Jennifer,+Tommy,+and+Kristen's+6-8+grade+page

There are four goals for the geometry standard and two goals for the measurement standard that are common across all the grade bands: You need to list the specific expectations for grades 6-8. the goals are common across all of the grade levels; the expectations are specific to grade bands. So please add all of those. Re-read the On-going reflection page set up. You're missing important criteria set forth on that page. =**__Geometry__**= - We talked about some characteristics of quadrilaterals. what motivated the talk? What did we do? Quadrilaterals are polygons with four sides and four angles. Some quadrilaterals have all congruent sides,right angles and parallel sides such as a square. Students in the 6-8 grade level need to be able to understand the relationships between the side lengths and angles. - We discussed characteristics of regular polygons. Again, how was this set up? Trying to connect what we do in class to what can happen in the middle school classroom. A regular polygon is a polygon with all side lengths, central and vertex angles are all congruent. We defined central angles as the angle from the center and the vertex angles are the angles formed at the vertices of these polygons. - We examined many different types of triangles and identified which characteristics all of them had and which ones only some of the triangles had. From these characteristics, we began to define what makes a triangle. Forming definitions of polygons is important so students know how polygons differ from each other and how they relate to one another. Many times, the names connect to the polygon's properties, thus helping make the connection with name, shape, and definition. So We defined a triangle and the different types of triangles. A triangle is a polygon with three sides. The different types of triangles are: acute, obtuse, scalene, isosceles, equilateral and right. An acute triangle is a triangle whose angles are smaller than 90 degrees. An obtuse triangle contains at least one angle larger than 90 degrees. An equilateral triangle is a triangle who has three congruent angles. An isosceles triangle has only two sides that are congruent. A right triangle has one right angle in it. -The big idea from class one was shapes and their features. This is not the summary of big ideas page! -The big idea from class two was the definition of a polygon which is a simple closed curve with straight sides. - We began coming up with area formulas. We found these by starting out with larger clarify "larger" (I thought we started with a rectangle and went to a parallelogram. How are they larger shapes?) shapes finding how we would find their areas and then using what we new to find the areas of shapes such as trapezoids. This is an expectation for grades 6-8, to be able to come up with these area formulas on their own and not just getting them from reading out of the text book. Now this begins to look at why important. Area rules: Rectangle A=b x h (length times width) Parallelogram A= b x h Triangle A= 1/2 b x h Trapezoid A= (b1+b2) h / 2 Circle A=(pi)r squared - We have started to talk about 3-d shapes including: Polyhedra-Polygon extended. to 3 dimensions Prism-Rectangular sides with polygon-shaped top and bottom. Cylinder//-// Flat, circular tops with curved edges. Cone-Circular base and vertex opposite the base. Pyramid-Square Bottom with four isosceles or equilateral triangles. Has a plat end and a point on the other end.
 * Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
 * precisely describle, classify,and understand relationships among types of two and three dimentiona; objects using thier defining properties.
 * understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects
 * create and critique inductive and deducive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the pythagerean relationship.
 * Feb 1**: So what corresponds to what?
 * Feb 15:**
 * Jan 27**:
 * Jan 11 and 13**:
 * April 7:**

> again, need to connect what is below to specific expectation - We used the coordinate plane and synthetic geometry to focus on isometries which are translations (slides), rotations (turns) and, transformations (flips). On the coordinate plane we used the four different quadrants to look at these isometries. Synthetic geometry is just like drawing on a piece of paper, to produce isometries this way we have to use tools such as rulers, angle rulers and protractors. - We tried to figure out how we could determine whether or not three random side lengths could be turned into a triangle. We came up with two statement s : 1. If the sum of the 2 shorter sides is greater than the longest side then we can make a triangle. 2. If the sum of the 2 shorter sides is less than the longest side then we cant make a triangle. We used what we learned about making triangles to see how we can determine whether or not four random side lengths would make a quadrilateral which lead us to these statements: 1. A quadrilateral can be made if the sum of the three smallest sides are greater than the longest side. 2. A quadrilateral will not be made if the sum of the three smallest sides are less than the longest side.
 * Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
 * use coordinate geometry to represent and examine the properties of geometric shapes
 * use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parellel lines or perpendicular sides.
 * March 31:** How does this connect to the above expectations.

-We started talking about reflection symmetry and rotational symmetry. We used the alpha-shapes describe, this won't mean much after a while and divided them into shapes having reflection symmetry, rotational symmetry or no symmetry. -The miras were used to find lines of symmetry and to reflect shapes over a line. Reflection symmetry is when a shape or an object is reflected over a reflecting line. This line will produce the same shape on both sides of the reflecting line. define both of the symmetries.
 * Apply transformations and use symmetry to analyze mathematical situations
 * describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling
 * examine the congruence, similarity, and line or rotational symmetry of objects using transformations
 * Feb 15 and 17:**

-For the visualization aspect, we used Geometer's Sketchpad in order to show how we can use simple and easy to use computer programs in order to visualize certain shapes, and how we can make those same shapes using the program. And how was this done? -**We started to look at three dimensional figures and their volumes on paper, so they were two dimensional representations of three dimensional objects. We had to work on our spatial visualization to be able to understand how many blocks there were in a 3-d shape when it was only represented as 2-d. How was this done? What shapes did we look at? -We also used such objects as calculators and calculator applications in order to figure out 3-dimensional cities and the size of different buildings. I speak from experience as to what sort of tools we had in Junior High. I remember having a TI-83 and using all of the different applications in order to figure different aspects of math including three dimensions, odds, or looking at a math problem in a different way. Great but focus on what we have used here initially. Be specific vs general. What about the use of Scratch? Or geoboard?
 * Use visualization, spatial reasoning, and geometric modeling to solve problems
 * draw geometric objects with specific properties, such as side lengths or angle measure
 * use two dimentional representations of three dimentional objects to visualize and solve problems such as those involving surface area and volume
 * use visual tools such as networks to represent and solve problems
 * use geometric models to reoresent and expain numerical and algebraic relationships
 * recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.
 * Feb 8**:
 * April 14:

=__**Measurement**__= -We talked about how we can measure angles without using the word degrees, or protractors. What did we talk about? -We talked about different ways to use units and how that affects what is being measured What did we talk about? -We stated that angles are measured in degrees. How did we come to know this? -Explained the differences between measuring the length of a side and an angle. Which is? -We used attributes of either three or four numbers in order to determine whether or not the three or four numbers would make a triangle or quadrilateral. We determined that if the two smallest (triangle) or three smallest (quadrilateral) numbers are larger than the largest number, then those particular numbers would make a triangle or quadrilateral, respectfully. **
 * Understand measurable attributes of objects and the units, systems, and processes of measurement
 * understand both metric and customary systems of measurment
 * understand realtionships among units and convert from one unit to another within the same system
 * understand select and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume
 * Jan 20:**
 * Feb 1:**
 * March 31:

- ** What idea is being developed here? ** We used two rubber bands tied together to trace a shape, using the elasticity of the rubber band to show how the new shape differs from the original shape, whether it's by doubling the perimeter or quadrupling the area. We didn't have enough time to use three rubber bands tied together, but the hypothesis is that the perimeter will be three times as big, and the area will be nine times as big. **We talked about dilation and used the rubber band stretcher to see how to make a dilation. We used a two rubber band stretcher which caused our objects perimeter to become twice is original size and the area to become four times its original size. This lead us into talks of scale factors and ratios. - We worked with circles today and how to figure out their radius, diameter and circumference. The diameter can be measured by measuring the largest part of the circle. The diameter is twice the radius or the radius is half the diameter. The formula for circumference is (pi)diameter. The way we found this out was by every group measuring certain circles around the room. We measured the diameter and the circumference. We then imported these numbers into our calculators, got every one else numbers as well and turned it in to a graph. plotted the data on a scatter plot. We noticed the data clustered in a very strong linear fashion so we fit a line to the points. We found an equation of the graph was about 3 times the diameter, y=3x, which is very close to the formula to find the circumference of a circle, C=πd. 3 and pi are about the same number.
 * Apply appropriate techniques, tools, and formulas to determine measurements
 * use common benchmarks to select appropriate methods for estimating measurements
 * select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision
 * develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapeziods, and circles and develop strategies to find the area of more complex shapes
 * develop strategies to determine to surface area and volume of selected prisms pyramids and cylinders
 * solve problems involving scale factors, using ratio and proportions
 * solve simple problems involving rates and derived measurements for such attributes as velocity and density
 * March 22:
 * April 7:**