Warm-Up What are the 8 Standards of Mathematical Practices? Make sense of problems and persevere in...
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Transcript of Warm-Up What are the 8 Standards of Mathematical Practices? Make sense of problems and persevere in...
![Page 1: Warm-Up What are the 8 Standards of Mathematical Practices? Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct.](https://reader036.fdocuments.in/reader036/viewer/2022072017/56649f005503460f94c163c5/html5/thumbnails/1.jpg)
Warm-UpWhat are the 8 Standards of Mathematical Practices?
Make sense of problems and persevere in solving themReason abstractly and quantitativelyConstruct viable arguments and critique the reasoning of othersModel with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
![Page 2: Warm-Up What are the 8 Standards of Mathematical Practices? Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct.](https://reader036.fdocuments.in/reader036/viewer/2022072017/56649f005503460f94c163c5/html5/thumbnails/2.jpg)
Today’s Objective:G.GPE.B.7 Use coordinates to
compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
![Page 3: Warm-Up What are the 8 Standards of Mathematical Practices? Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct.](https://reader036.fdocuments.in/reader036/viewer/2022072017/56649f005503460f94c163c5/html5/thumbnails/3.jpg)
Rectangle Area Conjecture:
The area of a rectangle is given by the formula ____________, where A is the area, b is the length of the base, and h is the height of the rectangle.
A = bh
![Page 4: Warm-Up What are the 8 Standards of Mathematical Practices? Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct.](https://reader036.fdocuments.in/reader036/viewer/2022072017/56649f005503460f94c163c5/html5/thumbnails/4.jpg)
Find the area of this shape
![Page 5: Warm-Up What are the 8 Standards of Mathematical Practices? Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct.](https://reader036.fdocuments.in/reader036/viewer/2022072017/56649f005503460f94c163c5/html5/thumbnails/5.jpg)
€
12(10) =5
€
12(6) =3
€
12(6) =3
€
12(18) =9
32
The area of the figure is 52 square units
![Page 6: Warm-Up What are the 8 Standards of Mathematical Practices? Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct.](https://reader036.fdocuments.in/reader036/viewer/2022072017/56649f005503460f94c163c5/html5/thumbnails/6.jpg)
Investigation: Area Formula for Parallelogram
A parallelogram
A straight edge
A compass
Scissors
• From the vertex of the obtuse angle adjacent to the base, draw an altitude to the side opposite the base. Label the parallelogram as shown.
![Page 7: Warm-Up What are the 8 Standards of Mathematical Practices? Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct.](https://reader036.fdocuments.in/reader036/viewer/2022072017/56649f005503460f94c163c5/html5/thumbnails/7.jpg)
Investigation: Area Formula for Parallelogram
• Cut along the altitude. You will have two pieces – a triangle and a trapezoid. Try arranging the two pieces into other shapes without overlapping them. Is the area of each of these new shapes the same as the area of the original parallelogram? Why?
• Is one of your new shapes a rectangle? Calculate the area of this rectangle. What is the area of the original parallelogram? State the conjecture.
![Page 8: Warm-Up What are the 8 Standards of Mathematical Practices? Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct.](https://reader036.fdocuments.in/reader036/viewer/2022072017/56649f005503460f94c163c5/html5/thumbnails/8.jpg)
Parallelogram Area Conjecture
The area of a parallelogram is given by the formula ____________________, where A is the area, b is the length of the base, and h is the height of the parallelogram.
A = bh
![Page 9: Warm-Up What are the 8 Standards of Mathematical Practices? Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct.](https://reader036.fdocuments.in/reader036/viewer/2022072017/56649f005503460f94c163c5/html5/thumbnails/9.jpg)
Let’s practice!!!A represents area and P represents perimeter.
A = 2508 cm2
P = ?
210 cm
![Page 10: Warm-Up What are the 8 Standards of Mathematical Practices? Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct.](https://reader036.fdocuments.in/reader036/viewer/2022072017/56649f005503460f94c163c5/html5/thumbnails/10.jpg)
Let’s practice!!!Find the area of the shaded region.
A = 42 ft2