Section 1
Concept: Regrouping Products
Property
When the result of multiplying in one place value is 10 or more, we regroup it into groups of the next higher place value.
For example, a product of 35 ones is regrouped as 3 tens and 5 ones.
In this Grade 5 Illustrative Mathematics lesson from Chapter 4, students apply whole-number multiplication and the standard algorithm to solve real-world problems involving the volume of rectangular prisms. Using birdhouse dimensions as context, they calculate products of multi-digit numbers and explore strategies such as the associative and commutative properties of multiplication. The lesson addresses standards 5.NBT.B.5 and 5.MD.C.5, reinforcing multi-digit multiplication within a measurement and volume context.
Section 1
Concept: Regrouping Products
When the result of multiplying in one place value is 10 or more, we regroup it into groups of the next higher place value.
For example, a product of 35 ones is regrouped as 3 tens and 5 ones.
Section 2
Concept: Decomposing into Partial Products
To multiply two two-digit numbers, you can decompose one number into its tens and ones.
Multiply each part by the second number to get two partial products, then add them together.
For two numbers and , where :
Section 3
Concept: The Placeholder Zero in Multiplication
Each place value is 10 times greater than the place value to its immediate right.
Therefore, multiplying a number by 10 shifts each of its digits one place to the left, increasing the number's total value by a factor of 10.
Section 4
Multiply First, Then Add the Carry
When composing a new unit in multiplication, you must multiply the digits first, then add the carried value to that product.
The rule is: (digit multiplier) + carried value.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter
Expand to review the lesson summary and core properties.
Section 1
Concept: Regrouping Products
When the result of multiplying in one place value is 10 or more, we regroup it into groups of the next higher place value.
For example, a product of 35 ones is regrouped as 3 tens and 5 ones.
Section 2
Concept: Decomposing into Partial Products
To multiply two two-digit numbers, you can decompose one number into its tens and ones.
Multiply each part by the second number to get two partial products, then add them together.
For two numbers and , where :
Section 3
Concept: The Placeholder Zero in Multiplication
Each place value is 10 times greater than the place value to its immediate right.
Therefore, multiplying a number by 10 shifts each of its digits one place to the left, increasing the number's total value by a factor of 10.
Section 4
Multiply First, Then Add the Carry
When composing a new unit in multiplication, you must multiply the digits first, then add the carried value to that product.
The rule is: (digit multiplier) + carried value.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter