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# Fraction, decimal and percentage match - ratio as a fraction in simplest form

In this co-operative card game, students have to match the equivalent representations of fractions, decimals and percentages, ranging in difficulty from simple to challenging. This activity encourages mathematical discussion within the classroom, mental arithmetic, and strengthens students’ understanding of decimals, percentages and fractions.

In the trial, use of this activity ranged between 50 minutes and 1 hour and 15 minutes.

Materials

• Sets of cards for each pair of students in the classroom (preferably laminated, and each set in a different colour, to avoid sets becoming mixed)
• Calculators
• Pencils and paper
• Large cards with sets of a fraction, equivalent decimal and percentage for warm up activity

Key Mathematical Concepts

• The different equivalent representations of a number, in fraction, decimal and percentage form.
• Conversion between fraction, decimal and percentage representations.
• Fractions as division (e.g. ½ = 1 ÷ 2 = 0.5 = 50%).
• Problem solving and estimation strategies.

Using the Activity

Warm-up activity

Give students each a card with a decimal, fraction or percentage written on them. Instruct students to find the other two people that match them, to make a set of three (this could be extended to include equivalent fractions, with the set then being made up of four cards). When students find their complete set, they are to sit on the floor.

Review of Warm-up Activity, and Instructions for Main Activity.

Discuss with students what strategies they used to find their partner. This will help them in the forthcoming task. It may be useful to make some strategies explicit such as how to convert a fraction to a decimal by using a calculator (or how to use the division algorithm rather than using a calculator), and how to convert decimals to percentages.

Group students into pairs, and give each pair a set of the laminated cards. Explain that they are to match the equivalent fraction, decimal and percentage for all 72 cards.

During the Activity

The teacher should move amongst the students to see what strategies are being used to solve the problems. If students are having difficulty, it may be necessary to pause the activity and ask groups to share how they are solving the problems.

Review – whole group

When students are finished (or when the time is right, it is not necessary to complete the task for students to have effectively learned the mathematics), ask students to share their strategies with the whole group. Depending upon class size, each pair could share their strategies for one of the sets of three equivalent representations.

Prerequisite Knowledge

• What a decimal number is
• What a percentage is
• What a fraction is
• Simple decimal and fraction equivalence.

|Dimension |Standard |
|Number (Level 4) |Students use decimals, ratios and percentages to find equivalent representations of common fractions|
| |(for example, 3/4 = 9/12 = 0.75 = 75% = 3 : 4 = 6 : 8). |
|Number (Level 4.25) |Expression of single digit decimals as fractions in simplest form and conversion between ratio, |
| |fraction, decimal and percentage forms |

|Dimension |Standard |
|Number (Level 3.5) |Representation of simple ratios as percentages, fractions and decimals |

Assessment

When demonstrating knowledge at VELS Level 4.0, students will be able to correctly identify the equivalent decimal numbers, percentage and fraction for the set of cards. Students will be able to explain their method, and an understanding of the mathematical principals involved in converting a number from one representation to another should be evident.

One teacher in the trial found that students had some experience with fraction equivalence, but little on decimals or percentages. As a result, many students found this challenging but learned from the activity, but a few students found it quite difficult.

Some students in the trial also wanted to know how to convert decimals to fractions, and the teacher used the opportunity of the questions asked to discuss when it might be that these calculations are useful – e.g. at shops, percentages of amounts of money and estimation of similar calculations.

This activity received a positive response from teachers in the trial.

Potential Student Difficulties

In the trial, one teacher noted that this activity is more complex than it may initially appear. Students need to be able to convert fractions to decimals before they can solve the problems.

Student Feedback

Almost all students considered they were challenged by this task (13 out of 14 respondents), learned some new mathematics (12 /14 respondents) and all felt they could use this maths on other problems. All students who responded to the survey identified that the key learning outcome was to be able to convert fractions to decimals and percentages.

Source

Activity Cards ‘Percentage Rummy’ from Trish Leigh (2005) Maths Tracks for Victoria Level 4B (Melbourne: Rigby Harcourt Education).

Acknowledgements

Thanks to teachers in the Berwick South Cluster Numeracy Team Action Research Project for their invaluable input through the use and feedback of this activity in their classrooms.

How do you find the ratio in simplest form? To find the simplest whole number ratio, divide each number by the smallest number of moles: C: 3.41 / 3.41 = 1.00. H: 4.53 / 3.41 = 1.33. O: 3.41 / 3.41 = 1.00.