Math History Tech Task2 PDF

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GKM1 TASK 2: STUDENT TECHNOLOGY LESSON A1&2. General Information Lesson Title: Subject(s):

Using GeoGebra to Solve a System of Equations

Algebra 1

Grade/Level/Setting:

Grade 9, total of 24 students, six groups of 4.

Prerequisite Skills/Prior Knowledge:

-Define each variable in an equation -How to write and solve system of equations -Different Methods in solving system of equations (Substitution, Equal Values, and Elimination) -Basic computer knowledge (internet access) Standards and Objectives

State/National Academic Standard(s): Oregon 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 Learning Objective(s):

Given access to GeoGebra, students will be able to successfully write, solve and graph a system of equations from a word problem, and explain their findings with an 80% classroom average. Materials

Technology

-Paper/Pencil

GeoGebra Calculator is a great tool to be used in order for students to check their work and fully visualize the problem. This tool will act as a substitute to working the problems by hand, but also have instant feedback if the student entered the equation wrong for example, it is a way for students to make sure their equations are correct and able to be graphed and solved properly.

-Notebook -Highlighters (2) -GeoGebra Calculator/ Graphing -Graphing/Scientific Calculator -Computers Language Demands Language Function(s):

By the end of this lesson, students will be able to explain and demonstrate how to solve a system of equations for the given word problem by using the provided technology, GeoGebra.

Vocabulary:

-Graph

-Solve

-Equal Values Method

-Justify

-System of Equations

-Analyze

-Add, Subtract, Multiply, Divide

-Define

-Explain Discourse and/or Syntax:

During the lesson, student will be following along with each step, asking questions to their groupmates or the teacher when clarification is needed, and participating to answer questions from the teacher to demonstrate understanding. Planned Language Supports:

GeoGebra, graphing calculator, word wall, example problem diagrams around the classroom, and notes.

Instructional Strategies and Learning Tasks Anticipatory Set: Activity Description/Teacher

Warm up: Highlight important information and set up for a system of equations (Equal Values Method). Do not solve. “A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.75, how many dimes and how many quarters does he have?” (OnlineMathLearning, 2020) ----------------------------------------Have warm up displayed as students come in, give them about 10 minutes to settle and complete the warm up -Ask students to take-out two different color highlighters, and highlight the important information. One color for each equation. -Ask students to not solve, this problem will lead to the lesson. -Not graded, just practice. How to Complete Warm up: -1. First highlight, “14 coins”, represents the total amount of coins, which only include dimes and

Student Actions

-Students will first write and highlight important information in the given warm up word problem in their notebooks -Define the variables (y) and (x) -Then, using what they highlighted create a system of equation that includes the two variables. -Have equations be ready for the Equal Values Method -Volunteers can share their results.

quarters -2. Second highlight, “the total value of his change is $2.75”, students will compare total amount of money to amount of coins -3. To write up the equations, first define the variables: (y)= dimes, (x)= quarters -4. We know there are 14 total coins, (y) is dimes and (x) is quarters so, x + y = 14 -5. We also know X (quarters)= $0.25 and Y (dimes)=$0.10 when it comes to money. So, 0.25x + 0.10y = 2.75 -6. Set up equations for Equal Values Method (both equations must be equal to the same variable) -7. Solve each equation to be equal to (y)

-8. Now we have equations: y = -x + 14

&

y = -2.5x + 27.50 Presentation Procedures for New Information and/or Modeling:

Activity Description/Teacher

Student Actions

-Make sure all students are ready to move on. Answer questions as needed

-Students will observe the model during the beginning of instruction.

-Through the projector introduce website GeoGebra Calculator to students.

-Then volunteers can share what they understood from the lesson introduction.

www.geogebra.org/calculator

-Show students… How to enter an equation on GeoGebra: -1. Press the (+) button towards the top left corner of the screen to enter equation: y=-x+14 -2. Notice a line graph appears instantly, which represents the entered equation ----------------------------------Ask students to open the webpage on their computers and enter the first and second equations Guided Practice: Activity Description/Teacher

Student Actions

-After a couple minutes, enter the second equation

-Students will access webpage and enter given equations, and familiarize themselves with GeoGebra

-1. Press (+) again to enter y=-2.5x+27.50

-Solve along with teacher, ask questions when clarification is needed.

-2. Line graphs appear on the right side of the screen

-Take notes in notebook

-3. Explain that the point of intersection (where the lines cross) is this problems answer in the form (x, y)

-Write answer in sentence form

- In this problem it is (9,5) where X (or quarters) = 9 & Y (or dimes) = 5

-Answer: There are 9 quarters and 5 dimes that total to $2.75 -Walk around the classroom to check understanding Independent Student Practice: Activity Description/Teacher

-Present new word problem

Student Actions

-Students will collaboratively work on the new word problem.

Independent Practice:

-1: highlight important information.

Create a system of equations in the Equal Values form and solve using GeoGebra. Write your answer in sentence form.

-2: Define the variables

“You are running a concession stand at a soccer game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night, you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?” (Hutchinson, 2020)

-4: Solve for a variable in order to use the Equal Values Method

------------------------------------------

-3: Create two equations comparing the two variables

-5: Solve both equations by using GeoGebra -6: Find how many sodas and hot dogs were sold to make $78.50 at the soccer game. -7: ADVANCED STUDENTS- Will create a table and graph using GeoGebra to prove their findings. Check answers by plugging in X & Y values into original equations

-Ask students to work together or ask to work independently. Culminating or Closing Procedure/Activity: Activity Description/Teacher

Student Actions

-Ask students to share their findings after the group collaboration/work.

-One person in each group will share their findings with the class.

Exit Ticket:

-Students will compare answers and ask questions if they arise.

-Introduce Google Form formative assessment as exit ticket the last 10 minutes of class -The formative assessment has a final word problem where students will need to create a system of equations using the equal values method and can use GeoGebra, and notes to solve. Results will be shown on the teacher Google Form page as students finish. Goal is to reach a class average of 80% accuracy.

-Access Google Form, and complete by using prior knowledge and GeoGebra -Complete Google Form independently

-Walk around classroom and ask facilitating questions to students who need assistance during the formative assessment “What is your first/next step?” “What are we comparing?” “Can you check your notes to compare the steps you took to solve the previous word problem?” Differentiated Instruction

Students will be able to solve the system of equations by hand, and use the technology provided, GeoGebra, to check their work and compare their answers. Students will also solve for Y in both equations and provide a table and graph. Checking the solution. Students may also facilitate other groups who are struggling and lead classmates to the answer.

Gifted and Talented:

EL: Students will be provided with vocabulary posters around the classroom that include examples and definitions of words like: Solve, Equation, Graph. Also provided on the board are a list of websites they may use to help solve the equations like, GeoGebra. These examples will help students understand the steps in order to solve a system of equations. Students with Other Special Needs: Students will have the opportunity to work in assigned groups or independently. Students will also be able to use notes with similar examples, and use highlighters to take note of the important information in the word problem. Students may also use the posters around the classroom with examples and definitions/pictures. Assessment Formative

Teacher circulation and listening to group collaboration, facilitating when needed, guided questioning. Students will demonstrate understanding by completing a Google Form that has a different word problem to create a system of equations. Students will also explain their reasoning, and give feedback on using GeoGebra. Summative

Given access to graphing calculators, students will create and solve a system of equations from a real-world word problem with 80% accuracy. B1.

In this example lesson plan, I mention using an online algebra and graphing software to solve

system of equations. Desmos and GeoGebra are good examples because they are free to use anywhere with internet access, which makes it a great option for students while studying at home or anywhere outside of the classroom setting. These sites enhance student learning by having students practice in writing a system of equation in its correct form to enter it on the webpage, if done incorrectly the website gives instant feedback and cannot solve the system. They also give instant visuals of what the graphs of the equations look like and noticeably shows the shared coordinate point, or answer, of the system of equations. These webpages are a great way for students to practice solving equations, compare their work instantly, and overall have a better understanding of how to solve a system of equations either in a classroom setting or at home while doing homework. B2.

Using this technology may limit student learning if used inaccurately since it does give

instant answers to the problems, students may just enter the needed information and not participate in the engaging and analyzing aspects of the material. This technology if used incorrectly can give students instant answers to the problems, but participating and comparing their answers to the webpage will solely be based on their own decisions of how to use the technology.

B3.

To overcome students using the technology to only receive answers and not engage in the

material, I can present the class with the expectations of using the technology and remind them that during their exams or tests, the technology will not be used. By having an open conversation with the students and making it clear of what I expect of them not only makes our teacherstudent relationship stronger it gives the students a sense of purpose since they are the ones choosing their own outcome, to fly by and struggle in the exams or to actually engage and understand the material being taught. C. Using

webpages like GeoGebra can be interacting and fun for students to demonstrate their

understanding in a creative way. One strategy to promote creativity in the classroom is by having the students make an image on a coordinate graph on GeoGebra and then find their own unique equations that represents each coordinate point of their design. This activity allows students to create their own problems, solve it, and analyze what was done correctly or incorrectly. After the assignment, students can ask themselves “What could I have done differently?” “Where was I stuck, and how did I figure out the next step?” “How did GeoGebra help in my problem?” The students can then share with a group or a partner their equations and have them solve to find the hidden image. By having creative and fun tasks that tie in with the students learning, it helps them build creative and divergent thinking skills, and staying engaged in the material.

Works Cited: Hutchinson, K. (2020). Solving systems of equations word problems. Algebra Class. https://www.algebra-class.com/solving-systems-of-equations.html.

OnlineMathLearning.com. (2020). Systems of equations - word problems (examples, solutions, videos, worksheets). https://www.onlinemathlearning.com/systems-equations-wordproblems-8ee8.html....