ML Geometry

Amusement Park 7.G.B

randituggle ML Modeling, Uncategorized ,

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

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

Image berrymanv Geometry Curriculum Aligned with CCSS-Math, HS Geometry, Picture Problems ,

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

cortneaaustin Common Core State Standards Mathematics ,

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

Image kristinthomas2 Uncategorized ,

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.