1. Differentiating Tasks
Math 412
February 11, 2009

2. 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

3. 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

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

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

6. 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.

7. 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

8. 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.
Example:
Multiplication
40 x 9 = 360
Two whole numbers multiply to make 360. What might the two numbers be?

9. Open-ended Questions Method 2: Adjusting an Existing Question
Identify a topic.
Think of a typical question.
Adjust it to make an open question.
Example:
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¢

10. 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.

11. 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.

12. 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?

13. 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.

14. 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?

15. 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

16. 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.

17. 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

18. Sample – 3D Geometry p. 11

19. 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.

20. 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).