Differentiating Tasks

Math 412February 11, 2009

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

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

Diversity in the Classroom

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

Open-ended Questions

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

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.

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

Open-ended Questions Method 1: Working Backward

1. Identify a topic.2. Think of a closed question and write down

the answer.3. Make up an open question that includes (or

addresses) the answer.

Example: 1. Multiplication2. 40 x 9 = 3603. Two whole numbers multiply to make 360. What

might the two numbers be?

Open-ended Questions Method 2: Adjusting an Existing Question

1. Identify a topic.2. Think of a typical question.3. Adjust it to make an open

question.

Example: 1. Money2. How much change would you get

back if you used a toonie to buy Caesar salad and juice?

3. 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 $1.15Caesar Salad $1.20Veggies and Dip

$1.10Fruit Plate $1.15Macaroni $1.35Muffin

65¢Milk

45¢Juice

45¢Water

55¢

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.

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.

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?

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.

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?

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.

Allowed Not Allowed

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.

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

Sample – 3D Geometry p. 11

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.

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).