Lesson plan

Topicm8f78fcb876bc54d9_1528449000663_0Topic

An absolute value – definition

Levelm8f78fcb876bc54d9_1528449084556_0Level

Third

Core curriculumm8f78fcb876bc54d9_1528449076687_0Core curriculum

I. Real numbers. The basic level. The student:

6) uses the concept of the number interval, marks intervals on the number linenumber linenumber line.

7) applies geometric and algebraic interpretation of the absolute valueabsolute valueabsolute value, does equations and inequalities of the following type: $| x + 4 | = 5, | x - 2 | < 3, | x + 3 | \geq 4 .$

Timingm8f78fcb876bc54d9_1528449068082_0Timing

45 minutes

General objectivem8f78fcb876bc54d9_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm8f78fcb876bc54d9_1528449552113_0Specific objectives

1. Applying geometric and algebraic interpretations of the absolute value of a number.

2. Solving equations and inequalities of the following type: $| x + 4 | = 5, | x - 2 | < 3, | x + 3 | \geq 4 .$

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesm8f78fcb876bc54d9_1528450430307_0Learning outcomes

The Student:

- applies geometric and algebraic interpretations of the absolute value of a number,

- solves equations and inequalities of the following type: $| x + 4 | = 5, | x - 2 | < 3, | x + 3 | \geq 4 .$

Methodsm8f78fcb876bc54d9_1528449534267_0Methods

1. Situational analysis.

2. Task tables.

Forms of workm8f78fcb876bc54d9_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm8f78fcb876bc54d9_1528450127855_0Introduction

Students revise information about number intervals – types, ways of marking them on the number line
and how to write them down.

The teacher introduces the subject of the lesson – the absolute value of a number.

Procedurem8f78fcb876bc54d9_1528446435040_0Procedure

Students work individually, using computers. Their task is to know the interactive illustration, that describes the absolute valueabsolute valueabsolute value of a number.

[Interactive illustration]

After having completed the exercise, they present results of their observations:

- the distance between the number a and zero on the number line is called the absolute value of the number a and is marked as $| a |$ ,
- for any real number a, $| a | = | - a |$ ,
- for any real number a, $| a | \geq 0$ .m8f78fcb876bc54d9_1527752263647_0- the distance between the number a and zero on the number line is called the absolute value of the number a and is marked as $| a |$ ,
- for any real number a, $| a | = | - a |$ ,
- for any real number a, $| a | \geq 0$ .

TASK STATIONS

Students work with the method of task stations. In groups, they solve tasks prepared earlier by the teacher.

Each group gets points for correct solutions and the time of doing exercises.

The best group gets marks from activity.

Station 1.

Task 1

Solve equations using the example presented in the frame.m8f78fcb876bc54d9_1527752256679_0Solve equations using the example presented in the frame.


$\| x \| = a, a \geq 0, x = ?$ [Illustration 1] $\| x \| = a \Leftrightarrow x = - a o r x = a$

a) $| x | = 5$ ,

b) $| x - 5 | = 10$ ,

c) $| 2 x + 3 | = 7$ .

Station 2.

Task 2

Mark on the number linnumber linenumber line all numbers x that satisfy the inequality, using the example presented
in the frame. Write the proper number interval.


$\| x \| < a, a \geq 0, x = ?$ [Illustration 2] $\| x \| < a \Leftrightarrow x \in (- a, a)$

a) $| x | < 5$ ,

b) $| x | < 10$ .

Station 3.

Task 3

Mark on the number line all numbers x that satisfy the inequality, using the example presented
in the frame. Write the proper number interval.


$\| x \| > a, a \geq 0, x = ?$ [Illustration 3] $\| x \| > a \Leftrightarrow x \in (- \infty, - a) \cup (a, + \infty)$

a) $| x | > 4$ ,

b) $| x | > 1$ .

Station 4.

Task 4

Solve equations using information presented in the frame.


The distance between numbers a and b on the number linedistance between numbers a and b on the number line is equal to the absolute valueabsolute valueabsolute value of their difference $\| a - b \|$ . The form $\| x - 2 \| = 4$ means that the distance between the number x and number 2 is equal to 4. [Illustration 4] Therefore x = -2 or x = 6.

a) $| x - 5 | = 3$ ,

b) $| x + 2 | = 4$ .

The teacher evaluates students’ work and clarifies doubts.

An extra task

Solve the equation: $| 2 (x + 1) - 1 | - 4 = 5$ .

Lesson summarym8f78fcb876bc54d9_1528450119332_0Lesson summary

Students do the revision exercises. Then together they sum‑up the classes, by formulating the conclusions to memorise:

Selected words and expressions used in the lesson plan

absolute valueabsolute valueabsolute value

closed intervalclosed intervalclosed interval

distance between numbers a and b on the number linedistance between numbers a and b on the number line

distance between the number a and zerodistance between the number a and zerodistance between the number a and zero

number linenumber linenumber line

open intervalopen intervalopen interval

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$\| x \| = a, a \geq 0, x = ?$ [Ilustracja 1] $\| x \| = a \Leftrightarrow x = - a l u b x = a$

$\| x \| < a, a \geq 0, x = ?$ [Ilustracja 2] $\| x \| < a \Leftrightarrow x \in (- a, a)$

$\| x \| > a, a \geq 0, x = ?$ [Ilustracja 3] $\| x \| > a \Leftrightarrow x \in (- \infty, - a) \cup (a, + \infty)$

Odległość liczb a i b na osi liczbowej jest równa wartości bezwzględnej ich różnicy $\| a - b \|$ . Zapis $\| x - 2 \| = 4$ oznacza, że odległość liczby x od liczby 2 wynosi 4. [Ilustracja 4] A zatem x = -2 lub x = 6.

m8f78fcb876bc54d9_1528450119332_0

number line1

absolute value1

distance between numbers a and b on the number line1

closed interval1

distance between the number a and zero1

open interval1

Scenariusz

Topicm8f78fcb876bc54d9_1528449000663_0Topic

Lesson stages

Selected words and expressions used in the lesson plan