Strand/Topic: Patterning and Algebra Grade: 5 Date: October 18, 2011 Expectations: Overall: - determine, through investigation using a table of values, relationships in growing and shrinking patterns, and investigate repeating patterns involving translations Specific: - create, identify, and extend numeric and geometric patterns, using a variety of tools (e.g., concrete materials, paper and pencil, calculators, spreadsheets); (http://www.n5tn.com/eng/curriculum/elementary/math18curr.pdf) Is there a Connection for Students? Connections to other Curricular Areas? Patterns identified in every day life Visual arts tessellations Equity/ Diversity and Social Justice (Teacher Actions) Tessellations ensure that it is clear that not all students need to have an interest in visual arts in order to succeed Instruction will alter and/or differentiate based on the need to address individual learning styles and/or abilities. This will be accomplished with the use of visuals, manipulatives, explanations, and possible review of prior knowledge. Individual and group work will also be implemented in order to achieve this. Questions to Ask Accommodations/ Modifications (content/process/product) Materials
Part 1: Minds Concept Attainment: Identifying patterns I am going to start to organize patterns into yes category and non patterns into no category" have the class identify what categories we are establishing (have patterns on certain coloured paper) In the YES column, mathematical patterns will be placed, and in the NO column those visuals and/or number representations that are not patterns will appear Have students then identify the remaining examples as patterns and not patterns (all numerical up to this point) To make it more engaging, introduce a series of visual patterns (tessellations (M.C. Escher, geometric, etc) Hand out with explanation of testers rules and why they are or are not a pattern (if needed) E.g. of Testers: What do you think these examples represent? Why are these considered patterns? How are the visual patterns a representation of a mathematical pattern? Can you give me an example of a numerical pattern? Is there only one rule to mathematical patterning? Manipulatives Paper and pens Recognizable patterns that should be understood from prior knowledge (eg 2,4,6,8,10 ) Provide hand out that explains each examples rule and why it is a pattern Chalk and chalk board Examples Masking tape Coloured paper (red, yellow, blue) (1, 4, 7, 10, 13, 16 ) (2, 4, 8, 16, 32 ) (3, 6, 9, 12, 15 ) (1, 5, 4, 12, 26) How do you find the patterning rule for each example? Compare to each other? (http://mathworld.wolfram.com/tessellation.html) (http://jbkk.blogspot.com/2009/06/mc-escher-tessellations.html) s
Part 2: Action 30 minutes Indentifying Mathematical Patterns Key Ideas: Geometric shapes and recognizing how to form a pattern Linear relationships Continuing the pattern whether it is numerical or created from geometric shapes and/or tessellations Able to solve patterning through recognition and algebra Base ten blocks Multiple solutions (if applicable) COMPLETE THE FOLLOWING: 1. Individual a. Create a numerical pattern, different from those on the board and that involves multiplication or division OR b. Create a visual pattern using manipulatives (patterned cubes provided by teacher) 2. Pairs/ Trio a. Solve each others patterns students switch their work with a partner who as chosen to do a different activity from their own (student who completes a) switches with student who has completed b.) - students will work individually to find the pattern in their partners work b. Put patterns and written solutions on chart paper (be sure all explanations are clear and concise) 3. Extend a. Record all possible solutions to solving patterns b. Ensure that each member is prepared to and able to explain all solutions gathered 4. All students post work for sharing a. Gallery walk to occur on following day How did you find the solution to the problem? What strategies were used? Did algebra prove to be helpful? What other strategies could you have used? Why did you choose your strategy? Are you able to continue the pattern? Manipulatives Assigning roles in pairs Providing more examples Showing ways of solving Markers Chart paper Masking tape manipulatives Graph paper (for students individual work) Base ten blocks Patterned cubes
Part 3: Consolidate Debrief 10 minutes Key Ideas: Organization Clear Have students create a pattern, with a set of numbers provided by the teacher. Have students continue and/or finish a pattern proposed by the teacher (using shapes) Additional problems will be handed out in the form of handouts/ worksheets Questions to Ask Accommodations / Differentiation (content/process/product) Manipulatives What is similar about this problem compared to the ones previously looked at? What are the differences? More examples Think pair share Materials Base ten blocks Hand outs Assessment Tools (diagnostic/formative/summative) Diagnostic what do the students know, do they have any misconceptions, are they familiar with the appropriate math vocabulary, are they able to recognize a pattern Formative what strategies are they implementing, can they use algebra to solve a pattern problem, can they recognize a pattern in geometric shapes, do they understand why algebra is more efficient in solving patterns than trial and error Next Steps review of concepts ensure they understand by assigning homework and allowing them to write a math journal entry on patterning and algebra extend to creating tessellations as an in class assignment Self Reflection What went well? What didn t go so well? What do I need to change? Work Cited: http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf http://cemc2.math.uwaterloo.ca/mathfrog/english/kidz/games5.shtml (worksheets obtained from this cite as well)