1. + Unit 2 EP210 Math Methods By Tanya Allen-Gaines “ Number sense can be described as a good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms.” -Hilde Howden Feel free to share together until class begins.

2. + Netiquette Review For seminar: Be on time and on topic Never post a message that is in all capital letters -- it comes across to the reader as SHOUTING! Use boldface and italics sparingly, as they can denote sarcasm. Be considerate. Rude or threatening language, inflammatory assertions (often referred to as "flaming"), personal attacks, and other inappropriate communication will not be tolerated. For discussions: Keep messages short and to the point. Be respectful and treat everyone as you would want to be treated yourself. Always practice good grammar, punctuation, and composition. This shows that you’ve taken the time to craft your response and that you respect your classmates' work. Keep in mind that threaded discussions are meant to be constructive exchanges. Wait to respond to a message that upsets you and be careful of what you say and how you say it. Use spell check!

3. + Unit Outcomes Explain concepts of number sense and use strategies to facilitate instruction Explain the whole-number place value system and identify effective teaching strategies Analyze the role of the paraprofessional in enhancing student performance

4. + Key Concepts: Number Sense and Early Number Concepts Number sense is the concrete understanding children develop that numbers actually represent physical amounts and how these numbers compare to one another Number sense is the precursor to more complex, abstract concepts and operations. Question: How might you help a child to develop a concrete understanding that numbers represent actual amounts? What activities would be appropriate?

5. + Number Relationships and Counting A young child that can count to 100 is simply repeating a pattern and not showing number sense or understanding Early concepts of “number” start in PreK and kindergarten Students need early exposure to number concept relationships such as “more”, “shorter”, “same” or “heavier” in a hands-on environment Hands-on experiences (such as manipulatives) are vital in forming a concept of numbers such as 5 or 8

6. + Count

7. + Dot Count How many dots? How did you come up with the number? Was this easy or difficult? What would have made it easier?

8. + Count

9. + Dot Count Which slide was easier to count? Why? We have a preconceived picture of 8. Students need to build that concept in order to do higher level math such as larger numbers, making 10s, and operations such as addition and subtraction Counting requires a “number-word” association and an understanding of “one-to-one” when counting – the number word must have an associated value

10. + Number Relationships Spatial: dice patterns Part-part-whole: numbers can be composed of various parts (e.g. 7 can be a set of 4 and 3 or a set of 5 and 2) One and two more; one and two less: Anchors of 5 and 10: using these key numbers to build to higher numbers (e.g. 8 is 3 more than 5; 12 is a full ten frame plus 2 more)

11. + Virtual Fieldtrip Open a new web browser but don’t close out Seminar Visit the following website and try several of the games You can copy the link or press CTRL and click on the website below Listen for my voice to come back and we will debrief (it should be about 5-10 minutes) http://illuminations.nctm.org/ActivityDetail.aspx?ID=75 NCTM-Illuminations

12. + Time to share Please share your thoughts about the field trip. What did you do while you were away? How could these help students?

13. + Patterns in Numbers We talk about math as the “science of patterns” Pattern recognition is a huge leap toward number sense This is a great starter to place value

14. + Virtual Field Trip Visit the site below. http://www.nctm.org/java/eexamples/4.5/standalone1.asp Start with 2 + 2 and keep hitting equals until you fill the board. Share what you see. Without clearing the board, do 4 + 4 and keep hitting equals until you fill the board (a red dot will show your second set of numbers). Share what you see. Or http://www.abcya.com/interactive_100_number_chart.htm Choose a color Start at 2 and continuously add 2 and shade – see what pattern you get. Choose a new color and start at 4(don’t erase the first ones) – continuously add 4. Share what you see.

15. + Patterns in Numbers On the next slide describe what patterns you see…

16. + The Pattern of Numbers

17. + Place Value and Beyond Our number system is a Base-10 system implying that we have 10 digits: 0-9 Place value is our system of grouping by tens and can help students to recognize patterns and be used to simplify later concepts (decimals/percents). This accounts for our place value system of ones, tens, hundreds, etc. Place value is a concept that can be too easily rushed without developing a true concept of 10

18. + Place Value and Beyond Topics in math often are approached in incremental understanding. This means that as students progress and mature developmentally, earlier topics can be expanded and elaborated upon for a more complex understanding. A weakness in any early skill can profoundly affect a student’s success in later math concepts Question: What higher level concepts depend on place value?

19. + 100s Board and Place Value Concepts Can be used to teach several concepts: basic patterns counting multiplication facts multiples (for common denominators) two digit addition (from left to right) or subtraction Teaches higher level math concepts without memorizing rules!!

20. + Strong Foundation Why is it important to build a strong foundation in the early learning years in the field of mathematics? How can the paraprofessional contribute to this foundation?

21. + To do List Reading You will read about some of the important early number concepts that students acquire including number relationships, counting, number relationships, and basic place value concepts in chapter 9 and 12. Video Watch the video "Using Manipulatives as Models". Web Resource You will explore the publisher’s website and consider how you can use it as a resource for further information on the lesson topics. Discussion We will discuss the importance of considering developmental stages of reasoning and understanding when teaching mathematical concepts to students. Note: There are two separate posting for this unit.

22. + Help is available! Remember, I am just an email away at tallen- gaines@kaplan.edu