How can a child who has not yet developed base-ten concepts understands quantities as large as, say, 85?
Contrast this with a child who understands these same quantities in terms of base-ten groupings.
A child who has not yet developed base-ten concepts can understand quantities like 85 by using different strategies or representations. Here are a few possible ways:
1. Counting: The child can count by ones to reach the desired quantity. For example, they might start at 1 and count up to 85, saying the numbers one by one.
2. Grouping: The child can understand quantities using grouping strategies. Instead of counting one by one, they can count objects in groups. For example, they might have 85 beads and count them in groups of 10 or 20 to determine the total quantity.
3. Visual Representations: The child can use visual aids to help them understand large quantities. They can represent numbers using objects, such as drawing 85 circles on a piece of paper or using physical manipulatives like blocks or cubes.
On the other hand, a child who understands quantities in terms of base-ten groupings has a more advanced understanding. They recognize that the base-ten system is based on powers of ten (e.g., 10, 100, 1000), with each place value representing a different quantity. This understanding allows them to easily comprehend larger numbers like 85 without having to count one by one.
For example, they might know that 85 is made up of 8 tens and 5 ones. They understand that the digit 8 represents eight groups of ten, and the digit 5 represents five individual units or ones. This knowledge enables them to quickly visualize and comprehend the quantity.
Understanding quantities in terms of base-ten groupings provides a more efficient and flexible way to work with numbers, as it lays the foundation for more advanced mathematical concepts like addition, subtraction, and place value.