Math Live – Multiplication of Whole Numbers: Assessment Task
Grade: 5
Strand: Number
Outcome: 5
SPECIFIC LEARNER OUTCOME – Number
N5
Demonstrate , with and without concrete materials, an
understanding of multiplication (2-digite by 2-digit) to solve
problems.
PROCESSES
Communication (C), Connections (CN), Mental Mathematics and Estimation (ME), Problem Solving (PS),
Reasoning (R), Technology (T), Visualization (V)
C, CN, PS, V
EVIDENCE the student has achieved the outcomes
Each student will:
•
•
Use an algorithm to find the product of a 2-digit by 2-digit multiplication problem.
Explain the process of multiplication of 2-digit by 2-digit whole numbers.
TEACHER NOTE
•
In this assessment task, students will be asked to demonstrate their understanding of
multiplication of whole numbers (2-digit by 2-digit). They will solve two multiplication
problems (52 x 17 and 57 x 12) in order to prove that switching digits between factors, even if
they represent the same place value, will change the product. Students then explain and
model how to use partial products in 2-digit by 2-digit multiplication.
•
•
Students should have easy access calculators or a multiplication chart.
Early finishers can try out the lattice or the array model of multiplication and try to describe
what is happening at each step.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 1 of 14
•
Students can represent multi-digit multiplication in many ways:
Lattice Multiplication: 57 x 12
5
7 1
0 7
2
0
5 1
4
1 0
1 000
6
8
4
100
10
1
Distributive Property: 57 x 12
57 = 50 + 7
12 = 10 + 2
50 x 12 = 600
7 x 12 = 84
684
10 x 57 = 570
2 x 57 = 114
684
Array (Distributive Property II): 57 x 12
50
7
10
500
70
2
100
14
50
7
10
500
70
2
100
14
600
84
+
684
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 2 of 14
Partial Products: 57 x 12
5
x 1
1
1
0
7
5
0
6
8
7
2
4
0
0
0
4
Standard Algorithm: 57 x 12
1
5
x 1
1
1
5
7
6
8
7
2
4
4
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 3 of 14
Math Live – Multiplication of Whole Numbers: Assessment Task
Tamara thought that she could switch digits in the factors of a multiplication
problem and still end up with the same product.
I’ll switch the numbers in the ones
place because 2 x 57 is easier than
7 x 52!
52
x17
57
x12
1. Show how you would find each of the products.
52 x 17
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
57 x 12
Page 4 of 14
2. Tamara still doesn’t understand why she can’t just switch the digits and
come up with the same product.
You decide to explain to Tamara that 17 groups of 52 is a lot bigger
than 12 groups of 57. Show how you would explain this to Tamara as
clearly as you can. Use words and drawings to explain your thinking.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 5 of 14
Scoring Guide – Multiplication of Whole Numbers
Level
Criteria
Uses an algorithm to find
the product of a
3-digit by 2-digit
multiplication problem
Question #1
WOW!
Accurately applies an
algorithm to find each of the
products and shows all
necessary steps including
regrouping
NO, BUT…
INSUFFICIENT /
BLANK
Question #2
Clearly explains the process
of multiplication of large
numbers with reference to
either partial products or the
distributive property
Explains the process of
multiplication of large
numbers as finding the total
of a given number of equal
groups
YES
YES, BUT…
Explains the process of
multiplication of whole
numbers (3-digit by 2-digit)
Applies an algorithm to find
each of the products with
minor calculation errors or not
showing all necessary steps
Explains the process of
multiplication of large
numbers using only
procedural knowledge such
as the steps to apply in a
given an algorithm
Applies an algorithm to find
each of the products with
major errors in place value
and/or regrouping
Unable to explain the process
of multiplication with clarity
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
Wow!
Math Live – Multiplication of Whole Numbers: Assessment Task
Tamara thought that she could switch digits in the factors of a multiplication
problem and still end up with the same product.
I’ll multiply 356 by 12 instead of 352
times 16 since it is easier to multiply
by 2 than 6!
35 2
x16
35 6
x12
3. Show how you would find each of the products.
352 x 26
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
356 x 22
Page 7 of 14
Wow!
4. Tamara still doesn’t understand why she can’t just switch the digits and
come up with the same product.
You decide to explain to Tamara that 26 groups of 352 is a lot bigger
than 22 groups of 356. Show how you would explain this to Tamara as
clearly as you can.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 8 of 14
Yes
Math Live – Multiplication of Whole Numbers: Assessment Task
Tamara thought that she could switch digits in the factors of a multiplication
problem and still end up with the same product.
I’ll multiply 356 by 12 instead of 352
times 16 since it is easier to multiply
by 2 than 6!
35 2
x16
35 6
x12
1. Show how you would find each of the products.
352 x 26
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
356 x 22
Page 9 of 14
Yes
2. Tamara still doesn’t understand why she can’t just switch the digits and
come up with the same product.
You decide to explain to Tamara that 26 groups of 352 is a lot bigger
than 22 groups of 356. Show how you would explain this to Tamara as
clearly as you can.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 10 of 14
Yes, but
Math Live – Multiplication of Whole Numbers: Assessment Task
Tamara thought that she could switch digits in the factors of a multiplication
problem and still end up with the same product.
I’ll multiply 356 by 12 instead of 352
times 16 since it is easier to multiply
by 2 than 6!
35 2
x16
35 6
x12
1. Show how you would find each of the products.
352 x 26
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
356 x 22
Page 11 of 14
Yes, but
2. Tamara still doesn’t understand why she can’t just switch the digits and
come up with the same product.
You decide to explain to Tamara that 26 groups of 352 is a lot bigger
than 22 groups of 356. Show how you would explain this to Tamara as
clearly as you can.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 12 of 14
No, but
Math Live – Multiplication of Whole Numbers: Assessment Task
Tamara thought that she could switch digits in the factors of a multiplication
problem and still end up with the same product.
I’ll multiply 356 by 12 instead of 352
times 16 since it is easier to multiply
by 2 than 6!
35 2
x16
35 6
x12
1. Show how you would find each of the products.
352 x 26
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
356 x 22
Page 13 of 14
No, but
2. Tamara still doesn’t understand why she can’t just switch the digits and
come up with the same product.
You decide to explain to Tamara that 26 groups of 352 is a lot bigger
than 22 groups of 356. Show how you would explain this to Tamara as
clearly as you can.
Math Live
© 2009 Alberta Education (www.learnalberta.ca)
Page 14 of 14