Step 3… Making The Connection. Connecting The CCSS-M To Your Step 3… Making The Connection Connecting The CCSS-M To Your Instructional Materials

Common Core Instructional Shifts for Mathematics Focus: Instructional time spent on critical areas in standards Coherence: Think across grades, and link to major topics within grades Rigor: Require fluency, application, and deep understanding

Review of Previous Steps Review the structure and shifts of the CCSS Math Understand the language of a grade specific CCSS critical area at a deeper level Learn a process to review any CCSS domain Step 2 Deepen understanding of a critical area at your grade level Analyze content and process standards Understand the learning progression for a critical area of focus

Step 3-CCSS & Your Current Instructional Materials Is the content in my current instructional materials deep enough? Does the cognitive complexity of the tasks in my materials encourage the standards for mathematical practice? How can I use the existing problems in my text to reach the needed content depth and support the standards for mathematical practice?

Is the Content of My Instructional Materials Deep Enough?

How Deep is the Content in Your Instructional Materials? Working in grade level teams: Review CCSS standards in the domain you focused on from the previous session. (Use Arizona CCSS document for additional examples and explanations + OSPI Transition doc) Using your instructional materials, look at how the content of that domain is introduced, developed, and applied. (depth vs breadth) Discuss with your team. Share out. Depth vs breadth

Cognitive Complexity

Martha’s Carpeting Task Martha was recarpeting her bedroom, which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?

The Fencing Task Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits. If Ms. Brown’s students want their rabbits to have as much room as possible, how long would each of the sides of the pen be? How long would each of the sides of the pen be if they had only 16 feet of fencing? How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

Comparing Two Mathematical Tasks Think privately about how you would go about solving each task (solve them if you have time) Talk with your neighbor about how you did or could solve the task Martha’s Carpeting The Fencing Task NOTE TO SPEAKER: If there is time, you may want to have participants share their solution strategies on a blackboard or on large pieces of chart paper before showing the solutions that appear on the upcoming slides.

Solution Strategies: Martha’s Carpeting Task

Martha’s Carpeting Task Using the Area Formula A = l x w A = 15 x 10 A = 150 square feet

Martha’s Carpeting Task Drawing a Picture 10 15

Solution Strategies: The Fencing Task

The Fencing Task Diagrams on Grid Paper

The Fencing Task Using a Table Length Width Perimeter Area 1 11 24 2 10 20 3 9 27 4 8 32 5 7 35 6 36 The table shows that all the configurations have a perimeter of 24, but different areas. The area for the 6 x 6 pen is the largest; both before and after that, the areas are smaller than 36 square feet.

The Fencing Task Graph of Length and Area

Comparing Two Mathematical Tasks How are Martha’s Carpeting Task and the Fencing Task the same and how are they different? NOTE TO SPEAKER: If there is time, you may want participants to generate similarities and differences before sharing the upcoming slide.

Similarities and Differences Both are “area” problems Both require prior knowledge of area Differences The amount of thinking and reasoning required The number of ways the problem can be solved Way in which the area formula is used The need to generalize The range of ways to enter the problem Way in which area formula is used: Martha’s Carpeting can be solved by knowing and using the area formula but this formula alone is not sufficient to solve the Fencing Task The need to generalize: Martha’s carpeting does not lead to a generalization but the Fencing Task does The range of ways to enter the problem: Martha’s Carpeting Task cannot be started by a student who does not know the formula for area; the Fencing Task can be started in other ways, such as sketches on graph paper.

Mathematical Tasks: A Critical Starting Point for Instruction Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking. Stein, Smith, Henningsen, & Silver, 2000

Level 1 (Recall) ….includes the recall of information such as a fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. That is, in mathematics a one‐step, well‐defined, and straight algorithmic procedure should be included at this lowest level.

Level 2 (Skill/Concept) ….includes the engagement of some mental processing beyond a habitual response. A Level 2 assessment item requires students to make some decisions as to how to approach the problem or activity, whereas Level 1 requires students to demonstrate a rote response, perform a well‐known algorithm, follow a set procedure (like a recipe), or perform a clearly defined series of steps.

Level 3 (Strategic Thinking) ….requires reasoning, planning, using evidence, and a higher level of thinking than the previous two levels. This may require a student to explain their thinking or make conjectures. The complexity does not result from the fact that there are multiple answers, a possibility for both Levels 1 and 2, but because the task requires more demanding reasoning.

Level 4 (Extended Thinking) ….requires complex reasoning, planning, developing, and thinking most likely over an extended period of time.”

Refer to the Carpeting and Fencing Tasks-What are their levels of cognitive complexity?

Sorting Activity Individually: Categorize tasks into Level 1, 2, 3, or 4 using Cognitive Complexity Levels. Record your responses on the provided worksheet. In table teams: Share your results and come to consensus at your table. One person will record results on the “master” copy. Whole group: Share results and review criteria groups used for low and high levels.

Sorting Questions to ponder…… How did you determine between levels 2 & 3? Does a task presented as a word problem always have a high level of cognitive complexity? Does using a manipulative indicate a higher level of cognitive complexity? If a task requires an explanation, does it have a high level of cognitive complexity?

Changing the Cognitive Complexity Level Each team member picks out a task that was placed in level 1 or 2. Individually determine how you would modify your task to be a level 3 task. Share out with your team & determine which task you will share with the entire group. Share out entire group.

Cognitive Complexity & Mathematical Practices Which levels of cognitive complexity allow students to develop the mathematical practices? Update your Domain Illustration column 5.

What level of cognitive complexity are these tasks? Are there various levels of Cognitive Complexity in Your Instructional Materials? Review several types of problems/tasks found in your instructional materials. What level of cognitive complexity are these tasks? Level 1 (Recall) Level 2 (Skill/Concept) Level 3 (Strategic Thinking) Level 4 (Extended Thinking)

Share at your table the types of problems/ tasks you found : What are the prevalent levels of complexity in your instructional materials? How will this impact meeting the standards for mathematical practice? Whole group share out

Who’s Doing the Thinking?

Who’s Doing the Thinking? Watch Dan Meyer video

Video Debrief How much is too much support, how much is too little? How does scaffolding interfere/promote the standards for mathematical practice?

Who’s Doing the Thinking Complete the Gas Mileage Activity Discuss responses Review “original” Gas Mileage Activity Compare/contrast both versions

Growing with Math Grade 2 CCSS-M 2.OA $35 $29 What is the difference in price between the glove and hat? Growing with Math Grade 2 CCSS-M 2.OA

Janey is planting 12 trees in her yard Janey is planting 12 trees in her yard. There are 5 maple trees and the rest are oak. What fraction of the trees is oak? Lucas ran ½ mile and Candace ran 4/6 mile. Did they run the same distance? Explain. Math Connects Grade 4 CCSS-M 4.NF

There are 26³ ways to make a 3-letter “word” (from aaa to zzz) and 26⁵ ways to make a 5-letter word. How many times more ways are there to make a 5-letter word than a 3-letter word? The diameter of a human red blood cell ranges from approximately 6 x 10-6 to 8 x 10-6 meters. Write this range in standard notation. Holt Course 3 CCSS-M 8.EE

The polynomial 3.675v + 0.096v2 is used by transportation officials to estimate the stopping distance in feet for a car whose speed is v miles per hour on a flat, dry pavement. What is the stopping distance for a car traveling at 30 miles per hour? Holt Algebra 1 CCSS-M A-APR 1

A toy rocket is launched from the ground at 75 feet per second A toy rocket is launched from the ground at 75 feet per second. The polynomial -16t2 + 75t gives the rocket’s height in feet after t seconds. Make a table showing the rocket’s height after 1 second, 2 seconds, 3 seconds, and 4 seconds. At which of these times will the rocket be the highest? Holt Algebra 1

Who’s Doing the Thinking? Identify a standard within the domain you’ve been focusing on. Find a task in your instructional materials related to that standard. Make an adjustment/subtle shift to the task that will increase the cognitive complexity and help deepen the student’s content knowledge.

Impact of Teachers Read case studies (scenarios) of how Fencing Task was implemented. Use worksheet to write your thoughts on cognitive complexity students experience. Share out in table teams Whole group share out

Who’s Doing the Thinking Brainstorming Session: What instructional strategies can be used to promote student thinking and develop mathematical practices? Shifts in Classroom Practice Handout

Step 3… Objectives Revisited Determine if the content of instructional materials is deep enough. Compare and contrast the cognitive complexity of tasks and the Mathematical Practices Adjust existing problems/tasks to increase content depth and support Mathematical Practices.

Clock hours reminder– turn in forms Wrap up – Step 3… As facilitators back in your districts, what questions do you have? What suggestions? What further support would you like? Clock hours reminder– turn in forms

Readiness to Implement Survey Complete Post-Learning section of survey……….. What is your current state??

CCSS-M Professional Development Working in district teams: Individually complete Reflection form Share responses with your team Draft a plan to “roll-out” the CCSS-M to your district Create a poster with your district’s name and your plan for “poster walk” Create a poster with “suggestions” for administrator training

Clock hours reminder– turn in forms Thank you………… Clock hours reminder– turn in forms