Ordering fractions with the same denominator (1/3, 2/3, 3/3, 4/3)
Number Sequence progression, 3rd step
The purpose of the activity
In this activity, the learners develop an understanding of fractions by cutting, naming and ordering strips of paper.
The teaching points
The learners understanding the names and symbols for fractions.
The denominator (bottom number) in a fraction indicates the number of equal parts a whole is divided into.
The numerator (top number) in a fraction indicates the number of those equal parts.
Whole numbers can be written as fractions (for example 1 = 3/3 and 1 1/3 = 4/3).
Discuss with the learners the contexts in which they see or use fractions.
Four (or more) strips of paper (card) for each learner approximately 5 centimetres by 25 centimetres. (It is useful, but not necessary, for each strip to be a different colour.)
The guided teaching and learning sequence
1. Ask the learners to prepare a ‘set of fraction strips’ by:
keeping one strip as a single-unit strip
cutting one strip into two equal parts
cutting one strip into three equal parts
cutting one strip into four equal parts.
2. Discuss and ask the learners to write the symbol and name on the strip for each fraction type.
3. Encourage the learners to look for a relationship between the symbol and the fraction piece. Listen for the idea that the bottom number represents the number of pieces the strip is cut into and develop and emphasise the idea that the pieces must be equal. You could do this by cutting a strip into two unequal parts and asking if each is half. Introduce the name “denominator”.
4. Ask the learners to work in groups. Ask one learner to put down a ‘third’ and a second learner to put one of their ‘thirds’ beside it. Discuss how many thirds are in the row and what symbol describes this. Continue with the learners adding ‘thirds’ to the row and recording the symbols (1/3, 2/3, 3/3, 4/3). Encourage the learners to look for a relationship between the symbol and the fraction pieces. Listen for the idea that the top number of the fraction represents the number of equal parts. Introduce the name “numerator”.
5. Ask the learners to place three ‘thirds’ in a row and think of another name for this. Listen for “ 3/3 is the same as 1” and ask the learners to check this against the single-unit strip. Repeat with four ‘thirds’ ( 1 1/3), five ‘thirds’, etc.
6. Repeat the sequence from step 4 above, this time working with quarters.
Ask the learners to work in pairs to choose a fraction (for example, fifths or tenths) and to write down its sequence, giving equivalent names where possible (for example, 5/5 = 1, 6/5 = 1 1/5).
Encourage the learners to keep the set of fraction cards for future lessons.