Brandie+And+Kyla's+page+for+grades+Pre-K+-2nd

The focus of this page is on grades Pre-K -2.

There are four goals for the geometry standard and two goals for the measurement standard that are common across all the grade bands:

=Geometry= Example: sorting shapes by the number of sides they have or if they are regular or irregular shapes. Example: Example: Example: Square and a Rhombus. Young children may not know all of these, but letting them explore and find out that a rhombus can also look like a square is important for their future learning.
 * ===Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships===
 * Being able to recognize what different shapes are and how to sort them into different category.
 * Being able to name different shapes and some of their distinct properties.
 * 1) We named triangles in class and talked about the attributes that all triangles have and what only some triangles have.
 * 2) Naming quadrilaterals and understanding that some quadrilaterals can be defined by being another quadrilateral. Ex: A parallelogram is a quadrilateral with two paris of parallel sides. A rectangle is a parallelogram (because it has two sets of parallel sides) with 2 right angles.
 * Knowing the difference in the number of sides and corners a shape has and putting a name with those shapes.
 * 1) Triangle has three sides and three angles.
 * 2) Quadrilateral has four sides and four angles. Quadrilaterals include: Parallelogram, Rectangle, Trapezoid, Kite, Rhombus, Square, Kite.
 * 3) Regular Polygons are polygons that have all side lengths congruent and all interior angles congruent. Regular Polygons include: Triangle, Square, Pentagon, Hexagon, Heptagon, Octogon, Decagon.
 * 4) Some Polygons that do not have congruent sides or angles: Star, Concaved Shapes.
 * Having children begin to recognize that some shapes have the same properties and actually could have more than one name.

In class we began talking about 3-D shapes. We put the different shapes into different categories like: Cone, Cylinder, Prism, Pyramid and Sphere. We talked about what is unique about shapes and what makes them different from each other. This is not just important for students to understand but also have different ideas of what these shapes look like. For example: there are many different types of Prisms; so, it is important students know a variety of different Prisms not just one or two different ones. Example: Being able to determine a line of reflection between two shapes.If this is one a coordinate plane, one could describe the line of reflection in terms of x and y. Example: How can it be helpful? Give one specific example.
 * ===**Specify locations and describe spatial relationships using coordinate geometry and other representational systems**===
 * Being able to describe, name, and interpret relative positions in space and apply ideas about relative position.
 * Being able to describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance.
 * Being able to find and name locations with simple relationships such as "near to" and in coordinate systems such as maps.
 * 1) In class we talked about using the program Scratch to draw different shapes and understand angles better. This may be hard for younger children to do but starting in the second grades, I think the students could begin to use this program with some help. If children start using this program young I believe it will be very helpful to them in the future with geometry becomes more complex and difficult.
 * 1) Using this program students start to use direct commands to draw a shape in a fun way. Another thing that is so cool about this is that it is free, so anyone can use it. For children it also is fun and colorful which I think is a plus!

We started to talk about Transformations and Dialations. Dilations It is important to know that Transformations stay congruent even thought they are reflected, rotated, or translated. All of these can happen on a coordinate plain plane. Specific language can be used when talking about using coordinates but it is important that students understand how to do these and their importance because it become important when you start talking about Dilations. What do you mean? This is when shapes are similar not congruent. It is also important that students understand previous language what previous language? when talking about Dilations because angles and side lengths are talked about frequently. When talking about Dilations in depth, I believe it become too in depth for very young students.

Apply transformations and use symmetry to analyze mathematical situations
Example: Example: Example: Example: Using the Angle game in SMILEMath on the calculators. In SMILEMath you are given the option to watch the calculator draw an angle and you guess the measure of the angle or the calculator gives you a measurement of an angle and you have to draw the angle with that measurement. Didn't we do quite a bit of this with 3D shapes and silhouettes and the applet Building Perspective? Example:
 * Be able to recognize and apply slides, flips, and turns.
 * 1) We used a Mira in class to apply reflections along a given line.
 * 2) We created rules for applying slides, flips and turns.
 * 3) When reflecting in the y-axis, (x,y) --> (-x,y)
 * 4) When reflecting in the x-axis, (x,y) --> (x, -y)
 * 5) When reflecting in line x=y, (x,y) --> (-x,-y)
 * 6) When sliding horizontally by b units, (x,y) --> (x + a, y)
 * 7) When sliding vertically by b units, (x,y) --> (x, y + a)
 * 8) When sliding in line x=y, (x,y) --> ( x + a, y + a)
 * 9) When rotating 90 degrees, (x,y) --> (-y, x)
 * 10) When rotating 180 degrees, (x,y) --> (-x, -y)
 * 11) When rotating 270 degrees, (x,y) --> ( y, -x)
 * 12) When rotating 360 degrees, (x,y) --> ( x, y)
 * Something important to remember about this is that the negative symbol does not mean that value becomes negative, it means that it becomes opposite. Would PreK-2 work with coordinates in such a fashion?
 * Be able to recognize and create shapes that have symmetry and also shapes that have none.
 * 1) Having children fold the shape to show the symmetry, so they can understand what symmetry is.
 * 2) In class we talked about how students could use patty paper to see if a shape has symmetry. Patty paper is easy to fold and you can see through it so they could also see if the shape has rotational symmetry.
 * 3) The same day we talked about how polygons can be regular and irregular. This is important for students to know the difference, when they are learning about symmetry.
 * Being able to draw a regular and irregular shape and know the difference between the two is important.
 * 1) Using the program Sketchpad young children can directly see lines of symmetry when shapes are reflected over one of the sides. I think that this does not work for all shapes. But if you reflect a shape over one of its side and it forms a quadrilateral, isosceles triangle or an equilateral triangle; where it was reflected is also a line of symmetry. This could be very helpful for a teacher and also for students.
 * 2) I think the earlier students start to use these programs the faster they will start to learn geometry. This is also a hands on way to learn, and most text books don't give you that option.
 * ===Use visualization, spatial reasoning, and geometric modeling to solve problems.===
 * Being able to create mental images of geometric shapes using spatial memory and spatial memorization
 * Be able to recognize and represent shapes from different perspectives.
 * 1) Building and playing with legos can give a student a perspective of their "shape" from a top, front, left, and right perspectives.
 * 2) Using Building Perspective on the calculator lets the user look at three different sized cities and they have to try to figure out the location of each building that is between 1-9 stories tall. The user can look at the buildings from front, left, right, and back perspectives. Aha!
 * 3) Working with 3D shapes. If a student can physically hold a 3D shape (manipulatives) and sort them into categories of Polyhedra, Prisms, Cylinders, Pyramids, and Cones. They can determine the attributes of each 3D shape by turning it to see different perspectives.

Example: Not clear how these ideas connect to number and measurement. Example: =Measurement= Example: 1. We talked about the difference between measuring an angle of a shape and the side of a shape. This led to the discussion of what is the difference between the length and area. Example: Trying to me a sure an angle using patty paper. The size of our units vary because of how large or small we folded the paper to fit into the angle. From this unit we created we determined that the smallest unit to measure an angle is a degree. A degree would the standard unit used to measure angles. Example:
 * Being able to relate ideas in geometry to ideas in number and measurement.
 * 1) Finding the measure of the interior and exterior angles of a regular polygon. Rule we came up with in class is that if you know the central angle of a regular polygon, you will know the exterior angle because they are the same. 180- (360/n)= central angle.N = the number of sides in the regular polygon.
 * 2) Translations, reflections, and rotations can be done on the coordinate system. Every point in a shape on the coordinate system is related to every point on the transformed shape.
 * Being able to recognize different shapes in different environments and specific locations.
 * 1) Stop Signs as being octagons, Bricks as being rectangles, Pizza Pie as being a circle and ect.
 * 2) Explaining and show students shapes at a different perspective. In class when we were talking about different ways you can draw an angle; that can be the same with shapes.
 * 3) In class we talked about drawing shapes different ways; so that the children recognize different polygons in different ways. As a teacher you could talk about how a square could also be a rhombus. A rhombus does not always have to be shown as a "tilted square."
 * 4) Again, Sketchpad could give students countless ways to view shapes and angles.
 * ===Understand measurable attributes of objects and the units, systems, and processes of measurement===
 * Understanding that measuring an angle is different than measuring a side of a shape.
 * Being able to recognize the attributes of length, volume, weight, area, and time
 * Being able to compare and order objects according to these attributes.
 * Being able to understand how to measure using nonstandard and standard units.
 * Being able to select an appropriate unit and tool for the attribute being measured
 * 1) When measuring angles we determined that making our own tool out of patty paper was not the same size of a unit for everyone. Using a protractor has the same size of a degree no matter which protractor you pick up.
 * 2) When measuring the Circumference of a circle, we used the method of taking a string and wrap p ing it around the edge of the cirlce circle and then measuring the string with a ruler. Another way we tried was using a measuring tape that could fit the curve of a circle. We then proceeded to find that if we knew the diameter of a circle we could find the circumference of a circle by multiplying it by pi. This last method would be the most appropriate but not with your age group to use because it is less time consuming.
 * 3) When talking about area and perimeter, students can explore the ruler. When finding the area you need to know height and base. This gives students are good chance to use a ruler both metric and American system. Measuring is a great tool to learn at a young age to too and when talking about perimeter and area it is the perfect time to learn and practice.

Example: In class we talked about how measuring angles you use the units in degrees and when measuring sides of shape you use inches, centimeters and more. Example: 1. Using Patty paper to create a unit of measurement to measure angles. 2. In class we talked about how measuring angles you use the units in degrees and when measuring sides of shape you use inches, centimeters and more. Example: Using a degree to measure the amount of degrees are in a single turn. One could use a compass which is made up of a number of degrees to measure an angle. Example: 1. Using patty paper to create a unit of measurement for measuring angles. 2. Talked about using protractors and how that may not always be the best method of measuring angles because someone can assume that the size of an angle can never be any larger than 180 degrees. 3. We used compass protractors in class that allowed us to make angles. 4. In class we used an angle ruler to measure the distance to prove that an image is a true reflection of a shape over any line. Example: 1. In class we talked about how all quadrilaterals interior angles add up to 360 degree. 2. We figured this out because every quadrilateral can be split into two triangles and we know that the sum of every triangle's interior angles is 180 degrees.
 * Understanding that different measurements use different units.
 * ===Apply appropriate techniques, tools, and formulas to determine measurements===
 * Being able to measure with multiple copies of units of the same size, such as paper clips laid end to end.
 * Being able to use repetition of a single unit to measure something larger than the unit
 * Being able to use tools to measure
 * Being able to develop common referents for measures to make comparisons and estimates.

When talking about area there were many formulas that were important to understand and know. 1. Square: Area= Base X Height. 2. Rectangle: Area= Base X Height. 3. Parallelogram: Area= Base X Height. 4. Trapezoid: (Base1 + Base2) Height X 1/2 5. Triangle: Base X Height X 1/2 6. Perimeter: The sum of all the side lengths. These are all very important to understand because area comes up all the time. Even very young children begin to know that area is the space with in a 2D shape. Also in class we made a puzzle tangram that we cut up different shapes to help explore area and perimeter more and exciting way. This helped students understand that different shapes have other shapes with in them and how the different area formula are figured out. This is all very helpful for young students. It is something they can visualize and that is very important.