Learn on PengiIllustrative Mathematics, Grade 5Chapter 4: Wrapping Up Multiplication and Division with Multi-Digit Numbers

Lesson 6: The Birds

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

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.

35 ones=3 tens+5 ones35 \text{ ones} = 3 \text{ tens} + 5 \text{ ones}

Section 2

Concept: Decomposing into Partial Products

Property

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 ABAB and CDCD, where AB=10A+BAB = 10A + B:

AB×CD=(B×CD)+(10A×CD)AB \times CD = (B \times CD) + (10A \times CD)

Examples

Section 3

Concept: The Placeholder Zero in Multiplication

Property

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.

Examples

Section 4

Multiply First, Then Add the Carry

Property

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 ×\times multiplier) + carried value.

Examples

Book overview

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Chapter 4: Wrapping Up Multiplication and Division with Multi-Digit Numbers

  1. Lesson 1

    Lesson 1: Estimate and Find Products

  2. Lesson 2

    Lesson 2: Partial Products: Diagrams and Algorithms

  3. Lesson 3

    Lesson 3: Standard Algorithm: Introduction and Practice

  4. Lesson 4

    Lesson 4: Standard Algorithm: Multi-digit Numbers with Composing

  5. Lesson 5

    Lesson 5: Build Multiplication Fluency

  6. Lesson 6Current

    Lesson 6: The Birds

  7. Lesson 7

    Lesson 7: World's Record Folk Dance

  8. Lesson 8

    Lesson 8: Partial Quotients: Strategy and Algorithm

  9. Lesson 9

    Lesson 9: Practice Division with Partial Quotients

  10. Lesson 10

    Lesson 10: Find Missing Side Lengths

  11. Lesson 11

    Lesson 11: World's Record Noodle Soup

  12. Lesson 12

    Lesson 12: Fractions as Partial Quotients (Optional)

  13. Lesson 13

    Lesson 13: Lots of Milk

  14. Lesson 14

    Lesson 14: Real-World Applications: Trash Problems

Lesson overview

Expand to review the lesson summary and core properties.

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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.

35 ones=3 tens+5 ones35 \text{ ones} = 3 \text{ tens} + 5 \text{ ones}

Section 2

Concept: Decomposing into Partial Products

Property

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 ABAB and CDCD, where AB=10A+BAB = 10A + B:

AB×CD=(B×CD)+(10A×CD)AB \times CD = (B \times CD) + (10A \times CD)

Examples

Section 3

Concept: The Placeholder Zero in Multiplication

Property

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.

Examples

Section 4

Multiply First, Then Add the Carry

Property

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 ×\times multiplier) + carried value.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 4: Wrapping Up Multiplication and Division with Multi-Digit Numbers

  1. Lesson 1

    Lesson 1: Estimate and Find Products

  2. Lesson 2

    Lesson 2: Partial Products: Diagrams and Algorithms

  3. Lesson 3

    Lesson 3: Standard Algorithm: Introduction and Practice

  4. Lesson 4

    Lesson 4: Standard Algorithm: Multi-digit Numbers with Composing

  5. Lesson 5

    Lesson 5: Build Multiplication Fluency

  6. Lesson 6Current

    Lesson 6: The Birds

  7. Lesson 7

    Lesson 7: World's Record Folk Dance

  8. Lesson 8

    Lesson 8: Partial Quotients: Strategy and Algorithm

  9. Lesson 9

    Lesson 9: Practice Division with Partial Quotients

  10. Lesson 10

    Lesson 10: Find Missing Side Lengths

  11. Lesson 11

    Lesson 11: World's Record Noodle Soup

  12. Lesson 12

    Lesson 12: Fractions as Partial Quotients (Optional)

  13. Lesson 13

    Lesson 13: Lots of Milk

  14. Lesson 14

    Lesson 14: Real-World Applications: Trash Problems