Mr. Miller's Algebra Class Page

This page is for the use of the students and parents of students who are in Mr. Miller's Algebra classes at Dr. Martin Luther King Middle School in San Francisco. The site includes:
 
 Algebra Class Information Slide Show
 (Note: It may take a few minutes for each slide to "load" as you go through them)
   Unit 1 Assignment List                Unit 2 Assignment List                Unit 3 Assignment List
 
  Unit 4 Assignment List               Unit 5 Assignment List                 Unit 6 Assignment List
 
  Unit 7 Assignment List               Unit 8 Assignment List                 Unit 9 Assignment List
 
   Unit 10 Assignment List                    Unit 11 Assignment List               Unit 12 Assignment List
 
         E-Mail Mr. Miller              Homework Help    Previous Test Answers & Solutions
 
 About the CPM Algebra Course                 Other Good Algebra Web Sites
 
 
 
    Mr. Miller, Rm 212

 
 
 
 
 
 
 

To send an email to Mr. Miller:  millerct@earthlink.net
To phone Mr. Miller at school: 415-330-1500 (ask for Rm 212)
 

 
 
 
 
 
 
 

FastCounter by bCentral

  (Back To Top Of Page)



 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 
 
Unit 1 Assignment List
DATE                                CLASSWORK                                                 HOMEWORK 
8/24   Introduction by Chris Miller   Shop for scientific calculator
8/25     GS 3, 4, 9    GS 10, 16, 17
8/26     GS 13, 20, 21    GS 15, 23, 26
8/27     SQ  1, 2, 4    (None)
8/30    (Give out textbooks)  SQ 14   SQ 5 - 7
8/31     SQ 8 - 11   SQ 13, 15 - 17
9/1       SQ 20 - 23   SQ 24 - 26
9/2       SQ 28, 29   (Discuss SQ 26)   SQ 31, 33, 34
9/3       SQ 30, 32, 35    (None)
9/7  Review Unit1 Pgs.7 & 15,  SQ 36 - 38   SQ 40, 41, 44, 50, 52
9/8       SQ 43 - 45   SQ 46, 47, 53, 55
9/9       SQ 48, 49, 57   SQ 62 - 64
9/10     SQ 58, 59, PZL-8   (None)
9/15    UNIT 1 TEST  (worth 40 out of 100 pts.)
 
  (Back To Top Of Page)
 
 
 
 
 
Unit 2 Assignment List
DATE                            CLASSWORK                                                                HOMEWORK 
9/13    SQ 74, 75 a & b only, 76, 77    SQ  78 - 80 
9/14    SQ 65 - 69   SQ  70, 72, 73, 81
9/15    SQ 82 - 84, 87    SQ  86, 88, 89 
9/16    (Unit 1 Test)    SQ 90 part b only
9/17    SQ 85   (none)
9/20    Finish SQ 85  & Present results to class by group    Skill 30 Ditto #1 - 17 
9/21    KF 1 , 2, 5 a-c only    KF  6, 7, 9
9/22    KF 8, 10, 11, 12    KF 13, 16, 17
9/23    KF 14 (needs group ditto), 19, 20    Skill 32 Ditto #1 - 17
9/24    KF 23, 24, 26, 27   (none)
9/27    KF  29, 31, 32, 41    KF 49, 51, 52
9/28    (catch-up day)   (none)
9/29    KF  35 - 37    (none
9/30    KF  42 - 44, 50   KF 60, 62, 64
 
  (Back To Top Of Page)
 
 
 
 
Unit 3 Assignment List
DATE              CLASSWORK                                                                  HOMEWORK
  10/1   KF  53 - 58   (none)
  10/4  KF  63, 66, 67   KF 68 - 71
  10/5  KF  72 a - d, 73, 74, 77   KF 75, 76, 80, 81
  10/6  (Unit 2 Test)   KF  85, 88, 89, 90
  10/7  KF  82, 83, 87, 91   KF 92, 97, 101, 102
  10/8  KF  94, 95, 100, 104   (none)
  10/12  KF 106   KF 109, 110, 116, 122
  10/13  (no class-- field trip)    (none)
  10/14  KF 111, 112, 115, 120   KF 118, 123, 125
  10/15  BC 1   (none)
  10/18  BC 3 a & b only, 4, 5, 6    BC  13, 14, 17, 18
  10/19  BC  8, 9, 10, 12    BC 15, 16, 23
  10/20  BC 19 - 22   BC 24, 26, 27
  10/21  BC  25, 28, 29   BC 33, 34 a & b only, 35

 (Back To Top Of Page)

 

Unit 4 Assignment List

DATE                          CLASSWORK                                                          HOMEWORK
  10/22   Skill 60 Ditto  (all)   (none)
  10/25   BC 31, 36, 38   Skill 61 Ditto
  10/26   BC 37, 39   BC 40, 41
  10/27  Skill Ditto 64 #1 - 20   Skill Ditto  62 # 1 - 32  E.C. #33 - 38
  10/28  BC 44 - 47   BC 49, 53, 54 a only
 10/29  Unit 3 Test  (none)
 11/1  BC 51, 52, 55, 56  BC 58, 59
 11/2  BC 61 - 65  BC 73 - 75
 11/3  BC 57, 66, 67  BC 76 - 78
 11/4  BC 68 - 71  BC 82, 86, 88
 11/5  BC 72  (none)
 11/8  CP 1 - 5  CP 7 - 11 
 11/9  CP 12,13,15 17  CP 22 - 25

 (Back To Top Of Page)

  Unit 5 Assignment List

DATE                      CLASSWORK                                                           HOMEWORK 
11/10   CP 16, 20, 21 CP 30, 31, 33, 35
11/12   CP 27, 28, 32  (none)
11/15   CP 37 - 39 CP 41 - 43, 47
11/16   (Unit 4 Test) CP 44 - 46, 47
11/17   CP 48 - 52 CP 56 - 59, 62
11/18   CP 60, 61, 63, 65 CP 66, 67, 70, 73, 76
11/19   CP 69, 71, 72, 74  (none, except CP 76)
11/22  CP 77 - 83 CP 85 - 88
11/23  CP 94, 95, 97 CP 89 - 91, 93, 96
11/24  CP 98-100, 104 (none)
11/29  CP 92 CP 101, 103, 106, 108
11/30 CP 110, 112 - 114 CP 117, 118, 121, 122
12/1  EF 1-6, 10 - 14 EF 15 - 17
12/2  EF 7 - 9, 18 EF 24 - 26, 29
E. C.  : The 10-day PhoneLog  Ditto

 (Back To Top Of Page)

Unit 6 Assignment List

DATE                   CLASSWORK                                                                  HOMEWORK
12/3  EF 19 - 22 (none)
12/6  EF 30 EF 34, 37 - 40
12/7  EF 32, 35, 36 EF 42, 43, 49
12/8  Unit 5 TestEF EF 50 - 53
12/9  EF 44 - 46 EF 62 - 65
12/10  EF 47, 48, 55, 56 (none)
12/13  EF 57 - 59 EF 66 a & b, 67, 69, 72
12/14  EF 60. 61, 68, 70, 71 EF 73 - 76
12/15  EF 78, 80, 81 EF 77, 83, 84, 86
12/16  EF 82, 85, 87, 91 EF 88, 89, 90, 93
1/3/00  EF 94, 96 - 100 EF 95, 102 - 104
1/4/00  EF 108 EF 106, 107, 111
1/5/00  EF 110, 112, 117, 126 EF 120, 121, 124, 125
1/6/00  WR 1 - 3 WR 5, 6, 8

 (Back To Top Of Page)

Unit 7 Assignment List

DATE                         CLASSWORK                                                        HOMEWORK
1/7/00  WR 11 & 13 (none)
1/10/00  WR 12, 20, 21 WR 14 - 16
1/11/00  (Finish 21) WR  19, 22 WR 18, 23, 25
1/12/00  WR 26, 28, 33, 34, 35 WR 37, 40. 47, 48
1/13/00  Unit 6 Test WR 49, 50, 56, 57
1/14/00  WR 29, 30, 31, 33  (none)
1/19/00  WR 39, 41, 42, 43 WR 44, 45, 53
1/20/00  (field trip- no class) (none)
1/21/00  WR  51 & 52 (none)
1/24/00  WR 59 & 62 WR 54, 65, 68
1/25/00  WR 66, 69, 70 WR 58, 63, 64, 67
1/26/00  WR 71 - 73 WR 74, 77
1/27/00  WR 78 - 81 WR 91, 93, 97, 101
1/28/00  WR 82 - 84 (none)
1/31/00  WR 95 WR  99. 103

 (Back To Top Of Page)
 

Unit 8 Assignment List

DATE                  CLASSWORK                                                               HOMEWORK
2/1  BR 1 & 2 BR  8 - 10
2/2  BR 3 - 5, 11 BR  6 & 7
2/3  Unit 7 Test BR  18, 19, 20 (skip d)
2/4  BR  12 - 14 (none)
2/7  BR 16. 17, 22 BR  27, 30 
2/8  BR 23 - 25 BR 29, 31
2/9  BR 26, 36, 39 BR 32, 33, 35
2/10  BR 38, 41, 48 BR 43, 44, 50
2/11  BR 40, 42, 47, 45 (none)
2/14  BR 49, 51, 53, 54 BR 55, 57, 58
2/15  BR 56, 59, 60, 62 BR 63, 67, 68
2/16  BR 61, 64, 70, 71 BR 72, 74, 77
2/17  BR 73, 78, 75, 79 BR 76, 80, 82
2/18  BR 81, 83 - 85 (none)

 (Back To Top Of Page)
 

Unit 9 Assignment List

DATE                 CLASSWORK                                                                 HOMEWORK
2/22   BR 86, 88, 94 BR 89, 95, 96
2/23  BR 90 & 91 BR 100, 101, 102
2/24  Unit 8 Test BR  99, 103
2/25  Finish BR 91, AP 5 & 7 (None)
2/28  AP 1 - 4, 10 AP 9. 13, 14
2/29  AP 11, 12, 17, 18 AP 15, 16, 22
3/1  AP 19 - 21 AP 25, 26, 28
3/2  AP 30 - 33 AP 35 - 37
3/3  Laws of Exponents Practuce Ditto  (none)
3/6  AP 34, 39 - 41  AP 45, 48, 49
3/7 Finish AP 41, then do AP 42 - 44 AP 46, 47 
3/8 AP 50 a & b, AB 51 a - d AP 52 - 54
3/9 AP 55, 56, 61, 64 AP 68, 69, 76
3/10 AP 57 - 60, 63 (none)

 (Back To Top Of Page)
 
 

Unit 10 Assignment List

DATE          CLASSWORK                                                                       HOMEWORK
3/13  AP 66, 67, 70 AP 73, 74, 77
3/14  AP 71 & 72 AP 80, 83, 84
3/15  AP 78 & 79 AP 81, 82, 88
3/16  AP 86, 87, 89 AP 90, 91, 92
3/17  Unit 9 Test  (none)
3/20  BP 2 - 4 BP 5, 9, 10
3/21  BP 6 - 8  BP 17 - 19
3/22  Test Ready -- Lessons 1 & 2 Test Ready - Lessons 3 & 4
3/23  Test Ready -- Lessons 5 & 6 Test Ready - Lessons 7 & 8
3/24  Test Ready -- Lessons 9 & 10 (none)
3/27  Boys vrs. Girls Contest/PracticeTest BP 16, 20, 21
3/28  BP 13 & 15 BP 23 & 25
3/29 or 3/30  BP 24, 26, 27 BP 30, 31, 32
3/31  BP 34, 35, 38, 39 (none)

 (Back To Top Of Page)

Unit 11 Assignment List

DATE              CLASSWORK                                                                   HOMEWORK
4/3  BP  41 - 43, 45, 46 BP 47, 51
4/4  BP 49, 50 BP 52, 54, 56
4/5 or 4/6  BP 53, 55, 57, 58 BP 63, 64, 66
4/7  Unit 10 Test (none)
4/10  BP 59, 61, 62, 67 BP 75, 78, 79
4/11  BP  69 - 73 BP 80, 81 
4/12  Review Ditto Pgs. 1 & 2  Review Ditto Pgs. 3 & 4
 4/13  BP 44, 60, 65, 76 BP 88, 89
 4/ 14  Video: Algebra Review (none)
 4/24  BP 83, 84, 86 BP 85, 93, 94
 4/25  BP 90, 91, 96, 97 BP 101 - 103
 4/26  BP 95, 100, 107 BP 98, 104, 105
 4/27  BP 99, 108 - 110 BP 113, 114, 116
4/ 28  BP 111, 112, 115, 117 (none)

 (Back To Top Of Page)

 

Unit 12 Assignment List

 DATE                        CLASSWORK                                                   HOMEWORK 
 5/1  YS 0 - 3, 6, 7 YS 9 - 12
 5/2  YS 8, 13, 14, 16 YS 5, 19, 20
 5/3  YS 17, 21, 23, 24, 25 YS 27 - 29
 5/4  YS 33, 34, 41, 42, 47 YS 30 - 32
 5/5  Unit 11 Test (none)
 5/8  YS 36, 37, 48, 49, 57 YS 39, 51, 56
 5/9  YS 53 - 55, 57 YS 59, 62, 70
 5/10  (Girl's Summit/ Boy's Field Trip) (none)
 5/11  YS 60, 61, 63, 69 YS 78, 81, 84
 5/12  YS 76, 77, 86, 87 (none)
 5/15  YS 88 a - c, 89, 92, 93 YS 91, 94, 97, 102
 5/16  YS 95 a - c YS 99, 105, 108
 5/17  Review for Semester Exam (none)
 5/22  YS 104 (none)

 

(Back To Top Of Page)

 
 
 
 
 
 
 
 
 

HOMEWORK HELP


This section features some hints for recent homework assignments.
1st HINT                                                 2nd HINT 
Please note: Some of the "BP" hints are still here, further down the chart!
YS 9   For a) look at BP 80 hints below.  For b) look at BP 98 hints.
YS 10  If the youngest daughter gets x money, then the oldest gets 2x and the middle gets x + 35.  The equation then add these to equal 775-- x + (x + 35) = 2x = 775.  Solve it and then use the answer to find what each girl gets.
YS 11   For a), b), & d) you can use the 4-box or FOIL methods. Part c) uses the distributive property. Part e) uses 4 boxes or FOIL but ends up with "xy"s in the answer.
YS 12  Use diamonds to solve a0 thru c) and see YS-1 for help with d).
YS 5  Use a diamond problem  & 4-boes to help factor these like in class.  The top of the diamond number is 270 (15 times 18!) and the bottom is -37.  The side numbers are then both negative: -10 and -27.  So the 1st box has 15x2 and the last box has +18.  Can you put -27x and -10x into the other two boxes so that workable factors can be found?  One of the factors is (5x - 9).  For b) the top of the diamond is -630 and the bottom is +17. The side numbers are -18 and + 35.  Finish the rest on your own.
YS 19  Instead of the generic triangle to find slope, you could find the "change in the y numbers" over the "change in the x numbers". Then draw the "direction of change" arrows to see if the slope is positive or negative.  To find the equation use the slope you found in part a) and then substitute x & y numbers from either of the 2 points (given at the start of the problem) to find "b"-- the y-intercept.  Theen write out your equation in the y+ mx + b form.  For part c) an equation would be the same as in b) except yuou change the "b" number to anything else. For d) the same equation again except change the slope number this time.
YS 20  For a) the area of a triangle = 1/2 of the base times the height or 1/2(x)(2x). That makes 1/2 2x2 =Area. To find x use the Pythagorean Theorem to write x2 + (2x)2 = 122 . That makes x2 + 4x2 = 144. Solve that to find x.  Then use that answer in part a)'s equation to find the actual area.
YS 27  Remember- when you multiply exponents with identical "bases" you add the exponents and kepp the same base. So x2 times x5 = x7. It works much the same for division with exponents except that you subtract the exponents to get your answer.
YS 28  But when you have an "exponent of another exponent", then you keep the bas and multiply the exponents to get your answer. So (x4)2 = x8.
YS 29  This one has some that are the same as YS 27 and some that are the same as YS 28.
YS 30  Use your calculator to find these answers just as they tell you-- there's no other cjoice on this one. Then answer b) & c) after you get your answers.
YS 31  Look back at YS-1 for help with these-- remember the top part of the diamond is created by muliplying two numbers.  Use the diamond and the 4-boxes to factor these.
YS 32  Parts a) & b) factor "nomally" into "parenthesis" times "parenthesis binomials. Part c) only factors into "9x" times a binomial in parenthesis. Parts d) & e) are perfect square binomials that factor using the 4 boxes BUT two of the boxes "cancel" out to 0x. (Remember for example that part d) could have been written as x2 + 0x - 25!)  To do part f) look back again at YS-1 for help.
YS 39  Use the "laws of Exponents" chart at the bottom of the sam page in the book to help you with this one.
YS 51  The first three are each "the same thing divided by the same thing"-- you know then that they all equal one. For think of it as two steps -- first find the 12 divided by 3, then what's left is x over x which works like part a) again.  To do e) just try it out out-- is it true or not?  And that should tell you the answer for f).
YS 56  The common factor for a) is either 4 or 4x-- use 4x if you can.  Parts b), c) and d) all need to follow the same long process shown in YS-1.
YS 59  Part a) uses a simple diamond to factor-- the top of it is -16 and the bottom is +6.  The find what x should be for each parenthesis to equal 0. Part b) needs to be factored as in YS-1, then again find what x need to be for each parenthesis to equal 0. Part c) factors into z(5x - 13)-- so z itself could either be 0 or the answer to 5z - 13 = 0.
YS 62  If x is the width then 3x is the height.  When mutliplied they equal the area of 588.  Write an equation an solve it.
YS 70  For most of these you can refer back to the laws of exponents listed in YS 40.  Remember for b) that the -2 in the first parenthesis is not squared. For part d) remember to find -8/-4 first.  For part f) remember that the 2 is also "to the power of 3".
YS 78  Use a diamond to first factor a)-- the top is +90, the bottom is +19. Then find what x is for each parenthesis to equal 0.  Part b) is already factored for you -- just find what x should be for each parenthesis to equal 0. Part c) needs to be factored first following the p[rocedure in YS 1, then find x such that each parenthesis equals 0.
YS 81  Refer to YS 40 for the laws of exponents if needed. Remember the 3 in part b) is also "to the power of 3" which makes 27.  Note that the first part of c), (5x)2 becomes 25x2! Remember that the 6 in part e) is NOT " to the power of 4"-- only the x is.
YS 84 You can cancel things that are "alike" such as the (x + 4) in part a).  For parts b) and c) you'll need to first factor what's on top and what's on bottom and then cancel the factors that are alike.
YS 91  The diagonal of a square is really the hypotenuse of a right triangle--two sides of the square are the legs. Therefor the legs, 15 inches, squared and then added together equal the diagonal squared.
YS 94  This should be pretty easy by now-- remember to use the distributive property first in b) and that d) needs a calculator.
YS 97  If one leg is x, then the other is x + 2.  The hypotenuse is 17 so the equation is x2 + (x + 2)2 = 172.  Remember that (x + 2)2  itself = x2 + 4x + 4.  So altogether you have 2x2 + 4x + 4 = 289.  Subtract the 289 from each side to get a quadratic equation equal to 0.  Factor it (or use the new quadratic formula) to get the 2 answers for x.
YS 102  Cancel what can be cancelled.  For b) remember to simplify what's in the parenthesis first, then use the outside exponent.  For c) you'll need to factor then both first.
YS 99 You know the equation for a line-- y = mx + b.  We the slope (2/3) is the M.  Find the b by using the point (-6, -1) as your x & y numbers in the equation. Solve -1 = 2/3(-6) + b.  For part b) solve the equation again but using the x & y numbers from the point (60, 400).
YS 105  As it says, if you can factor it to help find the two answers for x, then go right ahead.  But if you can.t thyen do what we've done in class for the last few days-- use the "quadratic formula" See YS 86. Use you calculator for the square root part.
YS 108  Remember, when you multiply exponents, you ADD the exponent numbers. When you have an exponent OF ANOTHER exponent you either multiply the numbers or write the thing out as many times as it's "to the power of" and then multply , remembering to ADD the exponents. For the ones with division-- look for things to "cancel", then divide by SUBTRACTING the exponents.
BP 98  Use the hypotenuse formula here even though we know the hypotenuse is 18. We still need to fin the leg that's length 3x.and the other leg that's x.  The formula would tell us that x2 + (3x)2 = 182.  Altogether that's 10x2 = 324. Divide both sides by 10 and then get the square root of the answer to find x.  Triple it to find 3x.
BP 104  You're given the slope already-- 1/2-- and the equation y = mx + b.  Substitute the x and y numbers from the point (2, 3) into the equation. It now reads 3 = 1/2(2) + b. Solve this for b, and then rewite the original equation including the new answer for b.  Part b) works much the same way.
BP 105  For part a) first add 140 to both sides so the equation reads like this: x2  = 144.  Solve by finding the square root.  Part b) has 3 answers for x.  The first one is when x = 0.  The second is found when (x + 1) = 0 and the third when (x + 2) = 0. For part c) use the fraction buster 6x. Multiply all threee parts of the equation by 6x,  then simplify and find lowest terms for each part and then solve the equation that's left. Remember that part d) can't be solved all the way-- The y will be inyour answer. You want to really adjust the equation until it reads x = some answer with y in it.
BP 113  To solve a) and d) you need fraction busters-- for a) multiply all three terms by 6. For b) you can add 8 to each side, and then multiply both sides bu x. For c) you need to factor and set each parenthesis = to 0, so you'll get two answers. For e) just do what you did for part d) in BP 105.
BP 114  For a) note that both equations equal y. So theparts on the right side equal each other. But is 9 - x = 9 + x, then x can only be one possible answer. You figure it out!  Part b) tells you that x = 5 - y so you can substitute that "5 - y" for x in the first equation. Then solve it for y.  Then use that answer for y in either eqaution to solve for x.
BP 116  use diamond problems to help factor these.  For a) the "side" numbers in the diamon must multiply to make 45 and add up to make 46. Remember you only need to factor these, not solve them for x.
 
AP 82  If the dimensions are to be 3 times as long it means you are tripling x + 2.  That makes the new length 3x + 6.  You also triple x - 1. So the new width is 3x - 3.  2 of these length & 2 of these widths added together make the perimeter.  Use the 4-box method to multiply the new length times the new width to get the new area.
AP 8U8 Remember that a) show a DIFFERENCE of 2 squares-- so it factors into the orm (x + ?)(x - ?) where you need to find the ? that multiplies to make 16. For b) & c) you can use a diamond to help you factor them.  For d) you'll first have to subtract 24 from each side, then use a diamond to factor it.
AP 90  They want you to estimate these answers with out using your calculator-- it's not so hard.  For a) you know your 11 times table, so you could even write the exact answer for 11 times 11.  And for b) you can see it's a square so the area is 8 times 8. For c) you might round the 1 .2 off to 1 and say it's area is 1 times 1 but I'd raise the answer to 1.5 just because you know the real answer has to be a little higher than 1. For the rest, you're estimating ? times ? will give you the area-- for e) you might think 2 times 2 is 4 so a little more, maybe 2.2 times 2.2, would give you 5.
AP 91  Use diamonds to help you factor these.  But first for b) - d) you'll first have to factor out the greatest common factor to go on the outside of the parenthsis. For c) the GCF is 5x, which leaves x-squared - x - 6 on the inside of the parenthesis and that itself can befactored into (x +1)(x - ?)-- you find the other number.
AP 92  You want to find the x & y numbers where the graphs of these two equations would cross. By using substitution for y, you can rewrite the first equation to say 3x + 5 = 2(6 -x).  Solve that for x.  Then put that answer for x back into one of the original equations to find y. For b) notice that both equations have a one side being equal to y + 6.  Therefore these two parts are also equal to each other-- 2(x + 5) = 12x.  then proceed like in part a).

 (Back To Top Of Page)



 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Previous Test Answers and Solutions


The next Algebra test in Mr. Miller's class is on Thursday May 4, 2000.
The tests can be scanned in here, but they take quite a while to load-- slowing the whole process of opening the site way too much-- so I'm working on a separate page for the test answers.

 (Back To Top Of Page)



























About  the CPM Algebra Course

             EXCERPTS FROM "THE PARENTS GUIDE TO (CPM) MATH 1

The College Preparatory Mathematics...program began in 1989...

Each course was field tested for 3 years with at least 10,000 students, (then) revised andpolished...(by) 1997 there (were) about 2,000 teachers using a...CPM curriculum in 700schools with at least 400,00 students. (Note from Mr. Miller: By now these figures are evenhigher.)

The universal use of calculators and computers is changing what is important
in mathematics itself as well as what students need to know to be prepared for future
college careers and jobs.

We have designed the CPM materials both to reflect modern reality about what math is
important and to implement current knowledge about how students learn.

This course is built around problems-- lots of problems-- ranging from routine review, toproblems designed to teach concepts, to short writing assignments which ask the student toexplain.

We have designed the course so that the...time in class can be spent doing the more
challenging problems...while the problems which are designed to reinforce
previously learned skills may be done for homework.

Certain skills need to be practiced frequently so that they are retained... for many major ideas monthsmay pass before concepts finally become internalized.

Students need to see important ideas in many contexts and be asked to explain the connectionsmany times before these ideas become second nature.

This course...emphasizes several big ideas...
    --  ratios
    --  writing equations from words or diagrams
    --  solving equations
    --  symbol manipulation
    --  understanding the relationships among equations, graphs, and solutions to
         equations

This course is designed to focus on understanding these key ideas and using them as
natural places to practice the more traditional algebraic skills.

Once an idea is introduced, it is used continually throughout the year.

Most of the algebraic skills will be developed by starting with real situations or questionsarising in science or other areas of mathematics...

Much of the time in class will be spent working in study teams (groups) rather than listening tolectures or working alone. Students should be encouraged to work together on homework.

Calculators will be used throughout the course and every student should have a scientificcalculator for use at home and at school.

We expect the teacher...in most situations to ask questions, rather than tell answers.

With CPM students are responsible for both thinking about and doing mathematics so thatthey understand what they study. You must resist the urge to show (a student) a rule or tellhim/her the answer. The key is asking good questions that help (a student) move forward with aproblem.
 
 

 (Back To Top Of Page)


























 
 

Other Good Algebra Web Sites

 Felicia's Algebra Tutorial

Algebra Online

 (Back To Top Of Page)