1. 4 th Grade

2. Grant Purpose and Background Partnerships Purpose of this Training Target: Increase content knowledge of identified Tennessee Education Standards for Math as measured through a STEM challenge. Introductions and Training Purpose

3. http://msptennessee.wikispaces.com Please take the time to visit the site later Contact us if you have any questions or need help. MSP Wikispace – Your Source for All Resources

4. Use the Instructional Alignment from your homework to discuss the implications across the grade levels Choose one to share out. Vertical Alignment (Instructional Alignment Chart, K-12 Vertical Progression book)

5. Fourth Grade Challenge Irrigation Ideas There has been a breach in the irrigation system on a large farm. You have been asked to design the model for an irrigation system to move water from a reservoir to another location where it can be used for farming with minimal evaporation and a constant temperature. What kind of materials would work best?

6. Standards Math 4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. 4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Science GLE 0407.8.1 Recognize the major components of the water cycle. SPI 0407.8.1 Identify the basic features of the water cycle and describe their importance to life on earth.

8. Fraction Bars “Match Mine”

9. Find a person or persons that have the same portion of the strip colored

10. Fraction Bars “Match Mine” Find a person or persons who have a bar divided into the same amount of parts.

11. Fraction Bars “Match Mine” Find a person or persons who have an equivalent part.

12. Clear Target: I can identify when two fractions are equivalent using models.

13. Equivalent Fractions Private think time: – Take a minute to explore your fraction bars. – What do you notice? Talk with your group. What are your observations?

14. Equivalent Fractions If you have not sorted your bars by color, do so now.

15. Using your fraction bars, find the equivalent fraction to the given fraction below. Look at the denominators of the fractions you are solving and use those two fraction bar sets to find the answer to the problem.

16. Using your fraction bars, find the equivalent fraction to the given fraction below. Look at the denominators of the fractions you are solving and use those two fraction bars to find the answer to the problem.

17. Using your fraction bars, find the equivalent fraction to the given fractions below. Look at the denominators of the fractions you are solving and use those two fraction bars to find the answer to the problems.

19. Clear Target: I can compare fractions using >,<, = and justify my conclusions using a visual model.

20. Fraction Tower Cubes

21. Fraction Pyramid Cubes Use a variety of representations to help students understand conceptually.

22. We Do Student A: Talk to your shoulder partner and prove your fraction comparison. Student B: Verify that your partner’s work is accurate using accountable talk. Switch roles.

23. Fraction Pyramid Cubes

24. You Do / Check For Understanding How do you compare one fraction to another fraction? Create a fraction comparison of your own. Use manipulatives and pictures to show your thinking.

25. Table Talk Talk at your table about other ways fraction pyramid cubes can be used……….. Share your ideas!

26. Assessment

28. Scaffolding to Mastery Talk at your tables about other scaffolding lessons that need to occur to get to the level of mastery of the assessment. Chart your scaffolding ideas. Share out

30. Math Tasks There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics. Lappan & Briars, 1995

31. Math Tasks A mathematical task is a problem or set of problems that focuses students’ attention on a particular mathematical idea.

32. Math Tasks Teachers must be able to choose appropriate mathematical tasks judge the advantages of particular representations of a mathematical concept help students make connections among mathematical ideas grasp and respond to students’ mathematical arguments and solutions. Doerr, H. M., & English, L. D. (2006); Hunting, R. P., & Doig, B. A. (1997); Britt, M. S., Irwin, K. C., & Ritchie, G. (2001)

33. What are the barriers to using math tasks appropriately? A lack of mathematical content knowledge can impede teachers’ abilities to – notice and analyze students’ mathematical thinking – design actions that respond to students’ understanding – engage in productive professional conversations Doerr, H. M., & English, L. D. (2006); Hunting, R. P., & Doig, B. A. (1997); Britt, M. S., Irwin, K. C., & Ritchie, G. (2001 )

34. Task Selection True or False? (Discuss your answer with a partner) 1.All tasks must be high-level? 2.Accountable talk is only used during a high-level task? 3.The main purpose of tasks is for assessment purposes only?

36. Identify standards and targets Vocabulary Frame for the task

37. John has 1/2 of a Star Bar. Sue has 3/4 of a Star Bar. You have 4/6 of a Star Bar. Who has the biggest share of a Star Bar? Be prepared to explain how you figured out the share or the part of the candy bar that each person receives and how you know who has received the most candy. Show your solution with a visual model and explain how you know who has the most candy. Star Bar

40. John has 1/2 of a Star Bar. Sue has 3/4 of a Star Bar. You have 4/6 of a Star Bar. Who has the biggest share of a Star Bar? Be prepared to explain how you figured out the share or the part of the candy bar that each person receives and how you know who has received the most candy. Show your solution with a visual model and explain how you know who has the most candy. Star Bar

41. Quick Write Question Stems: If all of the students want the same amount of candy then how much more will each student need in order to have the same amount of candy as Sue? After reviewing my work and others’ work, describe what I realized about my own thinking and solution. Share if you learned anything new or viewed another solution that you felt you would use in the future and explain why. Star Bar

42. Integrated Science and Math Lesson “Round and Round the Water Goes” Clear Targets -I can partition a whole into eight equal parts, four equal parts, and two equal parts. -I can explain and illustrate why fractions are equivalent or not equivalent. -I can draw conclusions about the effect of multiple uses on a water source, quantity, of a reservoir.

43. The Water Cycle The journey water takes as it circulates from land to sky and back down is called the water cycle. Heat from the sun provides energy to evaporate water from the Earth’s surface (ponds, lakes, rivers, and oceans). The water vapor eventually condenses, forming tiny droplets in clouds. When the clouds meet cool air over land (condensation), precipitation (solid or liquid) occurs and water returns to the land. Most precipitation which lands on the ground forms runoff whether it stays on the surface or sinks underground. The runoff flows underground or above into our ponds, lakes, rivers, and oceans. Then the cycle continues all over again.

44. Materials A large bucket to hold several gallons One container per student (can use milk carton) Household sponges to cut Various colors of food coloring colors (optional)

45. Fractional Sponges (I do) Why is one-half equivalent to two-fourths? Why is one-eighth not equivalent to one-fourth ? Which statement is correct? 1/4 > 1/2 2/8 < 1/2 2/8 = 1/4

46. Cut Sponges (We do) Fold and cut paper templates and use to: Cut 1 sponge into eighths Cut 1 sponge into fourths Cut 1 sponge into halves Leave 1 sponge whole (You can increase or decrease these numbers to fit the number of students that you have.)

47. Model of Water Amounts

48. Directions (You do) Fill a large bucket to the brim with water. (This represents water stored in the river.) Tell students they are going to simulate changes in a watershed over several time periods. (Each 20 second round represents a time period.) For each round students should be an equal distance from the water source when the round starts, students fill their sponges with water from the reservoir to represent consumption. They squeeze the water out of the sponges into their containers. They can refill as often as they like per round. At the end of each round, note how much water is still in the bucket. Students then empty half of the water from their container back into the bucket. This represents the water that comes back to the reservoir through run off and precipitation. The other half of the water goes into the separate container. This represents the water that is used by animals, plants, etc. that is still on Earth, but does not immediately return to the reservoir.

49. Fraction Key Each person is represented by one-eighth Each farm is represented by one-fourth Each service provider is represented by one-half Each industry is represented by one whole

50. Round 1 It is 200 years ago. A few homesteaders operating small farms inhabit the watershed. (Two people and one farm represent the homestead.) Give each person (two) one-eighth sponge and one person one-fourth sponge to represent the farm. Students then empty half of the water from their container back into the reservoir (bucket), and half goes into a container that represents part of the water cycle.

51. Round 2 One hundred years have passed. A large farm and a small town are now located in the watershed. Distribute sponges cut in eighths to five people (town’s people) and a half sponge to one person representing a service provider. Would the people use, = the amount of water used by the service provider? Students then empty half of the water from their container back into the reservoir (bucket), and half goes into a container that represents part of the water cycle.

52. Round 3 It is just after WWII. The size of the town has increased. Many residents are employed in a factory. A whole sponge represents the industry. Two farming areas supply milk or food. They get one-fourth sponge each. Give four people one-eight sponge. Would the people and the farm together use, or = to the amount of water used by the industry? Students then empty half of the water from their container back into the reservoir (bucket), and half goes into a container that represents part of the water cycle.

53. Round 4 It is now the present. The town has continued to grow. A new industry that makes household cleaning products has moved in (1 sponge). Two people represents two service providers with one-half sponge each. Represent residential expansion by giving six people one-eight sponge. Would six people use, = the amount of water used by two service providers? Why could you say that both the industry and service providers in the town use equal amounts of water? Students then empty half of the water from their container back into the reservoir (bucket), and half goes into a container that represents part of the water cycle.

54. Evaporation, Condensation, Precipitation

55. Assessment How does the water cycle work? How does the water in a pond, lake, river, or ocean replenish itself? How has the use of water changed from time period to time period, and what effect has that had on the water quality? What are some ways we can conserve water?

56. Irrigation Challenge Procedure Divide students into groups of 2-3 students. Teams will design an irrigation system to move two cups of water a distance of at least three feet. Plans must be approved by the teacher before gathering materials. Test irrigation system by measuring how much water is gathered in each of the two destination containers.

57. Closure TARGET: Increase content knowledge of identified Tennessee Education Standards for Math as measured through a STEM challenge. Remember to check out the Wiki Remember to share information with rest of team (Math and Science) Remember to bring back the composition book and Vertical Progression Book for future trainings Take with you: bucket, sponges, fraction bars, fraction cubes