Author: Gricelda Pedroza

HSF.LE.A Linear v. Exponential

Gricelda Pedroza Assessment of CCSS-Math, CCSS-Math Learning Progressions, Common Core State Standards Mathematics, HS Functions

linear-vs-exponential-growthexponential-growth-formula1

Keeping track of car payments, value of the car and amount of money in a savings account.

What each of the above statements have in common is that they are all real life situation in which either a linear or exponential equation is needed. When it comes to high school math it is important to make the math problems and concepts relevant to the students and the real world. The following learning progression and lesson plan are examples of ways to introduce and teach linear and exponential equations.

This learning progression is set for high school Algebra where students will learn about buying a motorcycle and how to represent the scenarios in linear or exponential equations. Through this learning progression students will understand how this math concept is applied to real life whether it be because they want to purchase a car or because they want to know how much money they will have after 12 months of having money in a savings account. Each of the lessons is also aligned with CCSS for math and there are activities for each lesson to help students reach the standards.

Learning Progression:Learning Progression Narrative

Lesson Plan:HSF.LE.A Lesson

6.NS Nana’s Lemonade

Gricelda Pedroza Assessment of CCSS-Math, Common Core State Standards Mathematics, ML Modeling, ML Number Systems, Technology Teaching Issues

Link to Nana’s Lemonade:  http://www.101qs.com/3043

This 3-Act Math Task is called “Nana’s Lemonade” by Dan Meyer. In this task there are three acts. Act one is a video that shows a small glass of water with only one lemon wedge, towards the end of the video a second glass comes in which looks like it can be about three to four times the size of the first glass. Along with act one is a questions asking students “How many lemon wedges should we use to make it taste the same?” it asks for the students’ guess as well as a guess that us too high and one that is too low. In act two there a couple questions asking “what information would be useful to know here?” and “guess the volume of the larger cup” in this act there are also two images showing the volume of the cups. With the information given in act two the students are able to get to act three which is a video with the answer.

This task is aligned to the Common Core State Standards:

CCSS.MATH.CONTENT.6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.

CCSS.MATH.PRACTICE.MP4 Model with Mathematics.

This activity can be taught in a lesson involving number and operations. This task is asking students to estimate first then use the information given and fractions to solve the answer. The way I would teach this activity is by introducing the standard and then showing the video in act one, I would also ask the students to answer the questions. Showing the students the first video is important so they can understand what the question is asking and the students also get a visual representation of what the problem is like. After the students have watched the video as many times as they desire I would then as them to turn and talk with their peers about what information they might need in order to answer the question. By having the students turn and talk I can ensure that they start to think about what the problem is really asking. Once the students have come up with ideas I can then show them act two which gives them very important information about the size of the cups. After the students have that information they can then set up the fractions to solve for the number of wedges needed. Once the students have solved for the missing term I can then show them act three which is the video with the answer. By going through the three acts I can help the students achieve the common core standard.

Students are also given an opportunity to challenge themselves with the sequel questions which range in difficulty. Since we are in the topic of numbers and operations I would maybe have the students answer “how many ounces of water are in each container?” The students already know how many cups of water each container has but now they will have to convert to ounces.

G.SRT – Map My Walk

Gricelda Pedroza Common Core State Standards Mathematics, Geometry Teaching Issues, HS Geometry, HS Modeling, Technology Teaching Issues

CCSS.Math.Content.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*

G.SRT.C.8 Map My Walk

It is no secret that society is using more and more on technology for everyday things. As teacher we need to try to incorporate this kind of technology that our students are using on a daily basis into our curriculum.

apps

One way to incorporate technology into a lesson is by having students use what they can’t live without, their cellphones. In both Google Play and the iTunes store the Walk with Map My Walk app can be downloaded for free. This app tracks where the person is walking, what distance they have traveled as well as the duration of the walk. One standard that can be met using this app is G.SRT.C.8, which is a modeling standard that uses trigonometry and the Pythagorean theorem to solve right triangles. Using this app two students can start at a marked point and then walk away from each other at a right angle (maybe walk on the sidewalk of an intersection), while the students walk away from each other the app will track the distance traveled by each student. Once the students have walked the desired distance they can come together and draw their triangle using the data from the app. Now with the triangle drawn the students can now use the Pythagorean theorem to solve for the hypotenuse, which is the distance between the two students when they stopped walking. Once the students have solved for the hypotenuse then they can now use that information to solve for the angles using trigonometric ratios. To challenge the students a bit more they can be assigned to make their own triangle using only one student.

app

This activity will get students out of the classroom and doing something they probably did not think could be done with their phones. If this standard was not taught using technology it would be taught just by story telling and having students draw out the triangle according to the story. This activity is not only getting students to learn math in a more practical way but it is also getting them to move around. This is also something the parents and the community can get involved in. Parents can use the app to assess their child when they are out on family walks or when they are at the store. Once the student is comfortable with the app they can involve their friends and community members in an activity.

The students will be exited to get an opportunity to go outside and move around rather than just sit at a desk and work from a textbook. This technology is very helpful because students always have their phones on them. Instead of trying to fight them to put it away why not incorporate this into the curriculum where they will be using their phone in a positive and productive way. When students are able to see the how math is really applied to the real world they tend to listen better and be more involved. If the students can see the correlation between the lesson and the community they will be more enthusiastic. When students start to get into higher-level math they tend to lose interest because they feel like that math does not apply to everyday life but by having students use things like their phone in lessons they will see that math is still apart of it.

Here is the worksheet where the students will collect and write all their information. MapMyWalk

For more pictures and information about the app go to http://www.mapmywalk.com/app/

F.IF – Electric Bill

Gricelda Pedroza Assessment of CCSS-Math, Common Core State Standards Mathematics, HS Functions, HS Modeling

Alignments to Content Standards

  • Alignment: F-IF.A.1
    • HSF: Functions
    • Domain: HSF-IF: Interpreting Functions
    • Cluster: Understand the concept of a function and use function notation.
    • Standard: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Task

Anthony’s electricity company charges him $0.12 per kWh (kilowatt-hour) of electricity, plus a basic connection charge of $20.00 per month. Let C(k) be the cost in dollars at the end of the month and k be the kilowatt-hour.

  1. Write the function using C(k) be the cost in dollars and k for the kilowatt-hour.
  2. Complete the table below.
k (kilowatt-hour) C(k) (dollars)
0  
15  
35  
47  
89  
125  
260  

 

  1. Sketch a graph of C for 0≤k≤280.
  2. What is the domain and range of the function?
  3. Is C a function of k? Explain you reasoning.

Commentary

The purpose of the task is to illustrate the meaning of a function in a real-world situation. This task is helping the students understand and visualize whether or not this is a function. Students are also getting a sense of what it means for an equation to be a function. While solving this problem students are also answering whether each input only has one output. In future classes students will be able to use their knowledge of functions to be able to derive them.

F-IF Electric Bill Solution

G.SRT-Using a Cube Picture

Gricelda Pedroza Common Core State Standards Mathematics, HS Geometry, HS Modeling, Picture Problems

Geo Pic

This picture elicits the following problem that aligns to the Common Core State Standard: CCSS.Math.Content.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

The problem to solve is: Use trigonometric ratios and the Pythagorean Theorem to solve for the legs of the right triangles.

The students would each be given a print out of the picture and a piece of grid paper. With the grid paper on top of the original picture they will draw each right angle they are able to pinpoint. While they trace each right angle they have to make sure that each is drawn separately so they can calculate each measurement. After the angles are drawn the students will then connect the legs to make a triangle. In order to figure out at least one leg the students have to make sure the right angle lines up with a point on the grid paper. From there the students will use trig ratios and the Pythagorean Theorem to solve for the legs and hypotenuse of the right triangles.

This activity will be entertaining for the students because the figure is very interesting to look at. This will also show the students that math can be used outside of the classroom in real-life. This picture and CCSS will keep the students engaged because they will be communicating with their classmates to compare answers and strategies.

G.GPE-Using Geogebra to Compute Areas and Perimeters

Gricelda Pedroza Assessment of CCSS-Math, Common Core State Standards Mathematics, HS Geometry, HS Modeling, Technology Teaching Issues

Meeting State Standards is always in the back of all math teacher’s mind. Teachers are always thinking of new ways that they can incorporate new ideas into the classroom. When standards have to be met and students are very interested the beast way to approach the topic is to use something that relates to them. Students love technology, it’s part of their everyday life. Now the challenge is “how do we bring technology into the curriculum?” Using Geogebra that’s how. Geogebra is a free software that teachers and students can use to meet State Standards.

Getting students to plot point on a grid isn’t always very interesting, but now instead of plotting points on grid paper students can use Geogebra to plot coordinate points on a coordinate plane. The free Geogebra software can be used to meet Common Core State Standards like the one in the sample Perimeter and Area Lesson Plan along with the lesson plan is the sample Perimeter and Area Worksheet. This lesson plan is designed to help students achieve various learning targets aligned with the Common Core. The following Geogebra Article goes into further detail of why Geogebra should be used to elicit student learning and aid student achieve the Common Core State Standard.

F.BF-Wolfram Demonstrations for Student Visualization

Gricelda Pedroza Common Core State Standards Mathematics, HS Functions, Technology Teaching Issues

The following is an article explaining how the Wolfram Demonstrations Project and Wolfram Alpha engines can be used to elicit student understanding of parent functions and transformations. Student will be able to show mathematical understanding by playing and manipulating the parent function on the Wolfram Demonstrations Project and visually see what each manipulation will do to the graph. Students will also be able to check their understanding by using Wolfram Alpha and inputting the function they want to see transformed. Teachers are also able to use these engines to teach the class and explain the manipulations to the students as part of their lessons.

Wolfram Demonstrations Article