World Population [Picture Problem] 8.F.B.5, L.8.3, and MP.1

By: Kimberly Younger

This image of the world, from World Mapper is skewed based off the current population in each country. Students will be assigned a country and will be asked to find out the population of the country in 1918 and the current population (2018) then they will compare the the change in population.

The lesson will focus on the standard CCSS.Math.Content.8.F.B.5 which is finding the functional relationship between two quantities, whether they are increasing or decreasing and for the this lesson they would be focusing on only linear functions. The lesson will be called Population Change Project, students will sketch the graph with the population data they collect and write a paragraph about the data the collect and interpret what it means. Including information about why they think the population increased or decreased.

This Lesson is culturally responsive because students will be learning about other countries and why the population may have increased or decreased over decade (1918 – 2018). Students could be supplied with websites which show the current population and the passed population or they can be given time to do the research on their own.

The students will use the mathematical practice of CCSS.Math.Practice.MP1 which focuses on students problem solve and preserve in solving math problems. CCSS.ELA-Literacy.L.8.3 is the use knowledge of language and its conventions when writing. The evidence of this standard would be found when students complete their write up about the change in population over the passed decade.

Rocket Math: 8.F.A.3, 8.F.B.5, MP4

 

 

Rocket Math

By: Natasha Smith, Mariana Rosas, Paloma Vergara, & Melisa Sanchez-Leyva

 

 

 

 

This modeling lesson is for an 8th-grade classroom and is focused on the standards CCSS.MATH.CONTENT.8.F.A.3 and CCSS.MATH.CONTENT.8.F.B.5. This lesson introduces students to the concept of nonlinear functions. In the lesson, students will be able to explore the concept of a nonlinear function and expand their knowledge of what a function can look like.

This lesson follows a similar format to Dan Meyers’ 3 Acts. Students will start by watching a video of a model rocket launch. Individually, they will quickly draw a graph of what they think the relationship between the height of the rocket and time is. Next, they will work in groups to plot the points estimating the relationship of the height of the rocket at each second. Lastly, the teacher will take them outside and launch a model rocket to prove or disprove students’ theories. The model rocket will have a Pocketlab attached to it which will provide an exact graph of the height of the rocket at each time point. Students will compare their graphs to the Pocketlab graph. We decided to launch the rocket again instead of providing students with a graph from the original launch in the final act as it adds an element of excitement to the activity and the students will enjoy going outside to watch the rocket launch.

This lesson incorporates multiple types of technology. For the video used in the lesson, teachers would achieve best results by filming their own rocket launch as they will want to use the exact same type of model rocket in both the video and the in-class launch. The video representation should be similar to this video. Students will also be using the website Desmos to graph points. Lastly, the teacher will be using a Pocketlab. The Pocketlab is a wireless sensor that can be attached to different objects and will record different types of data and output graphs. For this lesson, the Pocketlab can be attached to the model rocket and will record the height (altitude) of the rocket as time passes.

Lesson Plan and Worksheet.

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Bouncing Into Math CCSS.MATH.5.G.A.2

Some math teachers might ask the question “how can I adapt this curriculum to relate to real world scenarios?” One way to start is by taking an interest in what your students are interested in. There’s a time for lecture and there’s a time for, well, bouncing balls and having fun. This activity features measurement of a tennis ball bouncing and when it slows down, compared to a rubber ball bouncing and when it slows down, using the Ipad app called Video Physics. You might be asking yourself now “how in the world does this relate to the real world?” Well, once this activity is performed by questioning young minds, the students will want to know more. They’ll want to use the technology and math and relate it to people and if they were to keep jumping, at what point would those bounces become smaller and slower. This is an activity to get the students up out of their seats and “perform” mathematics in the classroom.

In this activity the students will need to get into groups of at least three and have an Ipad, a worksheet, a tennis ball, and a rubber ball. Each student will have his/her own job: recorder, video-taper, and ball bouncer. Each student will get to perform each task within the groups of three. The students will collect and record data pertaining to the tennis ball and the rubber ball and how each ball’s acceleration and height of the bounces differ slightly. Prior to the students gathering data, they will draw their prediction of what each ball’s graph will look like. This will give the students more insight to how the math aligns with reality. After they complete the worksheet given during this lesson, the class can discuss their findings as well as how else they could use this technology in their day to day lives.

This assignment relates to the Common Core State Standard

CCSS.MATH.5.G.A.2 Graph points on the coordinate plane to solve real-world and mathematical problems.

Bouncing Into Math Worksheet-1oj7bir

Where Do We Meet? REI

screen-shot-2016-12-02-at-12-47-21-pm

WHERE DO WE MEET?

Where do we meet is an interactive activity that uses technology and mathematical concepts to create and solve real life scenarios. One of the Vernier products to compliment this lesson is the Motion Detector. This device allows for data to be collected through a calculator (or a computer software) where students can then analyze their findings. For this activity students will be able to see a real life scenario of the usage of the mathematical concept of Solving Systems of Liner Equations using a motion detector, calculator and themselves. In this activity, students will be able to part of the creation of data that will be used to create equations. Students will then take part in solving the system of equations using technology and on writing (mathematically). Students will be able to use this activity that ties to the following Common Core State Standards:

INQB.2 Collect, analyze and display data using calculators, computers, or other technical devices when available

APPD.2 Use computers, probes, and software when available to collect, display, and analyze data.

M3.2.H Formulate a question that can be answered by analyzing data, identify relevant data sources, create an appropriate data display, select appropriate statistical techniques to answer the question, report results, and draw and defend conclusions.

H.A.REI.1– Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

H.A.REI.2– Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

H.A.REI.5– Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

H.A.REI.6– Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

vernieractivity-wheredowemeet

Using Geogebra to Show Triangle Congruences HSG.CO.B.8

This lesson is for teachers to use technology to invoke a thoughtful and engaging classroom experience with their students. It is designed to show concretely through Geogebra all of the triangle congruences and all of the combinations that don’t work. This is a fantastic way for a teacher to show this to their students because it is difficult on a white board or with pen and paper to prove to the students that these congruences work. The most insightful part of this lesson is where the combinations that don’t work are shown to the students and the students can see on the screen why.

Geogebra is an excellent source that teachers can use which can incorporate visual understanding of many geometry lessons. It is a completely free computer application which can be downloaded here: https://www.geogebra.org/download. This application specifically allows a person to manipulate different points, lines, angles, and other things in ways that a pencil and paper cannot. For this lesson specifically, it works fantastically because of the free motion that the program gives you.

Common Core State Standard:

HSG.CO.B.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Lesson plan: technology-lesson-plan_triangle-congruencies

Attached worksheet: http://cdn.kutasoftware.com/Worksheets/Geo/4-SSS%20SAS%20ASA%20and%20AAS%20Congruence.pdf

Velocity Test: Interpreting Velocity Graphs HSF.IF.C.7

Figure from experiment 12 from Real-World Math with Vernier

Students are notoriously difficult for teachers to engage in a lesson. With Vernier, teachers are able to use lessons on quick notice that involve technology and student attention. With technology, students become excited about something different in the classroom and are therefore more attentive. With Vernier, there are numerous different technologies with hundreds of ideas for lessons (not exclusive to math if you are a science teacher-or if you are a math teacher wanting to introduce some science into your lesson!). The product used in this lesson is the Motion Detector, which can be acquired through https://www.vernier.com/products/sensors/motion-detectors/md-btd/. This sensor is designed to collect data from the distance between the sensor and what it is pointing at. There are Image result for speednumerous more lessons involving it, and is especially useful for any movement-based projects/lessons that a teacher plans to do.

 

This specific lesson deals with velocity. Students are assigned to record their distance and time with the Motion Detector. After they have that, they are to formulate a graph based on that data of their motion and compare/contrast that graph to the graph that the motion detector collected from their motion.

CCSS.MATH.CONTENT.HSF.IF.B.6
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

CCSS.MATH.CONTENT.HSF.IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Lesson: velocity-test-interpreting-velocity-graphs

Resources from vernier.com

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.

Planning a Party HSA.CED.A.2

cupcakes

 

You have a big birthday party coming up soon. You invited 16 people for the occasion.  The problem is, you haven’t gotten cupcakes yet. While considering the number of cupcakes to buy, your rule is each person attending (including yourself) must have 2 cupcakes each. Assuming that each person you invite will come and have their 2 cupcakes, how many cupcakes should you buy to hold true to your rule (2 cupcakes for everyone)?

This problem can be manipulated in many ways. For instance, what if you wanted each person to have 3 cupcakes? 5? We can let the number of cupcakes you are buying to be y and the number of cupcakes per  person be x and create an equation for the number of cupcakes you should buy for your party (n) and the number of cupcakes per person (x).

Now you are having second thoughts. Instead of yourself having the same number of cupcakes as everyone else, you want to have one more (so you would have x+1 cupcakes and everyone else would have x). How would this change your equation above? Create a new equation demonstrating this new rule with the same variables.

Now that you have established how to manipulate the equation based on changing information, you want to create an equation for future parties that you host showing the amount of cupcakes (or other food items) you need to have based on: the number of food item you want for each person, the number of people that will be there, and the amount (if any) more you want to have for yourself. Let these variables be x, y, and z respectively and the number of food items you need be the variable n. Create a brand new equation given these variables for the number of food items you need.

At times, it can be very difficult to engage math students in a classroom. Story problems are somewhat recommended because they can bring relevance from the students’ lives into a math problem. What preceded is an extended story problem involving something that all students will love: food. Along with the problem, the picture should make students’ mouths water. This problem should be relevant to almost all students and possibly give them some party planning advice.

The Common Core State Standard this problem is aligned with is HSA.CED.A.2:
Create equations in two or more variables to represent relationships between quantities.