Spinning Sums

Return to Question 3 on the Spinning Sums page in the Student Guide. This question asks students to relate the data to the question posed at the start of the lesson—which do you think is more likely to happen: spinning a sum of 7 or spinning a sum of 18?

Using their graphs and class number sentence chart, students can now tackle this question based on data. For Question 3, they should be able to see that spinning a seven is more likely than spinning an eighteen because there are four ways to get a sum of seven and only one way to spin the sum of eighteen.

Check-In: Question 12 in the Student Guide provides students with an opportunity to transfer what they have learned to a new context. Give students time to discuss possible answers to Question 12 and then write their thoughts in a paragraph. Douglas wrote the following paragraph:

If we spun 40 more times we would get a lot more sums. All of our bars would probably be taller than they are now. The thing that would be the same is that the tallest bars would still probably be in the middle because the numbers in the middle have the most ways to make them, and our shortest bars would probably be on the outside because those numbers have the least ways to make them. But our graph would not look just like the chart because even if we spun 80 times we might not spin a 4 at all, or we might not get 11 as our most common spin even though it has the most ways to make it.

Douglas explained how the “shape” of the graphs would be alike (similar pattern of more common sums in the middle) and different (taller bars across the entire graph). He provided explanations for his answers (tallest bars correspond with sums that have the most number sentences). He pointed out that what is possible is not always guaranteed (a given sum might not be spun, even after 80 spins). Douglas's response shows a strong understanding of the main points of this lesson.

Students are asked to look at the possible number sentences for the sum of 12 that can be generated using the two identical spinners in Check-In: Question 13. After studying these number sentences, students are asked to write a paragraph explaining why there are seven possible number sentences that could be generated.