this is a grade 10 algebra learning task

1. Grade 10 Algebra

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)