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This document provides an algebra lesson plan for grade 10 students. The lesson covers simplifying, adding, subtracting, multiplying, and dividing algebraic fractions. It begins with defining algebra and explaining the learning objectives. The lesson consists of three group activities - simplifying algebraic fractions, adding/subtracting algebraic fractions, and multiplying/dividing algebraic fractions. For each activity, examples are provided and the students work through practice problems in their groups. At the end, students reflect on what they have learned about solving algebraic equations with fractions.
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Authentic learning activity
- 2. What is Algebra Algebra is: the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. Any of several algebraic systems, especially a ring in which elements can be multiplied by real or complex numbers (linear algebra) as well as by other elements of the ring. Any special system of notation adapted to the study of a special system of relationship:
- 3. Learning task Lesson presentation Topic: Algebra Activity1 (Group Activity) 1.Simplying algebraic fractions. Activity 2 (Group Activity) 2. Adding and Subtracting algebraic fractions. Activity3 (Group Activity) 3.Multiplying and dividing algebraic fractions. Reflection 1.Simplyifying algebraic fractions 2. Adding and subtracting algebraic fractions 3. Multiplying and dividing algebraic fractions Lesson objectives for the activity: *Learners must be Able to factorise a quadratic expression *Learners must be Able to simplify a simple algebraic fraction *Learners must be Able to Lesson objectives for the activity: *learners must be Able to simplify an algebraic fraction *learners must be Able to add/subtract simple algebraic fractions *learners must be Able to add/subtract Lesson objectives for the activity: *learners must be Able to add and subtract complex algebraic fractions *learners must be Able to multiply and divide simple algebraic fractions *learners must be Write a summary reflecting of what you have learnt from this lesson of algebra
- 4. Instructions Learners must divide themselves into group of fours The must choose one group leader within them. Every member of the group must contribute towards each given group class activities. Each members of the group will present their work to the fellow student All marks will be divided equally to each group members. Teacher will present the lesson by explaining and giving some examples Teacher will give learners some activities.
- 5. Which ones are you using? Always aim high! I AM TALKING TO YOU YES I MEAN YOU HIDING AT THE BACK You are the future. LET GET IT STARTED Effective Participator Self Manager Independen t Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills
- 6. Simplifying Algebraic Fractions Learning Objectives: Able to factorise a quadratic expression Able to simplify a simple algebraic fraction Able to simplify more complex algebraic fractions Grade 10
- 7. Simplifying Algebraic Fractions To simplify algebraic fractions you usually have to factorise the top and/or the bottom, then cancel common factors 3𝑥 + 6 3𝑥2 3(𝑥 + 2) 3𝑥2 𝑥 + 2 𝑥2
- 8. Simplifying Algebraic Fractions 4𝑎𝑏 + 8𝑎2 12𝑎 4𝑎(𝑏 + 2𝑎) 12𝑎 𝑏 + 2𝑎 3 3
- 9. Simplifying Algebraic Fractions 4𝑥 − 20 𝑥2 − 13𝑥 + 40 4(𝑥 − 5) 𝑥 − 5 (𝑥 − 8) 4 𝑥 − 8
- 10. ACTIVITY ONE: Working in groups of four simplify the following algebraic fraction 7𝑥 − 35 21 3𝑥2 + 15𝑥 27𝑥 6𝑥2 𝑦 + 18𝑥𝑦 21𝑥𝑦 𝑥2 + 7𝑥 + 10 3𝑥 + 15
- 11. Adding and Subtracting Algebraic Fractions Learning Objectives: Able to simplify an algebraic fraction Able to add/subtract simple algebraic fractions Able to add/subtract more complex algebraic fractions
- 12. Adding and Subtracting Algebraic Fractions Just as with numerical fractions, the denominators must be the same before you can add or subtract fractions 3𝑥 4 + 2𝑥 5 15𝑥 + 8𝑥 20 23𝑥 20
- 13. Adding and Subtracting Algebraic Fractions 25 3𝑥 − 7 𝑥 25 − 21 3𝑥 4 3𝑥
- 14. Adding and Subtracting Algebraic Fractions 6 𝑥 + 3 + 8 𝑥 − 4 6 𝑥 − 4 + 8(𝑥 + 3) (𝑥 + 3)(𝑥 − 4) 6𝑥 − 24 + 8𝑥 + 24 (𝑥 + 3)(𝑥 − 4) 14𝑥 (𝑥 + 3)(𝑥 − 4)
- 15. ACTIVITY 2: working in groups of four solve the following 1. a) 7 𝑥 − 5 𝑥 b) 8𝑥 3 + 4𝑥 3 c) 5𝑥+1 2 − 3𝑥 2 2. a) 7𝑥 3 + 3𝑥 4 b) 7𝑥 3 − 8𝑥 5 c) 12 5𝑥 + 3 𝑥 3. a) 𝑥+3 6 + 𝑥 −2 4 b) 2𝑥 −5 3 − 4𝑥+1 7
- 16. Multiplying and Dividing Algebraic Fractions Learning Objectives: Able to add and subtract complex algebraic fractions Able to multiply and divide simple algebraic fractions Able to multiply and divide more complex algebraic fractions
- 17. Multiplying and Dividing Algebraic Fractions Just as with numeric fractions, look to cancel diagonally before multiplying the numerators and denominators 4𝑥 5 × 15𝑦 16 3𝑥𝑦 4 3 1 1 4
- 18. Multiplying and Dividing Algebraic Fractions The same method applies to dividing algebraic fractions: Copy, change, flip. 11 9𝑥2 𝑦 ÷ 77𝑦 15𝑥 5 21𝑥𝑦2 11 9𝑥2 𝑦 × 15𝑥 77𝑦 1 5 3 7
- 19. Multiplying and Dividing Algebraic Fractions 𝑥 + 4 𝑥 − 3 × 3𝑥 − 9 5𝑥 + 20 𝑥 + 4 𝑥 − 3 × 3(𝑥 − 3) 5(𝑥 + 4) 3 5
- 20. ACTIVITY 3: in group of four solve the following. 36𝑥 55𝑦 × 33𝑦2 40𝑥 7𝑥+56 9𝑥−81 ÷ 5𝑥+40 3𝑥−27 𝑥2−121 𝑥2+21𝑥+108 ÷ 𝑥2−18+77 𝑥2+7𝑥−18
- 21. What have you learnt? In your brain, write or draw everything you can remember about solving algebraic equations involving fractions. It can be a skill or a reflection, or something else that might be prominent in your brain. Draw your brain What grade we working at? Where are we in our journey?
- 22. . How well do you understand the task? I don’t understand I nearly understand I fully understand Effective Participator Self Manager Independen t Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using?
- 23. REFLECTION ACTIVITY After your lesson reflection… Think about how you can improve your work. (What Went Well) (how do you feel working with a group) (Was the group effective) (how was the lesson) (how do u feel working with a group) (Was there any conflict) (write a summary of all your experiences of learning Algebra)