Numerical Fluency #79 by yIqCyW40

VIEWS: 11 PAGES: 36

									Austin Independent School District
Department of Curriculum and Instruction


                                                                               Mathematics



                 Numerical Fluency
                     Grade 6




                                          Mathematics
                                                 1st Six-Weeks
                                                   2009-2010

     Numerical Fluency Problems #1-1 through 1-25
                        (1-26 through 1-28 OPTIONAL)



   Austin ISD Secondary Mathematics Department       1st Six Weeks 2009-2010   Page 1 of 36
 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                   Numerical Fluency Specification Sheet
                                               1st Six Weeks: 29 Days
  NF       Matrix      TEKS      TAKS
                                                                                 Answer
Problem      #           #       Obj #
Discuss Numerical Fluency Problems by having students share their multiple strategies.
This sharing will help students become flexible, efficient, and accurate with numerical
reasoning while learning the TEKS deeply.

                                               Strategy #1: Changing the order of the factors does not change the
                                                product such as 4  5  20 and5  4  20 .
                                               Strategy #2: Double a column to obtain twice as much such as doubling
  1-1        128         L                      the products of the 3’s column gives the products to the 6’s column. For
                                                example, 3  4  12 so 6  4  212  24 .
                                               Strategy #3: Use the 5’s as a benchmark and add groups of a number to
                                                the product of the 5’s. For example, to recall 8  8 , do
                                                 5 × 8 + 3 × 8 = 40 + 24 = 64 .
             112       6.1E        1       There are many possible rectangular arrays for 36 students.
                                           1 row with 36 students, 2 rows with 18 students each, 3 rows with 12 students
  1-2        128         L                 each, 4 rows with 9 students each, 6 rows with 6 students each, 9 rows with 4
                                           students each, 12 rows with 3 students each, 18 rows with 2 students each,
             133       6.2C        1       and 36 rows with 1 student each


                                                                               Number of
             112       6.1E        1                     Number of
                                                                            Students in Each
                                                          Rows, r
                                                                                Row, s
                                                              1                   100
                                                              2                    50
                                                              4                    25
             133       6.2C        1
                                                              5                    20
  1-3                                                        10                    10
                                                             20                     5
                                                             25                     4
                                                             50                     2
                                                            100                     1
             225         L




                                           1 Since 5 groups of 8 are 40, one more group of 8 added to 40 makes 48.
             128                   L       2 6  8 = (5  8) + (1  8)
  1-4                                      3 Since 3 groups of 8 are 24, 6 groups of 8 would be twice as much or 48.
             205                   L       4 6  8 = (3  8)  2
                                           5 6  8 = 48, 8  6 = 48, 48  8 = 6, 48  6 = 8
                                           1 Since 5 groups of 8 are 40, two more groups of 8 added to 40 makes 56.
             128                   L       2 7  8 = (5  8) + (2  8)
                                           3 Since 10 groups of 8 are 80, three groups of 8 or 24 less than 80 makes
  1-5
                                            56.
             205                   L       4 7  8 = (10  8) - (3  8)
                                           5 7  8 = 56, 8  7 = 56, 56  8 = 7, 56  7 = 8




 Austin ISD Secondary Mathematics Department               1st Six Weeks 2009-2010                       Page 2 of 36
 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
  NF       Matrix      TEKS      TAKS
                                                                                Answer
Problem      #           #       Obj #
                                           1 Answers will vary. Here are some possible number sentences.
             121                   L       4  15 = (4  5) + (4  5) + (4  5)
                                           4  15 = (2  15) + (2  15)
  1-6
                                           4  15 = (4  10) + (4  5)
             610       6.12A       6
                                           2   4  15 = 60, 15  4 = 60, 60  4 = 15, 60  15 = 4
                                           1 Answers will vary. Here are some possible number sentences.
             121                   L       29  15 = (20  15) + (9  15)
  1-7                                      29  15 = (10  15) + (10  15) + (9  15)
             610       6.12A       6       29  15 = (30  15) – 15
                                           2 29  15 = 435, 15  29 = 435, 435  15 = 29, 435  29 = 15
                                           1 Answers will vary. Here are some possible factor pairs.
             112       6.1E        1       10  25, 3  25, 20  13, 5  13, 30  25, 7  25
                                           2 Answers will vary. Here are some possible number sentences.
  1-8                                      13  25 = (10  25) + (3  25)
                                           13  25 = (20  13) + (5  13)
             610       6.12A       6       13  25 = (30  25) - (7  25)
                                           3 13  25 = 325, 25  13 = 325, 325  13 = 25, 325  25 = 13
                                           1  50 groups of 18 is closer to the product of 47  18 because it is 3 groups
             135       6.2D        1
                                            of 18 more than the product, whereas, 40 groups of 18 is 7 groups of 18
  1-9                                       less than the product.
             136                   L       2 20(17) is closer to 22  17 because it is 34 less 22  17, whereas, 25  17
                                            is 51 more than 22  17.

             130         L                 1    2 pieces of rope
                                           2    3 buses
                                                  1
                                           3 2 dollars or $2.50
             133       6.2C        1              2
                                           Help students think about remainders. Depending on the context of the
 1-10                                      situation, remainders are dropped sometimes, sometimes they are rounded
                                           up, and sometimes a fractional remainder makes sense. Do NOT teach
             605       6.11A       6       division with fractions or decimals at this time. Help students make sense of
                                           the remainder by thinking about what the whole amount. In this case the
                                           whole amount were the 40 band students. The remainder of $20 was to be
                                           split evenly among the 40 band students; each of the 40 band students gets
             610       6.12A       6       $0.50 of that remainder of $20.


                                           1   4  26 = (2  26) + (2  26)
                                           2   4  26 = (4  20) + (4  6)
             133       6.2C        1
                                           3

                                                            26

 1-11        135       6.2D        1                  X       4
                                                            24    =     (4 x 6) =          4 rows of 6
                                                            80    =     (4 x 20) =         4 rows of 20
             136                   L                       104




 Austin ISD Secondary Mathematics Department              1st Six Weeks 2009-2010                         Page 3 of 36
 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
  NF       Matrix      TEKS      TAKS
                                                                                   Answer
Problem      #           #       Obj #
                                           1    The missing dimension on the left is 9. The missing dimension on the top
                                                is 20.
             133       6.2C        1       2    9  28 = (9  20) + (9  8)
                                           3
                                                                 28
                                                         X         9
                                                                 72     =       (9 x 8)   =      9 rows of 8
 1-12        135       6.2D        1
                                                               180      =       (9 x 20) =       9 rows of 20
                                                               252

                                           4    9  28 = 252; 28  9 = 252; 252  28 = 9; 252  9 = 28
             136                   L



                                           1     432 pencils
                                           2     The table below shows all the possible arrangements of cement squares
             112       6.1E        1           for the patio.
                                                                                    Number of Cement
                                                        Number of Rows, r          Squares in Each Row,
                                                                                             s
                                                                    1                       48
                                                                    2                       24
 1-13        128         L                                          3                       16
                                                                    4                       12
                                                                    6                        8
                                                                    8                        6
                                                                   12                        4
                                                                   16                        3
             133       6.2C        1                               24                        2
                                                                   48                        1


                                           1                                      2             26
                                                 10 x 20 = 200                                x 34
                                                 10 x 20 = 200                                  24   =    4x6
             133       6.2C        1
                                                 10 x 20 = 200                                  80   =    4 x 20
                                                  4 x 20 = 80                                  180   =    30 x 6
                                                 10 x 6 = 60                                   600   =    30 x 20
 1-14                                            10 x 6 = 60                                   884        34 x 26
                                                 10 x 6 = 60
                                                  6 x 4 = 24

             136                   L             34 x 26 = 884


                                           3 34  26 = 884; 26  34 = 884; 884  26 = 34; 884 34 = 26




 Austin ISD Secondary Mathematics Department                 1st Six Weeks 2009-2010                       Page 4 of 36
 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
  NF       Matrix      TEKS      TAKS
                                                                                  Answer
Problem      #           #       Obj #
                                           1
                                                 10 x 10    = 100           2
                                                 10 x 10    = 100                42
             133       6.2C        1             10 x 10    = 100                 X
                                                 10 x 10    = 100                17
                                                  2 x 10    = 20                 14   =7x2
                                                  7 x 10    = 70                280   = 7 x 40
                                                  7 x 10    = 70                 20   = 10 x 2
                                                  7 x 10    = 70                400   = 10 x 40
 1-15                                             7 x 10    = 70                714   = 42 x 17
                                                   7x2      = 14
                                                 42 x 17    = 714

             136                   L
                                           3 42  17 = 714; 42  17 = 714; 714  42 = 17; 714  17 = 42




                                           1 Answers will vary. Here is one possibility.
                                           45  39 = 40  39 + 5  39 = 1560 + 195 = 1755

             133       6.2C        1       2   Answers will vary Here is one possibility.

                                                             45
 1-16                                                      X 39
                                                             45   =9x5
                                                            360   = 9 x 40
                                                            150   = 30 x 5
             136                   L                       1200   = 30x 40
                                                           1755   = 45 x 39

                                           Strategies will vary. Efficient methods should be both accurate and quick.
                                           1 72  14 = 10  72 + 4  72 = 720 + 288 = 1008
             133       6.2C        1       2                 27
                                                           X 56
                                                             42     =6x7
 1-17                                                       120     = 6 x 20
                                                            350     = 50 x 7
                                                           1000     = 50x 20
             136                   L                       1512     = 56 x 27

                                           3   32(95) = 100  32 – 5  32 = 3200 – 160 = 3040




 Austin ISD Secondary Mathematics Department                1st Six Weeks 2009-2010                       Page 5 of 36
 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
  NF       Matrix      TEKS      TAKS
                                                                                Answer
Problem      #           #       Obj #
                                           1
                                                441           2     10
                                                420           3     10
             112       6.1E        1            399           4     10
                                                378           5     Answers will vary. Here are a
                                                357               few possibilities.
                                                336
                                                315                           a      b
                                                294                            3     63
                                                273                            5    105
                                                252                           10    210
                                                231                           13    273
                                                210                           15    315
 1-18                                           189
                                                168
                                                147
             133       6.2C        1            126
                                                105
                                                 84
                                                 64
                                                 42
                                                 21




                                           1    420
             112       6.1E        1       2    20
                                           3    20
                                           4    210
             133       6.2C        1       5    420
 1-19
                                           6    630
                                           7    840
                                           8    1050
             136                   L       9    1680
                                           10   2100
                                               1
                                           21 crayons
 1-20        133       6.2C        1           2
                                           Students should be using division strategies that make sense to them, but are
                                           also efficient strategies.
                                           1 Both Marta and James arrange their division problems vertically and write
             133       6.2C        1          their groups of 21 to the right side of the problem. Both Marta and James
                                              subtract groups of 21 until no groups of 21 remain of the original 504.
 1-21                                         James method is different than Marta’s method because he subtracts 20
             136                   L          groups of 21 as a first step, whereas Marta only subtracts 10 groups of 21
                                              as the first step.
                                           2 n = 24




 Austin ISD Secondary Mathematics Department              1st Six Weeks 2009-2010                       Page 6 of 36
 Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
  NF       Matrix      TEKS      TAKS
                                                                                    Answer
Problem      #           #       Obj #
                                           1
                                                          2       38  18 = 20  18 + 10  18 + 8  18 = 360 + 180 + 144 = 684
                                                 378
                                                 360
                                                 342          3    Miguel’s method

             135       6.2D        1
                                                 324
                                                 306
                                                                   n
                                                 288
                                                 270
                                                              18 576
                                                 252                     - 180          10 groups of 18
                                                 234                        396 left over
                                                 216                      - 360           20 groups of 18
                                                 198                         36 left over
                                                 180                      - 36            2 groups of 18
                                                 162                          0         32 groups of 18
                                                 144
 1-22                                            126
                                                               4     Gloria’s method
                                                 108
                                                  90
                                                  72
                                                                       n
                                                  54              18 576
                                                  36
                                                                    -540
             136                   L              18                                       30      groups of 18
                                                                             36   left over
                                                                           - 36             2   groups of 18
                                                                              0           32    groups of 18




                                           1    10 x 18 = 180; 20 X 18 = 360; 30 x 18 = 540; 40 x 18 = 720; 50 x 18 =
                                               900; 100 x 18 = 1800
             133       6.2C        1
                                                     n
 1-23                                      2    18 954
                                                   900 = 50 group of 18
             136                   L                54
                                                    54 = 3 groups of 18
                                                     0
             133       6.2C        1       1  54
 1-24
             136                   L       2  86
                                             Strategy #1: Changing the order of the factors does not change the
                                              product such as 4  5  20 and5  4  20 .
                                            Strategy #2: Double a column to obtain twice as much such as doubling
                                              the products of the 3’s column gives the products to the 6’s column. For
 1-25        128         L         1
                                              example, 3  4  12 so 6  4  212  24 .
                                             Strategy #3: Use the 5’s as a benchmark and add groups of a number to
                                                        the product of the 5’s. For example, to recall 8  8 , do
                                                                       5 × 8 + 3 × 8 = 40 + 24 = 64 .
 1-26        108         L
                                   1       1 $47.16      2 $12.89         3 0.124       4 $70.01
optional     127       6.2B



 Austin ISD Secondary Mathematics Department                  1st Six Weeks 2009-2010                             Page 7 of 36
  Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
   NF       Matrix      TEKS      TAKS
                                                                                 Answer
Problem       #           #       Obj #
  1-27       108          L
                                    1       9.5 – 2.75 = 6.75 inches
optional     127        6.2B
             108          L
 1-28                                       1   C
             227        6.2B        1
optional                                    2   $50.05
             223        6.5A        2




  Austin ISD Secondary Mathematics Department              1st Six Weeks 2009-2010          Page 8 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                    Numerical Fluency 1-1
Complete the following multiplication table.

X 1 2                         3 4 5 6 7 8 9                                    10       11         12
1     2                       3 4 5 6        8 9                               10       11
2 2                           6 8 10 12     16 18                              20       22
3 3 6                           12    18    24                                 30
4 4 8                        12    20 24                                       40
5 5 10                       15 20    30 35    45                              50                  60
6 6 12                       18 24 30          54                              60
7                                  35
8 8 16                       24
9 9 18                             45 54 63                                    90
10 10 20                     30 40    60 70    90
11 11 22
12                                            60

List 3 strategies you used to recall facts you did not
know.

1.

2.

3.



Austin ISD Secondary Mathematics Department        1st Six Weeks 2009-2010                Page 9 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                    Numerical Fluency 1-2
The Super Bowl is going to be held in Austin this year.
The Super Bowl Committee has decided that the 36
students in Ms. Grant’s class at Fulmore Middle School
will march in the pre-game parade. They will march in a
variety of rectangular arrays such as the one shown
below.




Write down as many of the possible marching
arrangements for the 36 students that you can.




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 10 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                    Numerical Fluency 1-3
The Super Bowl Committee changed their minds. They decided
all 100 sixth graders at Fulmore Middle School may march in the
pre-game parade. The 100 students will march in a variety of
rectangular arrays.

One of the Fulmore sixth graders wrote the following equation to
help find all the possible arrangements.

                                              r  s  100
A variable, often a letter of the alphabet, represents a quantity
that changes. In the equation above, the variable r represents the
number of rows. The variable s represents the number of
students in each row.

Create a table of data for the two variables. In the table write as
many possible marching arrangements for the 100 students that
you can.




Austin ISD Secondary Mathematics Department      1st Six Weeks 2009-2010                  Page 11 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                    Numerical Fluency 1-4

1        Describe in words how to use 5 8 to find the
         product of 6 8 .



2        Write a horizontal number sentence using 5 8
         that shows how to find the product of 6 8 .

                  6 8 = _______________________

3        Describe in words how to use 3 8 to find the
         product of 6 8 .



4        Write a horizontal number sentence using 3 8
         that shows how to find the product of 6 8 .

                  6 8 = _______________________

5        What is the multiplication and division fact
         family for 6 8 ?




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 12 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                    Numerical Fluency 1-5

1        Describe in words how to use 5 8 to find the
         product of 7 8 .



2        Write a horizontal number sentence using 5 8
         that shows how to find the product of 7 8 .

                  7 8 = _______________________

3        Describe in words how to use 10 8 to find the
         product of 7 8 .



4        Write a horizontal number sentence using 10 8
         that shows how to find the product of 7 8 .

                  7 8 = _______________________

5        What is the multiplication and division fact
         family for 7 8 ?




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 13 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                    Numerical Fluency 1-6

                                          Multiplication Cluster

                                                   45
                                                  2  15
                                                  4  10

                                                  4  15



1        Using one or more factor pairs from the Multiplication
         Cluster, write a horizontal number sentence that
         shows how to find the product of 4  15.

                  4  15 = ________________________________




2        What is the multiplication and division family for
         4  15?




Austin ISD Secondary Mathematics Department        1st Six Weeks 2009-2010                Page 14 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                    Numerical Fluency 1-7

                                          Multiplication Cluster

                                                 10  15
                                                 20  15
                                                 30  15
                                                  9  15

                                                 29  15



1        Using one or more factor pairs from the Multiplication
         Cluster, write a horizontal number sentence that
         shows how to find the product of 29  15.

                  29  15 = ________________________________




2        What is the multiplication and division family for
         29  15?




Austin ISD Secondary Mathematics Department        1st Six Weeks 2009-2010                Page 15 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                    Numerical Fluency 1-8

There are 13 classes of 6th grade mathematics at Porter
Middle School. Each class has 25 students.

1        Create a cluster of factors pairs that could be used to
         find the total number of students in the 13 classes.

                                              Multiplication Cluster

                                                ______________
                                                ______________
                                                ______________
                                                ______________

                                                     13  25


2        Using one or more factor pairs from the Multiplication
         Cluster, write a horizontal number sentence that
         shows how to find the product of 13  25.

                  13  25 = ____________________________




3        What is the multiplication and division family for
         13  25?




Austin ISD Secondary Mathematics Department           1st Six Weeks 2009-2010             Page 16 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                    Numerical Fluency 1-9

Without doing any calculations, decide which expression
is a closer estimate to the multiplication problem in each
rectangle. Explain your reasoning.


1                                             40 groups of 18

                 47  18
                                              50 groups of 18




2
                                              20(17)

                 22  17
                                              25  17




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 17 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-10

1        A rope is 100 feet long. How many pieces of
         rope, each 40 feet long, can be cut from the
         rope?




2        100 people from Lamar Middle School are going
         on a field trip. Each bus holds 40 people. How
         many buses are needed for the field trip?




3        A $100 prize was given to 40 band students who
         entering a marching contest. If the money is
         shared equally, how much will each student
         receive?




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 18 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-11
The array below models the multiplication problem 4  26.




1        The following array shows a way to divide the array above
         into groups.
                                                    26
                  2

                  2

    Using the dimensions from the array above, write a horizontal
    number sentence that shows how to find the product of 4  26.
           4  26 = ____________________________________

2        The following array shows another way to divide the array
         into groups.
                                               20                                 6

                  4


    Using the dimensions from the array above, write a horizontal
    number sentence that shows how to find the product of 4  26.
           4  26 = ____________________________________

3        Complete the following vertical number sentence for 4  26.

                    26
                  X 4
                                              (4 x 6)                         4 rows of 6
                                             (4 x 20)                        4 rows of 20



Austin ISD Secondary Mathematics Department         1st Six Weeks 2009-2010                  Page 19 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-12
The array below models the multiplication problem 9  28.




1        The following array shows a how to divide the array above
         into groups to find the product of 9  28. Find each missing
         dimension.

                                                                                8




2        Using the dimensions from the array above, write a
         horizontal number sentence that shows how to find the
         product of 9  28.
              9  28 = ____________________________________

3        Complete the following vertical number sentence for 9  28.
                    28
                  X 9
                                              (9 x 8)                        9 rows of 8
                                             (9 x 20)                       9 rows of 20


4        What is the multiplication and division family for 9  28?


Austin ISD Secondary Mathematics Department        1st Six Weeks 2009-2010                  Page 20 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-13
1        At the Austin ISD Warehouse, there are 72 pencils in
         each box. The Mathematics Department at Murchison
         Middle School ordered 6 boxes of pencils. How many
         pencils were ordered?

         Record your answer and fill in the bubbles below your
         answer. Be sure to use the correct place value.




2        Eric bought 48 cement squares to make a rectangular
         patio. He created an equation, r  s = 48, to find the
         different rectangular arrangements for the patio. If r
         represents the number of rows and s represents the
         number of squares in each row, what are all the
         possible arrangements for the rectangular patio?




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 21 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-14
1        To multiply 34  26, Janie used the following array model.
         Complete the multiplication equations and find the total
         product.

                        20                        6
                                                                    10 x 20 = ______
     10                                                             10 x 20 = ______
                                                                    10 x 20 = ______
                                                                     4 x 20 = ______
     10                                                             10 x 6 = ______
                                                                    10 x 6 = ______
                                                                    10 x 6 = ______
     10                                                              6 x 4 = ______

      4                                                             34 x 26 = ______

2        To multiply 34  26, Greg used the following array model.
         Complete the vertical multiplication strategy to find the total
         product.
                  20                          6                26
                                                             x 34
                                                                                4x 6
                                                                                 4 x 20
                                                                                30 x 6
30                                                                              30 x 20

                                                                                34 x 26

4                                                     3     What is the multiplication and division
                                                            family for 26 x 34?
Austin ISD Secondary Mathematics Department           1st Six Weeks 2009-2010             Page 22 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-15
1        To multiply 17  42, Roy used the following array model. Complete
         the multiplication equations and find the total product.
                    10            7
                                                                 10 x 10 = ______
                                                                 10 x 10 = ______
       10
                                                                 10 x 10 = ______
                                                                 10 x 10 = ______
       10                                                         2 x 10 = ______
                                                                  7 x 10 = ______
       10                                                         7 x 10 = ______
                                                                  7 x 10 = ______
                                                                  7 x 10 = ______
       10                                                         7 x 2 = ______
         2
                                                                 42 x 17 = ______
2        To multiply 17  42, Sandra used the following array model. Complete
         the vertical multiplication strategy to find the total product.
               10      7
                                                            42
                                                          x 17
                                                                              7x 2
     40
                                                                               7 x 40
                                                                              10 x 2
                                                                              10 x 40

                                                                              42 x 17

                                              3   What is the multiplication and division
     2
                                                  family for 42 x 17?

Austin ISD Secondary Mathematics Department         1st Six Weeks 2009-2010               Page 23 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-16
In recent Numerical Fluency problems you have used the
following multiplication strategies.

                 Clusters
                 Horizontal number sentences
                 Arrays
                 Vertical number sentences

1        Compute 45  39 using one of the above strategies.




2        Compute 45  39 using another one of the above
         strategies.




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 24 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-17

Use an efficient method to compute each of the following
problems. Be prepared to explain why your method
makes sense and why it is efficient.

1        72  14




2        27  56




3        32(95)




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 25 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-18

1        Complete the Multiple Tower below for 21.

                                              2   How many multiples of 21
                                                  does it take to get to 210?



                                              3   What value of x makes the
                                                  following equation true?

                                                                x  21 210
                                              4   What value of y makes the
                                                  following equation true?
                                                               210  21  y

                                              5   Use the Multiple Tower for 21
                                                  to find at least 3 pairs of
                                                  numbers that make the
                                                  following equation true.
                                                                   a 21  b
              _____
               63
               42
               21
                                              Save your Multiple Tower for use
                                              during the next few days.

Austin ISD Secondary Mathematics Department        1st Six Weeks 2009-2010                Page 26 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-19
                              Use the Multiple Tower you built for 21 to answer
                              the following problems.

                              1        After 210, what is the next multiple of 21 that
                                       has a 0 in the ones place value?


                              2        What value of a makes this equation true.
                                                     a  21 = 420

                              3        What value of r makes this equation true?
                                                     420  21 = r

                              Compute the following factor pairs to get some
                              Landmark Numbers for 21.

                              3        10  21 = ______

                              4        20  21 = ______

                              5        30  21 = ______
     _____                    6        40  21 = ______
      63
      42                      7        50  21 = ______
      21
                              8        80  21 = ______

                              9        100  21 = ______




Austin ISD Secondary Mathematics Department      1st Six Weeks 2009-2010                  Page 27 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-20

There are 129 crayons. Six children will share the
crayons equally. How many crayons will each child
receive?




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 28 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-21
Marta and James looked at the Multiple Tower for 21 and then
used different methods for the same division problem.

1        Be prepared to explain the similarities and differences of
         their methods.
2        Find the value for n that makes the division problem true.

           441                                Marta’s method
           420                                     n
           399                                21 504
           378                                 - 210           10 groups of 21
           357                                   294 left over
           336                                 - 210           10 groups of 21
           315                                    84 left over
           294                                  - 84            4 groups of 21
           273                                     0            n groups of 21
           252
           231
           210                                James’ method
                                                     n
           189                                21 504
           168
                                                - 420            20 groups of 21
           147                                      84 left over
           126                                    - 84            4 groups of 21
           105                                       0            n groups of 21
           84
           63
           42
           21
Austin ISD Secondary Mathematics Department       1st Six Weeks 2009-2010                 Page 29 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-22
                           1        Complete the Multiple Tower for 18. (Keep it
                                    for tomorrow’s Numerical Fluency.)

                           2        Solve 38  18 by using a horizontal number
                                    sentence.

                           3        Complete Miguel’s division problem below and
                                    find the value of n that makes the problem
                                    true.

                                              Miguel’s method
                                                   n
                                              18 576
                                               - 180           10 groups of 18
                                                 396 left over
                                               -               20 groups of 18
                                                           left over
                                                -                              ? groups of 18
                                                      1                        n groups of 18

                           4        Complete Gloria’s division problem below and
                                    find the value of n that makes the problem
                                    true.
                                              Gloria’s method
                                                    n
                                              18 576
                                               -              30 groups of 18
                                                           left over
        18                                       -                             ? groups of 18
                                                     0                         n groups of 18
Austin ISD Secondary Mathematics Department          1st Six Weeks 2009-2010              Page 30 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-23

1        Compute the following factor pairs to get some Landmark
         Numbers for 18.

                                       Landmark Numbers
                                       10  18 = _____
                                       20  18 = _____
                                       30  18 = _____
                                       40  18 = _____
                                       50  18 = _____
                                       100  18 = _____

2        Use your Multiple Tower for 18 and the Landmark Numbers
         for 18 to find the value of n that makes the following division
         problem true.

                 n
            18 954




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 31 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                   Numerical Fluency 1-24

Record your answer and fill in the bubbles below your
answer. Be sure to use the correct place value.

1        There are 972 seats in the Austin High School Theater.
         There are 18 seats in each row. How many rows of
         seats are in this theater?




2        There are 1806 peach trees in the orchard. There are
         21 rows of peach trees. How many trees are in each
         row of the peach orchard?




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 32 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                    Numerical Fluency 1-25

Complete the following multiplication table.

X           1         2   4 5 6 7 8
                                3                                         9      10 11 12
1                     2   4 5 6 3
2           2             8 10 12
                                6
3           3       6     12    18    2
4           4       8 12     20 24
5           5       10 15 20    30 35
6           6       12 18 24 30
7                            35
8                      24
9
10
11
12

List 3 strategies you used to recall facts you did not know.

1.


2.


3.




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 33 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                        Numerical Fluency 1-26

Use an algorithm to find the value of the variable that
makes each equation true.

1                 $ 35.17 + $ 11.99 = w




2                 15.7 – 2.81 = n




3                 z + 37.6 = 37.724




4                 $100 - x = $ 29.99




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 34 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                        Numerical Fluency 1-27
Harold made a drawing of his rectangular kitchen.
The length of the drawing was 9.5 inches, and the
width of the drawing was 2.75 inches less than the
length. Find the width of the drawing.




                                Kitchen
                                              9.5 inches




Austin ISD Secondary Mathematics Department      1st Six Weeks 2009-2010                  Page 35 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems

                                        Numerical Fluency 1-28

David bought 2 shirts at Foleys. One shirt cost $23.50.
The other shirt was on sale for $5.95 off of the original
price of $32.50.


1        Which equation can be used to find n, the total
         amount David paid for the 2 shirts?

         A        n = 23.50 + (5.95 + 32.50)
         B        n = (32.50 – 5.95) – 23.50
         C        n = (32.50 – 5.95) + 23.50
         D        n = (32.50 – 23.50) – 5.95



2        How much did David pay for the two shirts?




Austin ISD Secondary Mathematics Department    1st Six Weeks 2009-2010                    Page 36 of 36

								
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