Bimodal Histogram- Open Middle Problem

Directions: Using the integers 1 to 9, create a data list that produces the following graph.  (You may use an integer more than once)


What do you notice about the graph?  How does that help you with the problem?

Justify why your list works.

Are there any other data lists that produce the same graph?  Provide an example.


Box Plots- Open Middle Problem

Directions: Using the integers 0 to 9, create a data set that will produce the following Box Plot.  You may use the numbers more than once.



What is the least amount of points you need to create the graph?

What is the greatest amount of points you need to create the graph?

Can you have the same amount of points but different values?  (Could 1,1,3,3,5,5,7,7,9,9 product the same box plot as 1,1,3,4,5,5,6,7,9,9?) If so, provide an example.

Graphing Temperature Change- Open Middle Problem

Directions: Using the numbers 1-9 at most once each time, create a graph that represents the temperature change over seven days.

  1. Overall temperature change is six degrees
  2. The temperature increase or decrease can not exceed three degrees per day
  3. The temperature change (increase or decrease) alternates between days


Temperature for Day 1: ___

Temperature for Day 2: ___

Temperature for Day 3: ___

Temperature for Day 4: ___

Temperature for Day 5: ___

Temperature for Day 6: ___

Temperature for Day 7: ___

Interpreting Graphs- Open Middle Problem

Using the numbers 1 to 6, using a number only once, create a graph and fill in the blanks to make them true.


There are ___ bananas, ___ apples and ___ oranges.

There are ___ more apples than bananas.

There are ___ less oranges than apples.

There are ___ more oranges than bananas.


NOTE: I would suggest having this pre-printed for students and have numbers 1 to 6 printed on paper that students can use as a manipulative.


Special thanks to @gfletchy for input on this problem and accomodations