Agenda

1. Agenda • Why Unit Bars • Representing Quantities (larger and smaller) • Representing Actions (put together, take away, compare, missing part) • Model Drawing Procedure • Part I • Part II • Model Drawing in 4-Step Process

2. Why Unit Bars? Texas curriculum has increased in difficulty. It requires: • Application of concepts • Deep understanding of concepts • Knowledge of academic language

3. Why Unit Bars? • Use of concepts in worded problems • Use of multiple concepts in worded problems • Connection among different representations of concepts • Use of mathematics vocabulary • Explanation and descriptions of mathematics in words What does increased difficulty look like?

4. Why Unit Bars? • No successful strategy for helping students solve multi-operation problems • Connected words in the story to actions: • put-together, • take away, • compare, and • missing part • Students often only identified one operation • Students matched the operations to the incorrect numbers; ie., 12 – 5 + 3

5. 24 24 Using Unit Bars ξ • Show a smaller quantity(#) • Show a larger quantity (#) • Label the unit bar ξ 24

6. Using Unit Bars 24 ] • Putting together 24 and 15 • Putting together 24 and 5 • Take away 8 from 29 15 ξ ξ ] 24 5 29 X| 8 29 |X 8

7. Using Unit Bars 24 • Comparing 24 and 15 • Missing part ξ ξ 15 22 | 12

8. Don’t forget that “?” 24 ] • Label the quantity being found, as described by the main idea in the question, with a “?”. ? 15 ξ ξ ] ? 24 5 29 X| ? 8

9. Model Drawing Procedure • Developed in Singapore • Visual representation of details with actions which assists children with problem solving • Helps children logically think using visual models to determine the computations

10. Model Drawing Procedure • Teaches the importance of language within math problems • Supports all ability levels within the classroom • Provides for differentiated instruction

11. Characteristics of Model Drawing Procedure • Identifies Who and/or What. • Uses a specific type of picture: unit bar. • Read one sentence, label, and adjust the unit bars. Repeat the process until all sentences have been read. • Uses a “?” on the unit bar to show what question is being answered. Part 1: Part 2:

12. Practicing Who, What, Unit Bar

13. Main Idea and Who, What, Unit Bar Details Ms. Sweed baked 8 brownies, 5 pies, and 7 cakes. How many pies and cakes did Ms. Sweed bake? pies and cakes M S bake Ms S p c

14. Main Idea and Who, What, Unit Bar Details There are 23 toys in the donation box for BCAM. Sixteen of the toys were dolls. How many toys were NOT dolls? toys NOT dolls toys

15. Main Idea and Who, What, Unit Bar Details Javier, Matthew and Leonard each have 4 DS games. If Benton buys 3 DS games, which of the following shows how to find the number of DS games the 4 boys have? J M L B DSG DSG DSG DSG DG 4 boys

16. Main Idea and Who, What, Unit Bar Details Morris was reading a 53 page novel. The first day, he read 25 pages, the second day he read 18 pages, and on the third day he finished the book. Which is one method that can be used to find how many pages he read on the third day to finish the novel? Method pages read 3rd day M novel p

17. Points to Remember • Some problems have extra information. • Some problems may not have both “Who” and “What.” • Main idea often helps with the “who” and “what.”

18. Characteristics of Model Drawing Procedure • Identifies Who and/or What. • Uses a specific type of picture: unit bar. • Read one sentence, label, and adjust the unit bars. Repeat the process until all sentences have been read. • Uses a “?” on the unit bar to show what question is being answered. Part 1: Part 2:

19. Read, Adjust, and Label • Read one sentence at a time. • If the sentence is long and has commas, then read to the comma • If the sentence is a compound sentence (two sentences joined by AND) then read to “and” • Adjust and label the model to show the facts in the sentence or phrase • Read the next sentence. • Adjust and label the model. • Continue the “read, adjust, and label until the story is completed.

20. Main Idea-Who, What, Unit Bar-Read, Adjust, Label • Rachel baked 22 cookies, 19 pies, and 15 cakes. How many cakes and cookies did Rachel bake? • Rachel baked 22 cookies, 22 R ] co ca 19 pies, co & ca R bake ? 15 and 15 cakes. ξ How many cakes and cookies did Rachel bake?

21. Main Idea-Who, What, Unit Bar-Read, Adjust, Label Christian bought a box of 28 pens. He took 8 of them to school and put 12 in a desk at home. He left the rest of the pens in the box. Which number sentence shows how to find how many pens are in the box? 28 Christian bought a box of 28 pens. # sent pens box ? C pens 12 8 He took 8 of them to school B S H and put 12 in a desk at home. He left the rest of the pens in the box. Which number sentence shows how to find how many pens are in the box?

22. Main Idea-Who, What, Unit Bar-Read, Adjust, Label Robbie was reading a 17 page book. On day one he read 4 pages. The second day he read 10 pages. He finished the book on day three. How many pages did he read on day one and day two? On day one he read 4 pages. Robbie was reading a 17 page book. 17 bk pgs R 10 pgs read 1st and 2nd day 4 The second day he read 10 pages. D1 D3 D2 ? He finished the book on day three. How many pages did he read on day one and day two?

23. 13 21 ? Main Idea-Who, What, Unit Bar-Read, Adjust, Label Todd went fishing. He caught 13 big fish and 21 little fish. How many more little fish than big fish did Todd catch? Todd went fishing. T bf Hmm little fish than big fish He caught 13 big fish T lf and 21 little fish. How many more little fish than big fish did Todd catch?

24. Main Idea-Who, What, Unit Bar-Read, Adjust, Label Juan and Leo each have 11 video games to trade. Juan and Leo each have 11 video games to trade. If Bill brings 7 games to trade, how many video games do the 3 boys have? J L B vg vg vg 11 vg 3 boys 11 ? If Bill brings 7 games to trade, 7 ξ how many video games do the 3 boys have?

25. Let's practice-- 4 - Step Process

26. Four-Step Process Austin has 22 toys. Jeff has 33 toys. How many toys do they have together? Step 2 Step 1 22 ] Toys together Austin Jeff toys toys Austin has 22 toys. ? 33 Jeff has 33 toys. How many toys do they have together? Step 3 Step 4 22 + 33 Add 22 and 33. 55

27. Four-Step Process Cathy has 9 pencils. She gave John 4 pencils. Sue gave Cathy 2 pencils at lunch. How could you find how many pencils Cathy has altogether? Step 2 Step 1 Cathy has 9 pencils. 9 2 She gave John 4 pencils. X | pencils Cathy ] Find pencils Cathy Sue gave Cathy 2 pencils at 4 ? lunch. How could you find how many pencils Cathy has altogether? Step 3 Step 4 5 + 2 9 - 4 Subtract 4 from 9. Add 2 to the difference. 7 5

28. Four-Step Process Max had 5 marbles. He gave his friend 3 marbles. He bought 7 new marbles at the store. Which number sentence shows how to find how many marbles he has now? Step 1 Step 2 Max had 5 marbles. NS-Max marbles now 5 7 He gave his friend 3 marbles. X| M marbles He bought 7 ] new marbles at the store. 3 ? Which number sentence shows how to find how many Step 3 Step 4 5 - 3 2 + 7 1) I subtracted 3 from 5. marbles he has now? 2) I added 2 and 7. 2 9 5 – 3 + 7 = 9 Is there another way to compute? 5 + 7 - 3 = 9

29. Points to Remember • Read, adjust and label-one sentence at a time. • Break long sentences into parts—and or commas help with places to break. • If there is more than one number given in a sentence, adjust the model one number at a time. • To show “take away”, mark off the appropriate units and draw an “X.” • Don’t get distracted with extra information. Focus on what the question is asking. • Placing the ? on the model, keeps students from answering the wrong question. • In the drawing, list the variables (who, what, unit bar) in the order that each appears in the story. • The computation is the differentiated part of the lesson. The model looks similar for all students, but the way they achieve success with computation is differentiated.

30. Benefits of Model Drawing • Fosters quantitative reasoning (number sense). • Empowers students to think systematically. • Deepens students understanding of difficult concepts. • Makes multi-step and multi-concept problems easy to work.

31. Benefits of Model Drawing • Improves comprehension through visualization of math concepts • Read a sentence, label, and adjust the model • Builds the foundation for algebra • Proven procedure with documented success

32. Benefits of Model Drawing • Provides a record of student thinking which teachers can use to help diagnose errors in student thinking. • Allows students to see connections between the model drawing representation, the number sentence representation, and the language representation. • Using the model drawing, students can write multiple number sentences. • Using the model drawing, students can write multiple process statements.

33. Q & A • Your questions--