Part 2: 1,2 More Than and Less Than activities

Part 1: 1,2 More Than and Less Than activities

Children should develop the idea that numbers have relationships to one another. Working with elementary and middle school age children has reinforced that notion. I've noticed that as kids get older and not develop numeric awareness and other relationships, the more likely the child will resort to memorizing facts, require longer time or not fully develop later math concepts. This has nothing to do with capability or intelligence, rather, the child has not developed key number sense areas and this slows, impedes and/or restricts the child's future math growth. Adopting an approach to emphasize these skills early is preferable but these are skills that can be taught to a wide range of ages. Although, I'd stick to basic number recognition and number skills for children 4 and under.

The More Than, Less Than activities help to develop childrens sense of relationships between numbers. Rather than think of one particular number--and only that number--they view it as a range of related numbers. For example, the number 8 is 3 more than 5; 2 less than 10; 1 less than 9; 1 more than 7; 2 more than 6. This is a concept that is important in a wide range of operations; let's look at addition. A child working the problem 8 +13 can solve this problem in a number of ways. A child without a range of strategies or developed number sense will probably have to count out 8 and then add on 13 to arrive at an answer. A child who's developed the 'Counting On' strategy will start with 13 and count on 8 more. A child who's developed an anchor of 10, may think in terms of completing the Ten-Fact for '13'; 7 more completes the Ten-Fact (and gives us 20) and 1 more is 21. Another child who's developed a range of strategies and has some place value sense may know that 10+13 is 23 but 8 is 2 less than 10, so the answer is 21.

It may seem like an overwhelming thought process but children can learn and use a wide range of strategies. Some children may not pick up strategies so easily and need additional activities and modeling to pick up strategies. This is not to say that a child must use one specific strategy. Rather, it's the opposite. It's OK for a child to use a different strategy from another child--or from the adult in the room. I'm more concerned about concepts that a child may be familiar with. If I see a child can not make generalizations about numbers, I work on activities and games that help foster greater number sense.

Developing Math Foundations: Game-Counting On

Developing Math Foundations: Counting On

Counting on is an important strategy that we typically develop in childhood. What is counting on? Counting on is the strategy that if we have two addends, we count on after where the first addend ends.

For example, 17+3. Children who aren't automatic with numbers, haven't developed addition strategies, and haven't developed counting on as a strategy will count out 17 beginning from 1 (using their fingers or a manipulative) and then add 3 more to arrive at the answer, 20.

A child who counts on will start after where the first addend ends. Since the first addend is 17, he/she will count on 3 begining at 18; 18, 19 and 20. A child who develops a count on strategy will have typically developed the strategy after noticing that the sum remains the same using either the shorter, more efficient counting on strategy or the more laborious and time consuming strategy of individually counting out the first addend and then adding the second.

Some children figure it out on their own but others need explicit instruction and modeling to make sense of the strategy. I remember having problems with counting on up until elementary school. My main problem was uncertainty of where I begin counting on from. For example, 17+3. Do I count on beginning with 17 or after it beginning at 18? I eventually figured out the strategy by using logic and easy examples. I would do simple problems for which I knew the answer to--like 5+3. I would then experiment to figure out which was the correct strategy. Since I knew the answer was 8, only one model of the counting on strategy would give me that answer.

This is the kind of experience our kids go through to make sense of numbers and math. We should allow them to explore and make sense of it for themselves but at the same time provide activities, guidance and support for building key concepts.

Playing Spit to Develop Number Automaticity