By for all whole numbers and (A) The side is By for any whole number (B) So the two sides are equal. AIR Additional Supports Background knowledge for teachers To make this a more meaningful, memorable, and engaging portion of the lesson for ELLs, the proof should be organized into a T-chart and students should be provided with the opportunity to at various points during the explanation. Students also will compare and contrast cases and ii iii using a Venn diagram to highlight similarities and differences. Clarification of key concepts and key academic vocabulary By attending to the language load in the texts shared with students and in the explanations provided orally, key content can be highlighted and amplified. Some ways to clarify key concepts include using present tense, using shorter sentences, using examples related to school contexts, using graphics and arrows to illustrate points, and using white space and color to accentuate important information. AIR Routine for Teachers Structured opportunities to speak with a partner or small group T: To make this clearer, we will substitute integers into this equation. I will write it as a proof, in two columns. writing the first two lines of the proof (the given or definition,” and then the rewriting of the “by first fractional term), have students work with a partner to simplify it further, down to the final solution of 5-12. Explain each step of the reasons, and explain that the term is used to mean the same thing as by when referring back to earlier work or already proven examples. because T: Now that we have created the of this case with integers, you will work with your partner to create the proof of this case with variables. Your work will follow the exact same format. Have students work with partners to redraft the same proof but with variables instead of integers. Explore case iii (Exercise 4) in the same fashion, first with an integer substitute, and then with variables. Ensure that students have opportunities to speak with their partners. After completion of cases ii and iii: How are cases ii and iii similar and how are they different? Provide a Venn diagram (or have students draw it) and with partners, generate a few key ideas for each category.
By for all whole numbers and (A) The side is By for any whole number (B) So the two sides are equal. AIR Additional Supports Background knowledge for teachers To make this a more meaningful, memorable, and engaging portion of the lesson for ELLs, the proof should be organized into a T-chart and students should be provided with the opportunity to at various points during the explanation. Students also will compare and contrast cases ii and iii using a Venn diagram to highlight similarities and differences. Clarification of key concepts and key academic vocabulary By attending to the language load in the texts shared with students and in the explanations provided orally, key content can be highlighted and amplified. Some ways to clarify key concepts include using present tense, using shorter sentences, using examples related to school contexts, using graphics and arrows to illustrate points, and using white space and color to accentuate important information. AIR Routine for Teachers Structured opportunities to speak with a partner or small group T: To make this clearer, we will substitute integers into this equation. I will write it as a proof, in two columns. writing the first two lines of the proof (the given or “by definition,” and then the rewriting of the first fractional term), have students work with a partner to simplify it further, down to the final solution of 5-12. Explain each step of the reasons, and explain that the term by is used to mean the same thing as because when referring back to earlier work or already proven examples. T: Now that we have created the of this case with integers, you will work with your partner to create the proof of this case with variables. Your work will follow the exact same format. Have students work with partners to redraft the same proof but with variables instead of integers. Explore case iii (Exercise 4) in the same fashion, first with an integer substitute, and then with variables. Ensure that students have opportunities to speak with their partners. After completion of cases ii and iii: How are cases ii and iii similar and how are they different? Provide a Venn diagram (or have students draw it) and with partners, generate a few key ideas for each category.
Engage%20New%20York%20Scaffolding%20Instruction%20for%20ELLs%20Math.docx