Level 4: Partitioning
Materials
Instructions
Say, “I’m going to ask you a question which I would like you to think about in your head … Ready? … Which is bigger, three quarters or four ninths? … How do you know?” Note student’s response.
Place the Fraction Comparison cards in front of the student and say, “Which one of these is smaller? … How do you know?” Note student’s strategy.
Place the Fraction Mat and the Fraction Mat Cards in front of the student. Use the number cards to make 1 quarter on the mat as shown, and say, “These cards can be used to make fractions like this (indicate the 1 quarter) … Please make two fractions that when added together are as close as possible to one.” Note student’s choice.
Place the Decimal Word cards in front of student and say, “Please put these in order from smallest to largest.” Indicate that the smallest card should go to the student’s left. Once student is satisfied with order, ask him/her to explain their reasoning.
Place Decimal Symbol cards in front of the student and say, “Can you put these in order from smallest to largest please?” Indicate that the smallest card should go to the student’s left. Once student is satisfied with order, ask him/her to explain their reasoning.
4.6 Advice rubric
Comparing and ordering fractions and decimals requires a sound understanding of how these numbers are represented, named, recorded, and renamed. Far too many students rely on inappropriate rules and procedures to interpret and rename these numbers which results in misconceptions such as the larger the denominator, the larger the fraction, the more digits after the decimal point the larger (or smaller) the number is and so on.
This task examines the extent to which students have a sense of the relative magnitude of fractions and can use this to estimate and make comparative judgements. It also examines the extent to which students understand how decimal numbers can be renamed and their strategies for ordering decimal numbers.
| Observed response |
Interpretation/Suggested teaching response |
|---|
May recognise or guess which fraction is larger (3 quarters) or smaller (48/80) but unable to say why, may choose inappropriate fractions for Fraction Mat task, generally unable to order decimal cards |
Suggests fractions and decimals not well understood in terms of how they are represented, named, recorded, and/or renamed
- Check the extent to which students can make, name and record common fractions and decimals (see Tools 4.1 to 4.5)
- Model and practice sequencing common fractions and decimals using a rope and pegs, play appropriate games, eg, How many wholes can you make? (pdf - 14.17kb)
- Use partitioning strategies to make and name models of ones and tenths (eg, 3 ones and 7 tenths), record using common fractions and decimal notation (see Partitioning (pdf - 199.51kb) paper)
- Review tenths as a place-value part and the idea more generally that 1 tenth of these is one of those, consolidate by providing opportunities to compare, order, sequence, count forwards and backwards in place-value parts, and rename
- Consolidate fraction renaming using partitioning strategies (see Partitioning (pdf - 199.51kb) paper)
|
Identifies and weakly justifies (eg, based on rough estimation) larger and smaller fraction, makes a reasonable choice for Fraction Mat task (eg, 1 quarter and 3 fifths), and correctly orders some of the Decimal Cards |
Suggests some understanding of how fractions and decimals are represented, named, recorded, and/or renamed
- Check the extent to which students can make, name and record an extended range of common fractions and decimals, including mixed fractions
- Consolidate the use of partitioning strategies to make and rename fractions and decimals to hundredths (see Partitioning (pdf - 199.51kb) paper)
|
Identifies and strongly justifies (eg, renames) larger and smaller fraction, makes a closely reasoned choice for Fraction Mat task (eg, 3 quarters and 1 fifth or 5 sixths and 1 seventh), and correctly orders most of the Decimal Cards |
Suggests relatively sound understanding of how fractions and decimals are represented, named, recorded, and/or renamed
- Extend comparing, ordering, sequencing and renaming activity to include more complex common fractions and decimals to thousandths
- Consider introducing/consolidating operations on common fractions and decimals (eg, addition, subtraction and multiplication)
|