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Two Grade 11 Mathematics teachers used the following learning activities to present their lessons. Read and reflect on the activities then answer questions that follow. |Teacher Tom Learning Activity Teacher Sam Cearning Activity Nature of the roots of a quadratic equation ax? + Consider the equations grven below: bx +c =0 are given byb² – 4ac, which is referred to as the discriminant and it is usually denoted by the symbol A (delta) a) 2x2 - 5x – 3 = 0 6) x2 + 3x = -2

Two Grade 11 Mathematics teachers used the following learning activities to present their lessons. Read and reflect on the activities then answer questions that follow. |Teacher Tom Learning Activity Teacher Sam Cearning Activity Nature of the roots of a quadratic equation ax? + Consider the equations grven below: bx +c =0 are given byb² – 4ac, which is referred to as the discriminant and it is usually denoted by the symbol A (delta) a) 2x2 - 5x – 3 = 0 6) x2 + 3x = -2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.5: Other Types Of Equations
Problem 69E
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13:03 ull LTE O Two Grade 11 Mathematics teachers used the following learning activities to present their lessons. Read and reflect on the activities then answer questions that follow. Teacher Tom Teacher Sam Learning Activity Learning Activity Consider the equations given below: Nature of the roots of a quadratic equation ax² + bx +c= 0 are given byb? – 4ac, which is referred to as the discriminant and it is usually denoted by the symbol A (delta). a) 2x2 – 5x – 3 = 0 6) x2 + 3x = -2 c) x2 + 9 = 6x d) 4y2 – 19y - 5 = 0 e) p(p + 5) = -8 If A >0 the roots are real If A >0 and a perfect square, the roots are real and rational If A <0 the roots are non-real IfA =0 the roots are equal For each of the equations do the following: olve for t (Note: the ansuer(s) you get here is (are) the roots of the equation). Decide whether the roots are real or non-real. i. unknown variable. Determine the nature of the roots for each of the following equations: a) 2x2 - 5x - 3 = 0 6) x2 + 3x = -2 c) x2 + 9 = 6x d) 4y2 – 19y - 5 = 0 e) p(p+ 5) = -8 ii. (Hint: If an equation has no solution, then it has no roots, we say the roots are non-real) Examine the roots and classify them as either rational or irrational. i. Examine the roots and say whether they are equal or unequal. tv. 1.1 In what way(s) is the learning outcome/objective guiding the two teac'iers' learning activities similar and different? 1.2 Make a list of the immediate or prior mathematical knowledge and skills that the learners must have in order to succeed in carrying out Teacher Sam's learning activity. 1.3 Make a list of mathematical knowledge and skills that could be assessed as learners carry out Teacher Tom's learning activity. 1.4 Which learning activity has more strength in developing learners' mathematical proficiency? In particular, the strands listed below. Justify your decision fully in each case. 1.4.1 Conceptual understanding 1.4.2 Adaptive reasoning Add a caption.. > Keletso Mashilo
Transcribed Image Text:13:03 ull LTE O Two Grade 11 Mathematics teachers used the following learning activities to present their lessons. Read and reflect on the activities then answer questions that follow. Teacher Tom Teacher Sam Learning Activity Learning Activity Consider the equations given below: Nature of the roots of a quadratic equation ax² + bx +c= 0 are given byb? – 4ac, which is referred to as the discriminant and it is usually denoted by the symbol A (delta). a) 2x2 – 5x – 3 = 0 6) x2 + 3x = -2 c) x2 + 9 = 6x d) 4y2 – 19y - 5 = 0 e) p(p + 5) = -8 If A >0 the roots are real If A >0 and a perfect square, the roots are real and rational If A <0 the roots are non-real IfA =0 the roots are equal For each of the equations do the following: olve for t (Note: the ansuer(s) you get here is (are) the roots of the equation). Decide whether the roots are real or non-real. i. unknown variable. Determine the nature of the roots for each of the following equations: a) 2x2 - 5x - 3 = 0 6) x2 + 3x = -2 c) x2 + 9 = 6x d) 4y2 – 19y - 5 = 0 e) p(p+ 5) = -8 ii. (Hint: If an equation has no solution, then it has no roots, we say the roots are non-real) Examine the roots and classify them as either rational or irrational. i. Examine the roots and say whether they are equal or unequal. tv. 1.1 In what way(s) is the learning outcome/objective guiding the two teac'iers' learning activities similar and different? 1.2 Make a list of the immediate or prior mathematical knowledge and skills that the learners must have in order to succeed in carrying out Teacher Sam's learning activity. 1.3 Make a list of mathematical knowledge and skills that could be assessed as learners carry out Teacher Tom's learning activity. 1.4 Which learning activity has more strength in developing learners' mathematical proficiency? In particular, the strands listed below. Justify your decision fully in each case. 1.4.1 Conceptual understanding 1.4.2 Adaptive reasoning Add a caption.. > Keletso Mashilo
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