Manipulatives and Technology

Minds On – Activities While the music plays, find your musical pattern partner. Choose a table (6 people per table) and try the table activity (some people may be observers). Be prepared to share: –a big idea that could connect to the activity –suggested modifications –consolidating questions for the big idea The music will start again when you have 2 minutes remaining.

Minds On – Activities (Remind me to distribute BLM 4.1) BIG IDEA 1 The study of the mathematical structure of patterns is a foundation to algebraic reasoning. BIG IDEA 2 The mathematical structure of a linear growing pattern can be represented in different ways. Different representations highlight different characteristics and can serve different purposes. BIG IDEA 3 Linear growing patterns can be distinguished from other patterns by the way they grow. BIG IDEA 4 Two pieces of information about a linear growing pattern can be sufficient information to fully describe the pattern.

Learning Goals Reflect on the process of building a math talk learning community (MTLC); Explore LGP activities that use manipulatives and/or technology; Connect existing activities to big ideas and learning goals, keeping struggling students in mind; Develop open and parallel questions for consolidating the manipulative/technology tasks; Create pages for the Important book for Linear Growing Patterns.

Group Norms All ideas will be listened to carefully and responded to respectfully; Everyone will have a voice; All suggestions will be presented with the intent to move the collective forward; Clarifying questions are welcome; Everyone will engage fully in the moment; Suffering is optional!

Minds On – Stumbling Blocks relying on looking down input/output columns in tables developing rules only based on only recursive thinking using proportional reasoning incorrectly tending to stick with a rule without testing it missing connections between the algebraic equation and its trend line tending to focus on specific points and not seeing the trend line as a representation of a rate of change missing the relationship between the x and y values of a point

Minds On – Technology The Ontario Curriculum Grades 9 and 10 Mathematics 2005 p. 27 Information and communication technology (ICT) provides a range of tools that can significantly extend and enrich teachers’ instructional strategies and support students’ learning in mathematics… Technology can help to reduce the time spent on routine mathematical tasks and to allow students to devote more of their efforts to thinking and concept development. (Remind me to show the Linear Rep Tool)

Minds On – Manipulatives The Ontario Curriculum Grades 9 and 10 Mathematics 2005 p. 15 Students should be encouraged to select and use concrete learning tools to make models of mathematical ideas. Students need to understand that making their own models is a powerful means of building understanding and explaining their thinking to others.

Minds On – “Clipping” Along Big Idea? Learning Goal?

Minds On – “Clipping” Along Example: BI: The study of the mathematical structure of patterns is a foundation to algebraic reasoning. LG: Making sense of linear growing patterns as just one of many mathematical structures

Minds On – “Clipping” Along Parallel Questions: 1.What are some examples of non-linear relationships? 2.What are some examples of linear relationships? 3.How do you know that the relationship between degrees F and degrees C is linear?

Action – “Clipping” Along 1.Establish Roles: a) Driver, b) Navigator, c) Recorder d) Time Manager, e) Participant, f) Participant 2.Explore the activity. 3.Select a Big Idea. 4.Form a Learning Goal. 5.Create consolidating questions.

Action – Gallery Walk Individually or with a partner, look at the variety of responses from other groups.

Action – SmartBoards Open Notebook File

Action – Different Algebraic Reps From Nelson Grade 8 Chapter 4, p. 126

Action – Musical Pause 1.Walk until the music stops. 2.Form groups of 3. 3.Answer the question.

Action – Musical Pause Question: 1) What’s the same and what’s different about the models?

Action – Musical Pause Question: 2) Answer the blue question on the sheet.

Action – Musical Pause Question: 3) How does the blue question compare to the questions beneath it?

Consolidate -Gizmos – a relatively new technology -When considering

Gizmos – a relatively new resource Consolidate

Consolidate – Gizmos Interactive PC and MAC (… but) Modifiable Supports Assessment

Consolidate – New Resource a)How does it connect to the big ideas and the math learning goals? b)How can it be used to help overcome the stumbling blocks? c)What open or parallel questions can be asked so that all students have an entry point? d)How can it be used to promote math discourse?

Consolidate - Reflection Three Stars … and a wish!