Problem Solving Using the Four Operations

Primary Standards:

MAFS.3.OA.4.8 Solve two-step word problems using the four (addition or subtraction) operations. Represent these problems using equations with a letter (symbol) standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

MAFS.3.OA.1.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Connecting Standards:

MAFS.3.OA.1.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = [] ÷ 3, 6 × 6 = ?.

Content Knowledge:

In prior grades, students solved a variety of one- and two-step word problems using addition or subtraction.  In 3rd grade, with the introduction of multiplication and division, they will be challenged to solve one- and two-step problems with all four of the operations.

Knowing which operation makes sense to solve a problem is a foundational problem-solving skill.  This is not achieved by identifying key words that tell students what to do, but instead, by recognizing the story situation or structure.  When students understand what is happening in a story problem and know the actions of the operations, they are able to match the operation to the problem situation.

A critical skill in solving word problems is the ability to represent the problem situation with equations.  In prior situations, students used symbols such as a blank space, a box, or a question mark to represent missing information.  In 3rd grade, they are introduced to the use of a letter to stand of unknowns in equations.  Students may be accustomed to representing a problem with an equation, but in two-step problems they may need to build two equations as they work through the steps of the problem.


GCG 1 – Learning Goal:  As a mathematician, I will be able to model and solve one-step problems; represent problems using equations with a letter for the unknown

  • Step 1: Represent a problem-solving situation with an equation, using a letter for the unknown
  • Step 2: Solve one-step equations, using a letter for the unknown

GCG 2 – Learning Goal:  As a mathematician, I will be able to model and solve two-step problems; represent problems using equations with a letter for the unknown

  • Step 1: Explain and directly model the steps of a two-step problem with concrete models or drawings
  • Step 2:  Represent a two-step problem-solving situation with an equation (or equations), using a letter for the unknown
  • Step 3: Solve two-step problems using models, drawing, or equations
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