October/November Math Update
November 4, 2010
First and second graders have ended their geometry unit of study. A great deal of new math language was used as we explored two-dimensional geometry in first grade. Second graders spent time with activities that reviewed the two-dimensional work they did last year and then moved onto three-dimensional geometry concepts.
First Grade Geometry:
Pattern blocks, Power Polygons and tiles were the materials we used during this math study. Shapes, or polygons, studied included hexagons, trapezoids, rectangles (including squares), and a variety of triangles. The majority of our work focused on the following quadrilaterals: rectangles and a special kind of rectangle called a square. All rectangles and squares have four straight sides, with four corners, (also called vertices—vertex for a single corner or point), and the corners are square corners or square angles. We also investigated several types of triangles, including equilateral, isosceles, and right triangles. It’s not expected that first graders know the names of all of these triangles, but that a triangle is a closed shape that always has three sides and three vertices. Some children at this age believe that only an equilateral triangle is “the right kind of triangle”, or think that if a triangle is positioned in a certain way, such as on sitting on the tip or one of its vertices, that it's somehow no longer a triangle. Many types of triangles are presented and used throughout the unit to help avoid any later misunderstandings about triangles.
Second Grade Geometry:
Second graders reviewed all of the above language and concepts, and were introduced to angles—the space between where two sides come together at a vertex or meeting point. The 3-D geometry explored used several blocks known as prisms. Face, edge and vertex were terms that were used as they were challenged to create the same block using a variety of other blocks. One of the most challenging activities of all was attempting to draw a block from a particular angle. Although this wasn't easy, everyone was excited and eager to give it a try, and kept working on their drawings after studying their blocks, re-examining their drawings, and making adjustments after careful observation.
What's next? Both first and second graders will work with story problems for addition and subtraction, along with learning the steps of the problem solving process. Sometimes when we're faced with a problem—a real problem—something that we don't have the answer to right away, feelings can take over. We've discussed many of these feelings. Sometimes we can feel excited to take on a challenge, and other times we can feel frustrated, worried, angry, confused. So, the problem solving process we will be using acknowledges these feelings right up front. What we do with these feelings is also part of the process to becoming good problem solvers. Some of the strategies we are using for those negative emotions, includes breathing, taking some time to relax, repeating in our heads positive talk "I can try this." Our goal is to acknowledge the feelings, but to not let them take over and control our attitude about attempting a math problem, (or really any problem in life). Feelings may come up in the middle of the problem solving process also, especially if we've worked really hard for a while on a specific approach, but it doesn't get us to where we wanted to be. Sometimes we need to go back and deal with our feelings again before we accept we may have to try a different strategy or approach to the problem. Another part of the math problem solving process we will emphasize is Understanding What the Problem is Telling and Asking Us to Find Out. We will also be looking at the many strategies and materials that can be used to help us solve math problems, and then how to represent this on paper. All of this is an effort to support children as they learn to become more independent in their math work, understanding what a problem is asking and choosing ways to find solutions.
That's all for now until the next update!
Brenda
