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# Maths by Carmen Benedicto

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CAL Presentations. Carmen Benedicto. Teaching Maths

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### Maths by Carmen Benedicto

1. 1. I´m a math teacher in a bilingual secondary school (highschool).My students are of the first and second year (ESO).I have an assistant teacher in my class once a week. Thatday the whole class is in English. The assistant teacher isShannon, she corrects of the pronunciation and spellingstudents and She helps me in math class, to do games oractivitiesI want the students to try to speak and participate as muchas possible.I try to make the students feel more confident with English. Itell them; “try to say it in English and after if it is necessary, Iwill correct you or Shannon will correct you” .The students get used to asking and answering in Englishas much as possibleNO GRADE OR MARK FOR THIS!I try to teach the most basic concepts and then I introducemore complex ones (concepts)Normally, I teach a new concepts in Spanish class, then Itake advantage of English class to reinforce the concepts.Each student has two books, one of them is an Englishbook and the other is a Spanish one.This year for the second course I have tried to teach someconcepts in English first.I´m going to show you an example of the way I teach mymath class in English and tools I used.
2. 2. Firstly I´m going to show you useful sentences that I use inclass a lot.USEFUL SENTENCES-Raise your hand before speaking and wait until I call onyou.-Turn around and face forward (Ponte derecho).-Is there anyone that knows the answer?-Do you understand this?-Copy down the words that appear on the screen, please.- Copy down the table, please.-You have to copy all of it.-Write down the exercise-What is the meaning of….?- It means the same things.-Can you say that again, please? Or Can you repeat,please?-Can you repeat the last…….? (sentence, word, letter,number)-Be quiet, I can´t hear.-Don´t hide …………….I did this when I was a child in English class, I had tomemorize five sentences every week, one hundred in thewhole course. If you didn´t voluntarily say five sentences
3. 3. every week , the next week you had to say twice as manysentences and do it successfully. The topic for today is FRACTIONSFirst of all to introduce the topic I usually give them thevocabulary about the topic and sometimes, I brainstormwords for the topic.I´m going to show you activities that I usually do in my classPractice, practice……
4. 4. LOOK UP WORDS about the topic in the dictionary and inyour book.http://www.amathsdictionaryforkids.com/Link bookWord referenceGoogle traductorIf the student have a right computer, everyone look up theirword, but if their computers don´t work or don´t carry lot ofthem, I use the digital or whiteboard.
5. 5. FRACTIONFRACTION NOTATIONNUMERATORDENOMINATOR numeratorPROPER FRACTION; deno min ator numeratorIMPROPER FRACTION; deno min atorMIXED NUMBERRATIONAL NUMBERDECIMAL FRACTIONTERMINATING DECIMALREPEATING DECIMALEQUIVALENT FRACTIONSREDUCEAMPLIFYPERCENTAGE (PERCENT)when the student finish looking up the words, they have todo this exercise.
6. 6. FILL IN THE GAPS WITH THE RIGHT WORD:FRACTION (8)NUMERATOR (3)DENOMINATOR (4)PROPER FRACTION (1) numeratordeno min atorIMPROPER FRACTION (2)numerator deno min atorMIXED NUMBER (1)RATIONAL NUMBER (2)DECIMAL FRACTION (2)TERMINATING DECIMAL (2)REPEATING DECIMAL (3)EQUIVALENT FRACTIONS (2)REDUCE (3)AMPLIFY(2)PERCENTAGE (PERCENT) (2)The students have a clue, because I write down the numberof time that they have to use each word.-Any part of a group, number or whole is a _________
7. 7. -Number above the line of a fraction, showing number ofparts of the whole is _________.-_________ is bottom number in a fraction. Also, thenumber of parts the whole is divided into-In the _________ _________ numerator is less than thedenominator, Represents an amount less than the unit-In the _________ _________ numerator is greater or equalthan the denominator, Represents an amount more or equalthan the unit 1-Whole number and a fraction like this 3 is a _________ 2_________It is other way to represent or express __________________-_________ _________ a number that can be written as aratio or two integers (_________), excluding zero as a_________.-_________ _________a _________ written as a_________ or _________ DECIMAL, other decimal are not_________ _________. 1 = 0 .5Example: ___________ ___________ 2 1 = 0.333... = 0.3 ˆ __________ ___________ 3 1 = 0.1666... = 0.16 _________ ________ ˆ 6 a ≠ 0.123456 ... NOT _________ _______ b
8. 8. -To ___________ or simplify a ___________ divide the___________ and ___________ by their highest commonfactor.To ___________ a ___________ multiply the ___________and ___________ multiply by the same number.In both you get a ___________ ___________-When you ___________ a ___________ you get a___________ ___________, because you have the samevalue or amount-___________ can be represented by ___________;Example:1 = 25 = 0.25; 0.25·100 = 25%4 100_________-___________ can be represented by _________;Example: 20 120% ⇒ = 100 5 ________
9. 9. SOLUTION:-Any part of a group, number or whole is a FRACTION-Number above the line of a fraction, showing number ofparts of the whole is NUMERATOR.-DENOMINATOR is bottom number in a fraction. Also, thenumber of parts the whole is divided into-In the PROPER FRACTION numerator is less than thedenominator, Represents an amount less than the unit-In the IMPROPER FRACTION numerator is greater orequal than the denominator, Represents an amount more orequal than the unit 1-Whole number and a fraction like this 3 is a MIXED 2NUMBER-It is other way to represent or express IMPROPERFRACTION-RATIONAL NUMBER a number that can be written as aratio or two integers (FRACTION), excluding zero as aDENOMINATOR,-DECIMAL FRACTION a FRACTION written as aREPEATING or TERMINATING DECIMAL, other decimalare not DECIMAL FRACTION. 1 = 0 .5Example: TERMINATING DECIMAL 2 1 = 0.333... = 0.3 ˆ REPEATING DECIMAL 3 1 = 0.1666... = 0.16 REPEATING DECIMAL ˆ 6
10. 10. a ≠ 0.123456 ... NOT RATIONAL NUMBER b-To REDUCE or simplify a FRACTION divide theNUMERATOR and DENOMINATOR by their highestcommon factor.-To AMPLIFY a FRACTION multiply the NUMERATOR andDENOMINATOR multiply by the same number.-In both you get a EQUIVALENT FRACTION (no S)-When you REDUCE a FRACTION you get aEQUIVALENT FRACTION, because you have the samevalue or amountFRACTION can be represented by PERCENTAGE;Example:1 = 25 = 0.25; 0.25·100 = 25%4 100AMPLIFYPERCENTAGE can be represented by FRACTION;Example: 20 120% ⇒ = 100 5 REDUCE
11. 11. TO PRATICE AND WRITING FRACTIONS IN ENGLISH 1. Fill in the boxes:Half 1/2 Seven sixthsFive thirds Three eighthsThree quarters Five ninths /2Two fifths Three tenths 2. Write down how these fractions are read. 3/2 Three halves 3/5 _____ _____ 1/4 _____ _____ 1/3 _____ _____ 3/10 _____ _____ 5/7 _____ _____ 6/7 _____ _____ 1/8 _____ _____ SOLUTION:
12. 12. 1. Fill in the boxes:Half 1/2 Seven sixths 7/6Five thirds 5/3 Three eighths 3/8Three quarters 3/4 Five ninths 5/9/2Two fifths 2/5 Three tenths 3/10 2. Write down how these fractions are read. 3/2 Three halves 3/5 Three fifths _____ _____ 1/4 One quarter 1/3 One third _____ _____ _____ _____ 3/10 Three tens 5/7 Five sevenths _____ _____ _____ _____ 6/7 Six sevenths 1/8 One eighth _____ _____ _____ _____TO PRACTICE OPERATION WITH FRACTIONFill with appropriate numbers
13. 13. Remember: To add and subtract fractions you need the same denominator and after that you add or subtract the numerators 5−2=5−4= 1 6 3 6 6 6 To multiply fractions you have to multiply the numerator by the numerator and the denominator by the denominator. 5 . 2 = 10 = 5 6 3 18 9 To divide fractions you have to multiply the first numerator by the second denominator and the resoult is the numerator and multiply the first denominator by the second numerator and the result is the denominator. 5 : 2 = 15 = 5 6 3 12 4(The students copy the table in his or her notebook)When I need to distribute paper for an activities I give usedpapers that have writing on one side. ___ + ___ = 1 _ . ___ : ___ = 10 21 = = 3 6 7 35
14. 14. Explain the solution in English(Guide)FIRSTThe denominator in the whole first column and in whole firstrow is ……., using the addition and subtraction fraction.SECOND………TO FINISH …….. SOLUTION: 5 2 7 + 7 = 1 _ . 2 : 3 = 10 7 5 21 = = 3 6 7 35
15. 15. FIRSTThe denominator in the whole first column and the wholefirst row is seven, using the addition and subtractionfraction.SECONDThe numerator in the second row, second column is threeusing the division fraction.THIRDThe numerator in first row, second column is two using themultiply fraction.FOURTHThe numerator in first row, first column is five using the addfraction.FIFTHThe numerator in the second row, first column is two usingthe subtraction fraction.SIXTHThe denominator in the second row, second column is five,using the division fractionTO FINISH
16. 16. you check the multiply of second columnBINGO of summary or reviewThe most common activity I used is BINGO I used it toreview at the end of each lesson or whenever I haveenough time to do many activities . Actually, the bingoactivity incorporates all learning in a lesson (everything welearn in a lessonThe student write the date: April, Wednesday 18th 2012The numbers that you can choose
17. 17. 11 3 1 5 5 5 1 3 ; ; 5; ; ; ; ; ; .6 4 2 3 6 4 5 5In the first column, you put proper fraction, decimalexpression and the name of decimal number.In the second column, you put improper fraction, decimalexpression and the name of decimal number.What do you think about five?Proper fraction Improper fractionSOLUTION:Proper fraction Improper fraction3 11 ˆ = 0.75 TERMINATING DECIMAL = 1 .8 3 REPEATING DECIMAL4 61 5 = 5 .0 INTEGER NUMBER = 0 .5 TERMINATING DECIMAL25 ˆ 5 ˆ = 0 .8 3 REPEATING DECIMAL = 1 .6 REPEATING DECIMAL6 31 5 = 0 .2 TERMINATING DECIMAL = 1.25 TERMINATING DECIMAL5 4
18. 18. 3 = 0 .6 TERMINATING DECIMAL5After thatPut the fractions in order from least to greatest……. < ……. < ……. < ……. <……. <……. < ……. < ……. < …….SOLUTION:1 1 3 3 5 5 5 11 < < < < < < < <55 2 5 4 6 4 3 6You choose three numbers and put them in a table withthree squares. The numbers should be from least togreatestspend YOURFRACTIONSThe student chooses a numberDepending on how much time I want to spend, the studentschoose two, three or four fraction and I prepare the numberof exercises I want to do.SOLUCIÓN: 1) 3 + 1 = 9 + 2 = 11 = 1.83 ˆ 2 3 6 6 6 2) 3 − 2 = 9 − 4 = 5 = 0 .8 3 ˆ 2 3 6 6 6
19. 19. 3) 5 · 1 = 5 = 1.25 2 2 4 5 : 1 = 10 = 5 4) 2 2 2 75 3 5) What fraction represent 75%? 100 = = 0.75 4 20 1 6) What fraction represent 20%? 100 = = 0.2 5 7) What fraction represent the decimal number 0.6? 6 =3 10 5 2 = 1 = 0 .5 8) What fraction of omelette I have eaten? 4 2 9) Correct a mistake in the name of fraction: five third 5 ˆ five thirds. = 1.6 3 ……. DICTATIONShannon and I dictate a problem, if they are quiet andpaying attention we repeat it as many times as they need.I can ask the students to try to write what they hear word forword or only the data from the problem. Then, Shannon or Iread it very slowly.The first student who finishes the problem has to raise hisor her hand then, writes the data on the whiteboard, solves
20. 20. the problem and wins a positive (two tenths) to add to theirgrade for the evaluation.When I correct the problem in the whiteboard I show themwritten problem.Link bookI like doing many different activities with my students toenjoy ourselves.This year, all of the bilingual teachers, Music, History,Physical Education, English and myself, decided to worktogether on the same topic ANCIENT GREECE. In eachsubject we would work students during the same week, onthis topic we made a Web quest about Ancient Greece towork in class if possible or at home.http://carmenlaffon.blogspot.com.es/http://zunal.com/webquest.php?w=122044
21. 21. Some times you have many problems with the classroomcomputer or the student lap-top and the connection may notwork so I always a plan B prepared.Sometime I prefer to use the chalk. Technology is helpful,but it is not the solution to all problems.Perhaps I would like to research the relationship betweenMusic and Mathematics to prepare an activity for the nextyear.I also used some videos for my classes.Videos:Sequences 5: Golden Rectangleshttp://www.youtube.com/watch?v=-ncEEXekZek&feature=relmfuGolden numberhttp://www.youtube.com/watch?v=fmaVqkR0ZXg&feature=relatedhttp://www.youtube.com/watch?v=oLGbggE21sIThe Fingerprint of Godhttp://www.youtube.com/watch?v=-Ibc8sD5sgw&feature=relatedGolden numberhttp://www.youtube.com/watch?v=fmaVqkR0ZXg&feature=relatedhttp://www.youtube.com/watch?v=U2bAlIK4KkE&feature=relatedhttp://www.youtube.com/watch?v=gKzcDZswj5A&feature=relatedhttp://www.youtube.com/watch?v=fmaVqkR0ZXgA good teacher is not the one who iswiser, but the one whose students learnmore.