Solve It or Sink It

This activity integrates measurement of mass with technology in a problem-solving context. Students should measure the mass of the marbles in grams.
The boat will float well if it has a wide base. Students may need to push the bottom fold back up inside the boat a little to make this base.
Additional problem-solving instructions or questions could include:
“Explore ways of arranging the marbles to find the least mass and the greatest mass that the boat can hold.”
“Does the size of the marbles change the mass that the boat can hold?”
“Discuss a plan to explore this question with a classmate. Write down each step of the plan and explore your findings.”
In question 3, have the students estimate the mass of marbles that the smaller boat size may hold. All the class estimates could be recorded on a stem-and-leaf graph (see Mathematics in the New Zealand Curriculum, page 216).
When the students compare the number of marbles that each boat holds, they could record this as a ratio or fraction, for example:

Using fractions reduces the effect of variations in design and construction styles. This may help students when they are comparing their results. It is also a good context for finding and recording fractions.
Have the students explore the class results to see whether there is a pattern, such as a number of students with equivalent (or nearly equivalent) fractions. Positioning each fraction on a number line between zero and one may help the students to see whether there is a cluster effect in the comparisons, for example:

If the results do not show a pattern, discuss some possible reasons with the class.
Ideas may include:

• the way the marbles were placed in the boat
• boats used for the first time may float longer than boats used more than once
• the similarity or otherwise of the water conditions

Answers to Activity

1.–2. Answers will vary.
3. a.–b. Answers will vary. You will use
approximately half the number used in
question 1.
c. Discussion points will vary.