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S*M#FX좁  rD2\oZqm$8 asU(!ps2ra_[v߬4"P.e.Vyy'r4 gdjüzҪjq3z-E{TOzW(x@?ȅp7뾝Y.o҉ힵ(0\eRF)8Ձa""(@6jrRA=aYӁ}f"BeG!fAZlFIrLQC6;2rggHuZǔ{238$M0ĝ.c9p߸kwG4t: ,iMi^ftݞMS89w}`pHnJoK5Դ3H :I9z?=8g$MOI)n,p #딑t)`Ht2(b]UF19D9ؤG 1ע6o;N|iH3@:\VL[4N'sWdqB7vq/:i '-ƴqs-E:nwM:F,/S:L׋8A϶={,mcKmgtqe]>E[ړY=쬅VPOUaPT3ڼ+r(a Y:ȼu[e_MW W+a_dl)˭U-䫀Eݹ&Àa_p(;"!Ⰼ#Abwad3͆C~j'[rE;+M+)`{?#T+U[%w<'T~.iFs0!Q38LFNcrڰ~0a5QvbLhKa`]'rED֍Prc4mҀy PDƵ0{Zܴ9ll֓+ו"A+ v@p8P'ۯ;@تK1BS,!B \&CbfY!KCxĐK`ˋH$,݁dr~< gH>s 9Be WhI`wwG;8ur^q}KGv;$2T1֓c P{M{a09T!iJ0qXE ifHWːPqq0CEHN<^dS}n1 ѡ"O:c: hx^m[yd?Cau04`uT$'D~= CCxh9Om:Ԍ!IP7ڡļ 180Dk@9!rEZ fTz`HaBIr``:D·e9 Hm`:bzU Յ`4`4P:C!v@'I!0⁐81 b,`4|D0?ZKKssAC%WXZZe0d(nC1 f%!:)rHv:N'Qi3wMg}κu399)LOOCL,.݋E,//X]]DZ'OYԩS8s Ν;… x".]˗/ʕ+z*666wv_7n͛un߾;wݻw߿Çx?~'Oӧx?/^˗/+~o޼۷o;>|Ǐ'; u,3 A@@  v 2008, Agnes AzzolinotocPageContentThis title & info page.storage%] Backup copies of each of the stacks of "manipulative graphics" are saved in the spreasheet. On each page, manipulatives graphics are placed in stacks in the visible display area and also to the right, off-screen, in storage. There is also one more copy on the storage page.V As noted above, colored cells are hot, formula cells, and compute the labeled items.$ To create your own pages of notes:H1st: Save this spreadsheet in a location you can find on your computer.X2nd: Insert a new worksheet in the spreadsheet -- Insert, Worksheet, or Alt + I, then W.C3rd: Name the page -- right-click the tab at the bottom, then name.?4th: Copy and paste material from other worksheets as desired. a1208.xls100s Board Computation '98, '01, '04 Agnes Azzolino 2005, Agnes Azzolino/www.mathnstuff.com/papers/langu/100s/signed.htm 4 - 3 - 4 - 3 4 - -3 Subtract. - 4 - -3subtract4Subtraction Using "Take Away" and "Add the Opposite"0www.mathnstuff.com/papers/langu/100s/big100s.gifsolveSolve equationsSubtract by "Take Away."Subtract by "Add the Opposite."#To Subtract by ADDING THE OPPOSITE: 1st: Represent the first number.12nd: Represent the opposite of the second number.Q3rd: Simplify, if possible, by pairing a positive with a negative to make a zero.#4th: What's left is the difference.To Subtract using "TAKE AWAY.":2nd: Add enough zeros so the second number may be removed.3rd: Remove the second number. MUPLICATION1st:2nd:3rd:4th:Multiply a top tile by a side tile filling in the corresponding region of the display area with the required tile. These tiles represent the product and the area of the region.5th:,The product is produced in the display area.*Represent the sum of a number and 3. Then: double it triple itmultiply it by 4multiply it by xmultiply it by x - 26Use paper to create a storage area and a display area.URepresent the other factor (in descending order) vertically in the left storage area.NRepresent the first number in descending order in the horizontal storage area.multMultiplydivideDivideDivide 4x-12 by 4.Divide x2 + 4x + 3 by x + 3. Divide.DIVISION6th:7th:$Read the quotient and the remainder.?Use paper to separate the storage region from the display area.`Represent the DIVISOR (the divider) VERTICALLY in storage on the left edge of the display area.zRepresent the DIVIDEND (stuff to be divided) in the DISPLAY AREA in descending order beginning with the upper left corner.IArrange, if possible, the dividend in IDENTICAL rows in the display area.jRepresent the appropriate QUOTIENT (answer) HORIZONTALLY in the storage area as dictated by the dividend..ADD ZEROS as needed to fill the required area.Hint?Factor.Factor x - 4 Factor 2x-x-6To Factor An Expression: Represent the expression in the display area in descending order Awith leading terms in the upper left and constants on the right. <IF POSSIBLE, arrange the tiles in IDENTICAL horizontal rows ;(forming a rectangular display area) then complete step 5. .IF IT IS NOT POSSIBLE to form identical rows, Aarrange constants in the lower right, seeking a binomial factor. "If looking for a binomial factor, think FOIL.5Arrange the tiles in a rectangular array if possible.DIF IT IS NOT POSSILBE to form binomial factors with existing tiles, 1try adding additional zeros to the display area. SIF IT IS NOT POSSILBE to form a rectangular area even after adding pairs of zeros, 1the expression can not be factored. Skip step 6. 1Represent the dimensions of the rectangular area -on the left in the vertical storage area and $on the top horizontal storage area. 9These are factors of the expression in the display area. 4Record each expressions in the border storage areas Qthen factor each expression (mentally or manipulatively), beginning with step 1. 8th:+Review EACH factor in the final expression.$Check to see if it can be factored. CVerify that the product of the factors is the original expression. 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