Topicmc72becb84b16fff3_1528449000663_0Topic

The positionpositionposition of points on the number line

Levelmc72becb84b16fff3_1528449084556_0Level

Second

Core curriculummc72becb84b16fff3_1528449076687_0Core curriculum

X. The number line. The coordinatecoordinatecoordinate system in the plane. The student:

1) indicates the sets of numbers on the number linenumber linenumber line which fulfill the following conditions: x ≥ 1.5 ; x < $-\frac{4}{7}$.

Timingmc72becb84b16fff3_1528449068082_0Timing

45 minutes

General learning objectivesmc72becb84b16fff3_1528449523725_0General learning objectives

Interpreting and creating mathematical texts and presenting data graphically.

Key competencesmc72becb84b16fff3_1528449552113_0Key competences

1. Reading the positionpositionposition of points on the number line.

2. Specifying the points on the number line.

3. Communicating in English; developing mathematical and basic scientific, technical and digital competences; developing learning skills.

Operational (detailed) goalsmc72becb84b16fff3_1528450430307_0Operational (detailed) goals

The student:

- reads the position of points on the number line,

- indicates points on the number line.

Methodsmc72becb84b16fff3_1528449534267_0Methods

1. Method of exposition.

2. Situational analysis.

Forms of workmc72becb84b16fff3_1528449514617_0Forms of work

1. Individual work.

2. Pair work.

Lesson stages

Introductionmc72becb84b16fff3_1528450127855_0Introduction

The students bring the ruler and sticky notes with the following numbers written on them:

-  -300, -250, -200, -150, -100, -50, 0, 50, 100;

-  -0,4; -0,2; 0; 0,2; 0,4; 0,6; 0,8; 1; 1,2.

The teacher prepares pieces of paper with the following numbers:

-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

and the sign of an arrow $\to .$

Proceduremc72becb84b16fff3_1528446435040_0Procedure

The teacher informs the students they are going to read and mark the numbers on the number linenumber linenumber line.

The teacher chooses at random eight volunteers and gives them the cards with the numbers -3, -2, -1, 0, 1, 2, 3 and an arrow sign $\to$. The students have to stand in the ascending order according to the cards they hold. The student who holds the paper with the sign of an arrow $\to$, which means the orientation of the number line, stands to the left of the person holding the card with the greatest number.

The teacher explains to the students that the line with a specified orientation, the arbitrary pointpointpoint 0 (the begining) and the unit segment is called the number line.

The students answer the following questions:

What does the orientation of the arrow tell you about?

What numbers are at the same distance from the beginning on the number line? How are they called? 

Where can we use the models of the number lines in our everyday life?

The teacher chooses at random eight volunteers and gives them the cards with the numbers -3, -2, -1, 0, 1, 2, 3 and an arrow sign $\to$. The students have to stand in the ascending order according to the cards they hold. The student who holds the paper with the sign of an arrow $\to$, which means the orientation of the number linenumber linenumber line, stands to the left of the person holding the card with the greatest number.

The students discuss the samples of the numbers on the number line: the numbers -10, -8, -4, -2, 0, 2, 4 and the numbers -9, -6, -3, 0, 3, 6, 9.

They should come up with the following conclusions:

- The numbers on the number line are arranged in a systematic way.
- The direction of the axis shows the ascending order of numbers.
- The numbers which are at the same distance to the arbitrary point but lie at the opposite sides on the number line are called the opposite numbers.mc72becb84b16fff3_1527752263647_0- The numbers on the number line are arranged in a systematic way.
- The direction of the axis shows the ascending order of numbers.
- The numbers which are at the same distance to the arbitrary point but lie at the opposite sides on the number line are called the opposite numbers.

The students work in pairs. They use the numbers on the sticky notes.

Task 1

Draw two number lines. Mark the points corresponding to the numbers on the sticky notes. Stick the notes with the numbers in the appropriate places. Mark the opposite numbersopposite numbersopposite numbers with the same colour.

Example 1

Draw the number linenumber linenumber line. Mark the points 0, 1, 2, 3, 4, 5 and their opposite numbers.

[Illustration 1]

The points on the number line are marked with the dot. The number assigned to the point is called its coordinatecoordinatecoordinate.

Task 2

Draw the appropriate number lines and determine the points of the following coordinates:

a)-600, -300, -100, 0, 200,

b)-3, -1,5, 3, 4,5, 6,

c) $-\frac{3}{5},-\frac{1}{5},\frac{4}{5},1\frac{2}{5},2.$

Task 3

Place pointpointpoint M on the number linenumber linenumber line in the place specified with a given coordinatecoordinatecoordinate.

[Geogebra applet]

Example 2

Read the coordinatecoordinatecoordinate of point A.

[Illustration 2]

Notice that the distance between the numbers 0 and 20 is divided into four identical segments. Each of these segments equals five unit segments, i.e. 20: 4 = 5. The coordinate of point A equals 10,
because 2 ⋅ 5 = 10.mc72becb84b16fff3_1527752256679_0Notice that the distance between the numbers 0 and 20 is divided into four identical segments. Each of these segments equals five unit segments, i.e. 20: 4 = 5. The coordinate of point A equals 10,
because 2 ⋅ 5 = 10.

Task 4

Read the coordinates of point A:

a)

[Illustration 3]

b)

[Illustration 4]

An extra task:

Draw the number line and determine:

a) all integersintegersintegers greater then -6 and not smaller then 4,

b) all positive multiple of the number 13 smaller than 100,

c) the opposite numbersopposite numbersopposite numbers to the numbers $-1,-\frac{8}{9},-\frac{3}{9},0,\frac{1}{9},1\frac{5}{6}.$

Lesson summarymc72becb84b16fff3_1528450119332_0Lesson summary

Students do the summarising tasks.

Then, they together sum up the classes drawing the conclusions to memorise:

- The line with the specified direction, an arbitrary pointpointpoint 0 (the beginning) and the unit segment is called the number linenumber linenumber line.

- The number assigned to the point is called its coordinate.

Selected words and expressions used in the lesson plan

coordinatecoordinatecoordinate

integersintegersintegers

multiple of a numbermultiple of a numbermultiple of a number

number linenumber linenumber line

opposite numbersopposite numbersopposite numbers

orientation of the axisorientation of the axisorientation of the axis

pointpointpoint

positionpositionposition

straight linestraight linestraight line

unit lengthunit lengthunit length