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

Lesson 7: World's Record Folk Dance

In this Grade 5 Illustrative Mathematics lesson, students estimate and solve multi-digit division problems using strategies such as partial quotients and the relationship between multiplication and division. Set in the context of a world record Peruvian folk dance with 4,704 dancers arranged in groups of 8, students practice dividing multi-digit whole numbers in ways that build on their Grade 4 understanding of place value and division. This lesson from Chapter 4 prepares students for more efficient division methods aligned to standard 5.NBT.B.6.

Section 1

Strategic Placement and Maximum Carry

Property

To maximize a product, place the largest available digits in the positions with the highest place value.
The maximum value that can be composed (carried) in any single step of multiplication is 8.

Examples

Section 2

Applying Multiplication to Equal Groups

Property

To find the total number of items in a collection of equal-sized groups, you multiply the number of groups by the number of items in each group.

Total=(Number of groups)×(Number of items per group)Total = (Number\ of\ groups) \times (Number\ of\ items\ per\ group)

Examples

  • If there are 35 dance troupes and each troupe has 24 dancers, the total number of dancers is found by multiplying 35×2435 \times 24.
35×24=840 dancers35 \times 24 = 840\ dancers
  • A folk dance festival has 112 circles of dancers, with 18 dancers in each circle. The total number of participants is:
112×18=2016 participants112 \times 18 = 2016\ participants

Explanation

Multiplication is an efficient method for finding the total when combining multiple groups of the same size. In a word problem, one factor represents the number of equal groups, while the other factor represents the quantity within each group. The product of these two numbers gives you the total quantity across all groups. This concept is fundamental for solving real-world problems involving repeated addition.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Strategic Placement and Maximum Carry

Property

To maximize a product, place the largest available digits in the positions with the highest place value.
The maximum value that can be composed (carried) in any single step of multiplication is 8.

Examples

Section 2

Applying Multiplication to Equal Groups

Property

To find the total number of items in a collection of equal-sized groups, you multiply the number of groups by the number of items in each group.

Total=(Number of groups)×(Number of items per group)Total = (Number\ of\ groups) \times (Number\ of\ items\ per\ group)

Examples

  • If there are 35 dance troupes and each troupe has 24 dancers, the total number of dancers is found by multiplying 35×2435 \times 24.
35×24=840 dancers35 \times 24 = 840\ dancers
  • A folk dance festival has 112 circles of dancers, with 18 dancers in each circle. The total number of participants is:
112×18=2016 participants112 \times 18 = 2016\ participants

Explanation

Multiplication is an efficient method for finding the total when combining multiple groups of the same size. In a word problem, one factor represents the number of equal groups, while the other factor represents the quantity within each group. The product of these two numbers gives you the total quantity across all groups. This concept is fundamental for solving real-world problems involving repeated addition.