gr9_Square+Roots

= Square Roots =

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

-comparing and ordering rational numbers -solving problems that involve arithmetic operations on rational numbers. [C, CN, PS, R, T, V]
 * A3** Demonstrate an understanding of rational numbers by


 * A5** Determine the square root of positive rational numbers that are perfect squares [C, CN, PS, R, T]


 * A6** Determine an approximate square root of positive rational numbers that are non-perfect squares [C, CN, PS, R, T] ||
 * **Planning for Assessment** || **Assessment Strategies** ||
 * * Have students generate a list of 10 different rational numbers, in fraction and decimal form. Ask students to exchange lists with a partner and put the numbers in order by placing them on a number line. Have students develop a list of rules for ordering rational numbers.


 * Display two rational numbers on the board or overhead such as 0.125 and 0.126 or 3/4 and 4/5 and challenge students to determine a rational number that is between the two given rational numbers. Have the students come up with their own question similar to above then exchange their question with someone else and solve each others question. Students then can check to see if each solved their problem correctly.


 * Provide students with a list of 50 rational numbers and ask students to create 24 questions that involve arithmetic operations on rational numbers that would give an answer that is on the list of 50 numbers. Have students create bingo cards with their 24 questions. For example if -1/6 was one of the 50 numbers, a student might create (-4/3 - 1/2)÷11. Have students trade their bingo cards with a partner and verify that each other's questions are correct before playing the game.


 * Make up fraction "twisters" and have students determine whether they are true. For example: If a fifth of a fifth is less than a fourth of a fourth, then a fourth of a fifth must be less than a fifth of a fourth, of course. Is a third of a third more than a third and a third, or is it all absurd? Ask students to create their own twisters and challenge each other. Check for accuracy and understanding.

What are the square roots of 25? What is the principle square root of 25? What are the solutions to x^2=25? Which answer do you give when you see the notation sqr25?
 * Discuss the difference between rational numbers and irrational numbers as an introduction to non-perfect square roots. || Verify that students can:
 * order a given set of rational numbers, in fraction and decimal form, by placing them on a number line.
 * identify a rational number that is between two given rational numbers
 * solve a given problem involving operations on rational numbers in fraction and decimal form. ||
 * Review with students their knowledge about square roots from the previous grades:
 * Ask questions such as:
 * Ask students to explain how the prime factorization of a number can indicate whether or not a number is a perfect square.


 * Have students create a table of roots of perfect squares from 1 through 900, then estimate the square roots of non-perfect squares using the roots of perfect squares as benchmarks. || Verify that students can:
 * determine whether or not a given rational number is a square number and explain the reasoning.

sqr(1)= 1 sqr(1.21)= 1.1 sqr (1.44) =1.2 sqr(1.69)= 1.3 . . sqr(7.29)=2.7 sqr(7.84)=2.8 sqr(8.41)=2.9 sqr(9)= 3 -Then have students to use these perfect squares as benchmarks to estimate the square roots of other rational numbers between 1 and 9. Ask students to determine if there are any other numbers between 1 and 9 with a digit in the ones, tenths and hundredths place that are perfect squares.
 * estimate the square root of a given rational number that is not a perfect square, using the roots of perfect squares as benchmarks ||
 * * Explain that roots of non-perfect squares are irrational and therefore never terminate nor repeat thus technology can only provide an approximation of the root. || Verify that students can:
 * explain why the square root of a given rational number as shown on a calculator may be an approximation ||
 * * Have students complete a table of roots of perfect square similar to the following


 * Provide students with squares of various side lengths such as 3, 0.2, 3/4, and 4x and have them calculate the area of the square.


 * Provide students with squares of various areas such as 2.25, 16/9, and 16.9 || Verify that students can:


 * determine the square root of a given positive rational number that is a a perfect square
 * determine a positive rational number given the square root of that positive rational number
 * determine an approximate square root given a rational number that is not a perfect square using technology ||