Math Live Multiplication of Whole Numbers: Assessment Task. Grade: 5 Strand: Number Outcome: 5

Transcription

1 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 1 of 14

2 Students can represent multi-digit multiplication in many ways: Lattice Multiplication: 57 x Distributive Property: 57 x = x 12 = x 12 = = x 57 = x 57 = Array (Distributive Property II): 57 x Page 2 of 14

3 Partial Products: 57 x x Standard Algorithm: 57 x x Page 3 of 14

4 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 x Show how you would find each of the products. 52 x x 12 Page 4 of 14

5 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. Page 5 of 14

6 Scoring Guide Multiplication of Whole Numbers Level Criteria WOW! YES Uses an algorithm to find the product of a 3-digit by 2-digit multiplication problem Question #1 Accurately applies an algorithm to find each of the products and shows all necessary steps including regrouping 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 Explains the process of multiplication of large numbers as finding the total of a given number of equal groups YES, BUT 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 NO, 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 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 Page 6 of 14

7 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! x x Show how you would find each of the products. 352 x x 22 Page 7 of 14

8 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

9 Multiplication of Whole Numbers: Assessment Task Yes 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! x x Show how you would find each of the products. 352 x x 22 Page 9 of 14

10 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

11 Yes, but 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! x x Show how you would find each of the products. 352 x x 22 Page 11 of 14

12 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

13 No, but 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! x x Show how you would find each of the products. 352 x x 22 Page 13 of 14

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. Page 14 of 14