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Developing Number Sense Amy LeHew – Elementary Math

Welcome Teachers!. Developing Number Sense Amy LeHew – Elementary Math. August 2011 RTI Kathy Richardson Assessment Pilot Memorized knowledge is knowledge that can be forgotten. Internalized knowledge can’t be forgotten because it is a part of the way we see the world. Today’s Agenda.

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Developing Number Sense Amy LeHew – Elementary Math

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  1. Welcome Teachers! Developing Number SenseAmy LeHew – Elementary Math August 2011 RTI Kathy Richardson Assessment Pilot Memorized knowledge is knowledge that can be forgotten. Internalized knowledge can’t be forgotten because it is a part of the way we see the world.

  2. Today’s Agenda • 8:30-11:30 • Understand how children come to learn number • Discuss challenges to learning and methods to meet their needs • Explore Assessment Series • 11:30-12:30 • 11:45-1:00 Lunch • 12:30 – 1:30 computer lab

  3. FamilyTeaching (Iowa)MathOcean FamilyTeaching (Iowa)MathWater Amy LeHew

  4. Let’s Start with some MATH  • Welcome to Numeria my young Numeriticians! • Today is only our first day, so let’s count! X i k n XNun Xi Xk Xn

  5. Numeria • Let’s try this with manipulatives. Grab some cubes and lets try again… X, i, k, n, Xnun, Xi, Xk, Xn

  6. Let’s Start with some MATH  X, i, k, n, Xnun, Xi, Xk, Xn Ok, how would we write the next one?

  7. X, i, k, n, Xnun, Xi, Xk, Xn Hmmm, you clearly need another support. Let’s try filling our X-Frame

  8. Numeria X, i, k, n, Xnun, Xi, Xk, Xn Let’s try some simple addition and subtraction x + k= n – i Xi + ? = xn

  9. Place Value What base were we working in? At your table, discuss the importance of understanding base-ten structure. Where do students struggle? What can we do to help them?

  10. Expectations • Students learn to count in kindergarten. • Students leave first grade knowing some combinations to ten. • By the end of 3rd grade, students are expected to add 3-digit numbers. • Many students are unable to make this transition because they do not have a solid understanding of the structure of number.

  11. So how do students develop powerful number sense? • Counting videos

  12. Making Ten • How many? • How many more to make ten? What does a student need to know before they can engage in this type of activity?

  13. What happens when students struggle?

  14. The Curriculum • Developing Number Concepts by Kathy Richardson • Designed to help children internalize foundational math concepts • Utilize a variety of learning activities. • Provide ongoing assessment and activities designed to meet individual student needs.

  15. The Curriculum • Assessments: • Interview-style • Administered online • Take about 5 minutes (each) • Pinpoints what students understand about number • Based on Kathy Richardson’s Critical Learning Phases

  16. The Curriculum • Lessons: • Lessons to use • Designed to help children internalize foundational math concepts • Easily integrated into Math Workshop time • Based on student needs

  17. The Curriculum • Amcanywhere.com • Record as you assess • Provide detailed reports for each student and class

  18. Where should we start? • Assessment # 5: Number Combinations

  19. ByKathy Richardson Assessment #5 Combination Trains Overview & Description of Strategies

  20. Learning Number Combinations • Children need to see the basic facts as a set of interrelated concepts. • Children need to be able to look for relationships between the facts they know and other larger, more complex numbers or problems. • Emphasis needs to be on learning number composition and decomposition and number relationships – not just on getting the right answers.

  21. What are we trying to determine with this assessment? To determine what number combinations the student knows and to find out if they can use the answer to a combination they know to figure out one they don't know. Does student know the parts of numbers to 10? Can student use efficient strategies to solve problems to 20.

  22. What will my students be asked to do during the Combination Train assessment? • Students will be presented with connecting cube trains of different lengths – they will be asked to add a variety of number combinations. • Will assess their fluency with numbers to 6, to 10, and to 20.

  23. Use “Linking Assessment to Instruction” guides for instructional support from Developing Number Concepts Select Downloads Select Linking Assessment

  24. ByKathy Richardson Assessment #6 Hiding Assessment Overview & Description of Strategies

  25. Learning to Decompose Numbers • To subtract children need to know the parts of numbers and see the relationship between composition and decomposition. • Children must recognize that one number is contained within another number. • Children must understand that the number stays the same even when it is broken apart and recombined in various ways.

  26. What are we trying to determine with this assessment? Does the student… -know parts of numbers to 10 quickly, without counting to figure them out. Can the student… -use what they know about parts of numbers to solve subtraction problems.

  27. The Hiding Assessment: Video • Show video 24:10 • Look at student behaviors. What does it look like when they… • Don’t know? • Are confident? • 25:11 Kindergartener with 5 cubes • 26:36 First Grader: 5 and 6 • 28:42 Second Grader; 6 and 10

  28. What Strategies do Students Use? Knows Quickly: Does not hesitate or count to figure out. Related Combinations: Uses what they already know to figure out what they don't know. Ex: I see 2. 4 and 2 is 6 so 4 are hiding. Counts On or back: Starts with what they see and counts on or starts with the whole number and counts back for each counter they see. "I see 4...So, 5...6 are hiding. Two are hiding." Counts All: Uses fingers or visualizes the whole number. Counts On or back: Starts with what they see and counts on or starts with the whole number and counts back for each counter they see. "I see 4...So, 5...6 are hiding. Two are hiding."

  29. I’ve Assessed, Now What? Assessment book Page 52 – 54 2:2-5 Book 2 Chapter 2 Activity 5 Look in Developing Book 2 – page v

  30. ByKathy Richardson Assessment #6 Hiding Assessment What questions do you have?

  31. ByKathy Richardson Should we go back? (to assessment #5) Or Forward? (to assessment #6)

  32. ByKathy Richardson Assessment #5 Combination Trains Overview & Description of Strategies

  33. Learning Number Combinations • Children need to see the basic facts as a set of interrelated concepts. • Children need to be able to look for relationships between the facts they know and other larger, more complex numbers or problems. • Emphasis needs to be on learning number composition and decomposition and number relationships – not just on getting the right answers.

  34. What are we trying to determine with this assessment? To determine what number combinations the student knows and to find out if they can use the answer to a combination they know to figure out one they don't know. Does student know the parts of numbers to 10? Can student use efficient strategies to solve problems to 20.

  35. What will my students be asked to do during the Combination Train assessment? • Students will be presented with connecting cube trains of different lengths – they will be asked to add a variety of number combinations. • Will assess their fluency with numbers to 6, to 10, and to 20.

  36. Trains • How is this different from the Hiding Assessment? .

  37. ByKathy Richardson Assessment #7 Ten Frames Overview & Description of Strategies

  38. Learning about Numbers as One Ten and Some More • Understanding that numbers are made up of “ten and some ones” is a foundational skill students must learn to work with larger numbers. • To solve more challenging problems student must move beyond counting on strategies and be able to solve problems by using relationships and understanding the underlying structure of numbers to 20.

  39. What are we trying to determine with this assessment? To determine if the student can combine single digit numbers by reorganizing them into a 10 and leftovers. To determine if the student can use their knowledge of the parts of numbers to 10 to subtract numbers up to 20.

  40. What will my students be asked to do during the Ten Frames Assessment? • Using ten frames, students answer a series of addition and subtraction questions. • Assesses whether students know parts of numbers and can break numbers apart to complete the ten to solve the problem. • To complete assessment, students solve “what if” questions without the support of the ten frame.

  41. Overview of Ten Frames Assessment • Part 1 – Addition • Part 2 – Subtraction Each part divided into four areas: • Adding/Subtracting Ten and Ones • Knows Parts of Numbers • Making a Ten and Adding/Subtracting Ones • Recognizes Ten More Note: Ten frames to use during assessment are available in download section.

  42. Part 1, Addition Adding Ones to a Ten (10 +9 and 6 +10): Trying to assess if student can easily add the ones to the ten without counting on or counting all. These strategies are self-explanatory. If “N” assessment will end.

  43. Part 1, Addition continued Knows Parts of Numbers Making a Ten and Adding Ones 8 + 7, 7 + 6, 8 + 5 Recognizes Ten More 18 + 5 Student is presented with multiple problems and is asked to break apart the number to make ten (knows parts of numbers) and then asked how many altogether (making a ten and adding ones). The final question adds ten to the question (recognizes ten more). • Use practice question 9 + 3 to be sure student understand procedure.

  44. Part 2 - Subtraction • To determine if the student can decompose a teen number into a ten and leftovers. • To determine if the student can subtract by breaking up a number in order to get to ten and then subtracting what is left from 10. • Practice Problem: 12-3

  45. ByKathy Richardson Assessment #8 Grouping Tens Overview & Description of Strategies

  46. Learning about Numbers as Tens and Ones Children need to learn that numbers to 100 are composed of groups of tens and ones. Children must do more than label the digits in a number – they must understand that numbers are organized into groups of tens and ones. Children must recognize that a ten is both one ten and ten ones. This level of thinking is difficult for young children.

  47. What are we trying to determine with this assessment? Do students understand that numbers to 100 are organized into groups of tens and ones. Can they add tens without counting. Can they take away tens without counting. Do they understand that counting by groups doesn’t change the total quantity?

  48. What will my students be asked to do during the Grouping Tens assessment? • Students will be asked to identify tens and ones when presented with number cards. Note: Number cards available under downloads of www.amcanywhere.com. • Using counters, student will identify groups of ten and leftovers. • Student will use what they know about tens to find out how many altogether. • Students will be asked to add and take away tens without counters.

  49. Assessment #8: Grouping Tens • Video: 33:20 • First Grader and Second Grader: 33:50 – 37:10 • 40:12 Tad Second Grader

  50. ByKathy Richardson Assessment #9 Two-Digit Addition & Subtraction Overview & Description of Strategies

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