Cardinality
Cardinality:
When counting, knowing that the final number count represents all the objects in a set rather than just the last object.
Videos for Educators
Important Information:
Children’s growing skills in the accuracy of verbal and object counting support them as they grapple with cardinality, which is a necessary concept in operations. Struggling to remember what number comes next takes up a lot of working memory, and leaves little room for operations on even small sets. (Stanford University)
A child who understands this concept will count a set once and not need to count it again. They will automatically remember and know how many items in the set are represented.
Students who are still developing this skill need constant repetition of counting and explicit teaching through modelling so they understand they do not need to count over and over again when it will result in the same number. Students who have difficulty with their working memory may have difficulty with this concept.
Involving children in activities where they answer questions about ‘how many’, will help to develop the understanding of cardinality. They need to be able to say the counting names in the correct order, but also recognize the last number said is the total amount of items.
Strategies to Support Student Learning:
Labelling the total number of items then counting them (Label-first). For example, on a page with 3 elephants, saying, “Look there are 3 elephants. Let’s count them.” And counted them as, “one, two, three.”
Counting the items, then emphasizing and repeat the last word (Count-first). For example, on a page with 3 elephants, say, “One, two, three, t-h-r-e-e. There are three elephants.”
Encouraging students to show you a group of items to match a specific number.
Ask students to count a group of items in a set. Then, explicitly ask them to show you how many objects in that group represent that amount.
Things You Can Do In The Classroom
Games (Click Links Below)
In this activity, students develop through concrete to numerical representation of number to begin 'Counting on.' This game can be modified to support 'Counting on From a Larger Number' through slight changes to the game. (Lawson, pg 163)
In this activity students develop strategies for counting on and the key ideas of cardinality and hierarchical inclusion. (Lawson, pg 164)
In this activity students develop strategies for counting on by using the number die as a starting point and the dot die to assist in counting on. (Lawson, pg 164)
Children work through a set of cards. For each card, children think about the number of dots they see and the whole to determine the missing part. (Lawson, pg 165)
In this twist on the classic War game, students work to find the difference in value between the two cards that are drawn. They are deepening their understanding of the part whole relationship and developing the counting on strategy, as they count on of from the lower card until they reach the value of the higher card. Students use counters to represent the difference. (Lawson, pg. 165)
This fun activity can be used in a small group or whole group. For this activity, place tiles of two colours in a paper bag. Tell students how many tiles there are in total and how many there are of one of the colours. Then, ask how many there are of the other colour. Children suggest answers and provide their thinking. (Lawson, pg. 166)
In this 3 person game, students race to be the first person to figure out the playing card they have on their forehead! (Lawson, pg. 167)
All games and activities located above are directly linked. Some can be found in the Alex Lawson What to Look For Resource. Page locations have been included in the description of each activity.
