Wafers with Decimal fractions

Prior knowledge.

• Share n objects between r people by equally partitioning each object, and dealing out one piece from each
• Share n objects between r people by dealing out wholes, then partitioning the remaining pieces into equal pieces
• Name and identify tenths of a length
• Use symbols for tenths as fractions and as decimals
• Add tenths where the total is both less than and more than 1
• Convert improper fractions into mixed numbers
• Simplifying fractions

Background

Before starting these short activities, students should be comfortable with answering ‘sharing’ problems of the form found in the activity ‘wafers’. Early sharing strategies involve dealing, and where partitioning is required, some students will partition ‘leftover’ objects into half, then continue dealing, then halve each leftover piece (and so on). To work on these activities, students need to have more sophisticated dealing strategies and to have linked the concept of a sharing problem to obtaining a fractional answer. As such this activity is developing the quotient sub-construct of fractions.

Comments on the Exercises

Exercise 1
Asks students to share a number of wafers between 10 people. Solutions are improper fractions in some cases.

Exercise 2
Asks students to share a number of wafers between 15, 20 and 30 people. In this exercise answers are required to be given as tenths, but the original fractions generated have denominators like 20, 30 or 15.