Scaffolding EngageNY Mathematics for English Learners

1. Scaffolding EngageNY Mathematics for English Learners Anita Bright, Ph.D. Portland State University Portland, Oregon February 4, 2014 Visit http://goo.gl/Ua0fcf to access the electronic version of this document.

2. Our Agenda • Looking at a lesson • A few quick ways to scaffold INSTRUCTION • Questions? • Visit http://goo.gl/Ua0fcfto access the electronic version of this document. abright@pdx.edu

3. Let’s look at part of a lesson. • What do you notice that might be problematic for English learners? • What might you do to modify this lesson? http://goo.gl/Ua0fcf abright@pdx.edu

4. Grade 6, Module 5, Lesson 11: Volume with Fractional Edge Lengths and Unit Cubes abright@pdx.edu

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7. How many 1 in x 1 in x 1 in cubes will fit in the following prism? Have students discuss their solution with a partner. How many 1 in x 1 in x 1 in cubes would fit across the bottom of the rectangular prism? How did you determine this number? abright@pdx.edu

8. How many layers of 1 in by 1 in by 1 in cubes would fit inside the prism? • If each cube represents dice that need to be shipped, how many 1 in x 1 in x 1 in dice will fit in the box? • How did you determine this number? • How is the number of cubes or dice related to the volume? • What other ways can you determine the volume of a rectangular prism? abright@pdx.edu

9. Example 1 (5 minutes) • The same package in the opening exercise will be used to ship miniature dice whose side lengths have been cut in half. The dice are ½ in x ½ in x ½ in cubes. How many dice of this size can fit in the box? How many cubes could we fit across the length? The width? The height? abright@pdx.edu

10. Now let’s look at how to improve it… abright@pdx.edu

11. How many 1 in x 1 in x 1 in cubes will fit in the following prism? Have students discuss their solution with a partner. How many 1 in x 1 in x 1 in cubes would fit across the bottom of the rectangular prism? How did you determine this number? abright@pdx.edu

12. How many layers of 1 in x 1 in x 1 in cubes would fit inside the prism? • If each cube represents dice that need to be shipped, how many 1 in x 1 in x 1 in dice will fit in the box? • How did you determine this number? • How is the number of cubes or dice related to the volume? • What other ways can you determine the volume of a rectangular prism? abright@pdx.edu

13. Example 1 (5 minutes) • The same package in the opening exercise will be used to ship miniature dice whose side lengths have been cut in half. The dice are ½ in x ½ in x ½ in cubes. How many dice of this size can fit in the box? How many cubes could we fit across the length? The width? The height? abright@pdx.edu

14. Let’s look at another example. abright@pdx.edu

15. 3. A toy company is packaging its toys to be shipped. Some of the very small toys are placed inside a cube shaped box with side lengths of ½ in. These smaller boxes are then packed into a shipping box with dimensions of 12 in x 4 ½ in x 3 ½ in. a. How many small toys can be packed into the larger box for shipping? abright@pdx.edu

16. Here’s a re-wording: Original Scaffolded A toy company puts small toys into boxes. The boxes are cubes with side length of ½ in. These small boxes are put inside a bigger box with dimensions of 12 in. x 4 ½ in. x 3 ½ in. How many toys can be put into the larger box? A toy company is packaging its toys to be shipped. Some of the very small toys are placed inside a cube shaped box with side lengths of ½ in. These smaller boxes are then packed into a shipping box with dimensions of 12 in x 4 ½ in x 3 ½ in. How many small toys can be packed into the larger box for shipping? abright@pdx.edu

17. Another note on this lesson • Words are used interchangeably: • Long/ length • High/ height (and sometimes deep/ depth) • Width/ wide • Some words are have multiple meanings (like volume). These relationships between these words need to be taught! abright@pdx.edu

18. How can teachers scaffold this curriculum? abright@pdx.edu

19. Three* big ideas: Amplify key language (to increase accessibility). Use graphic organizers (to help students focus on the big ideas). Provide support for speaking and writing (to enrich their academic register). *More big ideas at the end! abright@pdx.edu

20. Amplify key language • Text is written in present tense and may be redundant for clarity. • Sentences are short with no or few clauses. (These may read awkwardly to fluent speakers of English.) • New sentences begin on a new line. abright@pdx.edu

21. Contexts are familiar to students in school. • Names chosen for examples should not be similar to content (including names like Ray and Mark). • Pictures/ visuals/ illustrations are used to make content clearer. abright@pdx.edu

22. Words with multiple meanings that might be confusing are not used (ie, a garden plot and the request to plot points on a coordinate plane). • Language is internally consistent (if practice problems ask students to solve, the assessments should use the same term). If language is not internally consistent, then different terms are highlighted and taught (add, plus, sum, combine, all mean the same thing). abright@pdx.edu

23. A Standard Example (Lesson 8.1, p. 12) Scaffolded Example A group of objects doubles every 8 hours. Today there are B objects in the group. How many objects are in the group after 2 days? (There are 24 hours in one day.) Suppose a colony of bacteria doubles in size every 8 hours for a few days under tight laboratory conditions. If the initial size is 𝐵, what is the size of the colony after 2 days? abright@pdx.edu

24. A Standard Example (Lesson 8.1, p. 12) Scaffolded Example Kim has a farm in the shape of a rectangle. The area of Kim’s farm is 𝟐𝟏𝟓 square miles. Kim divides her farm into pieces that are each 𝟖𝟑 square miles in size. How many pieces does Kim make? A rectangular area of land is being sold off in smaller pieces. The total area of the land is 𝟐𝟏𝟓 square miles. The pieces being sold are 𝟖𝟑 square miles in size. How many smaller pieces of land can be sold at the stated size?  Compute the actual number of pieces. abright@pdx.edu

25. Provide side-by-side texts. • Look at how useful this is! (Google translate will even provide a read-aloud.) • (Note: This is best for students who are already highly LITERATE in their first language. Do not assume this is the case with all students.) abright@pdx.edu

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27. Provide step-by-step instructions in student-friendly language & use visuals. • From a lesson on translating one-step word problems to algebraic equations. Directions: a) Definea variable for each problem. b) Write an equation to represent the information. c) Be sure the equation requires the use of one inverse operation to find the solution! d) Show a check for each solution. abright@pdx.edu

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29. 2. Provide graphic organizers. • Non-verbal displays of relationships • A way to visually organize thinking abright@pdx.edu

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32. Similarities and differences abright@pdx.edu

33. Graphic organizer abright@pdx.edu

34. Frayer model abright@pdx.edu

35. Foldables • These don’t have to be from a template. Anything can work! abright@pdx.edu

36. Have students identify similarities and differences. • Venn diagrams • T-charts abright@pdx.edu

37. Similarities and Differences Concept: Conic Sections parabola ellipse circle hyperbola abright@pdx.edu

38. Similarities and Differences Concept: ____________ abright@pdx.edu

39. Similarities and Differences Concept: Which does not belong? (Can you think of another term that would fit?) acute right obtuse parallel abright@pdx.edu

40. 3. Provide support for speaking and writing • Each day needs structured opportunities for students to speak and write in English. abright@pdx.edu

41. Give concrete guidelines for speaking, reading, writing or listening. “Turn to your neighbor and explain…” Write the day’s objective on the board and have students read it along with you. Point to each word as you read aloud. Provide sentence frames for anyone who may benefit. (“I know the area of parallelogram B is larger/ smaller ______ than the area of parallelogram A because _____.”) (More advanced students might be ready for some transition language like this: http://writing2.richmond.edu/writing/wweb/trans1.html) abright@pdx.edu

42. Sentence frames (perhaps with word banks) can support student explanations. • Visit this link for some elementary examples from Justin Johnson. • See also page 24 of this fabulous document from Kate Kinsella. abright@pdx.edu

43. “The volume of my prism is ___units cubed. I found this by ______. • “My idea is similar to _____’s because ____.” abright@pdx.edu

44. “I know the answer is a fraction because_____” Word bank: Added Less than one Combined Whole number Equal abright@pdx.edu

45. Have students chorally repeat key vocabulary or phrases. • Have students chorally repeat the key term in creative ways. • (“The word is pronounced hypotenuse. Again, hypotenuse. Repeat after me: hypotenuse. Whisper it: hypotenuse. This side of the room only: hypotenuse. Everyone wearing jeans, hypotenuse.” ) • Why? It lowers the affective filter since there are multiple voices speaking at once. It promotes fluency. It provides and accurate auditory imprint. abright@pdx.edu

46. Be direct about language. • EXAMPLE OBJECTIVE FOR A LESSON: • Identify perfect squares; determine square roots. • Discuss the word square. Ask students to describe what a square is: a shape with 4 equal sides and 4 right angles. Have students point out objects in the room that are squares. • Introduce expressions with the word square that students will use in this lesson – square number, perfect square, squared, square root. • Explain to students that the word square can be a noun or a verb. In the expression “the square of a number…”, square is a noun. In the expression “if we square the number…”, square is a verb. • Tell students that we will be using the word root in the mathematical expression square root. Ask students if they know any other uses of the word root (roots of trees or plants, family roots). Point out to students that in these cases, the word root relates to the beginning or foundation for something. abright@pdx.edu

47. Use online resources for key vocabulary. • How about a cool dictionary? • Or what about Google translate? abright@pdx.edu

48. Provide word banks. • These can provide appropriate and relevant vocabulary to use in speaking or writing about the content. Adjacent Complementary Congruent Equal Supplementary Vertical abright@pdx.edu

49. Other rich ideas abright@pdx.edu

50. Use manipulatives! • The more concrete and visual these ideas can be, the better! • Remember this thing? Use something from the classroom instead! abright@pdx.edu