I thought we should double-up this week since both of these Learning Standards are relatively brief and easy-to-understsand. Both of these can be found under State Goal 6 -Demonstrate beginning understanding of numbers, including names and numerals.
Learning Standard C – Begin to make reasonable estimates of numbers.
There is only one Benchmark for Learning Standard C
6.C.ECa Estimate number of objects in a set
The Example Performance Descriptors are:
Make reasonable estimates of small quantities of objects (e.g., goes “four” when asked how many peach slices are in the bowl).
Tell whether a set is more or less than 5.
Tell whether a set is more or less than 10.
This is interesting to me since I know that children like to “guess” at how many, or how old, or how long… However, we often see that children are not quite successful at most of their estimates. Remember, if a child is confused by appearances, that objects that are “big” may appear to be “many” and objects that are “small” may appear to be “few”.
With small sets, young children will have more success at estimating. However, looking at a group of around 10 objects and being able to “tell whether a set is more or less than 10” is a fairly lofty expectation. I can barely do that, depending on the objects in the set. I often have to count. Now, if they mean that I can reasonably know that 2 objects in a set are less than 10 and 100 objects in a set are more than 10, I can do that. It is when the set is around 10, that I would have difficulty estimating without counting.
I also think it is important for young children to verify if their estimate is correct. You can do this with simple counting. Frequent experience with estimation and counting will support both Learning Standard B and C.
Learning Standard D
Compare quantities using appropriate vocabulary terms.
6.D.ECa Make comparisons of quantities
6.D.ECb Describe the comparison with appropriate vocabulary, such as more, less, greater than, few, equal to or same as.
The Example Performance Descriptors
Match sets of things that go together 1-1 and determine whether one set has more, less, or an equal amount (e.g., compare the number of napkins to place setting at the table).
Demonstrate an understanding of equal when dividing materials (e.g., divide cars equally between self and friend).
Use appropriate vocabulary to make comparisons of quantity (e.g., acknowledge that another child has more blocks).
“More” and “less” are really interesting mathematical constructs for young children because they are deeply important to the egocentric child. Who has “more” and who has “less” cookies or Legos matters to the egocentric child. They care deeply about themselves and this construct feeds right into that part of their psyche.
Remember, using mathematical vocabulary, whenever you have an opportunity will reinforce the acquisition of the terms as well as the absorption of the meaning.
My husband told me that his father had a system for dividing fairly for he and his sister. If there was one cupcake left in the house his father would tell them that one had to cut and the other had to choose. That system required the cutter to think about dividing as equally as possible, fully knowing that if there was one side that was bigger, the chooser would select it. We use this system in our house and, for the most part, it works.
Children also have a deep sense of justice and fairness. This mathematical concept will also appeal to that system of “right” and “wrong”.