Shift of Application Math Training Sunnyside School District Focus 1 & 2; Mathematical Shifts & Practices; June 2014

Good Afternoon Discuss the following with a partner: 1. How many of the PARCC items were based in word problems? 2. What types of word problems do you see in most classrooms? How closely do they match the items you just looked at?

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

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.

Math Practice 4: Modeling with Mathematics Read MP 4, then answer: 1. What does modeling mean in the common core? 1. How can you assess this math practice standard?

Read Math Practice 1 1. What are some student actions when demonstrating this math practice? 2. What are some teacher actions that will lead to students demonstrating this practice?

Modeling/Application: The culmination of it all! 7

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) minutes to solve Every two weeks

Daily Word Problems Provide a structure for students.  What is the problem asking us to do?  What do we know?  Show your steps:  What is your solution and how do you know it’s correct? Remove the structure for basic word problems throughout the year.

Word Problem Example 1. John brought 90 cookies to school for his birthday. There are 30 students in his class. How many cookies can they each have? 2. Nine friends bought a box of video games. They paid $85 and received $24 in change. How much did each person pay if they share the cost equally? 3. Deer in the Park problem

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

Performance Task Attributes o Real world o Complex o Multiple Standards o Multiple Steps o Related to current or previous learning o Take a minimum of 45 minutes o Relevant and engaging o Multiple ways to solve

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. 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.

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

Garden Problem I’ve had enough of this winter weather and I’m ready for spring. Today I started to plan my garden. The length of the rectangle area that I am going to plant is three feet longer than it is wide. I decided to plant one-third of the garden area with Sunflowers. Another fourth of my garden will be planted with Brown-eyed Susans. Only one-fifth of my garden will contain Columbine. Exactly one square yard in the rectangular garden will be devoted to Foxglove. The last one-sixth of my garden will be filled with Trillium.

Garden Problem Find the area, as well as the length and width, of my fractional garden. Please be sure to include the units of measure in your answer.

Reflection 1. What can you do in your role to prepare teachers for increased problem solving in the classroom? 2. What are the key components of an effective problem solving session?

4 th Grade Performance Task

Assignment Design a plan to help teachers incorporate all types of word problems into their classroom this next year. Consider the following: Training needed Scaffolding of tasks School-wide expectations Supporting throughout the year