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Content Area: Math
Index: 4.1B Grade 8 CPI 2
Standard: 4.1 - Number and Numerical Operations
Strand: B - Numerical Operations
Cumulative Progress Indicator: 2 - The student will use exponentiation to find whole number powers of numbers.
Grade: 8
Sample Activities:
· Students play powers max out. Each student has a set of 5 blanks, into each of which will be written a digit. They are in the form VW^X + YZ. One student rolls a die and everyone must write the number showing into one of their blanks. Once written, a number can not be moved. Another roll - another number written, and so on. The object is to be the player with the largest-valued expression when all five digits have been written. If a player has the largest possible value that can be made from the five digits rolled, there is a bonus for maxing out.
· Students develop their own "rules" for operations on numbers raised to powers by rewriting the expressions without exponents. For example, 7^2 x 7^4 = (7 x 7) x (7 x 7 x 7 x 7) = 7 x 7 x 7 x 7 x 7 x 7 = 7^6. You just add the exponents!
· Students read The King's Chessboard, The Rajah's Rice: A Mathematical Folktale from India, or A Grain of Rice. All of these stories involve a situation in which a quantity is doubled each day. Students use the story to discuss powers of 2 and to look for patterns in the sums of the powers of 2.
· Students use the relationship between the area of a square and the length of one of its sides to begin their study of roots. Starting with squares on a geoboard with areas of 1, 4, 9, and 16, they then are asked to find squares whose areas are 2, 5, and 13.
· Students work through the Rod Dogs lesson that is described in the First Four Standards of this Framework. They investigate how the surface area and volume of an object changes as it is enlarged by various scale factors.
Vignettes (PDF Format):
· Rod Dogs
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