1 Math CAMPPP 2011 Math at the Beach!!! Grade 5-8 Sandra Fraser Erik Teather

Proportional Reasoning Breakout 2 2

Learning Goals Extend our understanding of the big ideas of proportional reasoning through a hands-on mathematical experience. Explore and experiment with learning goals and success criteria. 33

Placemat 4 Think-tank Space Personal Think Space

Definitions In your personal think space, capture some of your key learnings and/or prior knowledge about ___________________. (e.g., Learning Goals and/or Success Criteria) 5

Learning Goals & Success Criteria Rather than discuss these terms now, we will do some work around them and discuss them in more detail at the end of this Breakout session. 6

Lemonade Task 7

Lemonade Problem Sandra and Erik are in charge of making lemonade for the beach party. They make the lemonade by using lemon juice concentrate and mixing it with water. Unfortunately, they forgot to bring the recipe to the beach party, so they try a few options. Which mixture will be the most lemony? How do you know? 8 Mix B 1 cups juice concentrate 4 cups cold water Mix A 2 cups juice concentrate 3 cups cold water Mix C 4 cups juice concentrate 8 cups cold water Mix D 3 cups juice concentrate 5 cups cold water

Defining the Core of the Lesson Big Ideas/Enduring Understandings:Overall Expectation(s)Specific Expectation(s) Process Expectation(s) Learning Goal(s) Task Success Criteria Knowledge/UnderstandingThinkingCommunicationApplication 9 Assessment FOR/AS Learning Lesson Analysis and Planning Template Task

Explore and Experiment 1.As a group, use the 11x17 template provided to record your thinking. 2.We are going to complete the template in chunks. 3.Be ready to stop and discuss your thinking along the way. 10

Defining the Core of the Lesson and Task 11

Fill in each box in the following sequence: 1.Record the task. 2.What are the Big Idea(s)/Enduring Understanding(s) being developed through the task (consider using the Proportional Reasoning package provided to support your thinking). 3.Use the Ontario Curriculum document and/or the Proportional Reasoning package to determine the overall and specific expectations that you want to assess through this task. 12 Lesson Analysis and Planning

Defining the Core of the Lesson Big Ideas/Enduring Understandings:Overall Expectation(s)Specific Expectation(s) Process Expectation(s) Learning Goal(s) Task Success Criteria Knowledge/UnderstandingThinkingCommunicationApplication 13 Assessment FOR/AS Learning Lesson Analysis and Planning Template #2 #3 Task #1

14 4.Use the Ontario curriculum document, the Mathematical Processes package, and/or the DI Mathematical Processes cards to help you determine the process expectation(s) that could be explicitly taught through this task. Lesson Analysis and Planning

Defining the Core of the Lesson Big Ideas/Enduring Understandings:Overall Expectation(s)Specific Expectation(s) Process Expectation(s) Learning Goal(s) Task Success Criteria Knowledge/UnderstandingThinkingCommunicationApplication 15 Assessment FOR/AS Learning Lesson Analysis and Planning Template #4 Task

Learning Goal Brief statements that describe for a student what he or she should know and do with respect to a mathematical concept. These should be based on mathematical process and content curriculum expectations, and connected to a big idea or more fundamental essential understanding. Learning goals should be expressed in language that students understand. (CAMPPP/Ministry Definition) 16

17 5.Create your Learning Goals for this lesson using the information that you have collected so far on your template, the CAMPPP/Ministry definition, as well as think about the definition that you began to develop for learning goals from the beginning of this breakout session. (Keep in mind… What should students be able to know and to do by the end of this lesson?) Lesson Analysis and Planning

Defining the Core of the Lesson Big Ideas/Enduring Understandings:Overall Expectation(s)Specific Expectation(s) Process Expectation(s) Learning Goal(s) Task Success Criteria Knowledge/UnderstandingThinkingCommunicationApplication 18 Assessment FOR/AS Learning Lesson Analysis and Planning Template #5 Task

Lemonade Task 19

Math Congress 20

Success Criteria 21 Pulling out the essential ‘look fors’…

Success Criteria Descriptions of successful attainment of learning goals (i.e., ‘look fors’ for successful learning) developed by teachers that focus on important mathematics. Success criteria reflect the learning goal which is based on mathematical process and content expectations and draws on significant traits or characteristics identified in the achievement chart. (CAMPPP/Ministry Definition) 22

Defining the Core of the Lesson Big Ideas/Enduring Understandings:Overall Expectation(s)Specific Expectation(s) Process Expectation(s) Learning Goal(s) Task Success Criteria Knowledge/UnderstandingThinkingCommunicationApplication 23 Assessment FOR/AS Learning Lesson Analysis and Planning Template Task

24 KNOWLEDGE / UNDERSTANDING THINKINGCOMMUNICATIONAPPLICATION Achievement Chart

Guiding Questions - What makes a good solution for this task? know do - What evidence can students use to demonstrate the knowledge (know) and skills (do) being assessed based on the intended Learning Goal(s)? 25

Big Idea (BIN 4) Numbers are compared in many ways. Sometimes they are compared to each other; other times, they are compared to benchmark numbers. Numbers can be compared in different ways- sometime to each other and sometimes to benchmark numbers. 26

Curriculum Expectations (Grade 6) Overall Expectation: - demonstrate an understanding of relationships involving percent and ratio. Specific Expectations: represent ratios found in real-life contexts, using concrete materials, drawings, and standard fractional notation determine and explain, through investigation using concrete materials, drawings, and calculators, the relationships among fractions, decimal numbers, and percents 27

Mathematical Process Expectations Reasoning and Proving: develop and apply reasoning skills to make and investigate conjectures and construct and defend arguments Representing: create a variety of representations of mathematical ideas, make connections among them, and apply them to solve problems 28

Learning Goals I can compare ratios, fractions, and percents in real-life contexts. I can draw conclusions and give justifications. I can select an appropriate representation and defend my choice. 29

30 KNOWLEDGE / UNDERSTANDING ➤ I can use fractions or ratios or percents to compare the concentration of liquids. ➤ I can explain the difference between a part-to-part and a part- to-whole ratio. THINKING ➤ I can check the reasonableness of my answer. ➤ I can describe how the solution was reached and explain the solution. ➤ I can review the method used: Did it make sense? Is there a better way to approach the problem? COMMUNICATION ➤ I can create a model to represent the problem (e.g., numerical, algebraic, graphical, physical, or scale model).

Gallery Walk As a group, walk around to find one solution you would share to achieve at least one of your intended learning goal. 31

Consolidating our Learning 32 Chew and Digest

Learning Goals and Success Criteria When would be the most impactful stage (e.g., Minds On, Action, Consolidation) to reveal the Learning Goals and the Success Criteria for this lesson? Why? 33

Frayer Model 1.As a group, revisit your initial definitions on your Placement and draw on your learning from this Breakout session to create a Frayer Model for one of the terms explored today, i.e. Learning Goals, Success Criteria. 2.Post. 34

Placemat 35 Think-tank Space (Frayer Model) Personal Think Space

The Frayer Model 36 DefinitionFacts/Characteristics Non-ExamplesExamples TERM?

Consolidation Question What Consolidating Question could be used as an exit card to determine students’ understanding of the lesson goal, “ I can compare ratios, fractions, and percents in real-life contexts”? 37

What did we learn? …about the mathematics? …about teaching mathematics? 38