Number and Operations in Base Ten

1. Number and Operations in Base Ten Place Value

2. Place Value Task • Find a number greater than 0 and less than 1,000 that: • is closer to 500 than 0, and • Is closer to 200 than 500. • There are many correct answers to this problem. Describe all of the numbers that are correct. Illustrativemathematics.org (finish)

3. What is the Big Deal about Place Value? • The base-ten place value system is the way we communicate and represent anything that we do with whole numbers and later with decimals. (Van De Walle, 2013)

4. Strategies Place Value Understanding Strategies A Progression Cluster 2.NBT.A Cluster 2.NBT.B Cluster 3.NBT.A (varied algorithms)Cluster 4.NBT.A (standard algorithm) Algorithms

5. What Does Place Value Mean? • Video at LearnZillion – Replace – David is doing this one. • http://learnzillion.com/lessons/3225-understand-the-value-of-digits-using-pictures

6. Counting and Cardinality • Talk to your neighbor. • What do you know about the following terms: cardinality, one to one correspondence, subitizing? • Read the Counting and Cardinality progression in your group. • Share out – Can anyone tell us what one to one correspondence is and demonstrate it? How about cardinality? Subitizing?

7. Counting and Cardinality • Two Tasks: • K.CC.B.4 – Goody Bags • K.CC.B.4 – Counting Mats • How do these tasks help students prepare for place value study? • Tasks from www.illustrativemathematics.org

8. K.NBT.A.1 Work with numbers 11-19 to gain foundations for place value. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

9. Turn and Talk • What would this standard look like in a kindergarten classroom?

10. Find a good Example Replace – Stacie is working on this one.

11. Video • Discuss the teaching moves the teacher made in this video to lead to the conceptual understanding the standard requires.

12. How Can We Use These Tools?

13. The “Teen Numbers” • What special difficulties do the “teen” numbers present for both counting and place value? 17, for example, doesn’t sound like 1 ten (ten ones) and 7 ones.

14. Big Idea 1 • Sets of ten (and tens of tens) can be perceived as single entities or units. For example, three sets of ten and two singles is a base-ten method of describing 32 single objects. This is the major principle of base-ten numeration. • In the NBT progression, page 2, this idea is listed under Base-ten Units.

15. 1.NBT.A.2 Understand place value. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones — called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

16. Discussion • Is there a difference between the kindergarten standard and the first grade standard? • If so, what is the difference? • How does the teacher’s language help students with understanding the content of this standard?

17. Big Idea 2 • The positions of digits in numbers determine what they represent and which size group they count. This is the major organizing principle of place value numeration and is central for developing number sense. • In the NBT progression, page 2, this idea is listed under Position.

18. Layered Flash Cards Visual Supports 8 6 80 6 layered separated 86=80+6

19. Big Idea 3 • There are patterns in the way that numbers are formed. For example, each decade has a symbolic pattern reflective of the 0-9 sequence (e.g., 20, 21, 22 ...29). • This idea is discussed in the NBT progression in first grade, page 6.

20. Very Hungry Caterpillar Task • How does this task develop place value understanding?

21. 2.NBT.A.1 Understand place value. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens — called a “hundred.” b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

23. An Example • Stacie will do this one.

26. Big Idea 4 • The groupings of ones, tens, and hundreds can be taken apart in different but equivalent ways. For example, beyond the typical way to decompose 256 of 2 hundreds, 5 tens, and 6 ones, it can be represented as 1 hundred, 14 tens, and 16 ones but also as 250 and 6. Decomposing and composing multi-digit numbers in flexible ways is a necessary foundation for computational estimation and exact computation. • This idea is discussed in the NBT progression in Grades 1 and 2 in the place value clusters.

27. Base Ten Riddles • I have 23 ones and 4 tens. Who am I? • I have 4 hundreds, 12 tens and 6 ones. Who am I? • I have 30 ones and 3 hundreds. Who am I? • I am 45. I have 25 ones. How many tens do I have? • I am 341. I have 22 tens. How many hundreds do I have? • I have 13 tens, 2 hundreds, and 21 ones. Who am I? • If you put 3 more tens with me, I would be 115. Who am I? • I have 17 ones. I am between 40 and 50. Who am I? How many tens do I have. • Van de Walle, J. A., Karp, K.S., & Bay-Williams, J. M. (2013). Elementary and Middle School Mathematics: Teaching Developmentally, Pearson Education. P. 200

28. Teaching Channel Video • https://www.teachingchannel.org/videos/second-grade-math-lesson

29. 3.NBT.A.1 Use place value understanding and properties of operations to perform multi-digit arithmetic. Use place value understanding to round whole numbers to the nearest 10 or 100.

30. 3.NBT.A.1 Building upon the understanding that 10 represents a bundle of ten ones, and 100 represents a bundle of ten tens, students should be able to locate a given number on a number line and round to the nearest ten or hundred.

31. Background Knowledge for Rounding to Ten and Hundred David will get a background video

32. Rounding to Tens Which of the following numbers will round to 40? How do you know? Use two different strategies. 37, 32, 43, 46, 50

33. Rounding to Tens • What is the smallest whole number that will round to 40? How do you know? • What is the largest whole number that will round to 40? How do you know? • How many different whole numbers will round to 40? How do you know? Adapted from http://www.illustrativemathematics.org/illustrations/745

34. Rounding to Hundreds • Which of the following numbers round to 600? How do you know? 550, 575, 620, 645, 680

35. Rounding to Hundreds • What is the smallest whole number that will round to 600? • What is the largest whole number that will round to 600? • How many different whole numbers will round to 600? Adapted from http://www.illustrativemathematics.org/illustrations/745

36. 4.NBT.1 Generalize place value understanding for multi-digit whole numbers. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

37. Rounding to 100 • Watch this Learn Zillion video

39. 4NBT Place Value Task Sometimes when we subtract one number from another number we decompose a number, and sometimes we don't. For example, if we subtract 38 from 375, we can decompose a ten into ten ones: Find a 3-digit number to subtract from 375 so that: • You don't have to decompose any numbers. • You would naturally decompose a ten. • You would naturally decompose a hundred. • You would naturally decompose both a hundred and a ten. In each case, explain how you chose your numbers and complete the problem. From http://www.Illustrativemathematics.com

40. 5.NBT.A.1, 5.NBT.A.2 • Understand the place value system. • 5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. • 5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

41. Understand the Place Value System Stacie is working on a fifth grade video

43. 5th Grade NBT Task • Kipton has a digital scale. He puts a marshmallow on the scale and it reads 7.2 grams. How much would you expect 10 marshmallows to weigh? Why? • Kipton takes the marshmallows off the scale. He then puts on 10 jellybeans and then scale reads 12.0 grams. How much would you expect 1 jellybean to weigh? Why? • Kipton then takes off the jellybeans and puts on 10 brand-new pink erasers. The scale reads 312.4 grams. How much would you expect 1,000 pink erasers to weigh? Why?

44. Big Idea 5 • “Really big” numbers are best understood in terms of familiar real-world referents. It is difficult to conceptualize quantities as large as 1000 or more. However, the number of people who will fill the local sports arena is, for example, a meaningful referent for those who have experienced that crowd. (Big Ideas are from Van de Walle, 2013, pg. 192)

45. Very Large Numbers • How many people do you think are in this stadium?

46. Just Don’t Do This • http://www.youtube.com/watch?v=yOz8Fq0nNqg • There just isn’t any understanding. Just don’t do it!

47. Notes-Future modules • Place Value progression • Comparing progression • Operations using place value strategies (algorithm article) • Addition • subtraction • Multiplication • division