Overview
In this module, students use place value understanding and visual representation to solve multiplication and division problems with multi-digit numbers. As a key area of focus for Grade 4, this module moves slowly but comprehensively to develop students' ability to reason about the methods and models chosen to solve problems with multi-digit factors and dividends.
In Topic A, students begin by investigating the formulas for area and perimeter. They then solve multiplicative comparison problems including language such as "times as much as" with focus on problems using area and perimeter as context.
EXAMPLE:
A field is 9 feet wide. It is 4 times as long as it is wide. What is the perimeter of the field?
Students create diagrams to represent these problems as well as write equations with symbols of the unknown quantities.
In Topic B, students use place value disks to multiply single - digit numbers by multiples of 10, 100, and 1,000 and two-digit multiples of 10 by tow digit multiples of 10.
In Topic A, students begin by investigating the formulas for area and perimeter. They then solve multiplicative comparison problems including language such as "times as much as" with focus on problems using area and perimeter as context.
EXAMPLE:
A field is 9 feet wide. It is 4 times as long as it is wide. What is the perimeter of the field?
Students create diagrams to represent these problems as well as write equations with symbols of the unknown quantities.
In Topic B, students use place value disks to multiply single - digit numbers by multiples of 10, 100, and 1,000 and two-digit multiples of 10 by tow digit multiples of 10.
In Topic C, students use the distributive property and multiply using place value disks to model. Practice with place value disks is used for two-, three-, and four-digit by one-digit multiplication problems with recordings as partial products. Finally, the partial products method, the standard algorithm, and the area model are compared and connected by the distributive property.
Topic D gives students the opportunity to apply their new multiplication skills to solve multi-step word problems. Students write equations from statements within the problems and use a combination of addition, subtraction, and multiplication to solve.
In Topic C, students synthesize (use analyze known concepts) their Grade 3 knowledge of division types (group size unknown and number of groups unknown) wit their new, deeper understanding of place value.
In Topic C, students synthesize (use analyze known concepts) their Grade 3 knowledge of division types (group size unknown and number of groups unknown) wit their new, deeper understanding of place value.
In Topic F, students explore factors, multiples, and prime and composite numbers within 100, gaining valuable insights into patterns of divisibility as they test for primes and find factors and multiples.
Topic G extends the practice of division with three- and four-digit dividends using place value understanding. Place value disks support students visually as they decompose each unit before dividing. Students then practice using the standard algorithm to recored long division. The solve work problems and make connections to the area model as was done with two-digit dividends.
Topic H culminates at the most abstract level by explicitly connecting the partial products appearing in the area model to the distributive property and recording the calculation vertically.
Topic G extends the practice of division with three- and four-digit dividends using place value understanding. Place value disks support students visually as they decompose each unit before dividing. Students then practice using the standard algorithm to recored long division. The solve work problems and make connections to the area model as was done with two-digit dividends.
Topic H culminates at the most abstract level by explicitly connecting the partial products appearing in the area model to the distributive property and recording the calculation vertically.