Author: sumec

Learning Progression for Polynomial Arithmetic (A-APR)

sumec HS Algebra, Uncategorized

This learning progression covers the arithmetic involved with polynomials, mainly focusing on quadratics. Also attached with the learning progression is a lesson plan that highlights the formative assessments associated with this learning progression. Students will participate any numerous cooperative learning activities as well as be given the opportunity to show their understanding of the concepts to the rest of the class by demonstrating their work on the board. These lessons are engaging and informative for students who need to meet the following Common Core State Standards:

  • CCSS.MATH.CONTENT.HSA.APR.A.1
  • CCSS.MATH.CONTENT.HSA.APR.B.2
  • CCSS.MATH.CONTENT.HSA.APR.B.3
  • CCSS.MATH.CONTENT.HSA.APR.C.4
  • CCSS.MATH.CONTENT.HSA.APR.C.5

Here is the learning progression and the lesson plan:
Learning Progression
Lesson Plan

S-MD.4: Money Duck 3-Acts Math Task

sumec Assessment of CCSS-Math, Common Core State Standards Mathematics, ML Modeling, ML Statistics & Probability, Technology Teaching Issues

The Money Duck is a math problem found on Dan Meyer’s 3-Act math task website. The task first has the students watch a video about a soap bar in the shape of a duck with varying amounts of money on the inside. From there, students are then asked several questions about the possibility of the amount of money inside the duck, such as “how much would you pay for this duck?” The activity can be found using the following link:
http://www.101qs.com/2985

The Common Core State Standard that this problem addresses is “Using Probability to Make Decisions”. Furthermore, it focuses on S-MD.4 which states that students will “develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.”

To get the students to meet the standard previously mentioned, I would first show them the video that was used on the Money Duck website. If the students have any questions about what the Money Duck is exactly, I would answer those questions before I began asking the students questions. The questions associated with this task will get progressively harder and more complex as the students work through them. The eventual destination is that the students will have an understanding of what expected value is, which is the main objective of the CCSS S-MD.4. This assignment requires that the students demonstrate their understanding of the identified CCSS in question 6 which asks “what is the expected value of each of the following distributions?” Students will have to use what they have learned and discovered in the previous questions as well as their understanding of probability to answer this question.

This lesson will prove to be engaging for the students because it involves videos and money. Also, I would make this a small group assignment so that students will be able to discuss ideas with group mates and then present their ideas to the rest of the class when we come back together. I would also ask other groups to respond each others answers, whether they agree or disagree, to better the entire class’s understanding of expected value.

Questions 1-5 will serve as a great formative assessment to see the students’ progress towards the learning target of being able to calculate expected value. These questions, as Dan Meyer described it, will be “setting the ball on the tee” for expected value so that the students will be able to answer question #6. #6 will serve as a benchmark assessment to see where the students are at in terms of CCSS S-MD.4. Depending on how far the hit the ball of the tee, whether it be a home run or they completely miss the ball, I can tell what the next step will be in terms of trying to meet that standard.

8.EE – Cooling Off

sumec Common Core State Standards Mathematics, ML Expressions & Equations, ML Modeling, Technology Teaching Issues

Using Vernier Temperature Probes are a great way for teachers to integrate technology in their classroom. This project uses probes to measure the temperature of hot coffee and cold water and ultimately decides the perfect amount of cold water needed to enjoy your cup of coffee. Having the students complete this experiment to collect data will be more engaging for them compared to getting data from a textbook. Since students will be using their very own data, they will be eager to solve the given equation, which will strengthen the skills necessary to meet the learning target. That is because the students will solve the equation multiple times to answer different questions and the more practice they have and the higher their engagement level, the more likely they are to remember these skills.

http://www.vernier.com/products/sensors/temperature-sensors/
http://www.vernier.com/products/sensors/temperature-sensors/

The questions asked in this assignment start simple, strengthening the students’ ideas and concepts of how all of the different temperatures and volumes relate to each other. As the students become more comfortable with the data, they are asked to apply their knowledge and equation solving skills to answer more difficult questions. Also, this project will be very memorable for the students and the teacher can refer back to it in future assignments so the students can recall the skills used to complete this task.

Many of the children have parents who drink coffee and undoubtedly, some of those parents probably burn their mouths. Students can actually apply these skills at home and determine how much cold water their parent(s) should add to make their coffee more enjoyable.

Here is assignment sheet needed to complete the experiment Vernier Probes Cooling Off

http://www.vernier.com/experiments/rwv/6/mix_it_up_-_mixing_liquids_of_different_temperatures/
http://www.vernier.com/experiments/rwv/6/mix_it_up_-_mixing_liquids_of_different_temperatures/

7.G-Using A Picture To Identify Geometric Shapes In The Real World

sumec ML Modeling, Picture Problems

bridges

 

This picture was found at http://web.utk.edu/~wmorgan/Suttree/bridges.htm

A possible math problem that students could solve is “identify all of the different geometric shapes found in this picture and then describe the relationship of the areas.”

This problem would align with the following CCSS:
CCSS.MATH.CONTENT.7.G.B.6
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.

To solve the problem, the picture can each be given a copy of the picture where they will use the extra space to solve the problem. Students will be able to identify triangles, squares, rectangles, parallelograms, and more. From there, they will be able to see that all of the triangles are congruent and that the areas are in proportion to one another.

Having the students find geometric shapes in the real world will give them a real world application of the math they are learning. This is extremely important because it answers the most asked question in math, “what is the point of this?” Using this picture will be one way in which you can answer this question.

A.CED-Using Geogebra To Model Equations For Real Situations

sumec Algebra Teaching Issues, HS Algebra, HS Modeling, Technology Teaching Issues

This article “Is 2 Really Greater Than 1?” we see how you can use Geogebra to have students create models that represent situations in the real world. Direct instruction, group work, and a worksheet are all used to get the students involved in the process of finding the correct answer to the problem; is two wheels more efficient than one? Students will work together to create a model that represents the size of a wheel, the size of the tire, and the ultimate cost of the bicycle and the tricycle using Geogebra. At the end of the assignment sheet, students will be asked to explain the difference of cost for certain materials. This allows them to make a further connection to the problem by understanding where the independent and dependent variables came from.

Here is the lesson plan that explains how to teach the modeling activity 2 >1 Lesson Plan and here is the worksheet used for this assignment 2 >1 Worksheet. To grade the students, you can use this rubric 2 > 1 Rubric