Use Addition and Subtraction Within 20 to Solve Word Problems Involving Situations Of

1.OA.A.1

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Unpacked

Students develop strategies for adding and subtracting whole numbers within 20.Teachers should be aware of the three types of problems and provide multiple experiences for their students solving ALL three types of problems: Result Unknown, Change Unknown, and Start Unknown. Students should use symbols to represent the unknown numbers in ALL 3 positions. The unknown symbols should include boxes, lines, question marks, or pictures, but not letters. Students use a variety of mathematical representations (e.g., objects, drawings, and equations) during their work. Students should use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction and to develop strategies to solve arithmetic problems with these operations.

Combining the use of situations and models (counters, drawings, number lines) is important in helping students construct a deep understanding of these two operations.

Fosnot and Dolk (2001) point out that in story problems, children tend to focus on getting the answer. “Context problems”, on the other hand, are connected to children’s lives, rather than to school mathematics. They are designed to anticipate and to develop children’s mathematical modeling of the real world.

In Put Together/Take Apart situations, two quantities jointly compose a third quantity (the total), or a quantity can be decomposedinto two quantities (the addends). This composition/decompositionmay be physical or conceptual. These situations are acted out withobjects initially and later children begin to move to conceptual mentalactions of shifting between seeing the addends and seeing thetotal (e.g., seeing children or seeing boys and girls, or seeing redand green apples or all the apples).

The relationship between addition and subtraction in the AddTo/Take From and the Put Together/Take Apart action situationsis that of reversibility of actions: an Add To situation undoes aTake From situation and vice versa and a composition (Put Together)

undoes a decomposition (Take Apart) and vice versa.

Put Together/Take Apart situations with Both Addends Unknownplay an important role because they allow studentsto explore various compositions that make each number.

Equations with one number on the left and an operation on the right (e.g., 5 _ 2 ? 3 to record a group of 5 things decomposedas a group of 2 things and a group of 3 things) allow students tounderstand equations as showing in various ways that the quantities

on both sides have the same value.MP6

Another visual of problem structures:

(Van de Walle, 2013, pg.149)