The Addition and Subtraction unit focuses on how students develop conceptual and algorithmic understanding using multiple strategies and representations.
See the standards throughout the grades.
See this progression for Addition and Subtraction beginning in Kindergarten.
Overall Purpose: Preservice teachers need to be able to use multiple strategies to solve addition and subtraction, recognize and analyze word problem types, apply addition and subtraction to the concrete, representation, and abstract progression, and unpack students' strategies to determine solution pathways and mathematical understanding.
N3.a: Add, subtract, multiply, and divide in multiple ways. Compare advantages and disadvantages of each method.
N3.b. Examine hypothetical or actual student calculation methods and decide if the methods are valid or not.
N3.c. Explain how to use properties of operations to make some calculations such as 24 x 25 easy to carry out mentally and write strings of equations, such as 24 x 25 = (6 x 4) x 25 = 6 x (4 x 25) = 6 x 100 = 600, to show how properties of operations support the “mental math.”
N4.a. Describe advantages and disadvantages of different concrete, pictorial, and abstract representations. Make connections amongst these representations and make connections between the representations and the numerical written methods, including the standard algorithm.
O2.a. Make sense of models for addition, subtraction, multiplication and division that progress from concrete through pictorial to abstract. Justify the choice of model for the context of a problem. Write and solve equations with the unknown in each location.
O2.b. State, recognize and apply:
Associative property of addition
Associative property of multiplication
Closure of addition
Closure of multiplication
Commutative property of addition
Commutative property of multiplication
Distributive property
Identity property of addition
Identity property of multiplication
Zero property of multiplication
Additive inverse property
Multiplicative inverse property
O1.d. Explore and discuss the different ways remainders can be interpreted when solving division problems. In particular, identify the different meanings of the remainder in a partitive vs. a measurement context.
O1.b. Use all of the different problem types for addition and subtraction (Add To, Take From, Put Together/Take Apart, Comparison) to develop meaning for these operations.
Understand that students may add and subtract in different ways using multiple representations.
Connect the structure of addition to the properties of addition.
Connect addition with different representations.
The word problem structure types help students develop a schema to separate important information and to structure their thinking (Van de Walle, Karp, Lovin, Bay-Williams, 2018, p. 117).
Help students develop generalized strategies.
Making Sense Series - Addition and Subtraction Video (Graham Fletcher)
Developing Essential Understanding of Addition and Subtraction for Teaching Mathematics in Pre-K-Grade 2 Book (Janet Caldwell, Karen Karp, Jennifer Bay-Williams, and Rose Mary Zbiek)
Beckmann (2017) Resources:
Chapter 3
Billstein (2016) Resources:
Sections 3-2, 3-4
Sowder (2017) Resources:
Chapter 3
Van De Walle (2019) Resources:
Chapter 11