+ All Categories
Home > Documents > Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers:...

Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers:...

Date post: 16-May-2018
Category:
Upload: doanh
View: 215 times
Download: 1 times
Share this document with a friend
14
Page 1 of 14 Math Live © 2009 Alberta Education (www.learnalberta.ca) 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.
Transcript
Page 1: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

Page 1 of 14

Math Live © 2009 Alberta Education (www.learnalberta.ca)

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.

Page 2: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

Page 2 of 14

Math Live © 2009 Alberta Education (www.learnalberta.ca)

50

7

10

500

70

2

100

14

50

7

10

500

70

2

100

14

600

84

684

• Students can represent multi-digit multiplication in many ways:

Lattice Multiplication: 57 x 12 7 1

5 0 7 2

0 5 1 4

1 0

6 8 4

1 000 100 10 1

Distributive Property: 57 x 12

57 = 50 + 7

50 x 12 = 600 7 x 12 = 84

684

12 = 10 + 2 10 x 57 = 570

2 x 57 = 114

684

Array (Distributive Property II): 57 x 12

+

Page 3: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

Page 3 of 14

Math Live © 2009 Alberta Education (www.learnalberta.ca)

Partial Products: 57 x 12

5 7

x 1 2

1 4

1

0 0

7 0

5

0 0

6

8 4

Standard Algorithm: 57 x 12

1

5 7

x 1 2

1

1 4

5

7

6

8 4

Page 4: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

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!

5 2 x 1 7

5 7 x 1 2

1. Show how you would find each of the products.

52 x 17 57 x 12

Page 4 of 14

Math Live © 2009 Alberta Education (www.learnalberta.ca)

Page 5: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

Page 5 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 6: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

Page 6 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

Explains the process of multiplication of whole numbers (3-digit by 2-digit)

Question #2

Clearly explains the process of multiplication of large numbers with reference to either partial products or the distributive property

WOW!

Accurately applies an algorithm to find each of the

products and shows all necessary steps including

regrouping

Explains the process of multiplication of large

numbers as finding the total of a given number of equal

groups

YES

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

YES, BUT…

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, BUT…

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

INSUFFICIENT / BLANK

Math Live © 2009 Alberta Education (www.learnalberta.ca)

Page 7: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

Page 7 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.

Wow!

I’ll multiply 356 by 12 instead of 352 times 16 since it is easier to multiply by 2 than 6!

3 5 2 x 1 6

3 5 6 x 1 2

3. Show how you would find each of the products.

352 x 26 356 x 22

Math Live © 2009 Alberta Education (www.learnalberta.ca)

Page 8: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

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.

Page 8 of 14

Math Live © 2009 Alberta Education (www.learnalberta.ca)

Page 9: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

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.

Yes

I’ll multiply 356 by 12 instead of 352 times 16 since it is easier to multiply by 2 than 6!

3 5 2 x 1 6

3 5 6 x 1 2

1. Show how you would find each of the products.

352 x 26 356 x 22

Page 9 of 14

Math Live © 2009 Alberta Education (www.learnalberta.ca)

Page 10: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

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.

Page 10 of 14

Math Live © 2009 Alberta Education (www.learnalberta.ca)

Page 11: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

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!

3 5 2 x 1 6

3 5 6 x 1 2

1. Show how you would find each of the products.

352 x 26 356 x 22

Page 11 of 14

Math Live © 2009 Alberta Education (www.learnalberta.ca)

Page 12: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

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.

Page 12 of 14 Math Live © 2009 Alberta Education (www.learnalberta.ca)

Page 13: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

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!

3 5 2 x 1 6

3 5 6 x 1 2

1. Show how you would find each of the products.

352 x 26 356 x 22

Page 13 of 14

Math Live © 2009 Alberta Education (www.learnalberta.ca)

Page 14: Multiplication of Whole Numbers - Assessment Task · Math Live – Multiplication of Whole Numbers: Assessment Task Grade: 5 Strand: ... Tamara thought that she could switch digits

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.

Page 14 of 14 Math Live © 2009 Alberta Education (www.learnalberta.ca)


Recommended