ED2652 Lecture Notes - Lecture 3: Origami
Mathematics 2: Number and Algebra (ED2652)
Tutorial Three – Week Three
Fractions
• Questions from Readings
o What are the four key understandings about fractions?
▪ Equal parts are necessary
▪ The number of parts names the parts
• Language issue – not as uniform as we would like them to be
o 8 parts = eighths
o 7 parts = sevenths
o 4 parts = quarters
o 2 parts = Halves
▪ The larger the number of parts, the smaller each part
• In the number system, 14 is more than 5
• With fractions, 1/14 is smaller than 1/5
▪ The size of each part depends on the size of the whole
o Why does shading a pre-partitioned diagrams not always provide evidence of understanding of fraction
concepts?
▪ If students draw their own lines, the fractions they shade may not be equal
▪ The fractions are already broken down for the child, and they can just shade in the number of the
numerator
▪ This doesn’t show that children understand fractions
• Concrete Activities:
o Un-Partitioned fractions
▪ Allows teachers to understand how much their class knows
• Region fractions
• Area fractions
▪ Before and after assessment piece
o Paper Folding
▪ This is helpful as children are making them
• Appreciation of part-whole relationships
• Recognition of the necessity for equal parts for fair shares
• Recognition of the relationship between the name of the parts (denominator) and how
equal parts are counted (numerator)
• Recognition that the higher number in the denominator the smaller the piece
• The whole can be partitioned into a variety of fractional parts
• All of the whole must be used when partitioning into fractional parts
• Equal parts may not look the same, but are still equal in quantity
o Fraction Strips
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Language issue not as uniform as we would like them to be: 8 parts = eighths, 7 parts = sevenths, 4 parts = quarters, 2 parts = halves. The larger the number of parts, the smaller each part. In the number system, 14 is more than 5: with fractions, 1/14 is smaller than 1/5. If students draw their own lines, the fractions they shade may not be equal. The fractions are already broken down for the child, and they can just shade in the number of the numerator. This doesn"t show that children understand fractions: concrete activities, un-partitioned fractions, allows teachers to understand how much their class knows, region fractions, area fractions, before and after assessment piece, paper folding. The whole can be partitioned into a variety of fractional parts: all of the whole must be used when partitioning into fractional parts. The size of the whole determines the size of the fractions.
