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UPDATED: JUNE 30, 2023: Newsletters
Counting Three Times:
When a child is asked to add two sets of numbers, they count the first set, count the second set. Finally, they put the two sets together and count again from one.
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Important Information:
In the beginning stages of early addition and subtraction, many children may not yet be able to hold the two sets of numbers in their head in order to count.
It is important that students in this stage continue to build cardinality which will allow the student to trust that the final number stated while counting is also how many are in the set without having to recount.
Giving students a variety of manipulatives and multiple chances to 'act out' each stage of the problem may help them to keep the two numbers separated and arrive at an answer.
When determining if a student is ready to move on from counting three times, try covering up a set of tiles the student has already counted and ask "how many are covered up?". If the student is able to tell you without having to count again, they are beginning to develop the key idea of cardinality which will support the shift into the strategy of counting on.
Children develop an understanding of cardinality by counting a variety of objects into different sized sets. Counting the same set several times and in a different order develops children’s understanding that the number in a set stays the same unless items are added or taken away.
Key Ideas: One-to-One Correspondence, Cardinality
Examples of what students might do:
Example of what students might say: "I counted out 3 snowmen and I counted out 4 snowmen. I then counted them altogether."
Strategies to Support Student Learning:
When initially designing your own questions to support counting on, be sure to keep one of the numbers small enough to encourage counting on.
Using part-part-whole cards or missing-addend cards may help children develop their understanding of the part-whole relationship.
Encourage children to count a wide variety of concrete materials to solve number problems. Start by joining small sets, with a total of five and then ten items.
Children at this stage often benefit from acting out a problem (Lawson)
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)
The object of the game is to be the first player to fill all 50 squares on the game board. Players take turns rolling the die, then puts that number of chips on their game board, one per square. The game ends when one player successfully fills all squares on his or her game board; or, when played cooperatively, when all game boards are filled. This game can be played as early as Kindergarten, but you may consider using game boards with only 20 or 30 squares, then giving each child 20 or 30 chips. (Lawson, Pg. 160)
Use square tiles or linking cubes, take turns building towers on a game board (MK5). The towers are constructed by adding the number of tiles or cubes that have been rolled on the die. Pay close attention to building the towers to the correct height. The game ends when one player successfully fills all the towers on his or her game board. (Lawson, Pg. 161)
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.
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