Mathematics is one of the core subjects in the educational system, and the knowledge of basic mathematic is vitally important for each person as well as reading and writing. This essay is aimed at discussing how to teach pupils to deal with decimals, in particular, how to perform rounding to the nearest tenth. The essay also includes concepts and basic knowledge necessary for the pupils to master the topic, common tasks to show and to practice the idea of rounding decimals, as well as possible mistakes and keys related to the operations with decimals.
1. Grade levels
The lesson concerning rounding with mixed decimals to the nearest tenth is intended for students of 4-6 grades, depending on the curriculum. However, the supposed examples and tasks may be used for pupils from any of the above-mentioned grades.
2. Prerequisite knowledge
In order to understand the material of the lesson, the pupils need to have basic understanding of what a decimal is. They should know the definition of a decimal number: i.e. that a decimal is used to denote number smaller than one. Also, the pupils need to realize what tenths and hundredths are and distinguish between them. The pupils needs to understand which number is smaller, for example, 0.01 or 0.1, and they also need to read the decimals properly (for example, 5.4 should be read as “five and four tenths”¯).
The teacher also needs to remind the basic ideas of rounding numbers to pupils and then show the similarity of rounding decimals. But first of all the teacher needs to ensure that pupils understand the purpose of rounding and remember how to round whole numbers.
There are several key questions and tasks that should be used to ensure that pupils are ready for the new material. For example, the tasks may be the following:
- Show the number line between two whole numbers divided by step of 0.1
- Set analogy between this line and the line of whole numbers
- Count aloud from the minor number to major number
- Ask pupils to identify, write and name the decimals shown on the line
The same line may be useful to explain rounding, so it may remain (for example, at the blackboard or at the screen) until the new material is shown.
The teacher should also ask the pupils to round whole numbers (examples: 48, 32, 25 etc.) to nearest tens.
3. New skills presented in the lesson
The teacher should explain the necessity of rounding decimals and set examples where this knowledge may be used in everyday life.
The new skills that the pupils will gain during the lesson: they will learn how to round mixed decimals to the nearest tenth and will learn where they may need this knowledge.
4. Rounding with decimals to the nearest tenth
Then the rule for rounding may be shown and accompanied with examples. The rule for rounding may be expressed as the following: “rounding decimals is very similar to rounding other numbers. If the hundredths and thousandths places of a decimal is forty-nine or less, they are dropped and the tenths place does not change. If the hundredths and thousandths places are fifty or more, the tenths place is increased by one”¯.
5. Activities and tasks
It may be useful to mention rounding distances in meters and show them on the number line. The rules of rounding may also be shown on the line, and examples with meters, as well as other examples, related with sport (time measurement etc.) or financial examples may be used.
Then the class passes to working with numbers without indicating the origin of the number. The teacher has to explain that rounding applies to any decimals and write down examples.
The teacher should set different examples. There are some key tasks that the teacher should explain to the class:
- Rounding 0.762 to the nearest tenth gives 0.8 (because the hundredths and thousandths places are 62, and this is more than 49)
- Rounding 0.742 to the nearest tenth gives 0.7 (because the hundredths and thousandths places are 42, and this is less than 49)
- Rounding 0.750 to the nearest tenth gives 0.8 (because the hundredths and thousandths places are 50, and this is equal to 50)
- Rounding 0.749 to the nearest tenth gives 0.7 (because the hundredths and thousandths places are 49, and this is less than 50)
6. Possible problems and misconceptions
The most common mistake while learning rounding mixed decimals to the nearest tenth is mixing when the starting number is rounded to greater number, and when it is rounded to smaller number. While there are practically no mistakes concerning numbers with combination of hundredth and thousandths from 01 to 39, and from 60 to 99, there occur mistakes on the 40-59 border. The teacher needs to address possible misunderstandings connected with this, and set more examples where this possible mistake may appear.
Basic mathematics is important for everyone, thus the methods of teaching the main principles and the used examples should be various ”“ to reach the mind of any pupil, and should be practiced for a proper time, to ensure that the pupils do the necessary operations automatically without having to remind the necessary ideas. Therefore, the lesson construction should ensure the above-mentioned objectives.