ALEX Classroom Resources

ALEX Classroom Resources
Subject: Mathematics (5)
Title: Grade 5 Mathematics Module 1, Topic A: Multiplicative Patterns on the Place Value Chart
Description:

Module 1, Topic A begins with a conceptual exploration of the multiplicative patterns of the base ten systems. This exploration extends the place value work done with multi-digit whole numbers in Grade 4 to larger multi-digit whole numbers and decimals. Students use place value disks and a place value chart to build the place value chart from millions to thousandths. They compose and decompose units crossing the decimal with a view toward extending their knowledge of the 10 times as large and 1/10 as large relationships among whole number places to that of adjacent decimal places. This concrete experience is linked to the effects on the product when multiplying any number by a power of ten. For example, students notice that multiplying 0.4 by 1,000 shifts the position of the digits to the left three places, changing the digits’ relationships to the decimal point and producing a product with a value that is 10 10 10 as large (400.0) (5.NBT.2). Students explain these changes in value and shifts in position in terms of place value. Additionally, students learn a new and more efficient way to represent place value units using exponents (e.g., 1 thousand = 1,000 = 103) (5.NBT.2). Conversions among metric units such as kilometers, meters, and centimeters give students an opportunity to apply these extended place value relationships and exponents in a meaningful context by exploring word problems in the last lesson of Topic A (5.MD.1).

Subject: Mathematics (5)
Title: Grade 5 Mathematics Module 2, Topic A: Mental Strategies for Multi-Digit Whole Number Multiplication
Description:

Module 2, Topic A begins a sequential study of multiplication that culminates in Topic D. In order to link prior learning from Grade 4 Module 1 and Grade 5 Module 1 and to set the stage for solidifying the standard multiplication algorithm, students begin at the concretepictorial level. They use place value disks to model multi-digit multiplication of place value units, for example, 42 × 10, 42 × 100, 42 × 1,000, leading quickly to problems such as 42 × 30, 42 × 300, and 42 × 3,000 (5.NBT.1, 5.NBT.2). Students then round factors in Lesson 2 and discuss the reasonableness of their products. Throughout Topic A, students evaluate and write simple expressions to record their calculations using the associative property and parentheses to record the relevant order of calculations (5.OA.1).

Subject: Mathematics (5)
Title: Grade 5 Mathematics Module 1, Topic A: Multiplicative Patterns on the Place Value Chart
Description:

Module 1, Topic A begins with a conceptual exploration of the multiplicative patterns of the base ten systems. This exploration extends the place value work done with multi-digit whole numbers in Grade 4 to larger multi-digit whole numbers and decimals. Students use place value disks and a place value chart to build the place value chart from millions to thousandths. They compose and decompose units crossing the decimal with a view toward extending their knowledge of the 10 times as large and 1/10 as large relationships among whole number places to that of adjacent decimal places. This concrete experience is linked to the effects on the product when multiplying any number by a power of ten. For example, students notice that multiplying 0.4 by 1,000 shifts the position of the digits to the left three places, changing the digits’ relationships to the decimal point and producing a product with a value that is 10 10 10 as large (400.0) (5.NBT.2). Students explain these changes in value and shifts in position in terms of place value. Additionally, students learn a new and more efficient way to represent place value units using exponents (e.g., 1 thousand = 1,000 = 103) (5.NBT.2). Conversions among metric units such as kilometers, meters, and centimeters give students an opportunity to apply these extended place value relationships and exponents in a meaningful context by exploring word problems in the last lesson of Topic A (5.MD.1).

Subject: Mathematics (5)
Title: Grade 5 Mathematics Module 2, Topic A: Mental Strategies for Multi-Digit Whole Number Multiplication
Description:

Module 2, Topic A begins a sequential study of multiplication that culminates in Topic D. In order to link prior learning from Grade 4 Module 1 and Grade 5 Module 1 and to set the stage for solidifying the standard multiplication algorithm, students begin at the concretepictorial level. They use place value disks to model multi-digit multiplication of place value units, for example, 42 × 10, 42 × 100, 42 × 1,000, leading quickly to problems such as 42 × 30, 42 × 300, and 42 × 3,000 (5.NBT.1, 5.NBT.2). Students then round factors in Lesson 2 and discuss the reasonableness of their products. Throughout Topic A, students evaluate and write simple expressions to record their calculations using the associative property and parentheses to record the relevant order of calculations (5.OA.1).

Subject: Mathematics (5)
Title: Grade 5 Mathematics Module 2, Topic C: Decimal Multi-Digit Multiplication
Description:

Throughout Module 2, Topic C, students make connections between what they know of whole number multiplication to its parallel role in multiplication with decimals by using place value to reason and make estimations about products (5.NBT.7). Knowledge of multiplicative patterns from Grade 4 experiences, as well as those provided in Grade 5 Module 1, provide support for converting decimal multiplication to whole number multiplication. Students reason about how products of such converted cases must be adjusted through division, giving rise to explanations about how the decimal must be placed.

Subject: Mathematics (5), Mathematics (5)
Title: Grade 5 Mathematics Module 2, Topic E: Mental Strategies for Multi-Digit Whole Number Division