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Probability: Impossible to Certain

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The last topic taught in 7th grade is probability. They develop their understanding of probability through analyzing experiments, calculating theoretical probabilities, and designing and running their own simulations to model real-world situations. Standard: CCSS.Math.Content.7.SP.C.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 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.  Goal: I'd like to provide more visual representations of probability through out this topic include actual spinners, dice, coins. Additionally, I'd like to provide a better foundation in understanding of what is “fair” or likely or unlikely. Additionally, I'd like to make the connection between these understandings and the v...

Geometry: How to find the area of a parallelogram

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Standard: Goal: My goal for this topic was to identify misconceptions when finding the are of a given parallelogram. Additionally, I want to make a point during my mini lesson and guided practice to share and use a helpful list of 'Steps for Understanding.' Hopefully these strategies will accommodate more students and will allow for more independent thinking, especially when a student is stuck on a question. The 'Steps for Understanding' will be the first resources students will (with lots of practice and redirection) go to if they're confused on how to start a question or if they're in the middle of solving one. The following are a couple problems from the lesson packet related to this standard, beginning with finding the area of a parallelogram.  Additionally, I've provided the incomplete template (below) that my students will receive to be completed during the Mini Lesson/Guided Practice. I've additionally added my answer key which in...

Calculus: What is a function?

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CCSS. Math. Content. 8.F.A.1 : Define, evaluate, and compare functions.  Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Goal : My goal for the topic of functions is to have students understand inputs and outputs and use the vocabulary of domain and range. Specifically, I want this lesson to be more a student to student based discussion lesson. I'd like my students to observe and comment on the differences and similarities they see in the given diagrams. After their observations are made, the definition of a function will be given (if they are higher level thinkers, we can arrive at the definition together via the similarities observed) and students will then go back to identify which relations represent functions and also provide explanations. The following two example problems make for great visual representations of inputs, outputs a...

Functions: Defining, Understanding, Graphing and Using Function Notation

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During my Functions lesson, I'd like to challenge my implementation of outside sources into the classroom, specifically with technology usage and also have a project based learning activity. I'd like to reacquaint myself with all the different modes, buttons and additional uses of the TI calculators. Common Core Standard:  Goal for this Lesson: In addition to presenting students with different types of functions and how graph them, in this unit I'd like to incorporate more technology use. I'd like to include in class calculator tutorials and provide additional supplementary tutorials on how to graph a function (including how to limit it's domain and range on the calculator). Additionally, I'd like to search through the internet for a computer graphing tool that could lead students into a functions project. I found this resource and I'd show my students this resources as an application example for functions. This will allow them to connect how co...

Algebra: Solving Inequalities and Graphing on a Number Line

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For our Second Personal Learning Path, I have chosen to discuss Algebra, more specifically how to solve inequalities and graphing them on a Number Line.  The Common Core Standard is as follows: Teaching Goal: I want to get better at facilitating a discussion with my students in order to arrive at an answer together, as a class. This facilitation won’t happen until my students have a foundational understanding of inequalities. Additionally, when the students feel more comfortable with solving and plotting inequalities on a number line, I’d like to have students lead the discussion of a problem (during share outs). Attached, I have included some of the classwork and below is a partial answer key that I will facilitate. Below is also a sample problem from the same classwork packet.    Sample Classwork Problem:   Do Now:   Mini Lesson:   Exit Ticket: An additional resources that I would steer students towards is their Alef Education Co...