Place Value

1. Place Value Place Value & MathLine

2. Place Value Place Value builds the foundation for all elementary math!

3. Place Value Research shows: Students who understand Place Value tend to understand elementary math Students who struggle with Place Value tend to struggle with elementary math

4. PlaceValue Place Value is demonstrated many ways in curriculum, including: Expansion of numbers Understanding Ones, Tens, Hundreds and up Explanation of numbers within their different place

5. PlaceValue It is important to first understand on MathLine… blue rings indicate 5’s… red rings indicate 10’s

6. PlaceValue Here are some examples of Place Value exercises Starting with expansion of numbers…

7. Place Value – Expansion Simple Expansion of 17?

8. Place Value – Expansion How many tens and how many ones in 17? 10 1 2 3 4 5 6 7

9. Place Value – Expansion Simple Expansion of 46?

10. Place Value – Expansion Note the number of red rings

11. Place Value – Expansion How many tens and how many ones in 46? 10

12. Place Value – Expansion How many tens and how many ones in 46? 10 10

13. Place Value – Expansion RULE – if we begin a group on one bar, it continues on the next. 10 10 10

14. Place Value – Expansion RULE – if we begin a group on one bar, it continues on the next. 10 10 10 10

15. Place Value – Expansion How many ones in 46? 10 10 10 10 1 2 3 4 5 6

16. Place Value – Expansion Students struggle with understanding the values for similar numbers, example: 15 & 51

17. Place Value – Expansion Show the relationship between 15 and 51 Put 2 MathLines front to back

18. Place Value – Expansion Students can see the difference. 15 51

19. Place Value – Expansion First, identify the “1” in 51 15 51

20. Place Value – Expansion Next, identify the “1” in 15 15 51

21. Place Value – Expansion See how the “1’s” in each relate Students can see that the “1” in 15 is a ten, versus the “1” in 51 is a one 15 51

22. Place Value – Expansion Now, look at the “5’s”, what is the “5” in 51? It is 5 tens 15 51 3 1 2 4 5 3

23. Place Value – Expansion What about the “5” in 15? 15 1 2 3 4 5 51

24. Place Value – Expansion We can see the 5 in “51” represent 10’s 15 51 3 1 2 4 5 3

25. Place Value – Expansion Where as the “5” in 15 is only 5 ones 15 1 2 3 4 5 51

26. Place Value – Expansion MathLine builds a concrete picture so students who struggle with switching numbers like 15 and 51… can now understand their value.

27. Place Value – Expansion Now use MathLine to teach Place Value of 3-digit numbers

28. Place Value – Expansion Using multiple MathLine’s show relationship between 236 362 100 100 200 200 300 36 62

29. Place Value – Expansion How do the “2’s” relate in both numbers? 236 362

30. Place Value – Expansion The “2” in“236” is two groups of 100. 236 362 100 200 2

31. Place Value – Expansion While the “2” in “362” is two “ones” 236 362 100 100 200 200 300 62 62 62

32. Place Value – Expansion How do the “3’s” relate in both numbers? 236 236 362 362

33. Place Value – Expansion The “3” in “236” is three groups of 10. 236 362 3 2 1 3

34. Place Value – Expansion The “3” in “362” is three groups of 100. 236 362 362 100 200 300

35. Place Value – Expansion How do the“6’s” relate in both numbers? 236 362

36. Place Value – Expansion The “6” in “236” is six ones 236 362

37. Place Value – Expansion The “6” in “362” is six tens 236 362 1 2 3 3 4 5 6

38. Place Value – Expansion On MathLine, students clearly see what the 2, 6, and 3 represent to each of these numbers. Teachers use many MathLine’s in sequence to teach value of numbers up to 1000.

39. Place Value – Expansion MathLine allows for a concise yet clear strategy to model large numbers. Students who struggle with Place Value need a concrete picture to understand the abstract symbols and the place values of each digit.

40. Place Value – Expansion Teachers are very creative with MathLine & Place Value exercises … As MathLine fulfills a unique need in such a fundamental concept in elementary math.