Moving with Algebra Sampler

29 Lesson Plans 305 Objective: To find square roots of monomials. Materials: Black and white cubes (or positive and negative integer squares, Master 19) Vocabulary: squaring a number, square root, radical sign Squares and Square Roots Ask students to name everyday activities that are inverses, such as zipping and unzipping a jacket, tying and untying shoes. Then have them list mathematical operations and their inverses. (addition and subtraction; multiplication and division) Squaring a number is like knowing the length of the sides of a rug and finding its area. Example: A rug with 4 feet on each side has 4 squared or 16 square feet. Finding the square root is the opposite of finding the area. The square root means to find the length of the sides of the square. If you have 25 square inches and want to arrange them as a large square, how many inches on each side? Use 25 cubes, tiles or squares. Rearrange them as a square to find the number of units on each side. Draw on the board: The square root of 25 is 5. This special symbol that means to find the square root is called a radical sign. To find the square root of a monomial with a variable, break apart the numbers and letters. Then find the square root of each part. 25 = 5 5 5 25 4 4 2 = 16 sq. units 4 Write on the board: Read the explanations at the top of the page together. Use cubes or squares on an overhead to demonstrate the examples related to the dog’s pen and carpet. Emphasize that monomials with variables must be broken into separate parts. Work problems 1, 9 and 17 together with the class. Note: On this page, which begins with geometric examples, only positive square root values are given as solutions. Square roots not pertaining to geometric figures have 2 square roots, one positive and one negative, e.g., 16 = ± 4). Skill Builders p. 233 16 x 2 x 2 4 x 16 = = ©MathTeachersPress, Inc. 305 Find the square roots. 1. 16 5. 81 9. x 2 2. 25 6. 100 10. n 6 3. 4 7. 121 11. r 10 4. 49 8. 144 12. a 8 13. 16 y 2 17. 4 g 2 h 2 14. m 2 18. 25 x 2 y 6 15. 36 n 6 19. 64 m 4 16. 49 g 2 20. 16 x 2 y 2 z 2 21. List all the numbers between 1 and 100 that have whole-number square roots. ______________________________________________________________________ Squaring a number is the opposite of finding a square root. The pair of operations act as inverses.They “undo” each other. Square Roots of Monomials Kim tiled the floor of the dog’s pen. The pen is a square with 3-foot sides. How many 1-foot squares will she need? 3 2 3 • 3 9 sq. ft. James has 16 1-foot carpet squares. He wants to use them to make a large square rug. How many feet are on each side? 16 means the square root of 16 16 4 3 feet 3 feet 1. Break into numbers and variables. 9 x 6 9 x 6 2. Find the square root of each part. 9 x 2 x 2 x 2 3 • x • x • x = 3 x 3 To find the square root of a monomial with a variable, Think: Look for perfect squares. x 6 = x 2 • x 2 • x 2 The computer lab is a square room with 81 square feet of space. Ms. Wong wants to put a shelf along the entire length of the back wall. How long will the shelf be? A 9 feet B 18 feet C 81 feet D 11 feet Answer 4 9 10 11 12 x n 3 r 5 a 4 4y m 6n 3 7g 2gh 5xy 3 8m 2 4xyz 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 5 2 7 Algebra Sample Lesson Square Roots of Monomials Finding the square roots of monomials Sample Scripting (Bold Type) Objective: To find square roots of monomials. Materials: Black and white cubes (or positive and negative integer squares, Master 19) Vocabulary: squaring a number, square root, radical sign Squares and Square Roots Ask students to name everyday activities that are inverses, such as zipping and unzipping a jacket, tying and untying shoes. Then have them list mathematical operations and their inverses. (addition and subtraction; multiplication and division) Squaring a number is like knowing the length of the sides of a rug and finding its area. Example: A rug with 4 feet on each side has 4 squared or 16 square feet. Finding the square root is the opposite of finding the area. The square root means to find the length of the sides of the square. If you have 25 square inches and want to arrange them as a large square, how many inches on each side? Use 25 cubes, tiles or squares. Rear ange them as a square to find the number of units on each side. Draw on the board: The square root of 25 is 5. This special symbol that means to find the square root is called a radical sign. To find the square root of a monomial with a variable, break apart the numbers 25 = 5 5 5 25 4 4 2 = 16 sq. units 4 Write on the board: Read the explanations together. Use cubes or sq demonstrate the example pen and carpet. Emphasi variables must be broken Work problems 1, 9 an class. Note: On this page, wh geometric examples, only values are given as soluti pertaining to geometric fi roots, one positive and on 16 = ± 4). Skill Builders p. 233 16 x 2 16 = ©MathTeacher Find the square roots. 1. 16 5. 81 9. x 2 2. 25 6. 100 10. n 6 13. 16 y 2 17. 4 g 2 h 2 14. m 2 18. 25 x 2 y 6 21. List all the numbers between 1 and 100 ___________________________________ Squaring a number is the opposite of findin The pair of operations act as inverses. The Square Roots of Monomials Kim tiled the floor of the dog’s pen. The pen is a square with 3-foot sides. How many 1-foot squares will she need? 3 2 3 • 3 9 sq. ft. J s s 3 feet 3 feet 1. Break into numbers and variables. 9 x 2. Find the square root of each part. To find the square root of a monomial with The computer lab is a square room with 81 to put a shelf along the entire length of the b A 9 feet B 18 feet 4 9 10 x n 3 4y m 2gh 5xy 3 1, 4, 9, 16, 25, 36, 49, 64, 81, 5 Algebra & Functions Unit 6