Student Name _____________________________________________
School ___________________________________________________
Teacher __________________________________________________
Date (Form A) _______________
Date (Form B) _______________
Grade 5
Regina Public Schools
Mathematics
Value-Added Assessment
Diagnostic Numeracy Assessment #1
Multiplication Strategies Task
Teacher Scoring Guide
June 2010
Grade 5 Scoring – Form A
Refer to Teacher Booklet pages 10-11 for descriptions and examples of Common Multiplication Strategies
and page 12 for Scoring Instructions.
4x16 = 64
9x19 = 171
8x21 = 168
7x28 = 196
Beginning Strategies (*valid but inefficient for large numbers)
*Counting arrays
Draws an array of dots, then counts or adds to find a solution.
*Repeated addition
Uses addition to find a solution.
*Skip counting
6, 12, 18, 24…
tally
Flexible Strategies of Computation (varies with numbers and situations)
Traditional
Multiplies digits from right to left and carries the tens if needed (7 x 28
Algorithm
becomes 7x8=56, carry the 5, 7x2=14, plus 5 equals 19. 196
Open arrays
The area model: draws an array that uses groupings to visually show
friendly factors.
Partial Products:
Place V alue
(Tens and Ones)
Partial Products:
Halving
Breaks the number into tens and ones. Then multiplies and adds the
subtotals. (9x19 becomes 9 x 10 and 9 x 9)
Partial Products:
Doubling
Breaks one number into twos. Multiplies the other factor by those twos
(or doubles). Adds the subtotals. (4x16 becomes (2x16) + (2x16))
Partial Products:
Friendly Factors
Breaks one number into friendly parts other than place value or
halves. Multiplies. Adds the subtotals. (8x21 becomes (8x10) + (8x11)
Rounding up to a
Friendly Factor
Rounds one factor up to a friendly factor. Multiplies by the other factor.
Subtracts to compensate. (9x19 becomes 9x20 = 180, 180-9)
Repeated Doubling
If one factor in the equation is 4, 8, or 16, break it into twos, and double
the other number for each 2. (8x21 becomes 2x 21=42, double 42 is 84,
double 84 is 168)
Halving and
Doubling
If one factor is even, split it in half and double the other factor.
(4x16 becomes 2x32 or 8x8)
Breaks one number in half. Multiplies the other factor by the smaller
numbers. Adds the 2 subtotals. (4x16 becomes (4x8) + (4x8))
Level 1
Prior Knowledge
Level 2
Early Knowledge
Level 3
Developing
Knowledge
Level 4
Meeting Grade
Level Knowledge
Level 5
Established
Knowledge
Is unable to
accurately solve at
least 3 equations.
Accurately solves
at least 3 of the
equations.
Accurately solves
at least 3 of the
equations.
Accurately solves
the 4 equations.
Accurately solves
the 4 equations.
Is unable to use
flexible strategies of
computation.
Shows 1 or 2
flexible strategies
and may use the
same strategy for
all 4 equations.
Shows at least 3
different flexible
strategies
throughout the
task.
Shows at least 4
different flexible
strategies
throughout the
task.
Shows at least 5
different flexible
strategies
throughout the
task.
Grade 5 Scoring – Form B
Refer to Teacher Booklet pages 10-11 for descriptions and examples of Common Multiplication Strategies
and page 12 for Scoring Instructions.
6x24=144
9x29=261
8x31=248
7x38=266
Beginning Strategies (*valid but inefficient for large numbers)
*Counting arrays
Draws an array of dots, then counts or adds to find a solution.
*Repeated addition
Uses addition to find a solution.
*Skip counting
6, 12, 18, 24…
tally
Flexible Strategies of Computation (varies with numbers and situations)
Traditional
Multiplies digits from right to left and carries the tens if needed (6 x 24
Algorithm
becomes 6x4=24, carry the 2, 6x2=12, plus 2 equals 14. 144
Open arrays
The area model: draws an array that uses groupings to visually show
friendly factors.
Partial Products:
Place V alue
(Tens and Ones)
Partial Products:
Halving
Breaks the number into tens and ones. Then multiplies and adds the
subtotals. (9x29 becomes 9 x 20 and 9 x 9)
Partial Products:
Doubling
Breaks one number into twos. Multiplies the other factor by those twos
(or doubles). Adds the subtotals.
(6x24 becomes (2x24) + (2x24) + (2x24))
Partial Products:
Friendly Factors
Breaks one number into friendly parts other than place value or
halves. Multiplies. Adds the subtotals. (8x21 becomes (8x10) + (8x11)
Rounding up to a
Friendly Factor
Rounds one factor up to a friendly factor. Multiplies by the other factor.
Subtracts to compensate. (9x19 becomes 9x20 = 180, 180-9)
Repeated Doubling
If one factor in the equation is 4, 8, or 16, break it into twos, and double
the other number for each 2. (8x31 becomes 2x 31=62, double 62 is 124,
double 124 is 248)
If one factor is even, split it in half and double the other factor.
(6x24 becomes 3x48 or 12x12)
Halving and
Doubling
Breaks one number in half. Multiplies the other factor by the smaller
numbers. Adds the 2 subtotals. (8x31 becomes (4x31) + (4x31))
Level 1
Prior Knowledge
Level 2
Early Knowledge
Level 3
Developing
Knowledge
Level 4
Meeting Grade
Level Knowledge
Level 5
Established
Knowledge
Is unable to
accurately solve at
least 3 equations.
Accurately solves
at least 3 of the
equations.
Accurately solves
at least 3 of the
equations.
Accurately solves
the 4 equations.
Accurately solves
the 4 equations.
Is unable to use
flexible strategies of
computation.
Shows 1 or 2
flexible strategies
and may use the
same strategy for
all 4 equations.
Shows at least 3
different flexible
strategies
throughout the
task.
Shows at least 4
different flexible
strategies
throughout the
task.
Shows at least 5
different flexible
strategies
throughout the
task.