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Copyright © 3P Learning – These resources have been created in partnership with Dr. Marian Small.
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www.mathletics.comQuestions to facilitate the learning
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Are there more low values or high values in your data? How do you know?
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What do you know about the value that was not increased or decreased?
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How did you figure out your six values?
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How did the total amount of increase for the 4 numbers compare to the decrease for the 1 number?
Why did that happen?
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How do you know that there have to be HUNDREDS more answers?
Scaffolding the learning
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Could you use all equal values? Why or why not?
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Could you start with the cubes instead of the numbers? How?
What’s the point of this task?
Students are introduced to how to use manipulatives to determine a mean in case this was new to them.
But then they are asked to use what they see to solve a problem. One goal is for students to see that if
4 data values are increased and 1 is decreased, then the sixth data value must actually be the mean.
Another goal is to realise that a fairly high value must be decreased if 4 values had to be increased. A
third goal is to see that the total increase for the values that are increased matches the decrease for the
value that is decreased. There are many possible solutions including, for example, 5, 5, 6, 7, 10, 27.
Extending the learning
Students might explore what the data set could be if 3 values were less than the mean and 2 values were
greater than the mean.
Building a Mean
Patterns and Algebra