Hierarchical Inclusion
Hierarchical Inclusion:
The counting and quantity principle that refers to understanding that all numbers preceding a number can be or are systematically included in the value of another selected number.
Videos for Educators
Important Information:
Hierarchical inclusion is an important landmark that students must reach in order to fully understand cardinality and to begin composing numbers (i.e.: composing a set of 5 items by combining a set of 2 items with a set of 3 items) and decomposing numbers (i.e.: decomposing a set of 6 items by separating into a set of 4 items and a set of 2 items).
When students understand that smaller numbers are a part of bigger numbers and that numbers increase by 1 as you count up, and decrease by 1 as you count back, they have the idea of hierarchical inclusion. They understand that the number six contains all of the numbers before it.
Strategies to Support Student Learning
Ask children to name the number that is “one larger” or “one smaller” than a number.
Ask for a number that is “inside” the number 7.
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.