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Infusing Dynamism into Daily Problem Solving

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Method 1: Question-less Problems (4:50)

There is no singular method for delivering question-less word problems, but the following procedure often produces dynamic results.

  • Students chorally read a few sentences of information that does not include a question.

  • The teacher directs students to diagram what they read.

  • As students draw diagrams, the teacher probes the room, prompting individuals to do one or more of the following:

    • Label all parts of the diagram.

    • Position a question mark in the diagram.

    • Share and explain drawings with a classmate.

    • Fill in parts of the diagram that aren’t given in the information provided.

    • Draw a second diagram to represent the same information.

    • Create a list of questions that could be answered with the given information.

  • After a few minutes, the teacher demonstrates drawing a diagram to match the question-less problem.  To stimulate flexible thinking, they might create a model that differs from what most students drew.

  • Students share questions that they wrote, and the teacher chooses one for all students to solve.

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Audio excerpted courtesy of Penguin Random House Audio from MATH MIND by Shalinee Sharma, read by Shalinee Sharma. © 2024 Zearn, ℗ 2024 Penguin Random House, LLC. All rights reserved.

Method 2: Write a Question to Match a Diagram (11:07)

Sophie has $100. After spending some money, she has $85 left. How much money did she spend?

 
 

Sophie had $85. After earning some more money, she had $100. How much money did she earn?

Method 3:  Select a Diagram that Matches a Story Problem. (15:25)

 

  • How many toothpicks did she use? 24 toothpicks

  • Why is Diagram A incorrect? Diagram A shows that Hannah made 3 triangles with 8 toothpicks in each triangle.

  • How could you change the problem to make Diagram A correct? Hannah made 3 triangles for a math project. She used 8 toothpicks for each triangle. How many toothpicks did she use? 24 toothpicks

 

Method 4:  Problem Solving Ladders (19:49)

Michael decorated 4 Valentine’s Day cards with 28 stickers. He put the same number of stickers on each page.

  • Michael used _____ more than 20 stickers to decorate the Valentine’s Day cards.

  • How many stickers did Michael put on each card?

  • Eric had twice as many stickers and cards as Michael. He put 5 stickers on the first card, 15 stickers on the second card, and an equal amount on each of the remaining cards. How many stickers did Eric put on each of the remaining cards?

  • Eric’s stickers came in packs of 4. If each pack costs 50 cents, how much money did he spend to decorate his cards?

Method 5:  Robot Problem Solver (26:26)

  • Write the word Flour and to the right of the word, draw a long bar.

  • Above the bar, write 15 Pounds.

  • Subdivide the bar into 5 equal units.

  • Beneath the word Flour, write Sugar.

  • To the right of the word Sugar, draw a single unit that is the same size as each Flour unit.

  • Draw a bracket that stretches from the bottom end of the first Flour unit to the last Flour unit.

  • Draw a question mark below the bracket.

  • Now, take a minute or two to write a word problem that matches the diagram you just drew.  If needed, replay the instructions.

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