Bar Modeling- What is It?

1. Bar Modeling- What is It? A visual representation of details and actions which assists children with problem solving A tool to help children think logically when making computations.

2. Aren’t These Like Part/Part/Total Diagrams? • Part/Part/Total diagrams are not proportional • PPT diagrams do not reinforce problem solving or number relationships

3. Part/Part/Total Ted has 6 toys. Mary has 2 toys. How many toys do they have altogether? • When the parts are not represented in proportion, student do not reinforce the relationship between the numbers.

4. Bar Models Are Proportional • Bar models foster number sense because bars are proportional and have meaning

5. Let’s consider the same problem with bar modeling… • Fred has 6 toys. Mary has 2 toys. How many toys do they have altogether? • Like the Part/Part/Whole diagram, the bar model allows the students to put parts together to get the total number of toys, but the bar model • reinforces the notion that Ted has more than Mary. • requires students to be more thoughtful about where to put the numbers • It also allows for further exploration… • How many more does Ted have than Mary? • How many could Ted give Mary so they could have the same, etc….

6. Bar Modeling- Scaffolding the Notion of Proportion Number Model: _____________+_____________=_____________ _____________=_____________+_____________

7. Bar Modeling Number Model: _____________+_____________=_____________ _____________=_____________+_____________

8. Bar Modeling Number Model: _____________+_____________=_____________ _____________=_____________+_____________

9. Bar Models Provide a Foundation For Algebraic Understanding • Fred has 6 toys. Mary has 2 toys. How many toys do they have altogether? T is the same as 6+2 T=6+2 T=8 There are 8 toys altogether. *Since the parts are the same size as the whole, it reinforces that equal means ‘same as’. As bar models get more complicated, the bar models will continue to provide a visual for the algebraic relationships

10. Bar Modeling Teaches The Importance of Language When Solving Math Problems • Have you ever had students add when they should subtract? • John collects rocks. He started with 4. After his vacation, he had 10. How many rocks did he collect on vacation? Why do we add and subtract?

11. Bar Modeling Teaches The Importance of Language When Solving Math Problems Compa R e Change Parts Parts Parts Parts Parts Parts and Wholes

12. You start with an amount • You add or subtract an amount • You end with a total amount Addition and Subtraction- Change

13. Addition Problems:ChangeBar Modeling Number Model: _____________+_____________=_____________

14. Change-Addition Start Change End = + 4 butterflies were sitting on a branch. 2 more landed on the branch. How many butterflies were on the branch now?

15. Addition Problems:ChangeBar Modeling Number Model: 4+2=6

16. Bar Modeling Teaches The Importance of Language When Solving Math Problems • Change problems can be presented in different ways so… • Bar Models will help students to: • Think about what information they have been given and what information they will are being asked to figure out. * May require subtracting or ‘counting up’. The bar model will help students choose what to do.

17. Bar Modeling: Joining (Addition-Change)

18. Bar Modeling: Joining (Addition-Change)

19. Bar Modeling: Joining (Addition-Change)

20. Bar Modeling- Subtraction-Change Number Model: _____________-_____________=_____________

21. Change-Subtraction Start Change End = - There were 4 butterflies sitting on a branch. 2 flew away. How many were left?

22. Bar Modeling- Subtraction-Change Number Model: 5-2=3

23. Bar Modeling Teaches The Importance of Language When Solving Math Problems • Change problems can be presented in different ways so… • Bar Models will help students to: • Think about what information they have been given and what information they will are being asked to figure out. * May requires adding. . The bar model will help students choose what to do.

24. Bar Modeling: Separating (Change- Subtraction)

25. Bar Modeling: Separating (Change-Subtraction)

26. Bar Modeling: Separating (Change-Subtraction)

27. Bar Modeling- Part/Part Whole Number Model: _____________+_____________=_____________ _____________-_____________=______________

28. Part/Part/Whole 1st Part 2nd Part End = + There were 4 butterflies and 2 ladybugs sitting on a branch. How many insects were sitting on the branch?

29. Bar Modeling-Part/Part/Whole Number Model: 4+2=6 6-4=2 6-2=4

30. Bar Modeling Teaches The Importance of Language When Solving Math Problems • Part/Part/Whole problems can be presented in different ways so… • Bar Models will help students to: • Think about what information they have been given and what information they will are being asked to figure out.

31. Bar Modeling: Part/Part/Whole

32. Bar Modeling: Part/Part/Whole

33. Bar Modeling: Part/Part/Whole

34. Warning, Warning! • There are 3 types of addition/subtraction problems: change, part/part/whole and comparison. • Change and part/part whole problems are based on the concepts of parts building wholes. COMPARISON PROBLEMS DO NOT! • COMPARISON PROBLEMS ARE BASED ON FINDING THE DIFFERENCE BETWEEN TWO PARTS

35. Bar Modeling- Multiplication DIFFERENCE Number Model: _________-__________=_________ (more or less)

36. Bar Modeling- Comparison Larger Smaller Amount Amount - = Jim has 5 butterflies. Mary has 2. How many more butterflies does Jim have than Mary?

37. Comparison Difference 3 More Number Model: 5-2=3

38. Bar Modeling Teaches The Importance of Language When Solving Math Problems • Comparison problems can be presented in different ways so… • Bar Models will help students to: • Think about what information they have been given and what information they will are being asked to figure out. * May require adding. Bar Models will help students figure out what to do.

39. Bar Modeling: Comparison- All(Finding The Difference)

40. Bar Modeling: Comparison- Smaller Amount Unknown

41. Bar Modeling: Comparison- Smaller Amount Unknown

42. Multiplication Bar Modeling Number Model: _____________x_____________=_____________

43. Bar Modeling- Multiplication Number Model: _____________x_____________=_____________

44. Bar Modeling- Multiplication Start Join X = Jim collects butterflies. There were 3 butterflies in each container. He had 2 containers. How many butterflies does Jim have in his collection?

45. Multiplication Number Model: 6÷2=3

46. Bar Modeling Teaches The Importance of Language When Solving Math Problems • Multiplication can be presented in different ways so… • Bar Models will help students to: • Think about what information they have been given and what information they will are being asked to figure out. * May require dividing. . The bar model will help students choose what to do.

47. Bar Modeling: Joining Equal Groups (Multiplication)

48. Bar Modeling: Joining Equal Groups (Multiplication)(Remember to split bottom bar in TA and APG examples)

49. Bar Modeling: Joining Equal Groups (Multiplication)(Remember to split bottom bar in TA and APG examples)

50. Bar Modeling- Division Number Model: _____________÷_____________=_____________