# Carroll Diagrams

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 cross-classification. 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.

The following diagram shows an example of a Carroll Diagram. Scroll down the page for more examples and solutions on how to use Carroll Diagrams. Example:
Sort the following numbers in the Carroll Diagram provided:
953, 888, 1501, 8000, 201, 2542, 450, 9349 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

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

 Sort Shapes using Carroll Diagrams Sort a variety of 2d shapes on a Carroll diagram. Sort by one or two conditions. Sort triangles - scalene, equilateral and isosceles. Sort quadrilaterals, pentagons, hexagons, heptagons and octagons, as well as parallelograms, rhombus, kites and trapeziums. Also sort according to a shapes properties such as acute, obtuse, reflex or right angles and symmetry or whether it is a regular shape. Carroll Diagrams Odd and Even Develop an understanding of sorting numbers on a Carroll diagram using particular properties as criteria. Numbers are sorted by two conditions. In Level 1 numbers are sorted into odd or even and more or less than either a number up to 10 and in Level 2 up to 99. In levels 3 and 4 sorting numbers up to 99 or 999 respectively is by odd or even and by the place value of particular digits such as 7 tens. Carroll Diagrams Multiples Sort multiples of selected numbers on the Carroll Diagram. This game will test your times tables knowledge. 2D Shapes Carroll Diagrams Sort 2D shapes on Carroll diagrams. There are four levels of difficulty and sorting is by two variable criteria. Squares are classed as rectangles as they are special case rectangles.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 