1. Module 4 Shift of Application Sunnyside School District

2. Reflection on Word Problems Reflect on your use of word problems with students since the last training. Which problem types were your focus? What challenges have your students faced when doing daily word problems? What were possible solutions?

3. Word Problem Types

5. CCSS Math Shifts 1. Focus 2. Coherence 3. Rigor  Procedural Skill and Fluency  Conceptual Understanding  Application of Math Standards

6. Math Practice Standards 1. Make sense of problems and persevere is solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

7. Math Practice 2 Read MP 2, then answer: 1. Define quantitative reasoning. 2. Define abstract reasoning. 3. What do these look like when students are solving word problems?

8. Example of Quantitatively / Abstract O Quantitatively: 10 cows are eating grass, 4 walk away. How many cows are still eating? O Abstract: 10-4=6 O We need both in solving word problems.

9. Application (Problem Solving) 2 Levels with a full range of problems in between: 1. Word Problems Daily Related to standard you are teaching One and two step problems 2. Performance Tasks Multiple standards Complex problems (more than two steps) 45-60 minutes to solve (25-30 minutes K-1) Every two weeks

10. Example of WP/PT O Word Problem ( Put Together / Take Apart- both addends unknown ): Gina has 10 crayons. How many could she put it the red box and how many could she put in the green box? O Performance Task: There are two trains at the station. Both trains have the same number off passengers. One train has 14 passengers. The other train has 2 passengers on the first car, 5 passengers on the second car and third car and the rest on the last car. How many passengers are in the last car?

11. Performance Tasks Goal: By the end of the year, students will be able to solve a multi-step problem independently and communicate their process verbally and in writing. 11

12. Performance Task Attributes o Real world o Complex o Multiple Standards o Multiple Steps o 45-60 minutes (30 minutes in K-1) o Multiple ways to solve

13. Problem Solving Steps 1. Teacher and students read the problem together to determine what the problem is asking. 2. Students take 5-10 minutes to attempt to solve independently. O NOTE: The amount of time for independent work should increase throughout the year. 3. Students join a group and share their work thus far. 4. As a small group, they solve the problem by computation and/or graphic representation. 5. The group shares their solution with the class on poster paper or other methods. 6. Self Assessment/Reflection – group and problem solving

19. Application Challenges Frustration goes with problem solving. Students need to stretch and discover. Teachers need a new way to measure their success when doing problem solving: Not correct answers Not lack of frustration What to look for in problem solving: Perseverance, Questioning, Explanation, Tools, Communication Math Practices

20. Ten Flashing Fireflies

21. O Read story O Model jar in story with picture of jar and fireflies or ten frames O Students can model firefly jars from parts of the story O Solve word problems related to fireflies O number of fireflies in jar, number outside of jar, number of fireflies altogether, combinations of fireflies to make a number using problem types appropriate for your grade level

22. Ten Flashing Fireflies Performance Task O Performance task O You have 10 fireflies. Some are in the jar and some are in the sky. Create one picture to show your fireflies. Make sure each person in your group has a different number of fireflies in their jar. Add your picture to the firefly wall. O Look at the firefly wall. Are there any other ways that we could arrange fireflies in the jar and in the sky? How do you know?

23. Reflection 1. What are some things that your teacher did or did not do while you were solving the problem? 2. How difficult would the problem be if you couldn’t have worked with a partner? 3. Did you feel that you needed more or less independent work time before joining with a partner to solve? Why?

24. Choose a Task  Use your resources to find a task to use with students in the next month. Possible resources include:  Unit Plans (current and prior) – Unit 9 and 10  Illustrativemathematics.com  NCTM  Investigations  Other web resources – units from other states  Edit task if necessary  Add your task to the google doc and be prepared to share with the group http://tinyurl.com/perftaskk1

25. Closure 1. How can you make the task process match your teaching style? 2. When will you do these tasks with your students? Make a specific plan.

26. Standards Study When reading a standard, think about: 1. What are the procedures/skills students need to learn during instruction? 2. What are the conceptual understandings that students need to have during instruction (what do they need to explain)? 3. What are the details in the standard that will guide how far I go with it? Example: Only use denominators 2, 3, 4, 6, and 8 (3 rd grade).

27. Definitions Procedures : A list of the skills that students will master while learning this standard. It’s what they will do with the math. Concepts: A list of what students will understand while learning this standard. It’s what they will explain about the math. 27

28. Standards Study 1OA1:1.OA.1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. (See Table 1.) Procedures: Add, subtract objects within 20. Identify unknown numbers and position through objects and/or drawings. Concept: Explain Result Unknown, Total Unknown, Both Addends Unknown Change Unknown, Addend Unknown, Difference Unknown. Start Unknown. Compare Bigger/Smaller Unknown. Details: Word Problems. Add and Subtract within 20. 28

29. Standards Study K: K.NBT.1 1 st : 1.NBT4-6 ADE Flip Books 29

30. Have a great rest of your week!