Analyze patterns and relationships. 3. Generate two numerical patterns using AC

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Amie Oliver
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1 envision ah 2.0 5h Grade ah Curriculum Quarer 1 Quarer 2 Quarer 3 Quarer 4 andards: =ajor =upporing =Addiional Firs 30 Day andards: Operaions and Algebraic Thinking 5.OA Wrie and inerpre numerical expressions. 1. Use parenheses, brackes, or braces in numerical expressions, and evaluae expressions wih hese symbols. 2. Wrie simple expressions ha record calculaions wih numbers, and inerpre numerical expressions wihou evaluaing hem. For example, express he calculaion add 8 and 7, hen muliply by 2 as 2 (8 + 7). Recognize ha 3 ( ) is hree imes as large as , wihou having o calculae he indicaed sum or produc. Analyze paerns and relaionships. 3. Generae wo numerical paerns using

2 envision ah 2.0 wo given rules. Idenify apparen relaionships beween corresponding erms. Form ordered pairs consising of corresponding erms from he wo paerns, and graph he ordered pairs on a coordinae plane. For example, given he rule Add 3 and he saring number 0, and given he rule Add 6 and he saring number 0, generae erms in he resuling sequences, and observe ha he erms in one sequence are wice he corresponding erms in he oher sequence. Explain informally why his is so. andards: Number and Operaions in Base Ten 5.NBT Undersand he place value sysem. 1. Recognize ha in a muli-digi number, a digi in one place represens 10 imes as much as i represens in he place o is righ and 1/10 of wha i represens in he place o is lef. 2. Explain paerns in he number of zeros of he produc when muliplying a number by powers of 10, and explain paerns in

3 envision ah 2.0 he placemen of he decimal poin when a decimal is muliplied of divided by a power of 10. Use whole-number exponens o denoe powers of Read, wrie, and compare decimals o housandhs: a. Read and wrie decimals o housandhs using base-en numerals, number names, and expanded form, e.g., = (1/10) + 9 (1/100) + 2 (1/1000). b. Compare wo decimals o housandhs based on meanings of he digis in each place, using >, =, and < symbols o record he resuls of comparisons. 4. Use place value undersanding o round decimals o any place. Perform operaions wih muli-digi whole numbers and wih decimals o hundredhs. 5. Fluenly muliply muli-digi whole numbers using he sandard algorihm. 6. Find whole-number quoiens of whole numbers wih up o four-digi dividends and wo-digi divisors, using sraegies based on place value, he properies of

4 envision ah 2.0 operaions, and/or he relaionship beween muliplicaion and division. Illusrae and explain he calculaion by using equaions, recangular arrays, and/or area models. 7. Add, subrac, muliply, and divide decimals o hundredhs, using concree models or drawings and sraegies based on place value, properies of operaions, and/or he relaionship beween addiion and subracion; relae he sraegy o a wrien mehod and explain he reasoning used. andards: Number and Operaions-Fracions 5.NF Use equivalen fracions as a sraegy o add and subrac fracions. 1. Add and subrac fracions wih unlike denominaors (including mixed numbers) by replacing given fracions wih equivalen fracions in such a way as o produce an equivalen sum or difference of fracions wih like denominaors. For example, 2/3 + 5/4 = 8/ /12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

5 envision ah olve word problems involving addiion and subracion of fracions referring o he same whole, including cases of unlike denominaors, e.g., by using visual fracion models or equaions o represen he problem. Use benchmark fracions and number sense of fracions o esimae menally and assess he reasonableness of answers. For example, recognize an incorrec resul 2/5 + 1/2 = 3/7, by observing ha 3/7 < 1/2. Apply and exend previous undersandings of muliplicaion and division o muliply and divide fracions. 3. Inerpre a fracion as division of he numeraor by he denominaor (a/b = a b). olve word problems involving division of whole numbers leading o answers in he form of fracions or mixed numbers, e.g., by using visual fracion models or equaions o represen he problem. For example, inerpre 3/4 as he resul of dividing 3 by 4, noing ha 3/4 muliplied by 4 equals 3, and ha when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people wan o share a 50-pound sack of rice equally by weigh, how many pounds of rice should each person ge? Beween wha wo whole numbers does your

6 envision ah 2.0 answer lie? 4. Apply and exend previous undersandings of muliplicaion o muliply a fracion or whole number by a fracion. a. Inerpre he produc (a/b) q as a pars of a pariion of q ino b equal pars; equivalenly, as he resul of a sequence of operaions a q b. For example, use a visual fracion model o show (2/3) 4 = 8/3, and creae a sory conex for his equaion. Do he same wih (2/3) (4/5) = 8/15. (In general, (a/b) (c/d) = ac/bd.) b. Find he area of a recangle wih fracional side lenghs by iling i wih uni squares of he appropriae uni fracion side lenghs, and show ha he area is he same as would be found by muliplying he side lenghs. uliply fracional side lenghs o find areas of recangles, and represen fracion producs as recangular areas. 5. Inerpre muliplicaion as scaling (resizing), by: a. Comparing he size of a produc o he size of one facor on he basis of he size of he oher facor, wihou performing he indicaed muliplicaion.

7 envision ah 2.0 b. Explaining why muliplying a given number by a fracion greaer han 1 resuls in a produc greaer han he given number (recognizing muliplicaion by whole numbers greaer han 1 as a familiar case); explaining why muliplying a given number by a fracion less han 1 resuls in a produc smaller han he given number; and relaing he principle of fracion equivalence a/b = (n a)/(n b) o he effec of muliplying a/b by olve real world problems involving muliplicaion of fracions and mixed numbers, e.g., by using visual fracion models or equaions o represen he problem. 7. Apply and exend previous undersandings of division o divide uni fracions by whole numbers and whole numbers by uni fracions. a. Inerpre division of a uni fracion by a non-zero whole number, and compue such quoiens. For example, creae a sory conex for (1/3) 4, and use a visual fracion model o show he quoien. Use he relaionship beween muliplicaion and division o explain ha (1/3) 4 = 1/12 because (1/12) 4 = 1/3.

8 envision ah 2.0 b. Inerpre division of a whole number by a uni fracion, and compue such quoiens. For example, creae a sory conex for 4 (1/5), and use a visual fracion model o show he quoien. Use he relaionship beween muliplicaion and division o explain ha 4 (1/5) = 20 because 20 (1/5) = 4. c. olve real world problems involving division of uni fracions by non-zero whole numbers and division of whole numbers by uni fracions, e.g., by using visual fracion models and equaions o represen he problem. For example, how much chocolae will each person ge if 3 people share 1/2 lb of chocolae equally? How many 1/3-cup servings are in 2 cups of raisins? andards: easuremen and Daa 5.D Conver like measuremen unis wihin a given measuremen sysem. 1 Conver among differen-sized sandard measuremen unis wihin a given measuremen sysem (e.g., conver 5 cm o 0.05 m), and use hese conversions in

9 envision ah 2.0 solving muli-sep, real world problems. Represen and inerpre daa. 2. ake a line plo o display a daa se of measuremens in fracions of a uni (1/2, 1/4, 1/8). Use operaions on fracions for his grade o solve problems involving informaion presened in line plos. For example, given differen measuremens of liquid in idenical beakers, find he amoun of liquid each beaker would conain if he oal amoun in all he beakers were redisribued equally. Geomeric measuremen: undersand conceps of volume and relae volume o muliplicaion and o addiion. 3. Recognize volume as an aribue of solid figures and undersand conceps of volume measuremen. a. A cube wih side lengh 1 uni, called a uni cube, is said o have one cubic uni of volume, and can be used o measure volume. b. A solid figure which can be packed wihou gaps or overlaps using n uni cubes is said o have a volume of n cubic unis.

10 envision ah easure volumes by couning uni cubes, using cubic cm, cubic in, cubic f, and improvised unis. 5. Relae volume o he operaions of muliplicaion and addiion and solve real world and mahemaical problems involving volume. a. Find he volume of a righ recangular prism wih whole-number side lenghs by packing i wih uni cubes, and show ha he volume is he same as would be found by muliplying he edge lenghs, equivalenly by muliplying he heigh by he area of he base. Represen hreefold whole-number producs as volumes, e.g., o represen he associaive propery of muliplicaion. b. Apply he formulas V = l w h and V = b h for recangular prisms o find volumes of righ recangular prisms wih whole number edge lenghs in he conex of solving real world and mahemaical problems. c. Recognize volume as addiive. Find volumes of solid figures composed of wo non overlapping righ recangular prisms by adding he volumes of he

11 envision ah 2.0 non-overlapping pars, applying his echnique o solve real world problems. andards: Geomery 5.G Graph poins on he coordinae plane o solve real-world and mahemaical problems. 1 Use a pair of perpendicular number lines, called axes, o define a coordinae sysem, wih he inersecion of he lines (he origin) arranged o coincide wih he 0 on each line and a given poin in he plane locaed by using an ordered pair of numbers, called is coordinaes. Undersand ha he firs number indicaes how far o ravel from he origin in he direcion of one axis, and he second number indicaes how far o ravel in he direcion of he second axis, wih he convenion ha he names of he wo axes and he coordinaes correspond (e.g., x-axis and x-coordinae, y-axis and y-coordinae). 2 Represen real world and mahemaical problems by graphing poins in he firs

12 envision ah 2.0 quadran of he coordinae plane, and inerpre coordinae values of poins in he conex of he siuaion. Classify wo-dimensional figures ino caegories based on heir properies. 3. Recognize a line of symmery for a wo-dimensional figure as a line across he figure such ha he figure can be folded along he line ino maching pars. Idenify line-symmeric figures and draw lines of symmery. 4 Classify wo-dimensional figures in a hierarchy based on properies. andards: andards for ahemaical Pracice P ah Pracices and Problem olving: (Las lesson each uni.) Bolded =Prioriy 1. ake sense of problems and persevere

13 envision ah 2.0 in solving hem. 2. Reason absracly and quaniaively. 3. Consruc viable argumens and criique he reasoning of ohers. 4. odel wih mahemaics. 5. Use appropriae ools sraegically. 6. Aend o precision. 7. Look for and make use of srucure. 8. Look for and express regulariy in repeaed reasoning.

Decimal moved after first digit = 4.6 x Decimal moves five places left SCIENTIFIC > POSITIONAL. a) g) 5.31 x b) 0.

Decimal moved after first digit = 4.6 x Decimal moves five places left SCIENTIFIC > POSITIONAL. a) g) 5.31 x b) 0. PHYSICS 20 UNIT 1 SCIENCE MATH WORKSHEET NAME: A. Sandard Noaion Very large and very small numbers are easily wrien using scienific (or sandard) noaion, raher han decimal (or posiional) noaion. Sandard