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Differentiating Tasks. Math 412 February 11, 2009. Differentiating Instruction.

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Differentiating Tasks

Math 412

February 11, 2009

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Differentiating Instruction

  • “…differentiating instruction means … that students have multiple options for taking in information, making sense of ideas, and expressing what they learn. In other words, a differentiated classroom provides different avenues to acquiring content, to processing or making sense of ideas, and to developing products so that each student can learn effectively.”

    Tomlinson 2001

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Differentiating Instruction

Some ways to differentiate instruction in mathematics class:

  • Open-ended Questions

  • Common Task with Multiple Variations

  • Differentiation Using Multiple Entry Points

  • Example Spaces

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Diversity in theClassroom

  • Using differentiated tasks is one way to attend to the diversity of learners in your classroom.

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Open-ended Questions

  • Open-ended questions have more than one acceptable answer and/ or can be approached by more than one way of thinking.

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Open-ended Questions

  • Well designed open-ended problems provide most students with an obtainable yet challenging task.

  • Open-ended tasks allow for differentiation of product.

  • Products vary in quantity and complexity depending on the student’s understanding.

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Open-ended Questions

  • An Open-Ended Question:

    • should elicit a range of responses

    • requires the student not just to give an answer, but to explain why the answer makes sense

    • may allow students to communicate their understanding of connections across mathematical topics

    • should be accessible to most students and offer students an opportunity to engage in the problem-solving process

    • should draw students to think deeply about a concept and to select strategies or procedures that make sense to them

    • can create an open invitation for interest-based student work

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Open-ended Questions Method 1: Working Backward

  • Identify a topic.

  • Think of a closed question and write down the answer.

  • Make up an open question that includes (or addresses) the answer.


    • Multiplication

    • 40 x 9 = 360

    • Two whole numbers multiply to make 360. What might the two numbers be?

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Open-ended Questions Method 2: Adjusting an Existing Question

  • Identify a topic.

  • Think of a typical question.

  • Adjust it to make an open question.


    • Money

    • How much change would you get back if you used a toonie to buy Caesar salad and juice?

    • I bought lunch at the cafeteria and got 35¢ change back. How much did I start with and what did I buy? Identify a topic.

Today’s Specials

Green Salad $1.15

Caesar Salad $1.20

Veggies and Dip $1.10

Fruit Plate $1.15

Macaroni $1.35

Muffin 65¢

Milk 45¢

Juice 45¢

Water 55¢

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Common Task with Multiple Variations

  • A common problem-solving task, and adjust it for different levels

  • Students tend to select the numbers that are challenging enough for them while giving them the chance to be successful in finding a solution.

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Plan Common Tasks with Multiple Variations

  • The approach is to plan an activity with multiple variations.

  • For many problems involving computations, you can insert multiple sets of numbers.

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An Example of a Common Task with Multiple Variations

  • Marian has a new job. The distance she travels to work each day is {5, 94, or 114} kilometers. How many kilometers does she travel to work in {6, 7, or 9} days?

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Plan Common Tasks with Multiple Variations

  • When using tasks of this nature all students benefit and feel as though they worked on the same task.

  • Class discussion can involve all students.

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Measurement Example

  • Outcome D2 – Recognize and demonstrate that objects of the same area can have different perimeters.

  • Typical Question (closed task, no choice):

    • Build each of the following shapes with your colour tiles. Find the perimeter of each shape.

    • Which shape has the greater perimeter?

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Measurement Example (continued)

  • New Task (open, choice in number of tiles):

  • Using 8, 16, or 20 colour tiles create different shapes and determine the perimeter of each. Record your findings on grid paper.

    • What do you think is the smallest perimeter you can make?

    • What do you think is the greatest perimeter you can make?

    • Prepare a poster presentation to show your results.

    • Sides of squares must match up exactly.


Not Allowed

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Differentiation Using Multiple Entry Points

  • Van de Walle (2006) recommends using multiple entry points, so that all students are able to gain access to a given concept.

  • Diverse activities that tap students’ particular inclinations and favoured way of representing knowledge.

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Multiple Entry Points

Based on Five Representations:

Based on Multiple Intelligences:

  • Concrete

  • Real world (context)

  • Pictures

  • Oral and written

  • Symbols

  • Logical-mathematical

  • Bodily kinesthetic

  • Linguistic

  • Spatial

  • Musical

  • Naturalist

  • Interpersonal

  • Intrapersonal

Based on Learning Modalities:

  • Verbal

  • Auditory

  • Kinesthetic

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Example Spaces: Quadrilaterals

  • Draw a figure that has four sides

  • Draw another.

  • Draw one that is really different than the first two.

  • Share your three pictures with three other classmates.

  • Sort your pictures in a way that everyone can agree on.

  • Prepare a flip chart with your sorted pictures and be prepared to explain how you sorted them to the class.

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Example Spaces: Operations

  • Think of an number sentence that gives an answer of 12.

  • Think of another.

  • Think of one that is really different than the first two.

  • Share your examples with a partner and see if you have any similar examples.

  • Try to find new examples that are different than the ones you have. List a few more.

  • Partner with another pair and share again.

  • As a group try to find all the numbers sentences you can think of that give an answer of 12. (This could go on forever so decide as a group when you think you have enough).