Grade 4 Mathematics
Problem Solving

Developing Problem Solvers

Problems can be posed in many different ways. These problem solving situations are illustrated in the images to the right. Students must be able to solve problems of any situation.

Problem Solving everyday
Problem solving is not an isolated activity. It doesn't occur every Friday. Instead problem solving is a skill that favors every mathematics lesson. Problem solving is more than just one-step word problems. Problem solving should feature risk tasks, authentic purposes, and multiple ways to be solved.

More than Words
Solving problems goes beyond mathematics presented as word or story problems. Problem solving is the act of finding a solution when a method for solution is not obvious. It can be story problems or simply open-ended questions. These problem solving decks from the North Carolina State Department of Education offer wonderful opportunities for thinking and solving problems.

Problem Solving Decks

Deck B: Grades 3-4
Deck B: Grades 3-4 (Student Copy)
Deck B: Grades 3-4 Solutions

Avoiding key words
1. Key words are misleading. Some key words typically mean addition or subtraction. But not always. Consider: There were 4 jackets left on the playground on Monday and 5 jackets left on the playground on Tuesday. How many jackets were left on the playground? "Left" in this problem does not mean subtract.

2. Many problems have no key words. For example, How many legs do 7 elephants have? does not have a key word. However, any 1st grader should be able to solve the problem by thinking and drawing a picture or building a model.

3. It sends a bad message. The most important strategy when solving a problem is to make sense of the problem and to think. Key words encourage students to ignore meaning and look for a formula. Mathematics is about meaning (Van de Walle, 2012).

Solving Problems Relies on Thinking and Making Sense. Context Helps Make Meaning.
Context helps students make meaning to solve problems. The story problem links below can be connected to a variety of children's literature titles to build context. There are examples of each story structure for each context/theme. Story structures adapted from CGI, 1998. Spaces for quantity are left blank intentionally. Please use numbers that your students are appropriate for your students.

Numberless Word Problems

Start Change End Organizer

Equal Groups Organizer

Addition / Subtraction Problems by Theme

This is a zip file of more than 60 word problems arranged around themes aligned different problem solving situations.

Multiplication/Division Problems by Theme

This is a collection of more than 60 word problems arranged around themes aligned with Equal Group situations. Students must also work with area/array sand comparison situations (multiplicative comparison is introduced in 4th grade).

Other exemplary resources for problem solving include ThinkTank by Origo and Problem Driven Math.