Mathematics 4: Support

1. Mathematics 4: Support Differentiated Instruction

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

4. Differentiating Instruction • Some ways to differentiate Instruction in mathematics class • Common Task with Multiple Variations • Open-ended Questions • Differentiation Using Multiple Entry Points

5. Common Tasks 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.

6. 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.

7. 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?

8. 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.

9. Follow-up Activity 1 Outcome D2 – Recognize and demonstrate that objects of the same area can have different perimeters. • Materials: coloured tiles and centimetre grid paper • Differentiation: the choice will be the number of tiles they select. • Choose 6, 12, or 20 tiles. Model as many rectangles as you can using all of your tiles. Draw each rectangle on your centimetre grid paper. Record both the area and perimeter for each figure. • Do all rectangles with the same area have the same perimeter?

10. Follow-up Activity 2 • Materials: Coloured tiles and centimetre grid paper • Differentiation: the choice will be the number of tiles they select. • Choose 6, 12, or 20 tiles. Make as many different shapes as you can and record the perimeter of each shape. • Note: At least one side of each tile must abut the side of another tile. • Additional extensions: • Determine the greatest possible perimeter. • Determine the least possible perimeter.

11. Now You Try: • Choose an outcome(s) from your grade level curriculum and create a differentiated activity for your students.

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

13. 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.

14. 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

15. Open-ended Questions 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? 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¢

16. Open-ended Questions • Use your curriculum document or Math Makes Sense to find examples of open-ended questions. • Find two closed-questions from Math Makes Sense or from your curriculum document. • Change them to Open-ended Questions. • Be prepared to share one of your questions.

17. 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.

18. Multiple Entry Points Multiple Entry Points are diverse activities that tap into students’ particular inclinations and favoured way of representing knowledge.

19. 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

20. Sample – 3D Geometry

21. Creating Tasks With Multiple Entry Points Using the outcomes for decimals, create tasks with multiple entry points. Take into consideration the five representations: real world (context), concrete, pictures, oral/written, and symbolic and multiple intelligences: logical/mathematical, bodily kinesthetic, linguistic, spatial.

22. Possible Uses for the Grid • Introduce some of the activities to students being careful to select a range of entry points. Ask students to choose a small number of activities. Other activities can be used for reinforcement or assessment tasks. • Arrange 9 activities on a student grid: 3 rows of 3 squares. Ask the students to select any 3 activities to complete, as long as they create a Tic-Tac-Toe pattern. • Other ideas?