1. Place Value &MathLine

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

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

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

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

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

7. Simple Expansion of 17? Place Value – Expansion

8. How many tens and how many ones in 17? 10 1234567

9. Simple Expansion of 46? Place Value – Expansion

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

11. How many tens and how many ones in 46? 10

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

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

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

15. Place Value – Expansion 10 How many ones in 46? 265431

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

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

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

19. First, identify the “1” in 51 Place Value – Expansion 15 51515151

20. Next, identify the “1” in 15 15151515 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 15151515 51515151

22. Place Value – Expansion 12 3 3 45 Now, look at the “5’s”, what is the “5” in 51? It is 5 tens 15 51515151

23. Place Value – Expansion 1 What about the “5” in 15? 2345 15151515 51

24. Place Value – Expansion 12 3 3 45 We can see the 5 in “51” represent 10’s 15 51515151

25. Place Value – Expansion 1 Where as the “5” in 15 is only 5 ones 2345 15151515 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 236 100 200 300 100 200 36 62 Using multiple MathLine’s show relationship between 362

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

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

31. Place Value – Expansion 100 62 236 100 200 300 62 200 362 While the “2” in “362” is two “ones” 6262

32. Place Value – Expansion How do the “3’s” relate in both numbers? 236362 236236236236 362

33. Place Value – Expansion 236236236236362 The “3” in “236” is three groups of 10. 1 2 3 3

34. Place Value – Expansion 236362 362 The “3” in “362” is three groups of 100. 100 200 300

35. Place Value – Expansion 236 362362362362 How do the “6’s” relate in both numbers?

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

37. Place Value – Expansion 236 362362362362 The “6” in “362” is six tens 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.