ALGEBRAIC-EXPRESSIONS-Term-2-Lesson-7-Grade Download

Transcript
MATHEMATICS LESSON PLAN
GRADE 8
TERM 2: APRIL – JUNE
PROVINCE:
DISTRICT:
SCHOOL:
TEACHER’S
NAME:
DATE:
DURATION:
1 Hour
1. TOPIC: ALGEBRAIC EXPRESSIONS:
EXPRESSIONS (Lesson 7)
EXPAND AND SIMPLIFY ALGEBRAIC
2. CONCEPTS & SKILLS TO BE ACHIEVED:
By the end of the lesson learners should be able to use commutative, associative
distributive to determine the squares, cubes, square roots and cube roots of single
algebraic term or like terms.
Grade 8 Lesson Plan: 1+4 Intervention – Term 2
ALGEBRAIC EXPRESSIONS: EXPAND AND SIMPLIFY ALGEBRAIC EXPRESSIONS (Lesson 7)
(Draft)
3. RESOURCES:
DBE workbook, Sasol-Inzalo workbook, calculator, textbook
4. PRIOR KNOWLEDGE




squares
cubes
square roots
cube roots.
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time: 10 minutes)
Homework provides an opportunity for teachers to track learners’ progress in the mastery of
mathematics concepts and to identify the problematic areas which require immediate attention.
Therefore, it is recommended that you place more focus on addressing errors from learner
responses that may later become misconceptions.
6. INTRODUCTION (Suggested time: 10 Minutes)
Ask the learners to give the mathematical meaning of the following concepts and provide examples
of it:
square, cube, square root and cube root


A square number is a number that you get when a number is multiplied by itself once e.g. 4 ×
4 = 16. Therefore 16 is a square number.
The square root is a value that multiplies by itself once to give the original number
e.g. 4 × 4 = 16. Therefore √16 = 4
Note:
Discuss the following misconceptions with the learners:
32 = 3 × 3 not 3 × 2
3×2=2+2+2
(3)2 = 3 × 3
=3××3×
=3×3××
= 9 2

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A cube number is a number you get when a number is multiplied by itself two times e.g. 3 × 3 ×
3 = 27. Therefore 27 is a cube number
A cube root is a value that multiplies by itself two times to give the original number
3
e.g. 3 × 3 × 3 = 27. Therefore √27 = 3
Grade 8 Lesson Plan: 1+4 Intervention – Term 2
ALGEBRAIC EXPRESSIONS: EXPAND AND SIMPLIFY ALGEBRAIC EXPRESSIONS (Lesson 7)
(Draft)
Page 2 of 5
7. LESSON PRESENTATION/DEVELOPMENT (Suggested time: 20 minutes)
Learning activities
Teaching activities
(Learners are expected to:)
Let the learners complete the following activities individually:
Activity 1
Determine the value of each without the use of a calculator:
a) √25
3
d) √216
b) √144

complete the activity
individually

engage in class
discussion on the
solution to the
problems

follow teachers
explanations

engage in discussions
with the teachers
3
c) √64
Discuss the following with learners and with their assistance
complete the activities

The square root of a product of square numbers is equal to
the product of the square roots
e.g. √ 25 × 9 = √25 × √9
=5 ×3
= 15
 Discuss the misconceptions with learners.
The square of the sum of square numbers is not equal to the
sum of the square roots.
√25 + 9 ≠ √25 + √9
√34 ≠ 5 + 3
√34 ≠ 8

The square of the difference of square numbers is not equal
to the difference of the square roots.
√100 − 64 ≠ √100 − √64
√36 ≠ 10 − 8
√36 ≠ 2

The square root of a quotient of square numbers is equal to
the quotient of the square root.
81 √81 9
√ =
=
4
2
√4
Grade 8 Lesson Plan: 1+4 Intervention – Term 2
ALGEBRAIC EXPRESSIONS: EXPAND AND SIMPLIFY ALGEBRAIC EXPRESSIONS (Lesson 7)
(Draft)
Page 3 of 5
Activity 2
Demonstrate the following problems to learners.
a) √0,49
49
=√100
=
√49
√100
7
=
10
= 0,7
b)
3
√0,0027
8. CLASSWORK (Suggested time: 15 minutes)
Activity 1
1. Simplify the following
(a) √ 12
(b) √125 2 + 44 2
3
(c) √−27 3
2. Say whether the equation is true or false. Give a reason for your answer.
√7 2 × 7 2 = 7 2
3. Simplify the following:
a) (25 − 16)2
b) (2 3 )3
Grade 8 Lesson Plan: 1+4 Intervention – Term 2
ALGEBRAIC EXPRESSIONS: EXPAND AND SIMPLIFY ALGEBRAIC EXPRESSIONS (Lesson 7)
(Draft)
Page 4 of 5
9. CONSOLIDATION/CONCLUSION & HOMEWORK (Suggested time: 5 minutes)
(a) Emphasise that:

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
squaring and finding square roots are inverse operations.
if you want to find the square root of 16² you need to find out what you need to
multiply by itself to get 16². The answer is 4, because (4)(4) = 16². Therefore
√16² = 4
in this grade square root of a negative number cannot be determined, because there
are no equal numbers that will give you a negative. (−4)(4) = −16 and −4 and 4 are
two different numbers.
to find the cube root you need to multiply the number by itself twice. To find the cube
root of 27³ you need to find out what need to be multiplied twice with itself to get
3
27³. (3)(3)(3) = 27³. Thus √27³ = 3a
you can find the cube root of a negative number because you can multiply a negative
3
3
number by itself twice and get a negative answer. √−27³ = √−3 × −3 × −3 =
−3
(b) The primary purpose of Homework is to give each learner an opportunity to demonstrate
mastery of mathematics skills taught in class. Therefore Homework should be purposeful and
the principle of ‘Less is more’ is recommended, i.e. give learners few high quality activities
that address variety of skills than many activities that do not enhance learners’ conceptual
understanding.
Carefully select appropriate activities from the Sasol-Inzalo Books, DBE workbooks and/or
textbooks for learners’ homework. The selected activities should address different cognitive
levels.
Recommended Homework:
Simplify the following
3
a) √√64
7
b) √1 9
c) (13 − 6)3
Grade 8 Lesson Plan: 1+4 Intervention – Term 2
ALGEBRAIC EXPRESSIONS: EXPAND AND SIMPLIFY ALGEBRAIC EXPRESSIONS (Lesson 7)
(Draft)
Page 5 of 5