Author: nelsokar

CCSS Cluster: HSG Congruence Learning Progression

nelsokar Common Core State Standards Mathematics, Geometry Curriculum Aligned with CCSS-Math, HS Geometry, Uncategorized

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This learning progression would take place in a 10th/11th grade Geometry class and is aligned to multiple Common Core State Standards regarding “Congruence” – specifically HSG.CO.B.6, HSG.CO.B.7, and HSG.CO.B.8. This geometry courses uses the Holt Rinehart Winston Geometry textbook aided with an online resource, TeachersPayTeachers – All Things Algebra. This specific learning progression aligns directly with the TeachersPayTeachers worksheets. The guided notes and assignment are taken directly from this online resource.

 

Learning Progression – edTPA

Probability Learning Progression

nelsokar Uncategorized

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The central focus of this learning segment is to understand how to find theoretical and experimental probability and how they are used to calculate percent error. The purpose of this content is to give students the mathematical tools to use in order to solve real-world scenarios involving probability. The underlying concepts are probability, fractions (adding, dividing, and multiplying), and percent. The simple knowledge in this lesson includes the all the vocabulary relating to probability, percent, and fractions; and how they are used together, such as probability of flipping a coin heads is ½ which is 50%. The procedures in this learning segment are stating the theoretical probability, finding the experimental probability, and then calculating the percent error. This learning segment covers the following three Common Core State Standards: CCSS.MATH.CONTENT.7.SP.C.5, CCSS.MATH.CONTENT.7.SP.C.6, and CCSS.MATH.CONTENT.7.SP.C.8.A. It also addresses the following Math Practices: CCSS.MATH.PRACTICE.MP4 and CCSS.MATH.PRACTICE.MP6.

 Learning Progression

CCSS.MATH.CONTENT.8.G.B.7 I can identify a right triangle!

nelsokar Assessment of CCSS-Math, HS Geometry

Alignment to Content Standards: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Tasks:

The following rectangle, measuring 15 inches by 12 inches, has been divided into four triangles. The figure below has been filled in with a few other dimensions.

IM Assessment figure

 

 

There are three right triangles surrounding a fourth shaded triangle. Using the Pythagorean Theorem

1) Find the missing lengths in the diagram

2) Prove whether the shaded triangle is a right triangle or not.

 

The commentary and solutions for this task are included in document link below.

IM Assessment 2

 

HSG.SRT.B.5 & HSG.SRT.C.7 – Humor to Engage Students

nelsokar Picture Problems

One of the biggest struggles a math teacher can have is getting students engaged and excited about a lesson. Many students do not like math, do not find it fun, and/or do not see any relevance behind what they are learning. A great tactic to get students engaged in the lesson is to start the lesson with a picture. Instead of starting the lesson with the same old lecture and learning target, mix it up, start the lesson with a humorous picture. What student does not like to get a little giggle? It will not only get the students laughing, but it will help the students remember the lesson and material because they will recall the funny graphic they were shown at the beginning of the lesson. It will give the students a reference tool as well, so actually giving each a student their own copy of the picture would also be a good idea. The picture could even be attached to the top of the notes page as an easy reference/reminder.

Here are two examples that could be used when teaching triangle relationships. Both of these pictures would fit perfect with a lesson that was targeted towards the following standards.

  • CCSS.Math.Content.HSG.SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
  • CCSS.Math.Content.HSG.SRT.C.7: Explain and use the relationship between the sine and cosine of complementary angles.

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Bouncing Ball – MATH.CONTENT.6.EE.C.9 & MATH.CONTENT.6.EE.A.2.C

Link nelsokar Common Core State Standards Mathematics, HS Functions, Technology Teaching Issues

downloadBasketball, soccer ball, racquetball, bouncy ball; what child does not like to play with a ball!?

So why not have a math lesson that appeals to their interest of bouncing balls!

 

 

Picture a bouncing ball. As the ball makes contact with the floor, the ball rises and slows, then descends and speeds up. For any one of those bounces, the ball’s height can be plotted as a function of time, making a parabolic shape. Therefore, the relationship between the height and time for any bounce of the ball is a quadratic.

The relationship between the graph and the bouncing ball is expressed as

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where y is representing the height of the ball at any given time x. Another form of the quadratic equation is

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where h is the x-coordinate of the vertex, k is the y-coordinate of the vertex, and a is a parameter. This form of the quadratic equation is called the vertex form.

In this activity, students will use a Motion Detector, along with a TI-Nspire, to record the motion of a bouncing ball. Once the students have collected the data, they will analyze the data and model the ball’s height as a function of time during one bounce using the standard quadratic equation, as well as the vertex form of the quadratic equation.

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This activity’s objective meets two of the Common Core State Standards:

  1. MATH.CONTENT.6.EE.C.9
    Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
  2. MATH.CONTENT.6.EE.A.2.C
    Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

 

Bouncing Ball Activity

Motion Detector Tool

Kahoot! – Using Technology to Teach Math

nelsokar Uncategorized

Cellphones, cellphones, cellphones, it seems that’s all students talk about as well as the only thing they want to be on. Well now there’s a way to integrate their love of this technology to enhance and liven up the learning environment. Let’s face it, technology isn’t going to go anywhere, in fact technology’s influence in our education system is escalating with every year, so teachers will need to learn as many ways to take advantage of the technology available to them. The attached article is all about an interactive software, Kahoot, and the many ways in which a teacher can utilize this software to spark interest and engage students. So instead of cell phones being detractors to student’s education and learning allow them to start being facilitators! student-using-smartphone-during-class_192643727

Kahoot Article

Crazy Constructions! HSG.MG.A.3

Link nelsokar HS Geometry, HS Modeling, Technology Teaching Issues

Today’s students are surrounded by technology, most of them their lives revolve around technology even. So what better way to connect with the students then using what they know best, technology! Especially in math, where the majority of students already dislike the subject, it is important to find ways to keep them interested and involved. The attached lesson, Crazy Constructions, does just that. This lesson has students using a program called GeoGebra to perform their geometric constructions. Students start by performing the series of constructions on paper, then they will recreate them on GeoGebra. This is great way for all students, regardless of ability, a chance to complete the assignment and get a pattern/picture as their end result. Some students struggle with using a compass and straight edge, this is where GeoGebra is helpful because it is very user friendly and it will give tips/hints on how to perform the construction. All the tool in GeoGebra are along the top with the hints/tips given as soon as a student selects the tool.

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There are even tutorials on the program if students are really struggling. The other benefit to GeoGebra is their instant feedback and results, this allows the students to know right away if they missed something based on the picture being shown on the program. This lesson meets the high school modeling with geometry Common Core State Standard: CCSS.MATH.CONTENT.HSG.MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

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The pictures/patterns students can create on GeoGebra by performing geometric constructions is endless. It is definitely worth giving this lesson a try. Students have enjoyed the fun, interactive way of performing constructions through this lesson; as well as getting to use a computer and technology instead of just their tools and paper.

LessonPlan-crazy-constructions-1dzu4ss

GeoGebra Free Download: http://www.geogebra.org/cms/en/download/