Differentiating Mathematics Instruction Jane Silva, Mathematics Instructional Leader SW

1. Differentiating Mathematics InstructionJane Silva, Mathematics Instructional Leader SW

2. When I think about teaching mathematics, I feel like… Four Corners

3. Our Differentiation Framework • With your group, organize the terms in order to show a relationship among the words. • Using the provided blank cards, label your groups according to the relationship you identified.

4. TDSBs Differentiation Framework

5. Strategies I Use in Mathematics Describe a strategy you use to differentiate according to the number you roll. Record your strategies on sticky notes. 1  Readiness 2  Interest 3  Learning Profile 4  Content 5  Product 6  Process 7  Environment

6. Identifying similarities and differences (e.g., Venn diagram) Summarizing and note taking (e.g., mind maps, concept maps) Reinforcing effort and providing recognition (e.g., goal- setting) Non-linguistic representations (e.g., graphic organizers) Cooperative learning (e.g., jigsaw, think-pair-share) Setting objectives and providing feedback (e.g., exit card, rubrics) Questions, cues and advance organizers (e.g., anticipation guides) Differentiation Strategies

7. “The teacher does not try to differentiate everything for everyone every day.” Tomlinson

8. Differentiating Instruction… IS NOT… IS… Individualized instruction for each student Providing instruction to meet the range of student needs

9. Cubing Menus Choice Boards RAFTs Tiering Learning Centers Structures for Differentiating Instruction

10. Describe probability as a measure of the likelihood that an event will occur, using mathematical language Structure: Cubing Probability IMPOSSIBLE LIKELY CERTAIN

11. Structure: Cubing Geometry & Spatial Sense Compare & Contrast

12. Structure: Cubing Journal Prompts Face 1: I understand… Face 2: I don’t understand… Face 3: I find it easy to… Face 4: I find it difficult to… Face 5: I learned… Face 6: I still want to know…

13. Structure: Menu Patterning Appetizer (Everyone): What is a pattern? Main dish (Choose 1): Create a repeating pattern using pattern blocks. Create a growing pattern using pattern blocks? Side dishes (Choose 2): Describe a pattern that results from repeating an action. Describe a pattern that results from repeating an operation. Describe a pattern that results from using a transformation. Dessert (If you wish) Create a growing pattern. How is it the same as a repeating pattern? How is it different?

14. Structure: Menu Geometry • With a partner collect 1 basket of pattern blocks. Take turns sorting blocks into two different groups and ask your partner to guess your sorting rule? (Some rules could be shapes that stack, roll, slide, or shapes with 3 edges, 4 vertices, 6 faces) • Look around our classroom, draw: 2 things that are rectangles, 3 things that are square, 1 thing that is a triangle, and 4 things that are circles. • Use a set of tangrams to create a design. Trace around the outside of each shape. • Choose 2 different shapes. Write about how they are different and about how they are the same.

15. Structure: Choice Board Number Sense & Numeration

16. Structure: Choice Board Fractions

17. Structure: R.A.F.T Various

18. Structure: R.A.F.T Measurement

19. Structure: TIERING Fractions Tier 1: all fractions are proper; have common denominators; and can be modeled Tier 2: fractions are proper and improper; have different denominators, but all can be modeled Tier 3: fractions are proper and improper and not all can easily be modeled

20. Structure: TIERING Measurement Find the surface of the following shapes: Activity A: Provide simple rectangular prisms and cylinders with measurements provided. Activity B: Provide simple rectangular prisms and cylinders where students must first measure. Activity C: Provide pictures of simple rectangular prisms and cylinders with measurements provided. Activity D: Ask students to find examples of cylinders or rectangular prisms.

21. Structure: Learning Centres Data Management Describe what type of data could be represented by this graph (an image of the graph is depicted). Station 1: Pictograph Station 2: Bar Graph Station 3: Stem-and-Leaf Plot Station 4: Broken Line Graph Station 5: Histogram

22. Strategies I May Use To Differentiate Think about one strategies you can use to differentiate mathematics. Discuss your thoughts on implementing this strategy in pairs. Be prepared to share.

23. Two Core Strategies for Differentiating Mathematics Instruction

24. Allows for different students to approach it by using different processes or strategies. Allows students at different stages of mathematical development to benefit and grow from attention to the task. Is framed in such a way that a variety of responses or approaches is possible. Strategy: Open Question

25. You add fractions and the sum is 1. What could the fractions be? Strategy: Open Questions

26. 1/2 + 1/2 = 1 1/4 + 1/4 + 1/4 + 1/4 = 1 2/8 + 6/8 = 1 1/3 + 2/6 + 4/12 = 1

27. What makes it open? Assessment: To reveal what students understand about fractions. Big Idea: There are many ways to represent numbers when adding fractions. Choice: It allows students at different levels of readiness to respond to the question. Strategy: Open Questions

28. Centres: Open Questions Number Sense & Numeration Data Management & Probability Geometry & Spatial Sense Measurement Patterning & Algebra Visit at least 2 stations. Stations are organized by strand.

29. Centres: Open Questions Select and try an open question. Questions are grouped by grade: K-2, 3-5, and 6-8.

30. Centres: Open Questions Discuss with others how you might use this in your teaching practice. Decide which big idea most appropriately reflects the task.

31. Centres: Open Questions Visit at least 2 stations(stations are organized by strand). Select and try an open question (questions are grouped by grade clusters) Discuss with others how you might use this in your teaching practice. Decide which big idea most appropriately reflects the task.

32. Centre: Number Sense and Numeration K-2: Show the number 7 in as many ways as you can. 3-5: The sum is 42. What is the question? 6-8: Create a sentence that uses each of the following words and numbers. Other words and numbers can be used. 40, percent, most, 80 Big Idea: There are many ways to represent numbers

33. Centre: Geometry and Spatial Sense K-2: Draw a design or shape made up of three shapes. The design should have symmetry. 3-5: How many different shapes can you make by using five green pattern block triangles? Triangles must match along full sides. 6-8: Show how to put together squares to create shapes with eight sides. Big Idea: New shapes can be created by either combining or dissecting existing shapes.

34. Centre: Measurement K-2: Two shapes are the same size. What could they be? 3-5: A polygon has a perimeter of 44 units. Draw five possible shapes. 6-8: A shape has an area of 200 square metres. What could its length and width be? Big Idea: The same object can be described by using different measurements.

35. Centre: Patterning and Algebra ? ? ? ? K-2: The forth picture in a pattern consists of five squares as shown. What could the first, second, third and fifth pictures look like? 3-5: A pattern begins like this: 2, 6, … How might it continue? 6-8: A pattern is built by adding pairs of terms to get the next term. There is a 10 somewhere between the forth term and the tenth term. What could the pattern be? Think of as many possibilities as you can. Big Idea: A group of items form a pattern only if there is an element of repetition, or regularity, that can be described with a pattern rule.

36. Centre: Data Analysis and Probability Favourite Dinosaurs T-Rex 25 Triceratops 3 Stegosaurus 8 Brachiosaurus 2 K-2: What might this graph be about? 3-5: Select a graph type you would use to display these data. Why is your choice a good way to show the data? 6-8: Create a set of data that can be appropriately described by using a histogram. Create that histogram. Big Idea: Graphs are powerful data displays because they quickly reveal a great deal of information.

37. Strategies for Creating Open Questions Turn around a question Closed: What is the sum of 2, 4, and 6?  Open: The sum of three numbers is 12. What can these numbers be?

38. Strategies for Creating Open Questions Ask for similarities and differences Closed: What is perimeter? What is area?  Open: How are perimeter and area the same? How are they different?

39. Strategies for Creating Open Questions Change the question Closed: What number has 3 hundreds, 2 tens, 2 thousands, and 4 ones?  Open: You can model a number with 11 base ten blocks. What could the number be?

40. Strategies for Creating Open Questions Leave the Values Open Closed: Use 3 triangles to make a trapezoid. Draw the lines of symmetry.  Open: Draw a design or shape made up of three shapes. The design should have symmetry.

41. Strategies for Creating Open Questions Ask for a number sentence Create a sentence that includes the numbers 3 and 4 as well as the words “and” and “more”. Ex: the sum of 3and4 is more than 6; 4 is more than 3andmore than 1

42. Make your Own Open Questions Select a curriculum expectation. Determine the big idea (or learning goal). Consider student readiness, learning profiles, and interests. Use a “opening up” strategy to develop a question.

43. Sets of tasks, usually two or three, that are designed to meet the needs of students at different developmental levels, but get at the same big idea and are close enough in context that they can be discussed simultaneously. Strategy: Parallel Tasks

44. Strategy: Parallel Tasks Create a repeating pattern that begins with 3, 5,… Create an increasing pattern that begins with 3, 5,…

45. What makes it parallel? Assessment: Differ in sophistication. Big Idea: They both posses the same big idea: a group of items form a pattern only if there is an element of repetition, or regularity, that can be described with a pattern rule. Choice: It allows students at different levels of readiness to select a question. Strategy: Parallel Tasks

46. What makes it parallel? Consolidation Questions: They both possess the same set of consolidation questions: What is your pattern? What makes it a pattern? What would be your 10th number? Strategy: Parallel Tasks

47. Resources Guides to Effective Instruction (K-6) – www.eworkshop.on.ca Edugains (7-12) – www.edugains.ca National Library of Virtual Manipulatives – Google “nlvm”