"""'b" , "'" 00,gnt '"d "ggedl"' ｷ ＼ Ｂ ｾ 150 40 ,.,mbei or non""""' tnl', "';,, '""' "·"'' ''" numbet ol tagged ns\1:,5:)_ number Of Ufltagged ]ish: '34 : M0 ere enfa Unit VII I Math and the Mind's Eye Activities Modeling Percentages &Ratios Introduction to Percentages Areas and lengths are used to imroduce rhe meaning of percenrage Given the meaning of 100%), studenrs develop their own procedures for carrying out computations involving percentages ath and the Mind's Eye materials are intended for use in grades 4-9 They are written so teachers can adapt them to fit student backgrounds and Fractions, Decimals and Percentages A pardon of a quantiry can be described in terms of a fraction, a decimal, or a percentage Ways of doing chis, and of converting from one way to another, are investigated Ratios The concept of ratio is introduced as a way comparing the number of black pieces to the number of red pieces in collccrions of counting pieces Percentages and Ratio Problems Diagrams and sketches are used to solve story problems involving percentages and ratios grade levels A single activity can be extended over several days or used in part A catalog of Math and the Mind's Eye materials and teaching supplies is available from The Math Learning Center, PO Box 3226, Salem, OR 97302, I 800 575-8130 or (503) 370-8130 Fax: (503) 370-7961 Learn more about The Math Learning Center at: "\VWw.mlc.p I I .l·····t·····t···-1 · 1·-·-t·····t· +-··1 -·t· t···-1-····l·····t· ·t· ·l· -·t···+····t 1··-··1···· Math and the Mind's Eye Unit VII • Activity • Action 1o 11 © Copyright 1991, The Math Learning Center Activity Sheet V/1-1-E For each of the following find what percent length SA is of length SB a 1 1 1 I I I I I I I I I I I I I I I I Find point A if the length of SA is 135o/o of the length of SB I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1 1 1 1 1 S b I s c I s 1 1 1 1 1 1 B I I I I I I I I I I I I I I I I I I B I I I I I I I I I I I I B I 1 1 I I I A I I I I I I I I I I I I I I A I I I I I I A Find point A if the length of SA is 150°/o of the length of SB I S I I I I I · I I I I I I I I I I I · -·B I I I S I I I I I I I B Find point A if the length of SA is 460°/o of the length of SB I I I I I S I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I B Find point A if SA is 25o/o longer than SB I I I I I I I I I I I I I I I I I I I S B Find point A if the length of SA is the length of S8 increased by 125°/o I I I I I I I I I I I I S I I I I I I I I I 'I I I I I I I I I I I I I I I I I I I I B Find point if the length of SA is 200°/o of the length of S8 I I I I I I I I I I I I I I I I I I I I I I I I I I I S A Find point if the length of SA is 120°/o of the length of SB ｾ I I I I I I I I I I I I I I I I Math and the Mind's Eye Unit VII• Activity • Action 13 I I I I I I I I I I I I I i ©Copyright 1991, The Math Learning Center Math and the Mind's Eye Unit VII • Activity • Action 1, © Copyright 1991, The Math Learning Center A B D E F H G I Activity Sheet V/1-2-A Math and the Mind's Eye Unit VII • Activity ã Action âCopyright 1991, The Math Learning Center B A 80% of the area is shaded of the area is shaded D C 75% of the area is shaded F E mw 45 of the area is shaded G 5% of the area is shaded .725 of the area is shaded H .075 of the area is shaded I .4375 of the area is shaded 66 %% of the area is shaded Activity Sheet V/1-2-8 Math and the Mind's Eye Unit VII• Activity ã Action âCopyright 1991, The Math Learning Center A B C 10 10 10 E D 23 F G 12 19 H 22 31 Activity Sheet V/1-2-C Math and the Mind's Eye Unit VII ã Activity ã Action â Copyright 1991, The Math Learning Center Ratio of Black Number of Number of Total Number to Red Pieces Black Pieces Red Pieces of Pieces to to 3 to 4 to 20 10 30 12 - 14 10 11 12 Math and the Mind's Eye Unit VII· Activity ·Action 4, ©Copyright 1991, The Math Learning Center Math and the Mind's Eye Unit VII • Activity • Action © Copyright 1991, The Math Learning Center Complete square so the ratio of the length of its side to the side of square A is to What is the ratio of the area of square to the area of square A? r , -T -; ; -; -; , -, -; -r , -, -; , -; -1 I I I I I I ｌI Ｍ Ｍ ｾ IＭ Ｍ Ｍ I I I ｾ Ｍ ﾷ ｾ I I I I I ' I r I r , - -r , r - I I I I I I I I I I I I I I I I Iｾ I I I I I I I I I I I I I I I I I I I I I I I Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｌ I Ｍ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｌ l Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｬ I I I I I I I I I I I I I I I I I I I I I I I Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ Ｔ IＭ Ｍ Ｍ Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ Ｔ Ｍ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ ＭI Ｍ ｾ Ｍ IＭ Ｍ Ａ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ Ｔ Ｍ I Ｍ Ｍ Ａ Ｍ I Ｍ Ｍ ｬ ·- I I I I I I I I I I I I I I I I I l I I Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｾ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｔ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｔ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ ｾ ｾ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ Ｑ I I I I I I I I I I I I I I I I I I I I I I I Ｍ Ｍ Ｍ ｴ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｴ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ Ｋ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ Ｋ Ｍ Ｍ Ｍ Ａ I I I I I I I I I I I I I I I I I I I I I I I I I Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ IＫ Ｍ Ｍ Ｍ I ｾ Ｍ Ｍ ｾ I Ｍ Ｍ Ｔ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ Ｍ I Ｍ Ｔ Ｍ I Ｍ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ﾷ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ I I I I Iｾ I I I I I I I I I I I I I I I I I I I I I I I I I I I I Ｍ Ｍ Ｔ I Ｍ Ｍ Ｍ I ｔ Ｍ Ｍ I Ｍ ｾ Ｍ ＭI ｾ Ｍ Ｍ I ｾ Ｍ Ｍ I Ｍ ｾ Ｍ IＭ ｾ Ｍ Ｍ ｆ ｆ Ｍ I ｾ Ｍ Ｍ I Ｔ Ｍ Ｍ IＭ ｾ Ｍ Ｍ I Ｍ ｾ Ｍ I Ｍ ｾ Ｍ I Ｍ ｾ Ｍ I Ｍ Ｍ Ｑ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I r -+ -r -+ -t E3 - -+ -r -+ -r -+ -l I I Iｾ Ｍ Ｍ ｾ I I ｾ Ｍ Ｍ ｾ IＭ Ｍ Ｍ I I Ｍ Ｍ Ｍ I I I Iｾ Ｍ Ｍ Ｍ I I Ｋ Ｍ Ｍ Ｍ I I I I I I Iｌ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ I I I I ｾ Ｍ Ｍ ｾ Ｍ Ｍ ｾ I I I IＭ Ｍ Ｍ ｾ I I Ｍ Ｍ Ｍ ｾ I I I I I Ｍ Ｍ ｾ ＭI Ｍ ｾ Ｍ I I I I Ｍ Ｍ ｾ Ｍ Ｍ ｾ Ｍ I I I I I I IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ I I I I Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｾ I I I I I I IＭ Ｍ ｾ Ｍ I I Ｍ Ｍ ｾ Ｍ I I I I I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｌ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ I I I I I I I ·)- I I I I I I I I I I I Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｾ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ Ｑ I I I I I I I I I I I I I I I I I I r , -T -r . -; -; , -, -T -; , -; -; , -, -1 I I I I I Iｌ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Iｾ I I I I I I I I I I I I I I I I I I I I I I I I I I Ｍ Ｍ ｊ _ l _ L JL ｬ I Ｍ Ｍ Ｍ I ｾ Ｍ Ｍ I ｾ Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ ｬ I Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ ｊ Ｍ Ｍ ｾ IＭ Ｍ Ｍ I I I I r + I I I I I I I I I I I I I I Ｍ I I Ｍ ｾ I I Ｍ I I I Iｾ Ｍ Ｍ ｾ I Ｍ Ｍ I I I ｲ Ｍ I I I Ｍ ｾ I Ｍ I I I I Ｍ ｾ I I I I I I Ｍ Ｍ ｾ Ｍ I I I ｾ Ｍ I Ｍ ｾ I I I I Ｍ Ｍ ｾ I I Ｍ Ｍ I I Ｍ ｲ I I Ｍ ｾ Ｍ I I Ｍ ｲ I I I I I Ｍ Ｍ Ｌ Ｍ I I Ｍ ｲ I I I Ｍ Ｍ Ｌ Ｍ I I Ｍ ｾ I I I I I I I I I I I I I I I I I I I I I I I I ｾ Ｍ I I I I I Ｍ ｾ Ｍ I I Ｍ ｾ I I I Ｍ Ｍ I I I I I ｾ Ｍ Ｍ I I I I I Ｍ ｲ Ｍ I I Ｍ ｾ I I I Ｍ Ｍ I I I I I Ｍ ｲ Ｍ I I I I I Ｍ ｾ Ｍ I I I Ｍ ｲ Ｍ I I I ｾ Ｍ I I I Ｍ ｾ I I I I I ｾ Ｍ Ｍ ｾ IＭ Ｍ Ｍ I Ｍ I I Ｍ Ｌ I I I I I Ｍ ｾ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I ｾ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ I Ｍ Ｍ Ｋ IＭ Ｍ ｾ Ｍ I Ｍ Ｋ Ｍ I Ｍ ｾ Ｍ IＭ Ｋ Ｍ Ｍ I ｾ Ｍ Ｍ I Ｍ Ｋ Ｍ IＭ ｾ Ｍ Ｍ I Ｍ ｲ Ｍ I Ｍ ｾ Ｍ IＭ Ｍ ｲ Ｍ I Ｍ ［ Ｍ I Ｍ Ｍ ｾ I Ｍ Ｍ ｾ I r T -r T -r T . -r ; -; ; -; , -; , -r , I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Iｾ I Ｍ ｔ I I I I Ｍ Ｍ ｾ ｲ I I Ｍ I I Ｍ ｔ I I I I Ｍ Ｍ ｾ ｾ I I Ｍ I I Ｍ ｾ I I I I Ｍ Ｍ ｾ Ｍ I I I I Ｍ Ｍ ｲ I I I I Ｍ Ｍ ｾ Ｍ I I Ｍ Ｍ I I ｲ Ｍ Ｍ I I I Ｌ Ｍ I I I I I I I I I I I I I I I I I I I I I I Ｍ ｾ I I I I I I I I I I Ｍ ｾ t_ l I I I I Ｍ Ｍ Ｍ I I I ｾ Ｍ Ｍ ｾ I I I Ｍ Ｍ ｾ I Ｍ Ｍ ｾ I I Ｍ Ｍ I I I I ｾ Ｍ I I I Ｍ ｾ Ｍ Ｍ I I I ｾ Ｍ _II _ J.I _II _ l _I, _ J_I ｾ Ｍ I I Ｍ I I Ｍ Ｍ ｲ Ｍ ｌ Ｍ Ｍ I I I Ｍ Ｍ Ｔ Ｎ I Ｍ Ｍ I Ｎ Ｍ ｊ I I I ｲ Ｍ I I I Ｍ ｾ Ｍ Ｍ I I I Ｍ ｾ Ｍ I Ｍ I I Ｍ Ｌ I I I I Ｍ ｾ Ｍ I Ｍ ｾ I I I I I I I I Ｍ I I I I I I I I I I I I I IＭ I I I Ｍ Ｍ I I I I Ｍ Ｍ Ｌ I I I Ｍ ｾ I I Ｍ I I I I I I I ｾ Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ Ｑ I I I I I I I I Ｍ ｔ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｾ Ｍ Ｍ Ｌ Ｍ Ｍ Ｍ Ｌ 1 I I I I I I I I I Ｍ Ｍ Ｑ IＭ Ｍ Ｍ Ｋ I Ｍ Ｍ Ｍ ｲ I Ｍ Ｍ Ｍ ｲ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｬ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Ｍ ｾ I Ｍ Ｍ Ｍ ｔ I Ｍ Ｍ Ｍ Iｾ Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ Iｾ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ Ｍ I Ｍ Ｍ Ｑ I Ｍ Ｍ Ｍ Iｾ Ｍ Ｍ Ｑ IＭ Ｍ Ｍ Ｋ I Ｍ Ｍ Ｍ ｲ I Ｍ Ｍ Ｑ IＭ Ｍ Ｍ Ｋ IＭ Ｍ Ｍ ｲ I Ｍ Ｍ Ｑ Ｍ I Ｍ Ｍ Ｑ Ｍ I Ｍ Ｍ ｬ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ I Ｍ Ｍ ｾ ＭI Ｍ Ｍ Ｔ I Ｍ Ｍ I I Ｍ I Ｍ Ｍ Ｍ Iｾ Ｍ Ｍ ｾ IＭ Ｍ Ｍ Ｔ I Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ Ｔ Ｍ I Ｍ Ｍ Ｔ IＭ Ｍ Ｍ Ｑ I ' I I ｾI Ｍ Ｍ Ｍ Ｚ I Ｍ Ｍ Ｍ Ｔ I Ｍ Ｍ Ｍ ｾ I I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｬ I I D Ｍ Ｋ I Ｍ Ｍ Ｔ Ｍ I Ｍ Ｍ ｾ I Ｍ Ｍ Ｋ IＭ Ｍ Ｔ IＭ Ｍ I I _! _ L JL J _ ｌ I I I _ LI JI _ L JI _ L JI I I I I I I -; -; , -, -1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ Iｌ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ Ｍ I Ｍ Ｍ ｬ I I I I I I I I I I Ｍ Ｍ Ｍ ＱＭ Ｍ Ｍ Ｒ Ｍ Ｍ Ｍ ｬ Ｍ Ｍ Ｍ ｌ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｬ Ｍ Ｍ Ｍ ｌ Ｍ ｟ ｊ ｌ J _ J Ｍ ｾ I I I I I I I I I I I I I I I I I I I I I I I I I I I Ｍ Ｍ Ｍ Ｍ I I ｾ I I I I Ｍ Ｍ Ｍ Ｍ I I Ｍ I I Ｍ Ｍ ｾ I I Ｍ ｾ I I I I Ｍ ｾ I I Ｍ ｔ Ｍ I I Ｍ I I Ｌ Ｍ I I I I I I I I I I Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ ｩ I I I Ｍ I I I I Ｍ Ｍ ｾ I I ｲ I I ｾ I I ｾ Ｍ I I Ｍ Ｍ Ｍ I I I Ｍ Ｌ I I I I Ｍ Ｍ Ｍ ｲ I I Ｍ Ｌ I I I I I I Ｍ I Ｍ Ｍ Ｍ ｾ I I I Ｍ Ｍ Ｌ I I Ｍ Ｍ ｾ I I Ｍ Ｍ I I Ｍ Ｍ Ｍ I I ｾ I I I I I I I I Ｍ Ｍ ｾ I I I I Ｍ Ｍ Ｍ ｲ I I Ｍ ｾ I I Ｍ Ｍ ｲ I I I Ｍ Ｍ Ｌ Iｌ Ｍ Ｍ ｾ I I ｾ Ｍ Ｍ ｾ Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ Iｌ Ｍ Ｍ Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ ｾ Ｍ I Ｍ Ｍ ｾ Ｍ I Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｌ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｌ I Ｍ Ｍ ｾ I I ｾ Ｍ Ｍ ｻ I I I I Ｍ I I I I I Ｍ Ｍ Ｋ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ I I I I I I I I I I I I I I I I I I I I I I I I I I I I • I I I I I I I I I I I I I I I Ｍ Ｍ ｾ Ｍ Ｍ ｽ Ｍ Ｍ Ｔ Ｍ ＱＭ Ｍ ｈ I Ｍ ｴ Ｍ Ｍ Ｔ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ Ｔ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ ｩ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Ｍ Ｍ Ｍ I I I I ｲ Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ ｲ I Ｍ Ｍ Ｋ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｴ IＭ Ｍ Ｍ ｲ I Ｍ Ｍ ｴ IＭ ﾷ ｾ ﾷ I Iｾ Ｍ I I ｲ Ｍ I I Ｍ Ｍ Ｑ I Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ ｩ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｩ I Ｌ I I Ｍ Ｍ Ｍ ｲ I I Ｍ Ｍ ｔ I I Ｍ Ｍ Ｍ ｾ I I Ｍ Ｍ I I I I I I I ｔ I I Ｍ Ｍ ｾ Ｍ I I Ｍ ｔ Ｍ I I Ｍ ｾ Ｌ Ｍ I I Ｍ Ｌ Ｍ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｲ I Ｍ Ｍ Ｑ I Ｍ Ｍ Ｍ ｲ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｲ I Ｍ Ｍ Ｑ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ ﾷ Ｍ I Ｍ ｾ Ｍ IＭ ﾷ Ｍ Ｍ I ｾ Ｍ Ｍ I Ｍ ｾ Ｍ IＭ ｾ Ｍ ＭI Ｍ ｾ Ｍ I Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ Ｔ Ｍ I Ｍ Ｍ ｾ I Ｍ Ｍ ｾ Ｍ I I I I I I I I I I I I I I I I I I I I I I I I I Ｍ Ｍ ｾ Ｍ Ｍ Ｋ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ ［ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｾ I I Ｍ Ｍ I I I I I Ｍ -+- I I I I I Ｍ Ｍ Ｍ Ｋ I Ｍ Ｍ Ｍ Iｾ Ｍ Ｍ IＭ I I I I Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ ｾI Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ I I Ｍ I I Ｍ I I I Ｍ Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ I Ｍ I I Ｍ ｾI Ｍ Ｍ Ｋ I Ｍ Ｍ I I t - Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ Ｑ Ｍ Ｍ ｾ I Ｍ Ｍ ﾷ IＭ Ｍ Ｍ I I Ｍ I I I Ｍ I I Ｍ I I I Ｍ I I Ｍ I I Ｍ ｔ I I I I ｾ I I ｾ I I I Ｍ I I Ｍ Ｍ ｬ I Ｍ Ｍ Ｍ ｾI Ｍ Ｍ ｾ I Ｍ Ｍ ｊ Ｍ I Ｍ Ｍ ｬ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｬ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ Ｍ Ｍ ｊ I Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｌ I Ｍ Ｍ ｾ I Ｍ I I Ｍ I I Ｍ I I I ｾ Ｍ I I I Ｍ I I Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ Iｾ Ｍ Ｍ I I I I I I Iｾ Ｍ Ｍ ｾ I Ｍ Ｍ I I ｲ Ｍ I I Ｍ Ｍ Ｋ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ I I Ｍ I I ｲ Ｍ Ｍ Ｋ Ｍ ｾ I I ｾI Ｍ Ｍ ｾ I Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ ﾷ Ｍ I Ｍ ｾ Ｍ IＭ ｾ Ｍ Ｍ I ｾ Ｍ Ｍ IＭ ｾ Ｍ ＭI ｾ Ｍ Ｍ I Ｍ ｾ Ｍ I Ｍ ｾ Ｍ IＭ Ｍ ｾ Ｍ I Ｍ ｾ Ｍ I Ｍ Ｍ ｾ I Ｍ Ｍ ｾ I ｾ Ｍ I I I I I ｲ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ ｴ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｴ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ Ｑ I ｲ I I Ｍ I I I I I I I I I I Ｌ I I Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ Iｾ Ｍ Ｍ ｾ I Ｍ Ｍ Ｔ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｔ Ｍ IＭ Ｍ Ｋ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ f -+ I I I Ｌ Ｍ Ｍ I I I L J- I I I Ｍ I I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｬ r , -, -; , -, -; , -, -T -r . -. -; , -, -1 I I I Ｍ I I I I L j I Ｍ Ｍ ｾI Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｋ Ｍ IＭ ｾ Ｍ Ｍ I Ｍ ｾ Ｍ I Ｍ ｾ Ｍ IＭ Ｍ ｾ Ｍ I Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ Ｔ Ｍ I Ｍ Ｍ ｾ I Ｍ Ｍ Ｔ I I ｾ ｌI Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ I ｌ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｌ I Ｍ Ｍ I ｲ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｴ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｴ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ Ｑ Iｾ Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ I ｾ I I I I I I ｲ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｲ Ｍ I I I I I I Ｍ Ｍ Ｍ ｾ I I I I I I Ｍ I r , - ; , -, -; , -, -T I I Ｍ I I I I I I I I I I I I ｾ Ｍ Ｍ ｾ IＭ Ｍ Ｍ I I I I I Ｍ Ｍ Ｍ Ｍ Iｾ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｲ I Ｍ Ｍ Ｍ Ｍ ｾ IＭ Ｍ Ｍ I I I I I I Ｍ Ｍ Ｍ Iｾ Ｍ Ｍ ｾ I I I I I I I I I I Iｾ I I I I I ｲ -r -+ - ' I I Ｍ ｾI Ｍ Ｍ Ｑ IＭ Ｍ Ｍ I I I I I I I I I I I I I Ｍ Ｍ Ｍ Ｍ Iｾ Ｍ Ｍ ｾ I Ｍ Ｍ Ｔ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ I Ｍ Ｍ Ｔ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ I I I I I Ｍ Iｾ I I I I I ｾ Ｍ Ｍ Ｍ ｲ I Ｍ Ｍ Ｍ Iｲ Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｴ I Ｍ Ｍ Ｑ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｴ I Ｍ Ｍ I I I I I I Ｍ ｾ Ｍ Ｍ Ｑ IＭ Ｍ Ｍ I I I I I I I Ｍ I I I I Complete figure K so it has the same shape as figure J and the ratio of the perimeter of J to the perimeter of K is to What is the ratio of the area of J to the area of K? I I I I ｾ I I I Ｍ I I I I I Ｍ I I I Ｍ I r , -r T -r H r ; -; ; -; , -r , -r , L J _L l_·G·- JL l J _ L j _ L J _ L j _ L J I I I ｔ Ｍ Ｍ I I I I I Ｍ I I I I I I Ｍ I I I I I I I I Ｍ I I I Ｍ Ｍ ﾷ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ ｾ Ｍ IＭ Ｍ ｾ Ｍ I Ｍ ｾ Ｍ I Ｍ Ｍ ｾ Ｍ I Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ Ｔ Ｍ I Ｍ Ｍ ｾ I Ｍ Ｍ ｾ I Ｍ I I I I I Ｍ I I I I I I I I Ｍ I I Ｍ ｲ Ｍ I I I I I I I Ｍ I I I Ｍ Ｍ ｾI Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ ｾ Ｍ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ I I I I I I Ｍ I I I I I I I I I I I I I I I I I I I I I I I I _ l _ L JL l _ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｴ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ Ｑ I I I Ｍ Ｍ I I I Ｍ Ｍ Ｋ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ I I I I I I I I Ｍ r + I I I I I ｾ I I I I I Ｇ Ｍ Ｍ ｊ I Ｍ Ｍ Ｍ ｌ I Ｍ Ｍ ｊ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｊ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ I I I I I I I -Ｍ I I ｾ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ I I I I I I I I I Ｍ Ｍ Ｋ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｴ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ Ｑ Ｍ Ｍ Ｍ ｲ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ ｩ L- f=I I I I I I I I I I r , -T -; , -; -; , -, -T -r , -T -; , -; -1 I I • ｾI Ｍ Ｍ ｾ Complete figure G so it has the same shape as figure F and the ratio of the perimeter ofF to the perimeter of G is to What is the ratio of the area of F to the area of G? I I I I Iｌ I I Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ IＫ Ｍ Ｍ Ｍ I ｾ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ Ｍ I Ｍ Ｔ Ｍ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ Ｔ ｾ r , -; -; , -, -; , -, -T -; , -, -; , -, -1 I I I Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ Iｾ Ｍ Ｍ Ｍ I ｌ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ Ｍ I Ｍ ｾ Ｍ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｌ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｌ I Ｍ Ｍ ｾ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｬ I I What is the ratio of the perimeter of triangle C to the perimeter of triangle D? What is the ratio of the area of triangle C to the area of triangle D? I I Ｍ Ｍ ｲ Ｍ I I Ｍ Ｌ Ｍ I I Ｍ Ｍ ｲ I I Ｍ Ｍ Ｌ Ｍ I I Ｍ Ｍ ｾ I I Ｍ Ｍ Ｌ ｲ Ｍ Ｍ Ｋ I Ｍ Ｍ Ｍ ｲ I Ｍ Ｍ Ｋ IＭ Ｍ Ｍ ｾ I Ｍ Ｍ Ｋ IＭ Ｍ Ｌ ｟ I Ｍ Ｍ Ｋ IＭ Ｍ Ｑ Ｍ I Ｍ Ｍ ｴ IＭ Ｍ ｾ Ｍ I Ｍ Ｍ ｲ IＭ Ｍ ｾ ＭI Ｍ Ｍ ｲ I Ｍ Ｍ ｾ IＭ Ｍ Ｍ ｲ I Ｍ Ｍ Ｑ I I I I I I I I I I I I I I I I I I I I Iｾ Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ ｾ I Ｍ Ｍ Ｍ ｾ I Ｍ Ｍ Ｋ I Ｍ Ｍ ｾ Ｍ I Ｍ ｾ Ｍ I Ｍ ｾ Ｍ IＭ Ｍ ｾ Ｍ I Ｍ ｾ Ｍ I Ｍ Ｍ ｾ Ｍ I Ｍ ｾ Ｍ I Ｍ Ｍ ｾ I Ｍ Ｍ Ｔ Ｍ I Ｍ Ｍ ｾ I Ｍ Ｍ ｾ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I ｾ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ ｔ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ ｔ Ｍ Ｍ ｾ Ｍ Ｍ ｾ Ｍ Ｍ ［ Ｍ Ｍ Ｍ ｔ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｔ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ ｾ Ｍ Ｍ Ｍ ｾ Ｍ Ｍ Ｌ I I IL lI I I I I I I I I I I I I I I I I ! I _II _ J I _II _ ! I ,!I _ ! I ,!I _ L I JI _ L I JI _ IL J.I _ I_ Activity Sheet Vll-3 Math and the Mind's Eye Unit VII ·Activity ·Action a © Copyright 1991, The Math Learning Center Percentage & Ratio Problems ONE SIX At a clearance sale, the price of a VCR was discounted 40% The discounted price was $375 What was the original price? A telethon for a local charity raised $45,000 This was 125% of the goal What was the goal? TWO SEVEN The ratio of children to adults at the circus is to If the total attendance is 285, how many children are present? The ratio of two numbers is to Their difference is 45 What are the numbers? THREE The price of a large chocolate bar was increased by 20% It now costs $1.50 What did it cost before the increase? FOUR Two numbers are in the ratio to One number is 17 more than the other What are the numbers? FIVE In a certain town, 16% of the population lives in apartment buildings If 2800 people live in apartments, what is the town's population? Math and the Mind's Eye Unit VII ·Activity ·Action 1, 2, EIGHT Sandra sold 40% more Campfire Girls cookies than her sister Together they sold $408 worth How much did each girl sell? NINE Three numbers are in the ratio to to and their total is 720 Find the numbers TEN A length of string that is 180 em long is cut into pieces The second piece is 25% longer than the first and the third piece is 25% shorter than the first How long is each piece? ©Copyright 1991, The Math Learning Center More Percentage & Ratio Problems ONE SIX Jane paid $17.49 for a book, including tax If the sales tax is 6%, what was the price without tax? The ratio of Sue's age to her father's age is to In three years their ages will total 60 How old is each now? TWO SEVEN If gallons of a mixture with a 30% concentration of ammonia is added to 20 gallons of water, what is the concentration of ammonia? If 50 gallons of cream with 20% butterfat is mixed with 150 gallons of milk with 4% butterfat, what percent butterfat is the mixture? THREE EIGHT The ratio of the length of a rectangle to its width is to Its area is 300 square inches What are its length and width? Clara is 31 years old Her sister Molly is 47 In how many years, will their ages be in the ratio of to 5? FOUR NINE In a collection of dimes and nickels worth $6.40, the ratio of the number of dimes to the number of nickels is to Find the number of each type of coin Mrs Howe drove 320 miles in hours If she continues at that rate, how many hours of driving will it take her to complete a trip of 1400 miles? FIVE TEN The population of Multnomah County is 20% of the population of Oregon Also, 65% of the population of Multnomah County is within the Portland city limits What percent of the Oregon population is in Multnomah County within the Portland city limits? Of 50 students in a school who took part in a survey, 14 said they had moved within the last year If this is representative of the school as a whole and there are 425 students in the school, how many of them moved within the last year? Math and the Mind's Eye Unit VII ·Activity ·Action © Copyright 1991, The Math Learning Center Still More Percentage & Ratio Problems ONE SIX During its January clearance sale, a gift shop offered all its merchandise at a 20% discount Arnold paid $33.39 for an item, including a 5% sales tax What was the original price of the item? The ratio of two numbers is to If the smaller number is increased by 18, the ratio becomes to What are the numbers? TWO Last week, a state park employee caught 50 fish, tagged them and threw them ｢ ｡ ｣ ｫ ｾ Today he caught 40 fish from the same lake and were tagged About how many fish are there in the lake? THREE How much milk with 4% butterfat should be added to 10 gallons of cream with 20% butterfat to obtain a mixture that is 8% butterfat? FOUR There are 2820 cars in Smithtown The ratio of intermediates to compacts is to and the ratio of compacts to full-size cars is to How many full-size cars are there? FIVE A car is sold with a $1000 rebate and a 15% discount Which gives the better price for the buyer: (a) rebate and then discount the price after rebate, (b) discount the price and then rebate? Math and the Mind's Eye Unit VII • Activity • Action SEVEN The population of the United States is 60% of the population of the NorthAmerica and 5% of the population of the World What percent is the population of North America _of the population of the World? EIGHT A 15-gallon radiator contains 40% coolant and 60% water How much of this mixture should be replaced by coolant to increase the percentage of coolant to 50% NINE A baseball team has played 3/4 of its season and won 45% of its games What percent of its remaining games must it win to have a br(fak-even season? TEN The ratio of Alex's cycling speed to John's is 6:5 John leaves school3:00 p.m and Alex leaves at 3:10p.m By 3:30, Alex is only km behind John How fast is each boy going? ©Copyright 1991, The Math Learning Center ... collections, the product of the number of black in the first and the number of red in the second is the same as the product of the number of red in the first and the number of black in the second The. .. examples of the use of percentages they find in newspapers and other popular media Have the students share their findings with the class 52.6% 53.8% 54.3% 55.6% 56.2% 57. 1% 57. 3% 57. 7% The language... PO Box 3226, Salem, OR 973 02, I 800 575 -8130 or (503) 370 -8130 Fax: (503) 370 -79 61 Learn more about The Math Learning Center at: "VWw.mlc.p