In Grade 5, students build fluency with the standard algorithm for multiplication, connecting the algorithm to strategies learned in fourth grade, and continue developing proficiency with dividing multi-digit numbers, using strategies based on place value and the properties of operations. In addition, from the start of fifth grade, they are expected to fluently add and subtract multi-digit numbers using the standard algorithm they learned in fourth grade. The tabs identify key strategies for adding, subtracting, multiplying, and dividing multi-digit numbers, and provide links to documents that fully describe and illustrate these strategies.
Addition Strategies Based on Place Value and Properties of Operation
Fluency is grounded in understanding. Developing an understanding of the algorithm for multi-digit addition involves connecting physical and visual models to numeric representations. In fourth grade, students use a variety of tools, models, and strategies that students to build fluency with addition:
Use number lines to add multi-digit numbers
Add multi-digit numbers using partial sums
Adjust multi-digit numbers to add (pictured)
Explain and connect strategies for adding to the standard algorithm
Add multi-digit numbers using the standard algorithm
Determine when an algorithm is efficient and when it is not
For full descriptions and illustrations of these strategies, download the file linked below:
Subtraction Strategies Based on Place Value and Properties of Operations
Fluency is grounded in understanding. Developing an understanding of the algorithm for multi-digit subtraction involves connecting physical and visual models to numeric representations. In fourth grade, students use a variety of tools, models, and strategies that students to build fluency with subtraction:
Use number lines to subtract multi-digit numbers
Subtract multi-digit numbers using partial differences by adding up or counting back (pictured)
Adjust multi-digit numbers to subtract
Explain and connect strategies for subtracting to the standard algorithm for subtraction
Subtract multi-digit numbers using the standard algorithm
Determine when an algorithm is efficient and when it is not
For full descriptions and illustrations of these strategies, download the file linked below:
Multiplication Strategies Based on Place Value and Properties of Operations
Fluency is grounded in understanding. Developing an understanding of the algorithm for multi-digit multiplication involves connecting physical and visual models to numeric representations. The learning targets for 5.NBT.5 identify the tools, models, and strategies that students should use to build fluency with multiplication:
Use partial products to multiply multi-digit numbers.
Connect partial products to the standard algorithm for multiplication.
For full descriptions and illustrations of these strategies, download the file linked below:
Division Strategies Based on Place Value and Properties of Operations
Fluency is grounded in understanding. Developing an understanding of multi-digit division involves connecting physical and visual models to numeric representations. The learning targets for 5.NBT.6 identify the following tools, models, and strategies that students should use to build fluency with division:
Represent division of multi-digit whole numbers with base ten models (equal groups) and arrays/area models.
Relate division of multi-digit numbers to multiplication of those numbers.
Connect representations to a partial quotient algorithm.
Use partial quotients to divide multi-digit whole numbers.
Explain partial quotients.
For full descriptions and illustrations of these strategies, download the file linked below: