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More Lessons for Grade 4 Math
More Lessons on Statistics
Venn Diagrams and Sets
In these lessons, we will learn how to use Carroll Diagrams. We also have some Carroll Diagram games that involve objects and numbers.
Carroll diagrams are tables that work like Venn diagrams and are used for the purpose of crossclassification. For Carroll diagrams, two attributes are being used for sorting, with one attribute of each characteristic being the focus.
The categories of a Carroll diagram should be mutually exclusive (do not overlap), for example even
and not even numbers. In a Carroll Diagram, numbers or objects are either
categorized as having an attribute or not having an attribute.
A table is created with four cells to show the four possible combinations of these two attributes. Either the items themselves, or the count of how many items of each type, are put in the cells.
Example:
Sort the following numbers in the Carroll Diagram provided:
953, 888, 1501, 8000, 201, 2542, 450, 9349
Example:
Put the following numbers into the correct place on the Carroll diagram.
1, 2, 3, 4, 5, 6, 10, 14, 15, 20, 21, 27, 28, 35, 47, 55

1digit Numbers 
2digit Numbers 
Even Numbers 
2, 4, 6 
10, 14, 20, 28 
Odd Numbers 
1, 3, 5 
15, 21, 27, 35, 47, 55 
Carroll Diagram Example
Using a Carroll Diagram to sort numbers based on divisibility rules.
Example:
Which of the following numbers are divisible by 4? by 9?
by 4 and 9? by neither 4 nor 9?
144, 128, 153, 235, 68, 120, 361, 424, 468
How to use Carroll Diagrams to Organize Numbers?
Odd, Even, Multiple of 3 and Not multiple of 3
Carroll and Venn diagrams
Example:
Organize the following numbers: Odd, Even, Multiple of 6, Not multiple of 6 using a Carroll diagram and a Venn diagram.
12, 15, 10, 17
Venn and Carroll Diagrams
Example:
Organize the following numbers: Divisible by 3, divisible by 5 using a Venn diagram and a Carroll diagram.
6, 8, 10, 15, 18, 25
Carroll Diagram Games
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with stepbystep explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the stepbystep explanations.
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