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Unit 2 EP210 Math Methods

“ 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

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Unit 2 EP210 Math Methods

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  1. “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. Unit 2 EP210 Math Methods By Tanya Allen-Gaines 

  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 (original posts 150 word minimum). • 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. UnitOutcomes • 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. Number Sense Chapter 9

  5. 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?

  6. 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

  7. Count

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

  9. Count

  10. 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

  11. 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)

  12. 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

  13. Timeto share • Please share your thoughts about the field trip. • What did you do while you were away? • How could these help students?

  14. Place Value Chapter 12

  15. 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

  16. The Pattern of Numbers

  17. 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.

  18. Patterns in Numbers • On the next slide describe what patterns you see…

  19. 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

  20. 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?

  21. 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!!

  22. 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?

  23. 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.

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

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