gr8_squares+and+roots

= Squares and Roots =

//It is expected that students will://
 * **Prescribed Learning Outcomes**

A1 Demonstrate an understanding of perfect square and square root, concretely, pictorially, and symbolically (limited to whole numbers). [C, CN, R, V]

A2 Determine the approximate square root of numbers that are not perfect squares (limited to whole numbers). [C, CN, ME, R, T] || Ask students to explain in writing why some of the numbers are perfect squares and others are not using evidence that they have generated. Students should address why one factor in a list of factors is the square root and others are not; how the prime factorization of a number reveals whether or not a number is a perfect square; and how a regional representation of a perfect square differs from the representations of numbers which are not perfect squares. || Verify that students can:
 * **Planning for Assessment** || **Assessment Strategies** ||
 * Provide student with several numbers such as these: 168, 196, 240, and 256. For each number have students
 * create a list of all factors
 * calculate the number's prime factorization
 * represent the number on grid paper to prove whether or not it is a perfect square
 * represent perfect squares as a square region
 * determine the factors of the numbers and explain why one particular factor of a perfect square is the square root
 * use reasoning to explain why the prime factorization of a number reveals whether or not the number is a perfect square. ||
 * Have students work in small groups to create a list or table of perfect squares from 10^2 up to and including 26^2. Have students roll three regular dice and from the digits generated create a three-digit number. (For instance, after rolling 3, 6, and 2 the students may create the number 236.) Have the students then estimate the square root of the number based on the benchmarks which were initially recorded. (Thus, in the example students should recognize that the root of 236 must be larger than 15 whose square is 225 and smaller than 16 whose square is 256. The students may even estimate to the nearest tenth by noting that 236 is closer to 225 than to 256. They may reason that 15.3 or 15.4 are reasonable estimations.) Have students check their estimation using technology. || Verify that students can:
 * Use the benchmarks to estimate the roots of numbers
 * Use technology to find the (possibly approximate) square root of a number

Note: It is important that when students are learning about the square root function they understand that there is only one answer. For example even though both -3 x -3 =9 and 3 x 3 =9 the sqr(9) only equals positive 3. This root is called the principle root and this positive root is the answer the calculator provides. Addressing this now will help prevent misconceptions and misunderstandings later on. ||