fewer the better) Alberta Program of Studies Students will understand… There are restrictions on values for the variable in a radical. *NL 3.6 Students will know … the square root of a negative number is not a real number Students will understand… There are appropriate forms of communications in mathematics. NL 3.2, 3.3, 3.5 Students will know … when the expression is simplified Students will understand… Radicals are more precise, efficient, concise and accurate. NL 4.5 Students will know … when it is appropriate to use an exact value versus a rounded decimal Students will understand… Operations can be performed on radicals, as with other numbers or algebraic expressions. NL 3.4 Students will know … what like terms are the rules for operations on radicals I*NL = Number and Logic Skills: Enduring Understanding List enduring understandings (the fewer the better) Specific Outcomes List the reference # from the Alberta Program of Studies Description of Skills The paraphrased outcome that the group is targeting Students will understand… There are restrictions on values for the variable in a radical. *NL 3.6 Students will be able to… identify values of the variable for which the radical expression is defined Students will understand… Some equations have extraneous roots, and NL 4.1, 4.3 Students will be able to… determine any restrictions on values for the variable in a radical equation
why. verify, by substitution, that the values determined in solving a radical equation are roots of the equation Students will understand… There are appropriate forms of communications in mathematics. NL 3.2, 3.3, 3.4, 3.5, 4.5 Students will be able to… simplify radical expressions with numerical or variable radicands rationalize the monomial denominator of a radical expression model a situation with a radical equation Students will understand… Radicals are more precise, efficient, concise and accurate. NL3, NL4 Students will be able to… answer questions with exact values Students will understand… Operations can be performed on radicals, as with other numbers or algebraic expressions. NL 3.4, 4.2 Students will be able to… perform operations with radicals solve radical equations to determine the roots I*NL = Number and Logic STAGE 2 Assessment Evidence 1 Desired Results Desired Results Teacher Notes There are three transfer tasks to evaluate student understanding of the concepts relating to radicals. A photocopy-ready version of each transfer task is included in this section. The first is not as open ended as many of the other transfer tasks have been. Glossary – Represents how far the number is from zero entire radical – A radical with a coefficient of 1 [Math 20-2 (Nelson: page 515)]
Level Excellent Proficient Adequate Limited Insufficient Criteria 4 3 2 1 Blank Math Content Part A All required elements are present and correct All required elements are present but may contain minor errors Some required elements are missing, or contain major errors Most required elements are missing or incorrect No score is awarded as there is no evidence given Math Content Part B All required elements are present and correct All required elements are present but may contain minor errors Some required elements are missing, or contain major errors Most required elements are missing or incorrect No score is awarded as there is no evidence given Math Content Part C All required elements are present and correct All required elements are present but may contain minor errors Some required elements are missing, or contain major errors Most required elements are missing or incorrect No score is awarded as there is no evidence given Math Content Part D All required elements are present and correct All required elements are present but may contain minor errors Some required elements are missing, or contain major errors Most required elements are missing or incorrect No score is awarded as there is no evidence given When work is judged to be limited or insufficient, the teacher makes decisions about appropriate intervention to help the student improve
Assessment Mathematics 20-2 Spiralling Out of Control Rubric . Component Description of Requirements Assessment Mathematical Content Part A Determines length of radical spiral in proper form IN 1 2 Part B Draws 3 radical spirals Determines total length of each of the spirals Makes generalization based on results of findings IN 1 2 3 4 Part C Determines solution to radical equation IN 1 2 3 4 Presentation of Data Part B Spirals are properly and neatly drawn IN 1 2 Explanation of Findings Part C Explains existence of and reasons for extraneous roots IN 1 2 3 4
Level Excellent Proficient Adequate Limited Insufficient Criteria 4 3 2 1 Blank Math Content Part A All required elements are present and correct Some required elements are missing or incorrect No score is awarded as there is no evidence given Math Content Part B All required elements are present and correct All required elements are present but may contain minor errors Some required elements are missing, or contain major errors Most required elements are missing or incorrect No score is awarded as there is no evidence given Math Content Part C All required elements are present and correct All required elements are present but may contain minor errors Some required elements are missing, or contain major errors Most required elements are missing or incorrect No score is awarded as there is no evidence given Presents Data Part B Presentation of data is clear, precise and accurate Presentation of data is vague and inaccurate Presentation of data is incomprehensible Explains Findings Part C Provides insightful explanations Provides logical explanations Provides explanations that are complete but vague Provides explanations that are incomplete or confusing. No explanation is provided
Determine any restrictions on values for the variable in a radical equation. Card 8: Outcome 4: Achievement indicator 4.2 Determine algebraically, the roots of a radical equation Card 9: Outcome 4: Achievement indicator 4.3 Verify, by substitution, that the values determined in solving a radical equation are roots of an equation. Card 10: Outcome 4: Achievement indicator 4.5 Solve problems by modeling a situation with a radical equation and solving the equation. Card 11: Outcome 4: Achievement indicator 4.4 Explain why some roots determined in solving a radical equation are extraneous. Note: Outcome 3: Achievement indicator 3.6 was not included as it was felt that the concept was sufficiently covered with achievement indicator 4.1 Glossary – Represents how far the number is from zero entire radical – A radical with a coefficient of 1 [Math 20-2 (Nelson: page 515)] extraneous root – A number obtained in the process of solving an equation that does not satisfy the equation mixed radicals – A radical with a coefficient other than 1 [Math 20-2 (Nelson: page 516)] – A number, from a given number system, that can be expressed as the square of a number from the same number system – The positive square root rationalize the denominator – The process used to write a radical expression that contains a radical denominator into an equivalent expression with a rational denominator [Math 20-2 (Nelson: page 517)] restrictions – The values of a the variable in an expression that ensure it to be defined [Math 20-2 (Nelson: page 517)]
Exemplar: Location List Harry Ainlay High School Location 1: Exit 1 Location 12: Exit 15 Location 23: South entrance to the West Court yard Location 34: Office Entrance Location 2: Exit 2 Location 13: Exit 16 Location 24: Wellness Centre Desk Location 35: South entrance to east courtyard Location 3: Exit 5 Location 14: Exit 17 Location 25: Dance studio Entrance Location 36: Outside entrance to the Auto Location 4: Exit 4 Location 15: Outdoor class room Location 26: Cosmetology Parking Propane tank storage Location 37:Inside Entrance to Construction Location 5: Exit 6 Location 16: Exit 14 Location 27: North east corner of the temporary library Location 38: Inside entrance to Design Studies Location 6: Exit 8 Location 17: Exit 13 Location 28: Southeast corner of the rotunda Location 39: Centre Table of the Rotunda Location 7: Visitor Parking Stall # 116 Location 18: North East Parking lot Student Bench Location 29: Book Room 304 Location 40: Room 384 Location 8: Exit 10 Location 19: Exit 19 Location 30: Drama room Location 9: Bike Racks Location 20: Exit 20 Location 31: Theatre Entrance Location 10: Exit 11 Location 21: South entrance to student activities Location 32: Athletics Office Location 11: Exit 12 Location 22: North East corner of the Rotunda Location 33: Student Services and Career Centre
Assessment Mathematics 20-2 Radical Race Rubric Level Criteria Excellent 3 Adequate 2 Limited 1 Performs Calculations Performs precise and explicit calculations. Performs appropriate and generally accurate calculations. Performs superficial and irrelevant calculations. Explains Choices Shows a solution for the problems; provides an insightful explanation. Shows a solution for the problem; provides explanations that are complete but vague. Shows a solution for the problem but no supporting mathematics.
M20-2 Lesson 2 Converting Entire to Mixed Worksheet (Variable Radicands) Simplify the following. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Extra Problem Answers: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Extra Problem