Math Live – Division of Whole Numbers: Assessment Task
Grade: 5
Strand: Number
Outcome: 6
SPECIFIC LEARNER OUTCOME – Number
N6
Demonstrate, with and without concrete materials, an understanding of
division (3-digit by 1-digit), and interpret remainders to solve problems.
PROCESSES
Communication (C), Connections (CN), Mental Mathematics and Estimation (ME), Problem Solving (PS),
Reasoning (R), Technology (T), Visualization (V)
C, CN, ME, PS, R, V
EVIDENCE the student has achieved the outcomes
Each student will:
• Analyze the process of division by considering the effect of changing the divisor
(single-digit) in a problem.
• Apply an algorithm to divide a 3-digit number by a 1-digit divisor.
• Explain the meaning of division of whole numbers.
TEACHER NOTE
•
In this assessment task, students will be asked to demonstrate their understanding of the
division of whole numbers (3-digit divided by 1 digit). They will first find all the possible
divisors of 345 that lead to a quotient less than 50 (7, 8 and 9). Then students chose one
of these divisors and use an algorithm to find an exact quotient. Finally, students will be
asked to use pictures, words and symbols to communicate their understanding of division.
•
•
Students should have easy access to base-ten manipulatives and a calculator.
Early finishers can find all the numbers between 200-300 that are divisible by (2, 4, 6, and
8) with no remainder. They can then look for patterns. (E.g. they always end in an even
number 0, 2, 4, 6, 8). They can then investigate if divided by an odd number (3, 5, 7, 9)
yields the same kind of pattern.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 1 of 14
•
Models of Division:
Repeated Subtraction: 268 ÷ 6
Either:
268 – 6 – 6 – 6 – 6…. (Then count the number of times you subtracted 6), or
268 – 60 – 60 – 60 – 60 – 6 – 6… (Count each 60 as 10 groups of 6 then add the single
groups of 6)
Measurement Model: 128 ÷ 8 = 16 (groups of 8)
528
Partitive Model: 520 ÷ 4 = 130 (in each of the four groups)
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 2 of 14
Part-part-whole: 128 ÷ 8 =
16
8
128
Note: The teachers at St. Matthew Elementary School in Edmonton noticed the similarity
between the array above and the symbolic notation below. This discovery has helped
their students to understand “which number goes under the bar” and to connect
multiplication and division.
16
8 128
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 3 of 14
Math Live – Division of Whole Numbers: Assessment Task
1. Name all the one-digit divisors that will make a quotient less than 50. Show
your thinking below using words and symbols.
3
4
5
÷
=
A quotient less than 50
2. Chose one of the divisors that you found and show how to complete the
division problem to find an exact answer. Show all your thinking.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 4 of 14
3. Explain in your own words, what division is. Use pictures, words and
symbols to show your thinking.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 5 of 14
Scoring Guide – Division of Whole Numbers
Level
Criteria
Analyzes the process
of division by
considering the effect
of changing the
divisor in a problem
Uses an algorithm to
divide a 3-digit
number by a 1-digit
number and explain
the process used
Question #1
Question #2
Explains the meaning
of division of whole
numbers
Question #3
Wow!
Analyzes and
generalizes the effect
of changing the
divisor in a problem
on the quotient based
on logical
mathematical
reasoning
YES
Correctly applies a
division algorithm and
provides an insightful
explanation of the
process
Correctly applies a
division algorithm and
provides a logical
step-by-step
explanation of the
process
Provides an in-depth
explanation of division
which shows strong
evidence of both
conceptual and
procedural
understanding
Provides an
explanation which
shows evidence of
conceptual
understanding of at
least one model of
division (partitive or
measurement model)
Provides an
explanation which is
based solely on a
procedural
understanding of
division
YES, BUT…
Analyzes the effect of
changing the divisor in
a problem on the
quotient through
systematic trial and
error
Applies a division
algorithm with minor
errors or provides only
a superficial
explanation of the
process
NO, BUT…
Attempts to analyze
the effect of changing
the divisor in a
problem on the
quotient through
random guessing
Incorrectly applies a
division algorithm
and/or provides little
or no explanation of
the process
Provides a simplistic
explanation (“opposite
of multiplication”)
which contains
misconceptions of the
meaning of division
INSUFFICIENT /
BLANK
No score awarded
due to insufficient
evidence of student
learning based on the
requirements of the
assessment task
No score awarded
due to insufficient
evidence of student
learning based on the
requirements of the
assessment task
No score awarded
due to insufficient
evidence of student
learning based on the
requirements of the
assessment task
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 6 of 14
Math Live – Division of Whole Numbers: Assessment Task
Wow!
4. Name all the one-digit divisors that will make a quotient less than
50. Show your thinking below using words and symbols.
3
4
5
÷
=
A quotient less than 50
5. Chose one of the divisors that you found and show how to complete the
division problem to find an exact answer. Show all your thinking.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 7 of 14
Wow!
6. Explain in your own words, what division is. Use pictures, words and
symbols to show your thinking.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 8 of 14
Yes
Math Live – Division of Whole Numbers: Assessment Task
1. Name all the one-digit divisors that will make a quotient less than
50. Show your thinking below using words and symbols.
3
4
5
÷
=
A quotient less than 50
2. Chose one of the divisors that you found and show how to complete
the division problem to find an exact answer. Show all your thinking.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 9 of 14
Yes
3. Explain in your own words, what division is. Use pictures, words and
symbols to show your thinking.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 10 of 14
Math Live – Division of Whole Numbers: Assessment
Task
Yes, but
1. Name all the one-digit divisors that will make a quotient less than
50. Show your thinking below using words and symbols.
3
4
5
÷
=
A quotient less than 50
2. Chose one of the divisors that you found and show how to complete
the division problem to find an exact answer. Show all your thinking.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 11 of 14
Yes, but
3. Explain in your own words, what division is. Use pictures, words and
symbols to show your thinking.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 12 of 14
Math Live – Division of Whole Numbers: Assessment Task
No, but
1. Name all the one-digit divisors that will make a quotient less than
50. Show your thinking below using words and symbols.
3
4
5
÷
=
A quotient less than 50
2. Chose one of the divisors that you found and show how to complete
the division problem to find an exact answer. Show all your thinking.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 13 of 14
No, but
3. Explain in your own words, what division is. Use pictures, words and
symbols to show your thinking.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 14 of 14