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2. Looking for Pythagoras - CMS Goals |
Make connections among
coordinates, slope, distance, and area
Relate the area of a square to
the length of a side.
Develop strategies for finding
the distance between two dots on a dot grid or two points on a coordinate grid.
Discover and apply the
Pythagorean Theorem
Extend understanding of number
systems to include irrational numbers
Locate irrational numbers on a
number line.
Represent fractions as decimal
and decimals as fractions.
Determine whether the decimal
representation for a fraction terminates or repeats
Use slopes to solve interesting
problems.
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1. Locating Points (Inv 1) 1.1 Driving Around Euclid 1.2 Planning Emergency Routes 1.3 Planning Parks (ACE 1 - 13 ) |
To review the use of coordinates for specifying locations. To use coordinates to specify direction and distance. To connect properties of geometric shapes, such as parallel sides, to coordinate representations. |
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2. Finding
Areas & Lengths 2.1 Finding Areas 2.2 Looking for Squares 2.3 Finding Lengths(ACE 1 - 15 )
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To find area of polygons drawn on a dot grid using various strategies. To find the length of a line segment drawn on a grid by thinking of it as a side of a square. To begin to develop an understanding of the concept of square root. |
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3. The Pythagorean Thm 3.1 Discovering t Pythagorean T 3.2 Puzzling Through a Proof 3.3 Finding Distances 3.4 Measuring the Egyptian Way (ACE 1 - 27 ) |
To deduce the Pythagorean Theorem through exploration. To use the Pyth Thm to find area of squares drawn on a dot grid. To use the Pythagorean Theorem to find the distance between two points on a grid. To determine whether a triangle is a right triangle. To
relate areas of squares to lengths of sides.
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4. Using t Pythagorean Th 4.1 Stopping Sneaky Sally 4.2 Analyzing Triangles 4.3 Finding the Perimeter ACE Questions ( 1 - 12 ) |
To apply the Pythagorean Thm in several problem situations To investigate the special properties of 30-60-90 triangles and an isosceles right triangle. To use properties of special right triangles to solve problems. |
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5. Irrational
Numbers 5.1 Analyzing the Wheel of Theodorus 5.2 Representing Fractions as Dec 5.3 Exploring Repeating Decimals ACE Questions ( 1 - 31 ) |
To connect decimal and fractional representations of rational numbers. To estimate lengths of hypotenuses for right triangles. To
explore patterns in terminating and repeating decimals. |
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6. Rational & Irrational Slopes 6.1 Revisiting Slopes 6.2 Simulating Cookies ACE Questions ( 1 - 16 ) |
To review the concept of the slope of a line. To connect the concept of slope to the idea of irrational numbers. To
use slopes to test whether lines are parallel or perpendicular. |