Bansho (What is it?)

Bansho is a method of teaching developed in Japan that focuses on teaching math through problem solving.  It allows students to see connections and progressions of the thinking involved when developing strategies to solve a problem.

For an in depth explanation of bansho in the Ontario classroom visit:

Examples of student work and strategies (produced by students in the class) can be found at: or

Planning/Organization  quick notes:

Here is a blank planning sheet:

Bansho Planning Sheet blank

An excellent math resource:


The Lesson – The Teacher’s Role

Lessons are generally set up with an activation (no more than 5 minutes), a problem (30-40 minutes), and the consolidation (15-25 minutes).  

The students work in groups to solve the problem, and are not given “leading questions”, but rather allowed to work through the problem in order to develop perseverance.  As a teacher, when you circulate around the room, it is very important that if you see a student doing something wrong, you don’t correct them or ask them “leading questions” that you hope will make them see their mistake.  It is very important that they be allowed to make mistakes.  It is also good to put up work that is incorrect, because there is often excellent thinking going on in questions that are wrong!  (Focus on the excellent thinking) “Aha” moments will often occur during the consolidation.  You will discover that students will quickly self-correct on the next bansho question if they have discovered their mistake on their own.

Many of the strategies used by students to solve problems can be found in the Ontario Education document “A Guide to Effective Instruction in Mathematics”.

There are always other strategies that come up as well.  These are great opportunities for the students to make connections between strategies.

Questions should have multiple entry points.

When groups have answered the question using one strategy, if time remains, they are sent back to solve the problem again using a different strategy.

Before consolidation, it is a good idea to ask that all the students in every group be expected to be able to explain the strategy the group used.


The students’ work can be assessed according to the categories of knowledge and skills that are described as follows:

Knowledge and Understanding. Subject-specific content acquired in each grade (knowledge), and the comprehension of its meaning and significance (understanding).

Thinking. The use of critical and creative thinking skills and/or processes,3 as follows:
– planning skills (e.g., understanding the problem, making a plan for solving the problem)
– processing skills (e.g., carrying out a plan, looking back at the solution)
– critical/creative thinking processes (e.g., inquiry, problem solving)

Communication. The conveying of meaning through various oral, written, and visual forms (e.g., providing explanations of reasoning or justification of results orally or in writing; communicating mathematical ideas and solutions in writing, using numbers and algebraic symbols, and visually, using pictures, diagrams, charts, tables, graphs, and concrete materials).

Application. The use of knowledge and skills to make connections within and between various contexts.

Examples of tests will be made available on this site.

7 Responses to Bansho (What is it?)

  1. Krish Khurana says:

    Where do you post all of your tests and quizzes for the grade 5 and 4/5 split class? Can you give me the link please?

    • mrwendler says:

      All the tests and quizzes are located on the math pages (set up according to strands). For example, if you click on the Numeration tab, click on the Addition Unit (Grade 4/5), about half way down the page you will find some tests (e.g.: Mental Math Addition Test Grade 4).

  2. Logan Bayer says:

    Do you happen to have any resources/ unit for multiplication of decimals? I guess specifically esitimating products and getting their feet wet from that end

    • mrwendler says:

      Nothing specific as of yet. I often include money questions during my unit on multiplication, but I would like to include more of it at the end of my unit on fractions (and decimals). If you come across some good resources, please send them my way and I will post them for others to use 🙂

  3. Sara says:

    How often are students working in small groups on these problems, and how often is it independent work? Do you give them a choice?
    Thanks! 🙂

  4. mrwendler says:

    They mostly work in partners and small groups. I set up groups/lists in my class that are divided into “like” ability, and “different” ability. I usually start a unit with the students working in “different” ability groups (meaning a strong student works with a weak student) to allow the weaker students to acclimatize to what we are doing. As the unit moves along I switch to “like” groups to get all the students more involved (by this point the weaker students have found strategies that work for them, and the stronger students can come up with more efficient and creative solutions). When I feel things moving along, I might try having them work independently (usually if I plan on evaluating where they are at). Hope that helps 🙂

  5. Pingback: A-C … Alphabetical Signposts to Teacher Excellence – Teach innovate reflect

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