Rich Learning Tasks

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More and More Dots
Questions to facilitate the learning
• What makes your pattern a pattern?
• How does the number of dots change in your pattern?
• How many dots would be needed in the fifth picture?
• Do you think there are other possible patterns with 10 dots in the fourth picture? Convince me.
Scaffolding the learning
• How do the dots in the example form a pattern?
• Would it still be a pattern if you added a dot to each picture? Where would you put the added dots?
• How else could you have made a pattern starting with 1 dot?
Extending the learning
Students might create additional patterns where the fourth picture has 10 dots or might create patterns
where the fifth picture has 20 dots instead.
What’s the point of this task?
The study of increasing/growing patterns relates well to skip counting, to multiplication and eventually to
the study of linear relationships. Young students can play with patterns to set the stage for more formal
study of patterns later on.
Dots were chosen for this task to unveil how visual representations of mathematical situations can provide
another way in to looking at number relationships. For example, the pattern of dots shown in the example
models 1, 3, 5, … dots. If the student looked at just the numbers, he/she might see only that they are odd.
But the visual reinforces that odd means double something and one more (the horizontal line without the
left corner is repeated in the vertical line without the top corner and the corner is added in). It might also
make the pattern of adding 2 easier for the student to see—one dot added on the right and odd on
the bottom.
Because 10 dots are required in the fourth picture, the student cannot just copy the provided pattern, but
might still use it as a starting point: for example, adding 3 dots to each of the given pictures would make
the fourth picture have 10 dots. Many possible other patterns of dots are possible that would allow 10 dots
in the fourth picture, e.g. 4, 6, 8, 10, …; or 16, 14, 12, 10, …; or 5, 10, 5, 10, ….
Patterns