Multiplying Fractions
Building on from adding and subtracting fractions students will now look at how to multiply fractions. Students will be encouraged to investigate questions such as "why does multiplying a number by a fraction make it smaller?" This unit will involve the use of manipulatives and pictorial representations to develop conceptual understanding. Again a focus will be placed on realistic contexts and students spend much of their time solving problems based on probable scenarios.Key questions:
- Multiplying a number by a fraction less than one results in a product smaller than the original number.
- People can use fractions to solve real life mathematical problems.
- Mathematicians can reason abstractly and quantitatively.
One of the core understandings in this unit is that when you multiply a whole number by a fraction less than one, your product is smaller than the original number.
In the example below, students were given a problem involving basketball courts taking up space in playgrounds. The challenge was to work out which court was the biggest, given that all the information about how much space would be given over to basketball was provided in fractions of a larger playground space, which was also given as a fraction of an overall measured park area!
Whilst multiplying fractions together in itself is a largely nonsensical activity, multiplying fractions of things together that produce a useful outcome is certainly worthwhile. Take the following hypothetical, but realistic example:
Temple Garden Foundation has four key programmes that it supports in Cambodia-
G5 students raise $20,000 one year.
Ben wants to spend 1/2 the money on health schemes and then share the rest equally between the other three programmes.
Helen wants to spend 3/8 on health schemes, 2/8 on income generation projects and split the remainder between infrastructure and education.
Question- How much money does each programme receive under Ben and Helen's plans?
The point of the exercise is not to practise multiplying fractions per se, but to use a method that students are comfortable with to solve realistic problems. Many students would chose to prove their answers by making a graphical representation of their working out, to explain how they have arrived at their answers. Standard algorithms can be fast and useful; understanding why we use them is what good mathematicians are able to do.
Next unit... Connecting fractions, decimals and percentages
TGF Walkathon fundraiser problem
Temple Garden Foundation has four key programmes that it supports in Cambodia-
- infrastructure
- income generation
- health
- children's education
G5 students raise $20,000 one year.
Ben wants to spend 1/2 the money on health schemes and then share the rest equally between the other three programmes.
Helen wants to spend 3/8 on health schemes, 2/8 on income generation projects and split the remainder between infrastructure and education.
Question- How much money does each programme receive under Ben and Helen's plans?
The point of the exercise is not to practise multiplying fractions per se, but to use a method that students are comfortable with to solve realistic problems. Many students would chose to prove their answers by making a graphical representation of their working out, to explain how they have arrived at their answers. Standard algorithms can be fast and useful; understanding why we use them is what good mathematicians are able to do.
Next unit... Connecting fractions, decimals and percentages
