Fluently multiply multi-digit whole numbers using the standard algorithm.
Measurement Topic
This standard is reported on the report card in these quarters as follows:
5th Grade Students Learning 5th Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of multiplication and division of different number types.
4th Grade Students Learning 5th Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of multiplication.
Learning Targets (I can)
Use partial products to multiply multi-digit numbers.
Connect partial products to the standard algorithm for multiplication.
Explain the standard algorithm for multiplication of multi-digit numbers.
Use the standard algorithm to multiply 2-digit by 1-digit factors, 3-digit by 1-digit factors, 4-digit by 1-digit factors, 2-digit by 2-digit factors, 3-digit by 2-digit factors, and 4-digit by 2-digit factors.
Solve problems using multi-digit multiplication.
About the Math
Multiplication can be represented by arrays, area models, or by equal jumps on a number line. In order to teach the multiplication algorithm with understanding, models must be used to explain the procedure for using the standard algorithm.
Use partial products to multiply multi-digit numbers.
The Distributive Property can be applied to expressions to find partial products. Students should show a deep understanding of partial products and various decompositions of factors. Partial products can be recorded as an algorithm as well. However, as the number of place values grows partial products can lose its efficiency.
Connect partial products to the standard algorithm for multiplication.
Students must be able to use the standard algorithm and explain how it works. To do this, students should connect the standard algorithm process to partial products. Essentially, the standard algorithm consolidates partial products into a single step per place value. See the linked article for more information.
Explain the standard algorithm for multiplication of multi-digit numbers.
The standard algorithm consolidates steps. It is a digit-based process. It relies on use of single-digit factors as values are not expanded. In the image to the right, one sees 6 x 9 but the actual computation is 6 x 9 tens or 6 x 90. Students should speak to place value as they progress through the algorithm.
Use the standard algorithm to multiply 2-digit by 1-digit factors, 3-digit by 1-digit factors, 4-digit by 1-digit factors, 2-digit by 2-digit factors, 3-digit by 2-digit factors, 4-digit by 2-digit factors and 3-digit by 3-digit factors.
As noted above, students must be able to use and explain the standard algorithm. Additionally, students should be challenged to determine when the standard algorithm is or isn't efficient. For example, 32 x 3 might be more efficiently thought of as 30 x 3 (90) + 2 x 3 (6). The paper/pencil algorithm for this computation is likely inefficient for most students.
Essential vocabulary for this standard includes: standard algorithm, multiply, product, and factor.
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
Progression Throughout Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Use partial products to multiply multi-digit numbers.
Connect partial products to the standard algorithm for multiplication.
Explain the standard algorithm for multiplication of multi-digit numbers.
Use the standard algorithm to multiply 2-digit by 1-digit factors, 3-digit by 1-digit factors, 4-digit by 1-digit factors, 2-digit by 2-digit factors, 3-digit by 2-digit factors, and 4-digit by 2-digit factors.
Multiply multi-digit numbers using the standard algorithm.
Revisit with routines and independent work.
Revisit with routines and independent work. Make connections when teaching multiplying decimals and volume.
Revisit with routines and independent work. Make connections when teaching multiplying decimals and volume.
These tasks can be used with small group or whole group instruction.
Instructional Materials for the various computation strategies can be found in Figuring Out Fluency Multiplication and Division with Whole Numbers (this book has been provided to schools) as follows:
Book Cover for Figuring Out Fluency Multiplication and Division with Whole Numbers
Partial Products-- pages 80-88
Standard Algorithm for Multiplication-- pages 144-150
Provide opportunities for students to share their current strategies for multiplying two 2-digit numbers. After a sense of students' current level of performance is established, begin by revisiting the concept of multiplication as finding the total number of items in multiple groups, using base-10 blocks, arrays, and area models for visualization. For example, show students how to calculate the area of a rectangle with 12 rows and 15 columns on graph paper, with base 10 blocks, and by breaking apart into equations. Multiple representations will help students have a deeper understanding of why 12 × 15 equals 180. Students should then practice multiplying more challenging 2-digit numbers, such as 64 × 42, using partial products written as equations. Provide context to the expression (For example, find the total number of seats in a stadium with 64 rows of 42 seats in each row) and estimate a reasonable answer before students being solving.
Use base-10 representations and color coding to help students make the connection between partial products (breaking apart each factor by place value) and the standard algorithm. Color coding can be used to help students understand how the two strategies are connected. Consider creating anchor charts to support students' understanding of both strategies. See slidesLinks to an external site. for anchor chart ideas. Use the same connections when solving 2 digit × 2 digit expressions.
Provide students completed problems that were solved using the standard algorithm. The work should be flawed in some way and students should analyze the work and identify the incorrect calculations.
Write a 3-digit by 1-digit multiplication problem with a product close to 2,000?
List two numbers whose product is between 400 and 600.
Is 4,000 a reasonable estimate for 312 x 9? Explain your reasoning.
How does the order of the digits in the factors impact the product? (e.g. 452 x 7 compared to 425 x 7)
In a multiplication problem, what happens to the product if each factor is multiplied by 2? What happens to the product if one factor is doubled and the other factor is divided by 2?
Is the product of 42 x 63 over or under 2,400? Use what you know about place value in the standard algorithm to explain your answer.
You multiply two two-digit numbers and the product is close to 2,600.What two numbers did you multiply?
Use 1,2,3,4,5 to make the a multiplication problem with the greatest product? How does the placement of the numbers impact the product?
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first(often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
Print Resources
Book Thumbnail
Book Title
Grade
Pages
Teaching Student-Centered Mathematics
3-5
Expanded Lesson: Area Model for Multiplication, Pages 129-130
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.
Use partial products to multiply multi-digit numbers.
Connect partial products to the standard algorithm for multiplication.
Explain the standard algorithm for multiplication of multi-digit numbers.
Use the standard algorithm to multiply 2-digit by 1-digit factors, 3-digit by 1-digit factors, 4-digit by 1-digit factors, 2-digit by 2-digit factors, 3-digit by 2-digit factors, and 4-digit by 2-digit factors.
Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.