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Connecting percentages decimals and fractions


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Last updated 26 October 2012 15:30 by NZTecAdmin

Number Facts progression, 5th step;
Place Value progression, 5th step

The purpose of the activity

In this activity, the learners explore the connections between percentages, decimals and fractions and develop mental strategies for solving problems involving percentages.

The teaching points

  • Percentages are another way of representing fractions and decimal fractions.
  • Often the easiest way to find a percentage of a number mentally is to use the equivalent fraction.
  • The learners also find out how to estimate percentages of numbers by choosing comparable fractions.

Resources

  • Sheets of paper divided into 100 small squares (10 x 10).

The guided teaching and learning sequence

1. Ask the learners what 50% means. Possible responses include 50 percent, one-half, 50/100, or 0.5. Ask the learners to explain how 50% becomes one-half. Listen for and reinforce that percent means “per hundred” and that 50 out of 100 (50/100) is equivalent to one half (1/2). Ask the learners to explain how 50% becomes 0.5. Listen for and reinforce that 50/100 is 0.50, which is written as 0.5.

2. Give each learner a sheet of paper divided into 100 small squares (10 x 10) and ask them to fold this square in half and to check that the area of one half of the square is 50 out of 100. Show the learners how to record this on a number line and on a place-value table.

Image of number line and place-value table.

3. Tell the learners they are going to fold the same square in half again. Ask them to predict how many parts this will make and what each part is called (one-quarter, 1 /4). Ask them to predict what one-quarter and three-quarters will be as percentages by predicting the number of squares out of 100 that will be in one- and three-quarters (25% and 75% respectively).

4. Ask the learners to fold the paper and check their predictions. Model or discuss how to add these to the number line and place-value table.

Image of number line and place-value table.

5. Write the following fractions on the board, and ask the learners to express each of them as a percentage. Suggest learners use any representation (for example, 100-square paper, fraction/percentage number line or place-value table) they think will help them.

  • 1/10
  • 3/5
  • 3/2 (1 1/2)
  • 1/8.

6. Ask the learners to discuss their solutions. Highlight the strategies they used, for example:

  • equivalent fractions: 1/10 = 10/100 = 10%; 3/5 = 60/100 = 60%
  • fraction/percentage number line: 3/2 = 150%

    Image of number line.

  • halving

    Image of place-value table.

7. At this point, consider asking the learners to explain how they can calculate GST by dividing by 8, or multiplying by 0.125 or halving, halving and halving again.

Follow-up activity

When the learners have completed the sequence described above, further consolidate their ability to convert between percentages and fractions by giving them the following percentages to convert to fractions: 60%; 90%; 37.5%; 175%; 250%.

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