In this Grade 5 lesson from Illustrative Mathematics Chapter 4, students learn to apply the standard algorithm to multiply two- and three-digit numbers by two-digit numbers, including recording the composition of new units. Building on prior work with single-digit multipliers and multiplication without composing, students combine these skills to find products such as 251 × 34 using a structured written method aligned to standard 5.NBT.B.5.
Section 1
Visualizing Multiplication with Place Value Disks
When multiplying, we can model the numbers with place value disks.
If any place value has 10 or more disks after multiplying, we compose them into a single disk of the next larger place value.
This is also known as regrouping.
Section 2
Relating Place Value Regrouping to the Standard Algorithm
Regrouping 10 units of a smaller place value into 1 unit of the next higher place value on a chart (e.g., ) is represented by the 'carried' digit in the standard algorithm.
The carried digit is the number of new groups formed.
Section 3
Connecting Partial Products to the Standard Algorithm
The standard multiplication algorithm is a condensed version of the partial products method.
The regrouped (carried) numbers in the standard algorithm represent the higher place value parts of each partial product, combining the multiplication and addition steps.
Section 4
Applying the Standard Algorithm for Multiplication
The standard algorithm for multiplication is a procedure where you multiply numbers vertically.
You multiply the single-digit multiplier by each digit of the multi-digit number, starting from the ones place and moving left.
When the product in any place value is 10 or more, you regroup (or 'carry') the tens digit to the next place value column to the left.
Expand to review the lesson summary and core properties.
Section 1
Visualizing Multiplication with Place Value Disks
When multiplying, we can model the numbers with place value disks.
If any place value has 10 or more disks after multiplying, we compose them into a single disk of the next larger place value.
This is also known as regrouping.
Section 2
Relating Place Value Regrouping to the Standard Algorithm
Regrouping 10 units of a smaller place value into 1 unit of the next higher place value on a chart (e.g., ) is represented by the 'carried' digit in the standard algorithm.
The carried digit is the number of new groups formed.
Section 3
Connecting Partial Products to the Standard Algorithm
The standard multiplication algorithm is a condensed version of the partial products method.
The regrouped (carried) numbers in the standard algorithm represent the higher place value parts of each partial product, combining the multiplication and addition steps.
Section 4
Applying the Standard Algorithm for Multiplication
The standard algorithm for multiplication is a procedure where you multiply numbers vertically.
You multiply the single-digit multiplier by each digit of the multi-digit number, starting from the ones place and moving left.
When the product in any place value is 10 or more, you regroup (or 'carry') the tens digit to the next place value column to the left.