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Draw Pictures or Models to Solve


Mathematics All Ages Strategy


Verbal Reasoning Abstract Reasoning Spatial Perception

Draw Pictures or Models to Solve

If your student needs support in solving word problems and deepening conceptual understanding

Instruction And Practice

  1. Objective: Students will draw models or pictures to solve problems so they can visualize what is being asked and more easily identify what to do.
  2. Using visual representations such as models and/or pictures allows students to move their thinking from the concrete to the abstract. By drawing a model, students access the math concepts more easily and connect the mathematical concept to the operation needed to solve. The visual representation also deepens the student's conceptual understanding and, in turn, strengthens problem solving skills.
  3. Visual representations include pictures (concrete pictures), bar models or tape diagrams, number lines, and area models (arrays).
  4. Drawing a picture can be used when solving pure computational problems (e.g. 5 x 7) or for solving word problems. See the next slide for how to use visual representations with word problems.
  5. Keep models simple. Teach students how to draw a model or picture that represents the mathematical concept, but excludes artistic details or irrelevant information.

Using Models To Solve Word Problems

  1. Explain why pictures help. Word problems are like stories with math. You need to figure out which math operation(s) to do to understand the outcome of the story. Drawing out pieces of the problem will help you picture that information like a story.
  2. Model with the class. a) Read a word problem out loud without drawing. b) Ask and discuss: What is this problem about? c) Next, read the problem a 2nd time, stopping to draw a bar model, diagram, or representation of each piece of information (i.e. people, objects or spatial concepts) involved. Use lines and symbols to represent words where possible. Refer to vocabulary that indicates which operation they might use. d) Solve the problem together using the visuals.
  3. Class Activity: Give students a word problem to draw. Working in pairs, students share their drawings and discuss what was helpful in the drawings and what they might adopt next time. Repeat regularly for word problems in class. Make the visual representation part of the assignment, leaving space for it on any worksheets.
  4. Teacher Notes: Keep drawings simple. Use basic shapes such as bars, rectangles, circles, or stick figures. Use arrows and include labels as needed. Remind students that neatness and clarity are far more important than art skills. This is particularly important for students with weaker visual memory or spatial perception.

*print* Student Checklist: Drawing Word Problems

  1. Read the problem one time through.
  2. Read through the problem again and stop to draw each new piece of information into a model, picture, or diagram of the story.
  3. Keep the picture simple and neat. Use basic shapes such as bars, rectangles, circles or stick figures. Use arrows, labels or words to help you make connections to the problem you will solve.
  4. Use your model, picture or diagram to help you create an equation and solve.

Why It Works (the Science Of Learning)!

Picturing a problem offers a concrete way for students to organize the information, understand the question and identify a solution. Pictures enable students to more effectively visualize math problems. Note that students with a learning disability often do not create accurate visual representations or use them strategically to solve problems, so providing a picture or visual for them will be important in helping them effectively use visual representations when solving.

Best-suited for students with weaker: Attention, Inhibition/Impulsivity, Long-Term Memory, Reasoning, Working Memory, Processing Speed (Source: Digital Promise Learner Variability Project)