My First Week of School... slower than expected

I had my first several weeks of notes and assignments all planned out. I guess I thought it could be taught in one week.

It did not go as planned! (It never does.)

I used the "First Day of School" tangram for all my classes. It was a great way to determine the pace at which a class or student cuts, folds, and pastes things together. The pace of my previously taught classes is significantly more efficient than that of my new students.

The great thing about doing the reference chart on day one is that my students immediately use it without being reminded to. In Pre-Algebra, we began the year with a review of Geometry Formulas. I was concerned at first, but realized that this was a great review of basic algebra skills with something they were familiar with. And it was another way to bridge the arithmetic skills from by hand to calculator.

Every class then created a Unit Pocket for the first unit.

In Algebra 2, we started with Sets of Real Numbers. I reference the textbook partly for my information and loved the example they used-billiard balls.

For the sets and subsets of rational numbers I printed a concentric rectangles to give the look and feel of a Venn diagram. My original strategy was to teach rational numbers first and work towards natural, but my colleague suggested and explained how she teaches natural numbers first and works out towards rational. It made complete sense and it worked my kids!!

For Geometry, I have followed the original pages from older posts, but decided to add this page to clarify what happens to triangles in the different types of geometry.

This year for Taxi Cab geometry, I used google earth to show students where it originated-New York. For small town kids, this was an adventure. We then used google earth to find our small town, overlayed a sheet of posterboard on the Promethean, and tried to find the shortest route from school to the Snow Cone truck. Taxi Cab geometry was just about everyone's favorite.

 

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Geometry: Non-Central Angles, Interior and Exterior Angles, and Secant and Tangent Relationships of Circles

Pg 5. Non-Central Angles (Need to rethink the title now that I think about it.)

This page consists of a half page fold of two pages glued together with four half page folds on each page. This entire page is pulled from the CSCOPE curriculum and tweaked just a bit.

First, we completed a page/lesson using paper folding and making conclusion based on what we know. When complete, the students would make a conclusion based on the evidence. We wrote that on the front off that page. After we completed all four pages, we went to the front and wrote three summarizing conclusions. I think it went pretty well and soundly build and understanding.

First section:

Left side:

I drew up a general diagram for the following three pages. We then completed the lesson with the same diagrams.

Right side:

Second Section:

Left side:

Right side:

 

Pg 6. Circles, Lines, and Angles

I want to find a better way to present and organize the following two pages. My students understood, but it didn't make a lasting impact.

 

 

 

Pg 7. Secant and Tangent Relationships

 

 

 

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Venn Diagrams: Quadrilaterals and other Polygons

These activities are AWESOME! I love the discussions that come up, the type of thinking that occurs, and the multiple possibilities there are.

These materials were provided through a workshop. I have yet to use them in my classroom, but I have no doubt these would be an excellent addition to the unit of quadrilaterals.

You start with four different Venn Diagrams.

 

 

 

You have a selection of set titles and shapes.

Here are some examples of the use of these materials.

(Don't forget about the universal set on the outside of the circles.)

 

 

Some suggested strategies/conversations:

• Have a student demonstrate their Venn Diagram.
• Have students justify their decisions.
• Start with with set titles and categorize shapes.
• Start with categorized shapes and determine the set title.
• Ask students where they started and how they categorized the shapes.

 

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Geometry: Special Right Triangles

Pg 10. Rationalize Square Roots

Before we dived into Special Right Triangles, I though we'd go over rationalizing square roots. This went much smoother this year than in the past because my students were familiar and comfortable with square roots and simplifying them. Surprisingly, most of the students took this very well and rationalized square roots like it was nothing! (Still amazed!) It has been such a struggle in the past.

 

 

Pg 11. Special Right Triangles

This has always been my toughest area to teach to my students, until this year. When it was all said and done, I confessed to my students that this is one of the hardest concepts/lessons for me to teach. Then, they blew my mind. My students told me this was the easiest thing they've done so far and loved it. Throughout the rest of the year they chose to use the special right triangles method to solve most other problems over trigonometry!!

I think that part of reason for this is the method I used to teach this concept. I pulled several resources for notes, guided practice, and independent practice. I worked all problems myself to identify a pattern to the differing levelss of questioning. After this, I taught each question type as a lesson by itself.

For 45-45-90, I focused on finding the legs first and then the hypotenuse.

For 30-60-90, I began with the questions that required simple mathematical relationships in order to solve and then we worked up to the questions involving rationalizing.

We would work out an example with extensive explanations, then complete a student let guided practice. For the independent practice, I encouraged them to work as a team and I graded them immediately. I actively monitored for independent and collaborative work and I made sure to intervene when I saw attempted cheating.

Special Right Triangles

Cover:

Deriving the formulas:

Lesson examples:

Guided Practices: These were folded and tucked behind the above notes that were glued down like a pocket.

For each question, you'll notice a select number of homework problems. I assigned what my students thought was randomly selected problems. I would assign a small two to three problem practice and then the next day come back and do one to two more or the same. In the end, we completed the worksheet.

Honestly this whole journal page probably took us four or five days to complete. We looped through lesson, guided practice, and independent practice for each type of question. I felt that this was an important tool needed later for properties and measurement of two and three dimensional shapes.

Usually, the lesson using trigonometry to solve right triangles is introduced here. However, this lesson hit right before Christmas break. I looked through upcoming units and decided that I could make up the lessons and concept in Unit 8 Measurement of Two Dimensional Figures. It turned out great! Not sure if I will keep it this way next year or not. I guess it depends on timing.

This is a page from my second year journal.

Optional Pg. Right Triangle Solving Strategies

This foldable was used after the lessons on Trigonometry to summarize the strategies used to solve right triangles.

 

 

 

 

 

 

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Geometry: Pythagorean Theorem

Pg 6. Right Triangle Basics (Optional - Used this my second year, but not my third.)

 

Pg 7. Pythagorean Theorem

LEFT: We took a square piece of paper and folded it until the entire square is made up of small right triangles. We then selected a right triangle and the three surrounding squares to demonstrate the Pythagorean Theorem.

RIGHT: Another time, we selected, drew, and then cut out the diagram to demonstrate the Pythagorean Theorem.

I have seen other diagrams using all the pieces to make a square, but I have yet to understand them or see the purpose. Any suggestions for enlightening resources?

Pg 8. Pythagorean Theorem and It's Converse

This next year, I will use Anglegs and worksheet to introduce and classify triangles.

My students came with excellent prior knowledge of the Pythagorean Theorem.

Pg 9. Multistep Pythagorean Theorem

 

 

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