Strategies for Whole Number Computation

1. Strategies for Whole Number Computation TAMU-QUMethods for Teaching Mathematics

2. Computational Fluency What does it mean to be computationally fluent?

4. Steps to Computational Fluency Number Sense Place Value Development and Understanding Understanding of the Operations Computational Fluency

5. Number Sense� The awareness of the relationships between number, an ability to represent each number in several ways, knowledge of the effects of operations, and an ability to interpret and use numbers in the real world. Gradually develops as students explore numbers, visualize then in a variety of contexts, and relate them in ways other than the traditional algorithms.

6. Pre-Number Concepts Sorting and Classifying Comparison Order, Seriation, Sequences Seriation--Process of focusing on an attribute and then ordering a set of objects according to that attribute Sequences�meaningful arrangements of objects or events Order�arrange by height, size, length, or other measurable attribute Patterns Group Recognition--being able to recognize the number of things without counting techniques Conservation�the trait that a given number does not vary (arranging objects differently or spacing them out doesn�t change the number of objects in the set)

7. Spatial Visualization Skills Proximity and Relative Position --Ideas of near, far, above, below, next Separation --realizing that an object is made of separate parts or that a collection is made up of separate parts Order --Beginning to end and end to beginning; ideas of first, last, middle, next to last Enclosure --Items being between or inside other items (like point being between two others on a line)

8. Counting Stages Rote Reciting words memorized in order Not having the number names in the proper sequence A one-to-one correspondence between object and number is not present Rational Counts with understanding Exhibits the 5 counting principles

9. Five Principles of Rational Counting Abstraction Any set of objects can be counted Stable-order Sequence of counting numbers does not change One-to-One Matching numbers with the item in the set. Each item is assigned one and only one number name. Order-irrelevance Order in which the items are counted does not matter Cardinal Number Last number names identifies the total number in the set

10. Counting Strategies Counting On Can start with any number and count Example: starts with 5 balls and counts six, seven, eight Counting Back Count backwards correctly from a point Example: starts with 56 and counts back 55, 54, 53, 52 Skip Counting Counting by 2s, 3s, 5s, 10s, etc.

11. Number Relationships Spatial relationships One and two more; One and two less Number benchmarks of 5 and 10 Part-part-whole relationships

12. Steps to Computational Fluency Number Sense Place Value Development and Understanding Understanding of the Operations Computational Fluency

13. Models for Place Value Groupable Models Beans Counters Straws Popsicle sticks Pregrouped or Trading Models base-10-blocks Non-Proportional Models money

14. Flats, Longs, Unit (FLU) Board

15. Understanding the Operations� Three-Step Approach to Fact Mastery Develop a good understanding of the operations Help students devise efficient strategies for fact retrieval Practice the use of their efficient strategies

16. Computational Strategies Direct Modeling Counts number of items; use of base-ten models Invented Strategies Supported by written recordings; use of mental methods when appropriate Traditional Algorithms Usually requires guided development

17. Benefits of Invented Strategies Base-ten concepts are enhanced. Invented strategies are built on student understanding. Students make fewer errors with invented strategies. Invented strategies serve students at least as well on standard tests.