Counting On/Counting Back
Counting On/Counting Back:
Counting On is being able to "hold" a quantity in their head and then add on to it. Students start with one of the addends and count on by ones until the second addend is reached.
Counting back is used in subtraction. Students will start with the larger number and count backwards to the smaller number.
Videos for Educators
Important Information:
In order to develop a strong understanding of quantity, and eventually how to manipulate quantities (like adding, subtracting, or fair-sharing: what we call operations) children need an abundance of counting experiences. In order to provide our brains with the capacity to concentrate on the more sophisticated aspects of mathematics, counting needs to become almost automatic. (Stanford University)
Once children understand cardinality and the forward and backward number sequences they can count on or back to solve number problems.
Couting on is a critical prerequisite for success in addition. Students will become comfortable with counting on through experience.
Couting back is an extremely important skill to prepare students for later work in subtraction.
Key Ideas: One-to-one Correspindence, Cardinality, Part-Whole Relationship, Hierarchical Inclusion
Examples of what students might do
What students might say:
"I started with my group of 5 flowers and then counted up until I got to 12"
"I started at 6 and then counted up to 10. There were 4 jumps so the answer is 4."
Strategies to Support Student Learning
Give your students ample time to work with manipulatives such as base 10 blocks, rekenreks, and ten frames (preferably all three). Experience with these manipulatives will give your students a visual – and as they work with counting on activities, they will be able to visualize the math in their heads.
Being able to start counting at any number is important because it shows how well a student understands numerical order.
Counting On strategy reinforces the commutative property of addition where a pair of numbers can be switched around without changing the result, for example, 5+7=7+5.
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.