Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Bartomeu Ramon CC San Alfonso POWERS AND ROOTS Age of students: 12-13 Language Aims To present a lexical set of words for students to understand and work with powers and roots To practise pronunciation of the words with the class To reinforce the language by providing students with tasks which invite them to use the language Content Aims To introduce powers, index laws and roots, and the operations with powers working with practical activities in order to engage the students 1. REMEMBER WHAT YOU ALREADY KNOW Modeling new vocabulary Power and roots concepts 2. OPERATIONS AND PROBLEMS WITH POWERS LISTENING FOR THE RIGHT ANSWER NOUGHTS AND CROSSES INDEX FORM HANGMAN 3. TRY YOURSELF WITH A TEST 1 Bartomeu Ramon CC San Alfonso MODELING NEW VOCABULARY WORK IN PAIRS Vocabulary : 1. We are going to read some words and to repeat them aloud chorally and individually: Power /paʊər/ Square /skweər/ Cube /kjuːb/ Root /ruːt/ Base /beɪs/ Exponent /ɪkˈspəʊ.nənt/ Index /ˈɪn.deks/ 2. Now write down the words in the activity one in the blank spaces: _________ 5 3 _________ ________ ________ 3 √8 __________ ________ 2 Bartomeu Ramon CC San Alfonso POWER AND ROOTS CONCEPTS Powers 9 is a square number. 8 is a cube number. 3×3=9 2×2×2=8 3 × 3 can also be written as 32. 2 × 2 × 2 can also be written as 23 This is pronounced "3 squared". which is pronounced "2 cubed". Index form The notation 32 and 23 is known as index form. The small digit is called the index number or power. You have already seen that 32 = 3 × 3 = 9, and that 23 = 2 × 2 × 2 = 8. Similarly, 54 (five to the power of 4) = 5 × 5 × 5 × 5 = 625 and 35 (three to the power of 5) = 3 × 3 × 3 × 3 × 3 = 243. The index number tells you how many times to multiply the numbers together. When the index number is two, the number has been 'squared'. When the index number is three, the number has been 'cubed'. When the index number is greater than three you say that it is has been multiplied 'to the power of'. For example: 72 is 'seven squared', 33 is 'three cubed', 37 is 'three to the power of seven', 45 is 'four to the power of five'. 3 Bartomeu Ramon CC San Alfonso LISTENING FOR THE RIGHT ANSWER 1. Activity Working in pairs you have to read aloud to your partner the powers you have in your worksheet, how many times they are multiplied for itself and the result. Then, he or she has to write it correctly in her/his worksheet. Take in account you have different powers on your worksheets STUDENT A Index form Multiplied form Result 43 27 72 53 132 65 2. Activity: Some of you will have to listen powers readed aloud from your partners and write them at the board. 4 Bartomeu Ramon CC San Alfonso LISTENING FOR THE RIGHT ANSWER 1. Activity Working in pairs you have to read aloud to your partner the powers you have in your worksheet, how many times they are multiplied for itself and the result. Then, he or she has to write it correctly in her/his worksheet. Take in account you have different powers on your worksheets STUDENT B Index form Multiplied form Result 83 34 26 112 24 104 2. Activity: Some of you will have to listen powers read aloud from your partners and write them at the board. 5 Bartomeu Ramon CC San Alfonso POWER AND ROOTS CONCEPTS Square root The opposite of squaring a number is called finding the square root. Example The square root of 16 is 4 (because 42 = 4 × 4 = 16) The square root of 25 is 5 (because 52 = 5 × 5 = 25) The symbol '√ ' means square root, so √ 36 means 'the square root of 36'. Cube root The opposite of cubing a number is called finding the cube root. Example The cube root of 27 is 3 (because 3 × 3 × 3 = 27) The cube root of 1000 is 10 (because 10 × 10 × 10 = 1000) 3 The symbol √ means cube root, so √ ‘the cube root of 64’. 6 Bartomeu Ramon CC San Alfonso NOUGHTS AND CROSSES 1. You will split the classroom into two groups (Team A and team B) and choose a spokesperson for each team. In turns, the spokesperson of team A will have to read aloud a root and the other team will have to write the correct answer at the whiteboard so that ONLY if they answer right, they will be allowed to write a “nought or a cross”. After that will be the turn of team B. Important: each time has only ONE minut to guess the correct answer. Roots for Team A Write the correct answer Roots for Team B √ √ √ √ √ √ 3 3 √ 3 √8 3 √ Write the correct answer √ 3 √ 3 √ 7 Bartomeu Ramon CC San Alfonso INDEX LAWS Multiplying numbers with the same base We often need to multiply something like the following: 4 3 × 45 We note the numbers have the same base (which is 4) and we think of it as follows: 43 × 45 = (4 × 4 × 4) × (4 × 4 × 4 × 4 × 4) We get 3 fours from the first bracket and 5 fours from the second bracket, so altogether we will have 3 + 5 = 8 fours multiplied together. 43 × 45 = 43+5= 48 In general, we can say for any number a and indices m and n: Dividing numbers with the same base As an example, let's divide 36 by 32: So we have 36÷32=36-2=34 We cancelled out 2 of the threes on top and the 2 threes on the bottom of the fraction, leaving 4 threes on the top (and the number 1 on the bottom). In general, for any number a (except 0) and indices m and n: 8 Bartomeu Ramon CC San Alfonso Raising an index expression to an index As an example, let's raise the number 42 to the power 3: (42)3 = 42 × 42 × 42 From the multiplication example above, we can see that this is going to give us 46. We could have done this as: (42)3 = 42×3 = 46 In general, we have for any base a and indices m and n: (am)n = amn Raising a product to a power Number example: (5 × 2)3 = 53 × 23 In general: (a·b)n = anbn Raising a quotient to a power Number example: In general: 9 Bartomeu Ramon CC San Alfonso HANGMAN 1. Split the classrom into two teams. Each team choose a representative and team A start saying a letter to find out the unknown word. Each team can only fail 6 times. Then it is the turn of team B. Roots for Team A Write the correct answer Roots for Team B Write the correct answer 82 ·52 4 26 · 56 8 5 Team A ___ ___ ___ ___ ___ ___ ___ ___ Team B ___ ___ ___ ___ ___ 10 Bartomeu Ramon CC San Alfonso NOUGHTS AND CROSSES 1. You will split the classroom into two groups (Team A and team B) and choose a spokesperson for each team. In turns, the spokesperson of team A will have to read aloud a root and the other team will have to write the correct answer at the whiteboard so that ONLY if they answer right, they will be allowed to write a “nought or a cross”. After that will be the turn of team B. Important: each time has only ONE minut to guess the correct answer. Roots for Team A √ Write the correct answer Roots for Team B √ 3 √ √ √ √ 3 3 √ 3 √8 3 √ Write the correct answer √ 3 √ 3 √ 11