Topicme5d326510d846068_1528449000663_0Topic

Solving word problems with decimal fractions

Levelme5d326510d846068_1528449084556_0Level

Second

Core curriculumme5d326510d846068_1528449076687_0Core curriculum

XIV. Word problems. The student:

5) uses their knowledge in arithmetic, geometry, calculation skills and their own appropriate methods to solve problems in practical context.

Timingme5d326510d846068_1528449068082_0Timing

45 minutes

General objectiveme5d326510d846068_1528449523725_0General objective

Matching a mathematical model to a simple situation and building it in various contexts, also practical contexts.

Specific objectivesme5d326510d846068_1528449552113_0Specific objectives

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

2. Developing the ability to calculate decimal fractionsdecimal fractionsdecimal fractions.

3. Solving word problems with a realistic context.

Learning outcomesme5d326510d846068_1528450430307_0Learning outcomes

The student:

- builds a mathematical model in a situation presented in a task,

- solves word problems doing calculations with decimal fractionsdecimal fractionsdecimal fractions.

Methodsme5d326510d846068_1528449534267_0Methods

1. Educational game.

Forms of workme5d326510d846068_1528449514617_0Forms of work

1. Work in pairs.

2. Group work.

Lesson stages

Introductionme5d326510d846068_1528450127855_0Introduction

Using the “lucky draw” technique to recollect methods of performing operations with decimal fractionsdecimal fractionsdecimal fractions. The students write their names on pieces of paper and put them into a box. The teacher draws 5 names. Then, the chosen students draw a piece of paper each from another box. They find examples of addition, subtraction, multiplication and division with decimal fractions in the pieces of paper. The students solve the tasks on the board, giving explanation of used calculation techniques. The fifth piece of paper is the “lucky draw”. The student who has drawn this one, gets a calculator and checks if the other students did their calculations correctly.

The teacher informs the students that store chain “Surprise” has introduced a regulation which makes every customer calculate how much he owes the shop.

It is forbidden to use any calculators.

The aim of the class will be developing the ability to do calculations with decimal fractionsdecimal fractionsdecimal fractions.

Procedureme5d326510d846068_1528446435040_0Procedure

The students solve the tasks in groups.

Task 1
A grain of wheat costs 0,02 zł. Arek bought 126 grains of wheat for his white mouse. How much did he pay?

Task 2
Basia’s pig eats 2 watermelons for breakfast every day. ! kilogram of watermelon costs 2,64 zł. How much money does Basia spend every week on the watermelons?

Task 3
Cecylia bought a TV set for herself and some toys for her goddaughters.

Using the applet, match the objects she bought to their prices.

[Geogebra applet]

Task 4
Darek spent 140 zł on bones for his dog. How many bones did he buy if one costs 70 gr?

Task 5
- Can I have 9 pieces of cheese for my cat? - Ewa said.
- The ones 3,10 zł per item? - The shop assistant asked.
- Yes, please.- Ewa said and gave a 50 zł note to the shop assistant.

How much change did she get?

An extra task:
Marcin bought 2 bags of hay and 3 bags of carrots for his horse. A bag of hay costs 89 zł, and a bag of carrots 46,10 zł. The shop had a special offer, so Marcin paid 20 zł less. How much did he pay in total?

Having solved all the tasks, the student check correctness of their answers. They use a model of solutions prepared by the teacher.

Discussion – is it easy to do the calculations with decimal fractionsdecimal fractionsdecimal fractions without a calculator? What do you need to do to get the correct result?

Example conclusions

- It is best to do calculations with decimal fractions in the written form.me5d326510d846068_1527752263647_0It is best to do calculations with decimal fractions in the written form.

- You can use the commutative and associative properties of addition and multiplication.me5d326510d846068_1527752256679_0You can use the commutative and associative properties of addition and multiplication.

- It is a good idea to estimate the result of the calculations to avoid obvious mistakes.

Pair work. The students throw two dices one by one. The number on the first dice refers to the number of złotys, and the other dice refers to the number of tens of groszes. For example, the result 4 and 6 gives 4,60 zł. The student’s task is to decide how much change will he get if pays the given amount of money (e.g. 4,60 zł) and has 10 zł.
The other student checks the result using a calculator.

The students assess themselves and decide if they will be able to do the shopping in the store chain “Surprise”.

Lesson summaryme5d326510d846068_1528450119332_0Lesson summary

The students do the consolidation tasks. They summarize the class and formulate the conclusions that they should remember.

- is best to do calculations with decimal fractionsdecimal fractionsdecimal fractions in the written form.

- You can use the commutative and associative properties of addition and multiplication.

- It is a good idea to estimate the result of the calculations to avoid obvious mistakes.

Selected words and expressions used in the lesson plan

answeransweranswer

commutative property of additioncommutative property of additioncommutative property of addition

commutative property of multiplicationcommutative property of multiplicationcommutative property of multiplication

content of the taskcontent of the taskcontent of the task

decimal fractionsdecimal fractionsdecimal fractions

estimatingestimatingestimating

operations with fractionsoperations with fractionsoperations with fractions

word problemword problemword problem