allow students to first work on the task independently. This allows students to generate their own solutions to the task. When finished, have the students compare their answers with the rest of their table. If students end up with different answers, have students prove how they got their answer.
Have students complete Part C and Part D. Allow students to first work on the task independently. This allows students to generate their own solutions to the task. When finished, have the students compare their answers with the rest of their table. If students end up with different answers, have students justify how they got their answer.
Summarizing Strategy: Ticket Out the Door: Students create their own word problem that involves finding the area and circumference of a circle. They will answer the problem.
Practice problems will be assigned for homework.
4 / I can calculate volume of Prisms and Pyramids. / Geometric Solids
Guided Notes for Volume of Prisms and Pyramids (See Resource Folder)
Pyramid and Prism Extension (See Resource Folder)
Area Review (See Resource Folder)
Materials for Differentiated Instruction – Remediation:
Calculators
Materials for Differentiated Instruction – Enrichment:
Pyramids and Prisms Extension (See Resource Folder). / Essential Question:How do I calculate the volume of Prisms and Cylinders? / Differentiated Instruction –
Remediation:
Peer Tutoring
Questioning
Calculators
Differentiated Instruction –
Enrichment:
Questioning
Peer Tutoring
Pyramids and Prisms Extension (See Resource Folder). / Formative Assessment: Class discussion
Informal Observations
Exit Ticket
Guided Practice and Independent Practice
Summative Assessment:
Homework
Lesson Title: Volume of Prisms and Pyramids
Set: Have students complete some area review questions (See Resource Folder).
Teaching Strategy:
  1. Ask students to define volume. Many students will answer by giving formulas they already know. Encourage students to explain the definition (volume is how many cubic units a three-dimensional figure will hold).
  2. Show the students a rectangular prism. Ask the students what the formula is for finding the volume of a rectangular prism. Most students now this as , but they don’t know why. Lead the students in a discussion about why the formula is . The reason is because is the area of the base. The formula to find the volume of any prism is .
  3. Using the Guided Notes for Volume of Prisms and Pyramids (See Resource Folder), work through the prism section with the students. Balance between modeled problems, guided problems, and independent problems.
  4. After completing volume section, take out a prism and pyramid with congruent bases and heights. Ask students how many pyramids it would take to fill the prism. Demonstrate for students that it takes 3 pyramids to fill the prism. This can be done with sand or water. Since it took 3 solids, the formula for find the volume of a pyramid is .
  5. Continue with the Guided Notes for Volume of Prisms and Pyramids (See Resource Folder). Balance between modeled problems, guided problems, and independent problems.
Summarizing Strategy: Exit Ticket: Volume of Prisms and Pyramids (See Resource Folder)
Practice problems will be assigned for homework.
5 / I can calculate the volume of cylinders and cones. / Volume of Cylinders and Cones (See Resource Folder)
Cylinder and Cones Exit Ticket (See Resource Folder)
Materials for Differentiated Instruction – Remediation:
Calculator
Materials for Differentiated Instruction – Enrichment:
Extension Volume of Cylinders and Cones (See Resource Folder). / Essential Question:How do I calculate the volume of cylinders and cones? / Differentiated Instruction –
Remediation:
Peer Tutoring
Questioning
Calculators
Differentiated Instruction –
Enrichment:
Questioning
Peer Tutoring
Extension Volume of Cylinders and Cones (See Resource Folder). / Formative Assessment: Class discussion
Informal Observations
Exit Ticket
Guided Practice and Independent Practice
Summative Assessment:
Homework
Lesson Title: Volume of Pyramids and Cones
Set:Show students a prism and cylinder. Ask the students why the cylinder is not a prism. Think-Pair-Share this question with students. The reason is because circles are not polygons. Therefore, cylinders are not polyhedrons.
Teaching Strategy:
  1. After the set, ask the students if cylinders are not prisms simply because they are not polyhedrons, how will we find the volume of cylinders? Remind students that we find the volume of a prims by using the formula . Can we use this knowledge to find the formula for the volume of cylinder? Ask students to Think-Pair-Share this question. Since our base is a circle, and we find the area of a circle by using the formula , then we will find the volume of a cylinder by multiplying the area of the base times the height, .
  2. After discovering the formula, model some examples. Use the Volume of Cylinders and Cones (See Resource Folder) examples. After modeling some examples, do some guided examples, and finally some independent practice.
  3. Ask students how cones and pyramids are related. Students should find that cones and pyramids have the same relationship as prisms and cylinders. Remind students the formula to find the volume of pyramid is . Since the base is a circle, the formula is .
  4. After discovering the formula, model some examples. Use the Volume of Cylinders and Cones (See Resource Folder) examples. After modeling some examples, do some guided examples, and finally some independent practice.
Summarizing Strategy:Cylinder and Cones Exit Ticket (See Resource Folder).
Practice problems will be assigned for homework.
6 / I can calculate the volume of spheres. / Sphere Examples (See Resource Folder)
Materials for Differentiated Instruction – Remediation:
Calculators
Materials for Differentiated Instruction – Enrichment:
Sphere Extensions (See Resource Folder) / Essential Question:How do I calculate the volume of spheres? / Differentiated Instruction –
Remediation:
Peer Tutoring
Questioning
Calculators
Differentiated Instruction –
Enrichment:
Questioning
Peer Tutoring
Sphere Extension (See Resource Folder) / Formative Assessment: Class discussion
Informal Observations
Ticket Out the Door
Summative Assessment:
Homework
Lesson Title: Volume of Spheres
Set: Watch the Khan Academy video on Find the Volume of a Sphere.
Teaching Strategy:
  1. Show the students a sphere. Ask the students how they would find the volume of a cylinder with a base equivalent to the widest part of the sphere, and the height that was the same size of this sphere. The area of the base would be and the height would be . There the volume would be:
    The sphere is not the size of this cylinder. It’s actually smaller. It’s of the size of the cylinder. Therefore, we need to multiply the formula by .

  1. Have students open Sphere Examples (See Resource Folder). Balance between modeling, guiding, and allowing students to work independently.
Summarizing Strategy: Ticket Out the Door: Students will write directions on how to find the volume of a sphere. They are to include an example they created.
Practice problems will be assigned for homework.
7 / I can use volume to solve problems. / The Ice Cream Task (See Resource Folder)
Materials for Differentiated Instruction – Remediation:
Calculators / Essential Question: How do I use volume to solve problems? / Differentiated Instruction –
Remediation:
Peer Tutoring
Questioning
Calculators
Differentiated Instruction –
Enrichment:
Questioning
Peer Tutoring
Ask students what would happen to the volume if we doubled both the height and radius of the cone, and the radius of the sphere. / Formative Assessment: Class discussion
Informal Observations
Ticket Out the Door
Performance Assessment:
Task Sheet
Summative Assessment:
Homework
Lesson Title: The Ice Cream Task
Set: Watch the Virtual Nerd video titled “What is the Formula for the Volume of a Cone?”
Teaching Strategy: Introduce Part A of The Ice Cream Task to the students (See Resource Folder). Have students work on Part A of the task independently. This will allow students to generate their own answers. Walk around to guide students in the right direction. When students have completed Part A, have them compare their answers with their table groups. While each person is presenting his/her findings to the group, the rest of the group should be listening.
Introduce Part B of the Ice Cream Task to the students. Students may work with their table groups on Part B. Monitor students as they work in groups, asking them questions to help them recall previous material. Encourage students to defend the dimensions of their cone they design.
When groups have completed Part B, have each group present their cone that contains the smallest dimensions (Part B Question 2) to the rest of the class. Identify which group has the least amount of material needed for the cone.
Summarizing Strategy: Ticket Out the Door: Students will answer the following question: What did you learn about problem solving during today’s lesson?
Practice problems will be assigned for homework.
8
Project Day 1 – refer to Unit Plan
Topic – IA Maritime Challenge
9
Project Day 2 – refer to Unit Plan
Topic – IA Maritime Challenge
10
Project Day 3 – refer to Unit Plan
Topic – IA Maritime Challenge
STANDARDS / Identify what you want to teach. Reference State, Common Core, ACT
College Readiness Standards and/or State Competencies.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
8.G.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
7.G.4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.