Problem Solving: The student identifies key information, determines appropriate strategies, finds solutions, and solves new problems with existing knowledge.

Identifying Key Information

Every math problem we solve—whether a simple equation, or a real-world problem (a.k.a. word problem or story problem)—has enough information to determine what its correct solution should be. The key information is any information that will help us understand and solve the problem. It includes quantities, terms or symbols that may indicate a mathematical action (a.k.a. operations) that takes place in the problem, terms or symbols that may indicate multiple mathematical actions happen (e.g., in a multi-step problem), and what the problem is asking the mathematician to solve.

Identifying the most important information isn't always easy, and thus it is a skill that needs to be developed over time. Four factors that contribute to a child's ability to identify key information include:

Math Vocabulary

Understanding mathematical words and symbols is crucial to understanding a problem statement. Without knowing terms like equal, sum, difference, product, quotient, fewer, more, greatest, least, nearest, estimate, of, from, remaining, sold, in all, altogether, et al., and their relationship to mathematical operations, students will have a very hard time figuring out what to do when they see these words. For more information about vocabulary development and example problems, visit the Mathematical Vocabulary section of our Communication page.

Reading Comprehension

The ability to read and understand what a problem is about is also very important. Mathematical vocabulary development helps, but students also must making meaning from the sequence of words and the context they are presented in. For example, read the problem:

Jayme has 24 fewer chrysanthemums than Rajit. Jayme has 18 chrysanthemums. How many chrysanthemums does Rajit have?

Even though the solution can be obtained with a relatively simple addition calculation (18 + 24 = 42), students may get stuck because they have no idea what chrysanthemums are, or they haven't read or heard names like Jayme or Rajit. Oftentimes, replacing the names (e.g., Maria and Leo) or the objects in the problem (e.g. flowers) will help students focus more on the math happening than the story. However, we do not simplify the words that appear in problems ahead of time, as it is also a tiny opportunity for students to learn about our world and develop more general vocabulary.

With a majority of our students being non-native English speakers, our mathematics learning benefits greatly from our strong English Language Arts (ELA) and English as an Additional Language programs. Fortunately, our math teachers are also English language teachers, and they can apply strategies used in ELA to help students understand math problems.

Careful Reading

Related to Reading Comprehension, students may skip reading directions, or read problem statements too quickly and drop or replace words with ones they think should appear.

For example, take the problem:

Subtract 1.56 from 18.3

Students may quickly read it as "Subtract 1.56 and 18.3", and incorrectly set up their problem statement as

1.56 — 18.3

However, with careful reading, students should note the word from and its connection to subtraction: Taking away one amount from a second amount means you start your statement with the second amount and subtract the first amount, as in

18.3 — 1.56

We can help students read more carefully by asking them to read problems three times: once in their minds, once aloud at a normal pace, and once again in their minds. Many times, reading a problem aloud makes the student slow down and encourages them to think about each word being said. Re-reading afterwards can help solidify the students' comprehension of the problem.

Exposure to Different Types of Problems

Simply put, a lot of improvement to identifying key information (and problem solving in general) comes from practice working with different types of problems. The problems may vary in the operation(s) required to solve them, the sequencing of words, the use of related terms, the context in which a problem appears, or they may build upon simpler problems to create multi-step problems. With the repeated exposure that happens within a year and throughout our math program (due to Singapore Math's spiraling curriculum), students will get better at understanding directions and problem statements, and gain comfort with solving real-world problems over time.

Determining Appropriate Strategies

Through relational and instrumental understanding and systematic variation, students learn more than one way to approach solving problems. Some strategies are more efficient than others, but sometimes a student may be able to solve a problem in a different way than others (and that's OK!). Once a student has identified the key information, there are several general strategies we teach our students to use:

• Write down the key information in an organized manner (a teacher may ask, "What do we already know?")

  • Alternatively, highlighting the key information can work well with coordinated colors

• Write a sentence or an answer statement with a blank line for the final amount ("What are we trying to find out?")

• In Grades K-2: Draw a picture to represent the problem (see the Visualization page for more information)

• In Grades 2-5: Draw a bar model to represent the problem (see the Visualization page for more information)

• Write a problem statement (equation) using numbers and symbols

• Use charts or tables to help organize information and see patterns, if needed

Finding Solutions and Solving New Problems

Ultimately, the goal of problem-solving is to consistently solve problems. While the real-world problems in Singapore Math tend to be very challenging, the lessons always provide students with all of the skills and knowledge needed to successfully solve the problems in the program. It becomes the student's job to take the strategies, content knowledge, and math skills they have and apply them to solving real-world problems.