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Subtraction Really is Addition (3-9 thru 3-15) 1st and 2nd Graders

In the 1st and 2nd grade classes this week, we reinforced the notion that subtraction really is addition. For example, 12-8=4 is the opposite as 8+4=12; 101-98 is really the same as 2+1=3.  What do we have to add to 98 to get to 101.  Also, 85-48 is 2+30+5=37.

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Also, we worked on subtraction as compared to negative numbers. For example 11-7=4 is the same as -7 + 11 = 4. 

There is a detailed explanation of these concepts in the attached pdf as well as additional practice.

Olympic Standings: Who is the world's best? (3-2 thur 3-8)

It has always intrigued me to look at the Olympic standings in the New York Times and watch the United States in first place by total medals.  The first thing I think about is the relative unimportance of a gold vs. a bronze.

The Canadian papers show Canada in first place with Germany at second and the USA in third.  They go by number of gold medals.

Diagonals in Polygons (2-23 thru 3-1)

Finding patterns in the number of diagonals in polygons can be very challenging.  First, the Mathletes had to draw all diagonals from a square to a regular 15-gon.  Diagonals are segments that connect non-adjacent vertices.  In other words, diagonals cannot lie on the side of a polygon. Many of the Mathletes saw patterns in the number of diagonals as the number of sides increased.

Area of Figures in Square Units (2-9 thru 2-22)

Find the area in square units of figures that the Mathletes created last week with coordinate points.  There are many methods of determining area, but here our strategy was to sketch each rectangle within the figure until all that is left are triangles.  The area of each rectangle can be found by simply counting the squares or by multiplying the outside dimensions (length times width).

Coordinate Plane Pictures (2-2 thru 2-8)

This week the Mathletes explored the Cartesian coordinate system in all four coordinates.  Using the x-axis (horizontal) and y-axis (vertical), we can find any unique point in a plane by a pair of numerical coordinates such as (2, 3) which means start on the number 2 on the x-axis and go up three units.Coordinates such as (-3, -6) represents a location at three units to the left of the origin (0,0) and then 6 units down.  This coordinate system was created by Rene Descartes in the early 1600s and further developed by another French mathematician, Pierre de Fermat.