Author: richarta

7-SP Introduction to Probability

richarta CCSS-Math Learning Progressions, ML Statistics & Probability

The grade level that the learning progression will involve are high school students in an Algebra B classroom. This is a group of students that are behind in algebra. This is why grade level 7 common core state standards are chosen. These students need more time for practicing new activities and more time to master new skills. The book used in this classroom is titled Algebra 1: Applications, Equations, Graphs. This textbook was published in 2004 by McDougal Littell, a division of Houghton Mifflin Company. This book is not used very much during class time. This learning progression will be for three probability activities. The first lesson will be an introduction of how to find probability and identify the likelihood of an event. Students will make a connection that if an event has a high probability, the event is more likely to take place. The second lesson will have students perform their own investigation of finding probability. Finally, the third lesson will have students create their own probability project. Students will use a real world application that can be used to collect data that relates to probability. The three Common Core State Standards that are used in the learning progression are

1. CCSS.MATH.CONTENT.7.SP.5..Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

2. CCSS.MATH.CONTENT.7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

3. CCSS.MATH.CONTENT.7.SP.7.a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

The link to the learning progression and lesson plan are below.

Learning Progression Formative Assessment (1)

 

 

G-GMD 3-Acts Math Task: Water Tank

richarta Assessment of CCSS-Math, Common Core State Standards Mathematics, HS Geometry, HS Modeling, Improve Mathematical Thinking, Technology Teaching Issues

The Water Tank math problem was found on the Dan Meyer’s 3-Act Math task website. This problem has students figure out of fast it takes to fill up the water tank. This activity can be found at the following link:

http://mrmeyer.com/threeacts/watertank/

watertank

Students will first watch a 17 second video of a water tank being filled. After the students watch the video, they will make guesses, one that is too high and one that is too low, on how long they think it will take to fill up the tank. After making their guesses, students will then discuss what information is needed to solve this problem. Students will then work on the information discussed to see if they can determine how long the water tank takes to fill. After the students determine an answer from their information, another 12 second video will be displayed and students will determine if their answer was right or wrong. An additional exercise is determining how fast it takes the tank to empty.

The Common Core State Standards that are addressed in this problem are from High School Geometry: Geometric Measurement and Dimension:

G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

G-GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Students will reach these standards through the videos and through the investigation of information. I will begin the activity by showing the first video. Then I will ask my students what information is needed in order to solve the problem and what formulas are needed to find the answer to the problem. The students will meet the first standard by determining a volume equation that will give us the correct answer. The students will meet the second standard by determining what two-dimensional shapes make up the three-dimensional shape. This could help us create a volume formula that we could use to find the answer. Students will also need help converting from volume into desired units. After the volume is determined, students will then convert the volume into ounces, watch a video on how long it takes to fill 16 ounces, and then finally determine how much time it takes to fill the water tank. Students will be formatively assessed through classroom discussions, group discussions, and the use of a worksheet.

This lesson is a great way to get students engaged and enjoy the activity because the lesson is interactive and has videos. Students would work in small groups and as a class to determine the answer the question. I have found that students work better in small groups and work better when they can share their ideas with the class. This is a way to build respect and rapport between the students and with the teacher. Also, the teacher can better monitor the students learning progress and manage the classroom. Technology is integrated into the lesson when the students are viewing the videos and images from the website that was given above.

F.IF – What is my Heart Rate?

richarta Common Core State Standards Mathematics, HS Functions, HS Modeling, Improve Mathematical Thinking, Technology Teaching Issues

heart_rate_data

This is a great interactive activity that helps students determine their hear rate after doing certain physical activities. Students can determine which activity will raise their hear rate the most and the least. This is important to real world problems because if you want to burn calories and lose weight, it would be very helpful to know which physical activities get your heart rate up the most. Also, students can determine how long it takes for their heart rate to go back to its normal rate. This is important because after doing a certain physical activity, it would be helpful to know how long it takes for your heart rate to go to its rest rate.

In this activity, students will be measuring and graphing their heart rates using graphing calculators and a hand held heart rate monitor. Students will perform 3 trials. Trial 1 will consist of rest, marching, and jogging in place. Trial 2 will consist of rest, jogging in place, and running in place. Trial 3 will consist of rest, marching in place, and jumping jacks. Each activity is 1 minute long. Students will create three graphs based on the three trials performed. The hand held heart monitor will be connected to the graphing calculator and graphing calculator will be collecting constant data for each trial. After each trial is completed, the graphing calculator will display the graph for the student. The student will sketch the three graphs on a worksheet: on the worksheet, the students will talk about the rates of change of each parts of the graph (constant, increasing, or decreasing). This activity lines up with the Common Core State Standards by meeting standard CCSS.Math.Content.HSF.IF.B.6. Students will be interpreting the rate of change of the function of their heart rate. They will be interpreting the rate of change symbolically.

The materials needed for this activity are as follows:

This activity will work better if students work in small groups. Students should be put int groups of 2 or 3. Each student in the group will be completing an experiment of their own. That way each student can be engaged and evaluate their own data.

 

A-SSE Throwing a Ball

richarta Assessment of CCSS-Math, Common Core State Standards Mathematics, Improve Mathematical Thinking

Title: A-SSE Throwing a Ball

Alignments to Content Standard: HAS-SSE.B.3.a Factor a quadratic expression to reveal the zeros of the function it defines.

Problem:

A big ball is thrown from a top of a 24m building with an initial velocity of 20 m/s and as the ball is falling, gravity acts on the ball pulling it downward towards the ground. The speed of the ball changes by a rate of 4m/s^2. What is the time in seconds that the ball hits the ground?

Commentary:

The purpose of this task is for students to first build a quadratic equation from the information given, factor the quadratic equation, and solve for the zeros to find the correct time of the ball hitting the ground.

Solution:

The height of the ball starts at 24m.

It travels at an initial velocity of 20 m/s.

Gravity pulls the ball downward towards the ground, changing the speed by 4m/s^2.

t is for time.

 

 

 

The quadratic equation is -4t^2 +20t +24mathill

 

This can be factored into (4t + 4) (-t +6) = 0

Set both binomials equal to 0 and solve for t.

4t +4 =0                -t +6 =0

4t = -4                     t = 6

t = -1

Because you cannot have a negative time, the ball hits the ground after 6 seconds.

7.G-Picture Problem: Fireworks

richarta Common Core State Standards Mathematics, ML Modeling, Picture Problems

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When a firework goes in the air, it blows up in a circular shape.  One could use a compass and draw a circle around the entire firework explosion. When a complete circle is drawn, one could use a ruler to measure what the diameter of the circle is. After the diameter is determined, one could find the area of the circle. The Common Core State Standard that this picture problem would align with is CCSS.Math.Content.7.G.B4. The student would have to know what the formula is to find the area of a circle is in order to actually find the are of the circle.

A.SSE-Using the Quadratic Formula with Technology

richarta Algebra Teaching Issues, Common Core State Standards Mathematics, HS Algebra, HS Modeling, Improve Mathematical Thinking, Technology Teaching Issues

This is a lesson for teaching students how to use the quadratic formula with the use of a SMART Board. How the students learn to use the quadratic formula is broken down into three steps: identifying the coefficients (a, b, and c) in a quadratic equation, correctly plugging them into the quadratic formula, and executing the formula correctly. What the teacher is trying to accomplish is attempting to get the students to learn a new mathematical skill by the use of technology. The teacher hopes that students will be more engaged in this lesson rather than writing on a regular whiteboard. You can view this lesson by following the link:

LessonPlanTemplate(1)

  • Integrating Technology in the Mathematics Curriculum

How technology is integrated into the curriculum of mathematics is by using a electronic white board, otherwise known as the SMART Board, to conduct a lesson and do practice problems with the students. The SMART Board will allow multiple students, maximum of 6 at a time, to do physical work on a given problem using their hands or a pen. Also, the SMART Board has access to a presentation website called the SMART Exchange. This website contains mathematical presentations that teachers can access and use in their classroom and the students can work on problems from the presentation physically. This piece of technology could help students reach the Common Core State Standard by getting the students more motivated and excited to participate in the activities offered. Because students are more interested in their computers and phones, this is a touch screen whiteboard that is much like some of their phones. There are high hopes to get students more engaged and motivated when using this piece of technology.

  • Participation in Community of Mathematics Educators

SMART Boards are giving the community of mathematical educators a much easier and mess free experience when conducting a lesson. When using the SMART Board, the teacher can create her or his own presentation or find one on the SMART Exchange. If a teacher wants to add anything to the presentation they can right in the moment by just writing on the SMART Board. Also, your days or erasing chalk or expo pens and writing with chalk or expo pens are over. The SMART Board is a mess free board. This is a great piece of technology that is easy to use, easy to display lessons, and mess free.

  • Ability to Contribute to Program and School Improvement

The SMART Board will help contribute to school improvement and to the program by getting students to be more engaged and by giving teachers a better way to communicate lessons to students. Students already have a hard time paying attention in class because they are distracted by their own pieces of technology. In using an electronic whiteboard that has a touch screen, there are high hopes to get students more interested in participating class and using the SMART Board to solve problems. Teachers can also choose lessons that best fit their classroom. Based on the students’ knowledge and skill level, the teacher can find a lesson on the SMART Exchange website that best helps students learn. Or the teacher can create their own lessons on the SMART Board. The SMART Board can display easy to read instructions, practice problems, or pictures. For example, if a teacher need to show a picture of a graph but also write down what the different parts of the graph are, the SMART Board can easily display all the information needed or the teacher can display the picture through the SMART Board and write on it what the parts of the graph are. SMART Boards have the ability make teaching more effective and could get students more engaged in participating during class.

  • Planning for Mathematical Understanding

Learning targets will be discussed with students before the lesson begins. The teacher will set up the SMART Board presentation form the SMART Exchange website. Students have had practice with squaring binomials and solving quadratic expressions by factoring. Pre-assessment will consist of giving the students a quadratic that cannot always be factored into two binomials. This will show them that there is another way to solve quadratic equations. The teacher will then assess if the students can identify the coefficients, a, b, and c, in the quadratic equation and determine if the students can correctly plug them into the quadratic formula. Students will be asked to identify a, b, and c of a quadratic equation. One student can volunteer to come to the board and physically write on the board what a, b, and c are. If the students can correctly plug in the coefficients into the quadratic formula, then they can move on to executing the formula to find the zeros of the quadratic equation. Another student will be able to come to the board and plug a, b, and c into the quadratic equation correctly. After a few practice trials of identifying a, b, and c and correctly plugging them into the quadratic formula, the teacher will move forward to effectively solving for the zeros of the quadratic equation. Multiple students can come to the board to solve multiple problems displayed. The students can explain what they are doing as they are going through the problem solving process. Their peers can voice helpful tips or advice if it is needed. After the class activity with the SMART Board in completed, the students will be given a worksheet with more practice problems on them to help master this new skill. This is a step by step process to ensure each student can first identify the correct coefficients, plug them correctly into the quadratic formula, and to correctly execute the equation to find the zeros.

  • Planning to Support Varied Learning Needs

Students have a lot of trouble grasping new mathematical concepts and skills. To accommodate for a large difference in mathematical ability, the teacher will use a SMART Board and a SMART Exchange presentation to help students grasp this new skill. Because it is a new technology, the teacher hopes that the students will be more engaged and will have more fun coming to the board. The teacher will go over step by step how to use the quadratic formula to ensure that students know how to use it correctly and have students come to the board to practice. Also, using the SMART Exchange will give teachers presentations or practice problems to display. It gives the teacher extra tools to help her students learn. The students will also work individually and at their own pace to complete the problems on a worksheet. Students who have misconceptions will work with the instructor and with peers in order to guide the student in the right direction and get immediate feedback.

  • Using Knowledge of Students to Inform Teaching and Learning

Because students have had practice with squaring binomials and solving quadratic expressions by factoring, they need to see a quadratic equation that cannot be factored back into two binomials. The teacher will break up the lesson into smaller steps so the students can keep up and learn how to use the quadratic formula more easily. Pre-assessment will consist of giving the students a quadratic that cannot be factored. This will show them that there is another way to solve quadratic equations. The teacher will then assess if the students can correctly identify a, b, and c in the quadratic equation and determine if the students can correctly plug them into the quadratic formula. If the students can correctly plug in the coefficients into the quadratic formula, then they can move on to executing the formula to find the zeros of the quadratic equation. It is more effective to break up each step in using the quadratic formula because students can be easily confused of how to identify and plug in the coefficients into the formula and can make an error trying to execute the equation. By breaking up the process into smaller steps, students can better grasp how to correctly use the quadratic formula. Also because the students have a hard time participating in the activity, the teacher will use a SMART Board to conduct her lesson. By using the technology in the process of learning, the teacher hopes that the students will be more engaged in the activity. They get to use a touch screen whiteboard to do their work on that is easy to use and mess free. The students use technology everyday; since the teacher knows that the students enjoy using touch screens and using technology, she hopes that the students will have more fun and be more engaged in the lesson.

  • Planning Assessment to Monitor and Support Student Learning

There are no formal rubrics for this lesson. The learning targets are as follows:

  1. I can identify when to use the quadratic formula.
  2. I can identify the correct coefficients, given by the quadratic equation, and plug them into the quadratic formula correctly.
  3. I can execute the quadratic formula and find the zeros of the quadratic equation.

In this lesson, the formative assessment will consist of the students coming to the SMART Board to physically identify a, b, and c, correctly plug them into the quadratic formula, correctly execute the formula to find the zeros, and given practice problems on a worksheet to continue to master this new skill.  The teacher will be observing the students while they quietly work. The teacher will comment on the students’ work to help guide them in the right direction during the problem solving process. At the end of the class period, the worksheet will be handed into the teacher for further assessment. The teacher will then evaluate the worksheets to determine what the students still need to work on.