Amusement Park 7.G.B

During this lesson, students will  be put to the test, using their prior knowledge from the previous geometry unit on two- and three-dimensional shapes involving area and perimeter.

You and your team have just been hired by Walt Disney Parks and Resorts Worldwide to landscape a brand new amusement park with rides. WDPR has provided you with a blank map with letters E through M, representing the nine rides that you must include in your design. Your task is to map out the most effective design in order to maximize the number of visitors to each ride. Your job is to gather all of the information you can, map out each ride using GeoGebra to graph your park, and present a justification as to why your design will maximize visitors to each of your rides.

In order to complete this lesson, students will be split into groups of 3-5. The class as a whole will have a set number of rides they must include in their park, and a set area for the park itself, but each group will devise different ride sizes and configurations throughout the map in order to maximize visitors to each ride.

 

Modeling Lesson-1xyl8m6

Cookie Monster or Monster Cookie? 7.G.B.6, MP1, MP2

 

Cookie monster? More like monster of a cookie…

The world’s largest cookie was baked by Immaculate Baking Company in Flat Rock, North Carolina in 2003. The area of the top of this cookie was 8,120 square feet with a diameter of 101 feet and weighed 40,000 pounds. Assuming that the cookie is a perfect cylinder, and its height was 6 inches, what is its volume? Round to the nearest cubic foot.

If there was an oven that could fit this cookie inside, what is the smallest volume size that the oven could be? (Hint: the oven must be a cube).

In this lesson, students will be using their knowledge of area and volume as well as mathematical reasoning to solve a problem that involving circles, cylinders, and cubes. The picture and the problem will intrigue students because they won’t believe that a real cookie was this big until they see it for themselves. Plus, who doesn’t love cookies? The teacher could also gain incentive and interest from the students by bringing in or having the students bring in cookies after the lesson.

 

CCSS.MATH.CONTENT.7.G.B.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.

CCSS.MATH.PRACTICE.MP1

Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2

Reason abstractly and quantitatively.

Apartment Proportions 7.G.A.1

Apartment Proportions

Problem:

Congratulations! You just got your first apartment. It’s located right in the heart of downtown Ellensburg. You just realized you do not have anything to put in your new living room which is 14’ by 12.5’.

Sadly, the store you want to get your furniture from only has a few options but they come in multiple proportions. Make sure you have at least one item from each of the categories. If an item is too large or small, use ratios to change the proportions. You are only allowed to have ten of the following items in your living room!

Hint: Do some of the sizes seem odd? You should probably use ratios to change the size.

Show your work!

Below are the furniture you can select from with the measurements.

Seating                                                            Misc

Couch 8’x4’                                                    Lamp 4’x4’

Chair 2’x3’                                                     Fan 4’x2’

Bean bag square 3’x3’                                  Bookshelf 3’x2’

 

Table                                                              Entertainment

Coffee Table 16’x9’                                       TV with stand 12’x10

Side Table .5’x.5’                                           TV 10’x2’

                                                                           Gaming Consoles 4’x6’

Rug

Fuzzy Rug 15’x8’

Rug 14’x6’

 

This picture was found at Clipart-Library. This lesson will focus on the CCSS.Math.Content.7.G.A.1 which is solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

I would teach this culturally by understanding that all students come from different cultures and different cultures have different housing expectations.

Other standard:

CCSS.ELA-Literacy.W.7.4
Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

Yeah He Caught It, But How Far Was It? 8.G.B.7

Problem: For this lesson, students will be doing an extreme version of utilizing the Pythagorean Theorem. The number in the picture, 400ft, is the distance from home plate to dead center field at Miller Park in Milwaukee, Wisconsin. The goal of the lesson is for students to find the distance of the ball when it is caught by Keon Broxton. Almost all of the information is present in the picture without much background knowledge, but they will also be told that he was estimated to be about 4ft off of dead center when he caught the ball.

The beginning of the lesson will have students discussing what information they have and what information they will need to complete the assignment. The groups will realize that they need to use the Pythagorean Theorem to solve the problem. The groups will come together for a class discussion and asked what information they still need.

After that, students will do their own research to find the missing components. These components are things like where in the stadium the ball was caught, where the ball was when it was caught, etc. The students will use this information to solve the problem, and present to the class how they solved the problem and how they found the missing information.

Connected Math Standards:

CCSS.MATH.CONTENT.8.G.B.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

CCSS.MATH.CONTENT.8.G.B.8
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Extension: If students are grasping the content quickly, have them estimate the angle at which the ball entered Keon Broxton’s glove. This can be done using basic trigonometry, which is referenced in the standard CCSS.MATH.HSG.SRT.D.10. While this is technically beyond their grade level, they have a lot of the background knowledge needed to solve the problem so long as they have the height of the ball at the apex of its flight.

Cultural Relevance: This lesson is culturally relevant because baseball is widely played around the world, especially in Hispanic cultures like Mexico, Puerto Rico, Costa Rica, and especially in the Dominican Republic. Plus many students idolize baseball players in a way that they will like the opportunity to do extra research with certain players in them.

Standard from Another Content Area:
WA.EALR.5.4.1
Uses sources within the body of the work to support positions in a paper or presentation.

This standard will be used when students are finding extra information for the assignment.

Playground Shapes 7.G.B.4, 7.G.B.6

Problem:

For this lesson, students will be using the image of the playground to identify different two- and three-dimensional shapes they can find, and then estimating possible measurements to use to find the area, volume, and surface area of the shapes identified.

The first part of the lesson will be each student generating a list of what two- and three-dimensional objects they see. After about 5 minutes, students will have a chance to discuss and compare in groups. Once the groups have shared their findings, the class will come together to share all of the shapes and objects that are in the picture. Estimations will be determined for measurements, so that there are concrete numbers for the students to use when calculating area, volume, and surface area.

Based on the standards associated with this lesson, the main focus will be on two dimensional circles, triangles, quadrilaterals, and three-dimensional cuboid objects.

Connected math standards:

7.G.B.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.B.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.

Extension:

Students who quickly progress through the shapes and objects associated with these standards can be challenged with the triangular pyramids in the picture. Also, the standard 8.G.C.9 is about using the formulas for the volumes of cones, cylinders, and spheres and using them to solve real-world problems. This is a clear extension of this activity since there are cylinders in the image, and students can be challenged to use what they know to estimate the volume of the entire slide.

Cultural relevance:

This lesson is culturally relevant to students because playgrounds are usually a place of fun for younger students, so in this way students are finding the math associated with a place that hopefully inspires positive feelings for them.

Standard from another content area:

CCSS.ELA-LITERACY.SL.7.1 – Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 7 topics, texts, and issues, building on others’ ideas and expressing their own clearly.

El Castillo (Temple of Kukulkan) 7.G.3

Related image

Math Standard:

CCSS.Math.7.G.3 – Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Math Problem:

With this standard and picture, I would have students look at the different ways that this pyramid could be sliced. With each slice that they think of, I would have them draw  what the pyramid would look like from the side and top view based off of every slice they would make. This would be done in partners and  each partner group would have to come up with at least two ways that the pyramid could be sliced. As an extension, I would ask them to show what the pyramid would look like if they sliced it more than once.

Integration:

Science Standard:

MS-ESS1-1 Earth’s Place in the Universe – Develop and use a model of the Earth-sun-moon system to describe the cyclic patterns of lunar phases, eclipses of the sun and moon, and seasons.  [Clarification Statement: Examples of models can be physical, graphical, or conceptual.]

Science Problem:

After students have had the chance to look at this pyramid from different points of view as a whole piece and as slices, I would have them use the pyramid to show how the earth, sun, and moon rotate together. They would be in groups of four and have to build a physical representation of the pyramid. After they got their pyramid created, they would draw placements of the sun, moon and earth in which they would have to explain in a presentation to the class where each would be and how the placements of the earth, sun and moon would change the way the pyramid would look (e.g shadows). No one pyramid would look the same because Students would all have drawn different placement of the sun, moon and earth from the hat. After each group has presented, we then decide as a class what group’s pyramid representation would be first if we were look at it at 7:oo am and who would be next until we got to the last pyramid representation.

How this problem teaches culturally:

This problem teaches culturally because throughout this integrated unit, we would have conversations of how the pyramid was created and how the Mayans used it. We would also talk about where the pyramid is located and what the culture was like when the pyramid was built.

Baseball Geometry 8.G.B.7

The shape of the baseball field is full of math and geometry! This is a wonderful way to connect ideas from math class to the real world and the everyday lives of your students. Whether or not your students participate in the game of baseball, baseball has been a very large part of American culture and history.

Some of your students may have never thought of the baseball diamond as a square. Post a picture in your classroom of the bases from a birds eye view. Point out that when you connect each base with a line you have a perfect square!

Questions to ask your students:

How far is it from home plate to first base? 1st to second? 2nd to third? 3rd to home?

How far does the catcher have to throw the ball to get it to 2nd base?

How can we figure this out?

What information do we need?

Possible way to implement this in your classroom:

Have pictures of baseball fields posted around the room or on each students desks. Have students partner up in pairs or groups of three.  Have these questions written on the board and release them to figure it out! Make sure you have previously taught the Pythagorean Theorem, but do not tell them this is the method they should be using. Let your students decide that this is a real life application of the Pythagorean Theorem. Once students have found their answers have them present their answers, process, and how they know they are right!

 

CCSS.MATH.CONTENT.8.G.B.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

CCSS.ELA-LITERACY.WHST.6-8.7
Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration..

Build a playground 7.G.B.6 and MP4

By: Kimberly Younger, Rachel Van Kopp, Lizzie Englehart and Naomi Johnson

This lesson is focused on a 7th grade standard CCSS.Math.Content.7.G.B.6 but could be used for 6th through 8th grade depending on the application. This lesson focuses on the use of formulas to find area and problem solving of a real-world problem with the use of technology.

The prompt is “The school district is building a new playground for the new elementary school down the road. They have hired Playgrounds R’ Us to build it, but the supervisor wants to know what students would want on a playground. Create a playground with the following requirements.”

The students are building on their knowledge of area and perimeter formulas and applying it to a problem. The students are given a square footage for the playground, they must use three or more different shapes to represent their equipment, and the total square footage of the equipment must cover 30% of the playground’s area or more.

The students are given a packet which includes direction, a rough draft grid paper, final draft grid paper (submitted for approval), a screen shot of their Geogebra playground and a write up about their playground.

Below is an example of the packet students received. (link to the packet)

Below is a student’s sample playground

Rough Draft Blueprint                                Final Draft Blueprint                               Geogebra Blueprint

Table for Blueprint

Extension for “Build a Playground”:

As an extension to this lesson, students will later be able to work with 3 dimensional figures and nets to build the playground they have constructed in our lesson. This lesson emphasized finding and working with area of various geometrical figures and special reasoning. Using the knowledge, they have gained through our lesson, the students will be able to create the net that would best fit the equipment shape that they have presented to us on their “blue prints”.

In order to create the appropriate net, students will need to understand that the 3-dimensional shapes base will be the shape they have placed on their map in the lesson “Build a Playground”. This extension will cover CCSS.math.content.7.g.b.6 which states “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.” This extension will help students make connections to the relationships between 2-dimensional figures and 3-dimensional figures, and connect the concepts of surface area and volume to real-world scenarios.

Surface Area & Volume of 3D shapes 6.G.A.4

6.G.A.4: Solve real-world and mathematical problems involving area, surface area, and volume.

Tasks: Students will have to properly use the equations provided in order to calculate the surface area and volume of the following shapes.

When calculating the surface area of an object (examples 1, 2, and 4) how many faces are there in order to get the right answer?

Commentary

The goal of this task is for students to understand the concepts behind 3D shapes and have a visual representation of shapes. During the lesson is taken place, the teacher will require to show students how to properly label the parts of the shape in order to correctly use the information in the equations provided to them. This will allow the students to understand the different dimensions and sides of a shape. Once the students are able make connections, the students will be able to determine the surface are and volume of a shape. With this being said, it’s common that students make simple mistakes such as forgetting to add the right number of faces of a shape. At this point, the teacher will need to use this task to make sure that students are able to understand the dimensions of a figure and how they differ from a different shape. The teacher will provide the properties and cover example problems in order to calculate the surface are of the shapes and volume. The students will also have a visual representation of the shapes.

Solution:

  1. By looking at the shape, we can see that there are four faces/sides with the same dimension of 3×2. This implies that the dimension of 3×2 will be multiply by 4 or simply add (3×2=6) 4 times. This will result of 24 in². The remain 2 faces/sides have a dimension of 2×2 resulting in 8 in². To a total surface are of 32 in².In order to calculate the volume of the figure (Length x width x height) we get 2in * 3in * 2in = 12 in³.
  2. To calculate the surface area of this shape, the same procedure as solution 1 will be follow with the exception that in order to calculate the surface area of triangle will require the equation of (base*height)/2. To a total surface area of 29.6 in². In order to calculate the volume of shape the picture on the right illustrate the equation needed to do so and volume = 8 in³.
  3. In order to calculate the volume of a cylinder the picture on the left illustrate how to do it. The volume of the shape will be 230.91 in³. To calculate the surface area of the cylinder, it will require students to use the equation. Surface area = 209 in².
  4. In order to calculate the surface area, we can see that the shape has a right triangle and two of the faces make up a square resulting in 49 in². By adding to other 3 sides/faces we get a total of 240.2 in². To calculate the volume of the figure the equation of Volume = area of base x height will be needed. This indicates that area of the base is (7*7)/2 and the height is 8 in where the volume = 196 in³.

The Art of Geometry SRT

 

 

CCSS.Math.Content.HSG.SRT.B.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

This picture will be covered in my geometry class. The purpose of the picture is to start talking about how mathematics is a form of art. You can find mathematics in every type of art. The lesson that will be covered to relates to this picture is finding corresponding and supplementary angles. The assignment will be for the students to create their own drawings and label the types of triangles and angles in their picture.