The purpose of this activity is to engage the students to use proportional reasoning and their knowledge of volume to solve a problem involving fractions.
This activity assumes the students have experience in the following areas:
The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.
The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.
A 600 mL jar is ⅓ full of water.
If all that water is poured into a 300 mL jar, what fraction of the smaller jar will it fill?
The following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.
Introduce the problem. Allow students time to read it and discuss in pairs or small groups.
Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.
Allow students time to work through their strategy and find a solution to the problem.
Allow students time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.
The reasons with measures mentally. They calculate one third of 600 mL then compare the answer, 200 mL, to 300 mL. Finally they express 200/300 as an equivalent fraction, 2/3.
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The student creates a regions model on grid paper. The draw the 600 mL container two thirds full. The same amount (number of squares) is mapped into the 300 mL container. They express the part-whole relationship in the diagram as 2/3.
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The student uses proportional reasoning to solve the problem. As the small container is half the volume of the big container then the fraction in the small container must be twice that in the large container. This might be expressed as 1/3 x 600 = 2/3 x 300.
Printed from https://nzmaths.co.nz/resource/how-full-jar at 3:04am on the 5th May 2024