Differentiating Tasks Math Sept , 2008

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

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.Multiplication 2.40 x 9 = 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.Money 2.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$1.15 Caesar Salad$1.20 Veggies and Dip$1.10 Fruit Plate$1.15 Macaroni$1.35 Muffin65¢ Milk 45¢ Juice45¢ Water55¢

An Open Task: Decimals Model each decimal with base ten blocks. Make a sketch to record your work. a) O.46 b) 3.04 c) 1.9 d) 1.09 e) 3.35 From Math Makes Sense 5, page 118 Opening it up… If the flat represents 1, use flats, rods and little cubes to build a robot model. Record a picture of your model and the value as a decimal number. Repeat two more times. Share with a partner. Share with the group.

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.

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?

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. AllowedNot Allowed

Example Spaces: Subtraction Think of a subtraction question where the solution is a two or three digit number. Think of another. Think of one that is really different than the first two.

Example Spaces: Area Think of a shape with an area of 24 cm 2. Think of another. Think of one that is really different than the first two.

Think Multiple Representations Verbal: Explain it in Words Contextual: Write a Story Problem Concrete: Use Concrete Materials to Build It Symbolic: Write it in Mathematical Symbols Pictorial: Draw a Picture Model

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