Stage 2 fractions and decimals
- read and write common fractions
- label the numerator and denominator in any given fraction
- explain that the denominator tells how many equal parts make a whole and the numerator tells how many of these parts are used
- locate fractions and decimals on a number line
Activities to support the strategies
Activity 1 – modelled
Instruct students that decimals are a type of fraction and that in a decimal number place value indicates the number of equal parts. Explain the numerator is the upper number of a fraction and represents the number of fractional parts. Explain the denominator is the lower number of a fraction and represents the number of equal parts the whole has been divided into.
Write and on the board. Explain that in these fractions the denominator is a multiple of 10 and so these fractions can be written as a decimal fraction. Next to each fraction write the correct decimal (.6 and .36).
Explain that a decimal point is used and the number of digits after the point tells us if the fraction is tenths or hundredths. Explain that 1 digit after the decimal point tells how many tenths and 2 digits after the decimal point tells how many hundredths. Point to the decimal and read aloud 6 tenths and 36 hundredths.
Write these examples on the board.
Note: Using the same digit and zero in different positions makes the student focus on the number of digits after the decimal point.
Activity 2 – guided
Ask questions and encourage students to justify (explain) their answer such as:
- How many digits after the decimal point?
- How many hundredths?
- How do we know (a number) is in the hundredths place?
- How does the position of the digits change the value of the decimal? Why?
- What pattern do you notice?
Using the example above, point to .08 and ask:
- How many digits after the decimal point is the 8? Answer: 2
- Say: 2 digits after the decimal point tells us it is hundredths.
- How many hundredths? 08 tells us it is 8 hundredths.
Repeat with other examples.
Support incorrect answers by explaining the error and talking through students' thinking using the 'think aloud' strategy, e.g.
- If a student says .03 is 3 tenths ask: How many digits after the decimal point is the 3? (point and count)
- Answer: 2 places
- So what does the .03 tell us?
- Answer: Hundredths
Once students have demonstrated mastery of decimal notation to two places, introduce decimal notation to three places.
Note: It is important to check that students are saying the 'ths' on the end (tenths and hundredths) as this will avoid confusion when mixed numbers are introduced.
Attach a one metre long piece of paper or ribbon to the board. Label the length as one metre. Have students mark and initial where they think 0.5 m would be. Have other students estimate the position of 0.25 m and 0.75 m.
Select students to check the measurements.
- How did you know where to place 0.5? 0.25? 0.75?
Repeat for other decimals, such as 0.2, 0.3, 0.8.
Students can organise cards from smallest to largest number on a washing line set up in the classroom with 0 displayed at one end and 1 displayed at the other.
Start with decimals to one decimal place then repeat with decimals to two decimal places.
Pose this question - which decimal is larger, 0.7 or 0.07?
- How do you know?
- How can you prove it?
Have students demonstrate which decimal is larger, using blocks, grid paper or another strategy.
Activity 3 – dividing one whole into fractions
Students are given a worksheet with a large circle drawn on it. They imagine that the circle is the top view of a round chocolate cake (or pizza base) which they have to share between five people.
Ask: How would you cut the cake so you have five equal pieces and none left over?
- Students draw lines on the 'cake' to show where the cuts would be.
- They could use pencils to work out where the cuts would be, before they draw the cuts on the large circle.
Students discuss the strategy they used to cut the cake into five equal pieces.
- If you have five equal pieces cut from one whole cake, what would each piece be called?
- What if the same cake was divided into ten equal pieces, so that each person could eat one piece and take one piece home? How would you change the five equal pieces into ten equal pieces?
- If you have ten equal pieces, what would each piece be called?
2. Students are given three strips of paper of equal length.
- Strip A represents one whole. Students write ‘one whole’ on the paper.
- They fold strip B into fifths and label the strip ‘fifths’.
- They fold strip C into tenths and label the strip ‘tenths’.
Students place the three strips of paper one under the other and discuss these questions
- What can you tell about the size of each fraction?
- What strategies did you use to create your fractions?
- What strategies did you use to obtain equal parts?
Students use their folded strips of paper to count by fifths and tenths. They can complete the missing labels on worksheets showing fifths and tenths.
Write the missing fraction labels on these fraction strips.
ACMNA079: Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation
MA2-7NA: Represents, models and compares commonly used fractions and decimals