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14 Jan 2018•0 j'aime•10,243 vues

14 Jan 2018•0 j'aime•10,243 vues

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lesson exponents and powers is connected with fractions decimals squares and cubes

- 1. What does a good lesson plan look like? By Dr. Sushma Singh (Mentor - Assessment Unit Directorate of Education government of Delhi) E-mail: ss6440083@gmail.com My personal experiences of content making over the last couple of years: After completion of my M.Phil. on Teaching strategies and Ph.D. on multimedia and Self- learning Module for school children. I participated in Ramanujan Model lesson plan competition organised by DOE in 2012 and also received Rs. 1100/- cash prize. Lesson- Algebraic Expressions class VIII prepared by me was in digital form and a question what next, engaged me to search further opportunities. I uploaded the lesson on slideshare.com. Its viewership graph which is more than 81,000 as on date, further motivated me to do some more and I took non-commercial licence and started web portal selflearningwithssingh.pbworks.com. My team which included me and students of RPVV Rohini utilised it and worked on Project Based Learning. As a Mentor Teacher I also got the chance to work on the content of Pragati 2, 3 and 4 of classes 6, 7 and 8 and contributed my ideas in approx. 18 chapters. Comics, stories, games activities and worksheets were designed to make the content of “Pragati” for joyful learning. For joyful learning story can also be one method in mathematics, I tried to illustrate and create a story “Local Tour” in English Hindi and Punjabi Languages on storyweaver.com. The Present lesson plan is also next step of my endeavour of content creation. Presently I am posted at Assessment Unit of DOE GNCT of Delhi. So the content of this lesson plan reflects the shadow of my past experiences aligned with my present assignments to strengthen self and joyful learning among the children in Mathematics. EXPONENTS & POWERS (Class -8 Nishtha and Neo-Nishtha) Lesson is about connection of four topics Fractions, decimals, squares and square roots, cubes and cube roots with Exponents and powers and also with self-assessment. Recap of fractions is through the game introduce in the beginning of the chapter. Learning outcomes of squares and square roots and cubes and cube roots are taught using worksheets. Real life connect of Exponents and power is explained in comic form. Recap of Fractions: This game tests students’ understanding of representing fractions in their simplest form. The objective of the game is to pick out all the fractions that are in their simplest form and leave out the rest. In the game baby dinosaur is with the grid of fractions, some in their simplest form and some not. Every time the baby dinosaur eats a fraction that is not in its simplest form, it falls ill. Causing the game to end. The game has been successfully completed when the baby dinosaur has eaten all the fractions in their simplest form.
- 2. Which fractions should I eat to remain healthy? Help me please. I think I should eat all in this. Am I right? Should I eat all the fractions in this grid also? What do you think? help me! See that I should not fall ill.
- 3. Preparing a test for yourself & peers Fill the above grid with some decimal numbers to add and some to subtract . Write the answers of above grid in this grid baby dinosaur will check and learn with you.
- 4. 2 Levels and 6 learning outcomes (LO) LEVEL 1 Learning outcomes: By the end of this module students will be able to: LO 1. Find square roots and cube roots of perfect-square numbers and cube numbers, recall from memory. LO 2. Understand the symbolism and role of an exponent and base to find values. LEVEL 2 Learning outcomes: By the end of this module students will be able to: LO 1. Understand the symbolism and role of negative fractional exponents. LO 2. Understand the rules of exponents and apply them in simplifying simple expressions. LO 3. Demonstrate how to use the radical sign in multiplying, dividing and simplifying expressions. LO 4. Simplify complex fractions having exponents in both numerator and denominator using the rules and quick simplifying methods. LEVEL 1 Learning outcomes: By the end of this module students will be able to: LO 1. Find square roots and cube roots of perfect-square numbers and cube numbers, recall from memory. LO 2. Understand the symbolism and role of an exponent and base to find values. Methodology: LO 1. Introduce the radical sign. Square root has the symbol √ or 2 √ Cube root has the symbol 3 √ Distinguish between square and square root as students often get confused on which one is which. Hint to remember: The Square of the number is BIGGER than the number as it is its square. The square root of a number is smaller than the number as it is root. Same is with cube and cube root. Square roots are relatively easier to memorize. Cube roots are tougher. LO2: 52 → 2 is exponent and 5 is base 5x5= 25 43 → 3 is exponent and 4 is base 4x4x4=64 Level 2 Learning outcomes: By the end of this module students will be able to: LO 1. Understand the symbolism and role of negative and fractional exponents
- 5. LO 2. Understand the rules of exponents and apply them in simplifying simple expressions. LO 3. Demonstrate how to use the radical sign in multiplying, dividing and simplifying expressions LO 4. Simplify complex fractions having exponents in both numerator and denominator using the rules and quick simplifying methods. Methodology: Recap of level 1 LO 1: Which of the following can you find the value of? 52 51 51/2 50 5-1 5-1/2 Does the value of an exponent always have to be positive? What do you think latter four mean? Base Raised to the power of ……… 2 1/2 0 -1 -1/2 8 64 1 1/8 4 16 2 1/4 9 81 1 1/3 16 4 25 7 1 1/7 1/√7 Explain: 51/2 is square root of 5. As 5 is not a perfect square it can be written as√5 and we do not have to put down the exact value. Make a similar table of cubes and cube roots, and fractional power -1/3 53 51 51/3 50 5-1 5-1/3 Try to find answer from children: What do you think 51/3 means? Explain that it can be written as 3 √5. Base Raised to the power of ……. 3 1/3 0 -1 -1/3 8 512 3 √2 1 1/8 1/ 3 √8= 1/2 27 729 3 √27 =3 64 1 125 25 1/ 3 √25 7 1 1/7 Explain: 81/3 is cube root of 8 which is 2. What is the cube root of 5? As 5 is not a perfect cube we don’t have an exact value so we leave it with the radical sign: 3 √5 or 51/3 . Also give example of the cube roots of numbers that are perfect cubes have an exact value. i.e. 1251/3 or 3 √125=5. LO 1. Find square roots and cube roots of perfect-square numbers and cube numbers, recall from memory.
- 6. Worksheet-1 Find the value of the following by multiplying: 1. 23 = 2x2x2 = 8 2. 43 = 3. 63 = 4. 52 = 5. 103 = 6. 73 = 7. 113 = 8. 92 = 9. 83 = 10. 32 = Self -Assessment Number of questions Number of correct Total %
- 7. Worksheet-2 Find the value of the following by multiplying: 1. (-2)3 =-2x-2x-2=-8 2. (-1)3 = 3. (-2)2 = 4. (-3)2 = 5. (-5)3 = 6. (-6)2 = 7. (-4)3 = 8. (-4)2 = 9. (-5)2 = 10. (-7)2 = Self -Assessment Number of questions Number of correct Total % Worksheet-3 Match the following squares. 12 22 32 42 52 62 72 82 92 102 112 122 132 142 152 16 9 36 121 64 1 49 81 4 100 144 225 25 196 169 Self -Assessment Number of questions Number of correct Total %
- 8. LO 2: Understand the symbolism and role of an exponent and base to find values Worksheet-1 What do the following represent? Tick two correct answers: a. 42 52 22 16 4 b. 42 152 32 16 4 c. 25 52 42 16 32 d. 162 152 62 6 36 Self -Assessment Number of questions Number of correct Total % LO 2: Rules of exponents 1. Addition rule: 23 x 22 = 2x2x2x2x2 = 25 Rule: 23 x 22 = 22+3 (am x an = am + n)
- 9. 2. Division rule: 25 ÷ 22 = 2.2.2.2.2 2.2 = 2.2.2 = 8 Rule: 25 ÷ 22 = 25 -2 (am ÷ an = am - n) 3. Multiplication rule: (22 )3 = (2x2)3 = (2x2) x (2x2) x (2x2) = 26 Rule: (22 )3 = 22x3 (am) n = am x n LO 3: 1. How radical sign cancel each other out. √5 √5 =5 √5 √5√5 = 5√5 √5 √5 √5 √5 =5.5 = 25 2. How numbers under the radical sign can be multiplied √5 √5 = √25 =5, √4 √9 =√36 =6 3. How numbers under radical sign can be divided (√5)2 (√5)3 (√5)4 (√5)5 (√5)5 (√5)7 = 52+3+4+5-5-7=2 = 52 =25 LO: 4 Ensure students know how to solve complex fractions first of all. Give abundant practice. Inserting a denominator of 1 wherever required. Do of all 3 types Type 1: 2/3 5 = 2/3 5/1 = 2 . 1 3 . 5 = 2 5 Type 2: 2 3/5 = 2/1 3/5 = 2 . 5 I . 3 = 10 3 Type 3: 2/5 4/7 = 2 . 7 5 . 4 = 14 20 = 7 10
- 10. Handling negative exponents: explain that whenever they see a negative exponent to Step1: take a up or down (up to the numerator if it is in the denominator and down to the denominator if it’s is in the numerator) and Step2: while doing so change it to positive. Step3: then follow the rules of exponents and simplify The size of an atom: 10-10 meters Human: 1.8m A human body cell: 5 x 10-5 m Planet Earth:1.3x107 m Distance from Sun-Earth: 1.5 x 1011 m
- 11. Worksheet 2: (Scientific Notation) Write the number(s) given in each problem using scientific notation. 1. The human eye blinks an average of 4,200,000 times a year. 2. A computer processes a certain command in 15 nanoseconds. (A nanosecond is one billionth of a second.) In decimal form, this number is 0. 000 000 015. 3. There are 60,000 miles (97,000 km) in blood vessels in the human body. 4. The highest temperature produced in a laboratory was 920,000,000 F (511,000,000 C) at the Tokamak Fusion Test Reactor in Princeton, NJ, USA. 5. The mass of a proton is 0.000 000 000 000 000 000 000 001 673 grams. 6. The mass of the sun is approximately 1,989,000,000,000,000,000,000,000,000,000,000 grams. 7. The cosmos contains approximately 50,000,000,000 galaxies. 8. A plant cell is approximately 0.00001276 meters wide. Write the number(s) given scientific notation in standard form. 9. The age of earth is approximately 4.5 X 109 years. 10. The weight of one atomic mass unit (a.m.u.) is 1.66 x 10-27 kg. Scientific Notation Worksheet Key 1. 4.2 x 106 2. 1.5 x 10-8 3. 6 x 104 mi 9.7 x 104 km 4. 9.2 X 108 F 5.11 x 108 C 5. 1.673 x 10-24 g 6. 1.989 x 1033 g 7. 5 x 1010 8. 1.276 x 10-5 m 9.4,500,000,000 yr. 10. 0.000000000000000000000001673 kg Self -Assessment Number of questions Number of correct Total %
- 12. One of my Self-assessment strategies in the classroom: Adopted school: SV Sector - 7 Rohini. Class 9th Sections A to H, Subject Mathematics. Dated 6th Jan2018: discussed with students about their performance in the Mid-term exam2017-2018 and difficulties and strategies to improve their scores. Stared self-assessment process. Mock test of math held on 8 Jan 2018. All the students were asked to prepare a self- analysis chart on the following format. Mock Test Self-analysis Name of student:---------------------Class & Section:-------------------- Question Number Marks allotted Marks scored 1 1 2 3 4 5 6 7 2 8 9 10 11 12 13 314 15 16 17 18 19 20 21 22 23 424 25 26 27 28 29 30 Total-30 Total 80 Total Students are asked to select 10 chapters of their choice out of total 15 chapters. Then we will find the relation between scores of self-assessed questions and chapters in the discussion during the next visit. Will try to find out the strategies to improve the scores and on which lesson and how each one of them should work more. Thanks