A Standards Progression
How does the idea of multiplication grow across grade
levels?
(include contexts, representations, equations, models,
strategies, and number size)
How does the work in each grade level
build toward an understanding and
use of the distributive property to
justify strategies?
2.OA. Work with equal groups of objects to gain
foundations for multiplication.
4. Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and
up to 5 columns; write an equation to express the
total as a sum of equal addends.
Uses addition to find the total
Models: objects and rectangular arrays
Equations are repetition of equal addends (2+2+2+2=8)
Begins the concrete experiences of
multiplication
3.OA. Understand properties of multiplication and
the relationship between multiplication and
division.
5. Apply properties of operations as strategies to
multiply and divide. Examples: if 6x4 = 24 is known,
then 4x6=24 is also known. (Commutative property
of multiplication.) 3x5x2 can be found by 3x5=15,
then 15x2=30, or 5x2=10, then 3x10-30. (Associative
property of multiplication.) Knowing that 8x5=40 and
8x2=16, one can find 8x7 as
8x(5+2)=(8x5)+(8x2)=40+16=56. (Distributive
property.)
(Please note: There are many other standards that develop
multiplication. This is one standard that directly identifies the
Properties of Operations.)
 Commutative
 Associative
 Distributive
4.NBT. Use place value understanding and
properties of operations to perform multi-digit
arithmetic.
5. Multiply a whole number of up to four digit by a
one-digit whole number, and multiply two two-digit
numbers, using strategies based on place value and
the properties of operations. Illustrate and explain
the calculation by using equations, rectangular
arrays, and/or area models.
Number size increases from 4-digit x 1 digit, to 2-digit by 2digit.
5.NBT. Perform operations with multi-digit whole
numbers and with decimals to hundredths.
5. Fluently multiply muli-digit numbers using ‘the’
standard algorithm.
Students work in whole numbers.
Uses place value to support properties of the operations.
Models might include: open arrays, arrays, equations and
partial product notation
Gr. 3 Builds on understanding of arrays
to deepen thinking about commutative
property and distributive property.
Provides a scaffold from the concrete
array to the equation.
Gr. 4 Builds on a concrete
understanding of single digit numbers
to expand to larger whole numbers.
Uses models more abstractly to
scaffold use of properties to support
strategies.
Gr. 5 Fluency expectation in
multiplication of whole numbers.
Uses place value to support properties of the operations.
Models might include: open arrays, arrays, equations and
partial product notation