# Four Operations Using Decimals

Students are required to be fluent when using the operations addition, subtraction, multiplication and division with integers and decimals. This resource package contains a variety of activities designed to support the teaching and learning of the use of the four operations, including efficient written methods, applied to integers and decimal fractions.

Visit the secondary mathematics webpage to access all lists.

### Column Addition

Two videos explaining written methods for adding whole numbers and decimal numbers.

**Column addition of whole numbers** – Five examples of adding whole numbers using the column method. The examples progress in difficulty adding numbers with two and three digits. The third and fourth examples include the need to ‘carry one’ from one column to the next. The videos can be used in a variety of ways. Pause the video after the initial problem is presented, ask students to complete the calculation and then discuss the different methods used. Ask students to criticise the methods used on the video.

**Column addition of decimal numbers** – Four examples of adding decimals using the column method. The examples progress in difficulty adding numbers with one, two and three decimal places. The third and fourth examples include the need to ‘carry one’ from one column to the next. Students could be asked to make their own short video showing a different approach to solving the problem. Ideal activity if students have access to hand held technology.

### Addition

This resource contains games, investigations, worksheets and practical activities many of which make ideal starter activities. Addition pack three contains work cards in which students are required to add simple decimals.

**Exactly Ten** is a game in which two players add decimals to make a target number. This activity can easily be extended to increase the degree of difficulty.

**OXFAM Collection** involves the multiplication and addition of decimals in the context of dealing with money.

### Arithmetic: Addition and Subtraction of Decimals

This resource is useful for consolidation work covering addition and subtraction of whole numbers, dealing with brackets, addition and subtraction of decimals and dealing with money.

**Arithmetic**: contains exercises requiring students to add whole numbers and decimal numbers. There are questions in word form and in the context of money. The worded questions are particularly useful to ensure students can perform the correct calculation to solve the problem presented.

### Multiplication

Two videos explaining methods of performing division calculations.

**Short multiplication **– Four examples of multiplying numbers using the column method. The examples progress in difficulty multiplying two digit numbers by a single digit number, multiplying a three digit numbers by a single digit number and multiplying a decimal by a number with a single digit.

**Gelosia method of multiplication **– Four examples of multiplying numbers using the Gelosia method. The examples progress in difficulty multiplying a three digit number by a single digit number, a two digit by a three digit, a decimal by a decimal and a decimal by a whole number.

### Multiplying decimals

This resource is useful to illustrate the common mistakes students make when multiplying two decimal values. It is suggested that the language used be adjusted so that the term 'times' is interchanged with 'of', thus one-tenth of one-tenth is equal to one one-hundredth.

Practice of multiplying decimals is provided by follow-up exercises.

### Division

This resource contains two packs of games, investigations, worksheets and practical activities.

Pack One contains thirteen work cards with activities covering simple division by a single digit, dealing with remainders, finding patterns when dividing by 11 and 13, and estimating answers.

Pack Two contains many activities requiring students to explore what happens when numbers are divided. **Dividing Investigation** explores which numbers produce an answer of .25 when divided by 4. **Lost Divide** gives a decimal answer to a division calculation and requires students to decide what calculation was made. This activity can easily be extended. **Repeating Digits** uses a flowchart to spot patterns when dividing, and **ISBN's and Errors** explore how ISBN numbers work and the role division plays.

### Division

As with the addition videos, these videos should be used to generate discussion of the methods used and to encourage students to make their own videos showing alternate methods.

**Short division** – Six examples of dividing numbers using the short, or what is sometimes called the bus stop method. The examples progress in difficulty with the first two examples not requiring any remainders, the next two examples having remainders within the calculation and the last two examples having remainders in the answer. The method shows how to leave the last two examples as decimal answers.

**Division by chunking** – Four examples of dividing numbers using the chunking method where a multiple of the divisor is subtracted from the table in chunks. The examples all divide by a single digit and all give whole number answers.

### Arithmetic: Division of Decimals

This resource covers mental division of whole numbers, division methods for whole numbers and decimals and a variety of division problems. The text book provides a number of questions useful for consolidation or as inspiration for making their own video.The worded questions test whether students are able to conduct the appropriate calculation to solve the given problem.

The activity **Divisibility Rules **requires students to explore different rules for divisibility and **ISBN Numbers** explains an application of multiplication and division.