Grade 10 Algebra

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:

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

simplify more

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

more complex

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 Able to multiply

Write a summary

reflecting of

what you have

learnt from this

lesson of algebra

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.

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

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

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

Simplifying Algebraic Fractions

4𝑎𝑏 + 8𝑎2

12𝑎

4𝑎(𝑏 + 2𝑎)

12𝑎

𝑏 + 2𝑎

3

3

Simplifying Algebraic Fractions

4𝑥 − 20

𝑥2 − 13𝑥 + 40

4(𝑥 − 5)

𝑥 − 5 (𝑥 − 8)

4

𝑥 − 8

ACTIVITY ONE: Working in groups of four simplify the following

algebraic fraction

7𝑥 − 35

213𝑥2 + 15𝑥

27𝑥

6𝑥2𝑦 + 18𝑥𝑦

21𝑥𝑦

𝑥2 + 7𝑥 + 10

3𝑥 + 15

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

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

Adding and Subtracting Algebraic

Fractions

25

3𝑥−

7

𝑥

25 − 21

3𝑥

4

3𝑥

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)

ACTIVITY 2: working in groups of four solve the following

1. a) 7

𝑥−

5

𝑥b)

8𝑥

3+

4𝑥

3c)

5𝑥+1

2−

3𝑥

2

2. a) 7𝑥

3+

3𝑥

4b)

7𝑥

3−

8𝑥

5c)

12

5𝑥+

3

𝑥

3. a) 𝑥+3

6+

𝑥 −2

4b)

2𝑥 −5

3−

4𝑥+1

7

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

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

Multiplying and Dividing Algebraic

Fractions

The same method applies to dividing algebraic fractions: Copy, change,

flip.

11

9𝑥2𝑦÷77𝑦

15𝑥

5

21𝑥𝑦2

11

9𝑥2𝑦×

15𝑥

77𝑦

1 5

3 7

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

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

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?

.

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?

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)