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.

Interpreting the cross-sections of 3-dimensional objects: HSG-GMD.B.4

Image result for object cut in half

 

 

HSG-GMD.B.4 has to do with a student’s ability to visualize relationships between 2 and 3 dimensional objects. Given the example above you see that a 3-dimensional sphere is related to a 2-dimensional circle. This relation is this; a circle is the cross-section of a sphere. No matter where or at what angle you take the cross-section it will be a circle and not matter the size of the sphere is will be a circle as seen by the rings in the cross-section. This could be better represented with 3 spheres cut in different places showing that the resulting cross-section is always a circle.

Battleships and Mines HSG.GPE

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What better way to learn math than by playing Battleships and Mines!!!

This interactive activity will indulge your students into creating their own battleships and mines using geometry. Students will generate their battleships and mines using equations of circles that will be graph using GeoGebra. GeoGebra is a free and useful software where students can create circles with just two clicks! No more “I do not want to graph this!” With GeoGebra students will be able to fully engage in the activity while practicing the properties of the equation of a circle, without the hassle of graphing it. GeoGebra not only does it have functions that can be incorporated with algebra and calculus curriculum, but it comes at no cost to schools, teachers and students.

battleships-lesson-geometry-m325

 

Modeling a Digital and Global Age Learning Environment

Modeling a Digital and Global Age Learning Environment

 

Over the past decade our world has become increasingly more dependent on technology. Some school districts have made an effort to bring more technology into every classroom, but it is time for teachers to include technological tools in each of their lessons to assist each of their students’ needs. There are tools that can be used in the classroom such as clickers, smartboards, and document cameras. There are also so many web based resources that teachers can use in the classroom and that students can use at home, given they have internet access. Teachers need to take the time to be trained in technological tools that can improve their students’ learning environment and many will quickly find that these tools assist many of their teaching strategies.

Class Website

             A class website is a great communication tool for teachers, their students, and the students’ parents. My website includes a unit calendar that includes daily homework and quiz/test dates. Parents and students can check the website each evening to make sure all homework is being completed and to be made aware of future assignments. My website also includes links to online textbooks, helpful math websites and websites that provide fun games for extending each of my students’ mathematical skills. Many schools have web address set up for each teacher or more personalized websites can be created on KompoZer which is available for free download.

Math is Fun

Math is Fun is a resource website that makes learning mathematics fun and easy. The site covers k-12 curriculum and provides definitions and procedures for solving all types of math problems. This is a great review website as well as a resource for double checking equations and methods for solving problems you are not 100% comfortable with. This online website can help students complete their homework if they forget any needed equations and it can also help parents help their children. It is no secret that many parents have difficulty helping with their child’s math homework past the elementary years; this website will help parents quickly review some concepts and procedures and further their ability to help with homework.

Khan Academy

Khan Academy is another math resource website. This website is excellent for students who learn by example. There are 2-3 examples for each topic that begin with video instruction showing step by step procedures to solve a problem. After video examples there are practice problems that have to be correct before moving forward but also hints to help. My students love Khan Academy and many times when I know I will have a substitute I have them show the Khan Academy video as opposed to teach a lesson to my students. On my website I update the Khan Academy link to go directly to our current topic page.  This resource along with the textbook website, which also has instructional videos, is usually enough instruction for my advanced students to keep on top of work when they miss class. This allows me to not have to take time away from other students to teach students who were absent. For some of my struggling learners it is expected of them to review lessons on Khan Academy each evening because hearing the information twice greatly improves their success.

GeoGebra

When my students enter the geometry unit we spend a lot of time on laptops or in the computer lab. I have found that geometry is one of the toughest units for young middle school students to comprehend because it involves so much more than they are used to dealing with at one time. GeoGebra is a great resource for all students, but especially those who are just beginning their journey through geometry. My students use GeoGebra, which is an online resource that can help students create shapes and find their measurements. Students have difficulty with relationships between shapes and remembering differences between area and perimeter. GeoGebra helps students, especially visual learners, actually see what area means vs perimeter. I have GeoGebra linked on my class website so students can have quick access to it at home.

With an ever changing world technology allows teachers keep their lessons and students up to date with the latest mathematical tools. Providing students with the knowledge of how many resources are online and available for help with homework will make students more interested in completing their homework because going online and searching through websites is fun for young adolescents. It is important for teachers to be able to make the transition from paper and pencil, to online tools, and then back to paper and pencil. Resources such as GeoGebra are wonderful for helping students gain conceptual understanding of abstract concepts, but the procedures that are needed to solve problems without the help of technology cannot be forgotten. Students will be taught what a good digital citizen is and the importance of this will be reminded to students whenever we go online as a class. I will model each resource for my students before I expect, or encourage them to use it without my supervision. Trusting my students to make good choices usually makes them want to keep that trust and I rarely come across problems with online resources.

 

Resources

KompoZer

http://kompozer.net/

Math is Fun

https://www.mathsisfun.com/

Khan Academy https://www.khanacademy.org/

GeoGebra

https://www.geogebra.org/

Digital Citizenship

http://www.digitalcitizenship.net/Nine_Elements.html

How Tall is That? 6.RP.A.3

MATH VisualCan’t measure the height of that tree with your ruler? No problem! Let’s use ratio’s to find it’s height!

This lesson is a great modeling activity where students are able to apply ratios and proportions to real world situations. They will be using the concept illustrated above with objects they find around their school. The students will find their own height and shadow length, and use this ratio to find the heights of several tall objects. Some of these might be basketball hoops, portables, school buildings, soccer goals, railings, and even the height of their own teacher! Continue reading