Topicm966b2ca00f38c130_1528449000663_0Topic

Solving word problems – negative numbers

Levelm966b2ca00f38c130_1528449084556_0Level

Second

Core curriculumm966b2ca00f38c130_1528449076687_0Core curriculum

III. The integers. The student:

5) does simple calculations in the head.

Timingm966b2ca00f38c130_1528449068082_0Timing

45 minutes

General objectivem966b2ca00f38c130_1528449523725_0General objective

Interpretation and production of mathematical texts as well as graphical presentation of data.

Specific objectivesm966b2ca00f38c130_1528449552113_0Specific objectives

1) Communication in English, developing mathematical, IT and basic scientific and technical competence, developing learning skills.

2) Doing simple calculations on integers.

3) Solving word problems with the use of negative numbers.

Learning outcomesm966b2ca00f38c130_1528450430307_0Learning outcomes

The student:

- does calculations on integers,

- solves word problems with the use of negative numbers.

Methodsm966b2ca00f38c130_1528449534267_0Methods

1) Educational game – mathematical domino.

Forms of workm966b2ca00f38c130_1528449514617_0Forms of work

1) Individual work.

2) Work in pairs.

Lesson stages

Introductionm966b2ca00f38c130_1528450127855_0Introduction

Working in pairs, the students revise methods of doing operations on integers. In order to do it, they solve the mathematical domino puzzle, which the teacher gave them.

Mathematical domino:

$\boxed{7}\boxed{-3+1}$

$\boxed{-2}\boxed{-6-1}$

$\boxed{2}\boxed{-6:6}$

$\boxed{-1}\boxed{10:\left(-2\right)}$

$\boxed{-7}\boxed{4-5}$

$\boxed{-1}\boxed{7-0}$

$\boxed{-5}\boxed{3·\left(-1\right)}$

$\boxed{-3}\boxed{-2·\left(-5\right)}$

$\boxed{7}\boxed{-8:\left(-4\right)}$

$\boxed{-10}\boxed{-7·\left(-1\right)}$

The students check the correctness of their answers with calculators. They correct any mistakes themselves or as the teacher for an explanation.

The teacher informs the students that the aim of the class will be using the ability to do operations on integers to solve word problems.

Procedurem966b2ca00f38c130_1528446435040_0Procedure

The students continue working in pairs. They solve the task using the applet.

Task
Solve the task below which describes the changes of the sir temperature in a town. Check the correctness of your results using the applet. In each case, decide if the temperature is positive or negative.

1. In the morning the temperature was -4°C. In the afternoon it rose by 4°C. What was the temperature at midday?

2. In the evening the temperature was 0°C. At midnight it dropped by 10°C. What was the temperature at midnight?

3. At dawn the temperature was -3°C. During the day it dropped by 6°C. What was the temperature during the day?  

[Geogebra applet]

The students share their thoughts after solving the task. They define the mathematical sense of expressions: above zerozerozero, below zerozerozero, zerozerozero or below, zerozerozero or above.

They write down their conclusion:

- a number greater than zerogreater than zerogreater than zero or equal to zerozerozero is non‑negative,

- a number less than zeroless than zeroless than zero or equal to zerozerozero is non‑positive.

The students work individually. Their task is to find a hidden word made of letters corresponding to the worked out numbers.

Task
Solve the exercises. Write the letters corresponding to the worked out numbers into the table and read the hidden word.

Exercise 1
Irek had 10 zł. He bought icecream for 6 zł, biscuits for 7 zł and a notebook for 2 zł. How much money did he have to borrow from his friend to pay for his shopping?m966b2ca00f38c130_1527752263647_0Exercise 1
Irek had 10 zł. He bought icecream for 6 zł, biscuits for 7 zł and a notebook for 2 zł. How much money did he have to borrow from his friend to pay for his shopping?

[Table 1]

Exercise 2
Marek and Darek throw a dice in turns. For throwing the even number you get 2 points. For throwing the odd number 4 points are subtracted. Marek threw the dice three times. The first and second time he threw 5 pips and the third time he threw 4 pips. How many points has he scored if in the beginning he had 2 points?

[Table 2]

Exercise 3
At 1 p.m. the temperature in our town was 30°C. Every hour it dropped by 20°C. What was the temperature at 5 p.m.?m966b2ca00f38c130_1527752256679_0Exercise 3
At 1 p.m. the temperature in our town was 30°C. Every hour it dropped by 20°C. What was the temperature at 5 p.m.?

[Table 3]

Exercise 4
What number will I get if I will divide -20 by -5?

[Table 4]

Exercise 5
A fish is swimming in the sea at a depth of 10 m. A seagull is flying above the fish, at an altitude of 6 meters above the sea level. What is the distance between the fish and the seagull?m966b2ca00f38c130_1527712094602_0Exercise 5
A fish is swimming in the sea at a depth of 10 m. A seagull is flying above the fish, at an altitude of 6 meters above the sea level. What is the distance between the fish and the seagull?

[Table 5]

Hidden word:

[Table 6]

The fastest students to get the hidden word get a “plus”.

An extra task
Find in the available source what an absolute zerozerozero is.

Lesson summarym966b2ca00f38c130_1528450119332_0Lesson summary

The students do the consolidation tasks. They cooperate to summarize the class and formulate the conclusion to memorize:
- a number greater than zerogreater than zerogreater than zero or equal to zerozerozero is non‑negative,
- a number less than zeroless than zeroless than zero or equal to zerozerozero is non‑positive.

Selected words and expressions used in the lesson plan

air temperatureair temperatureair temperature

greater than zerogreater than zerogreater than zero

negative numbernegative numbernegative number

non‑negative numbernon‑negative numbernon‑negative number

non‑positive numbernon‑positive numbernon‑positive number

positive numberpositive numberpositive number

less than zeroless than zeroless than zero

zerozerozero