Ottawa Bansho



Basho - Patterning - Grade 6Overall ExpectationsBy the end of Grade 6, students will:? describe and represent relationships in growing and shrinking patterns (where the terms are whole numbers), and investigate repeating patterns involving rotations;? use variables in simple algebraic expressions and equations to describe relationships.Specific ExpectationsPatterns and RelationshipsBy the end of Grade 6, students will:– identify geometric patterns, through investigation using concrete materials or drawings, and represent them numerically;– make tables of values for growing patterns, given pattern rules in words (e.g., start with 3, then double each term and add 1 to get the next term), then list the ordered pairs (with the first coordinate representing the term number and the second coordinate representing the term) and plot the points in the first quadrant, using a variety of tools (e.g., graph paper, calculators, dynamic statistical software);– determine the term number of a given term in a growing pattern that is represented by a pattern rule in words, a table of values, or a graph (Sample problem: For the pattern rule “start with 1 and add 3 to each term to get the next term”, use graphing to find the term number when the term is 19.);– describe pattern rules (in words) that generate patterns by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term (e.g., for 1, 3, 5, 7, 9, ..., the pattern rule is “start with 1 and add 2 to each term to get the next term”), then distinguish such pattern rules from pattern rules, given in words, that describe the general term by referring to the term number (e.g., for 2, 4, 6, 8, ..., the pattern rule for the general term is “double the term number”);– determine a term, given its term number, by extending growing and shrinking patterns that are generated by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term (Sample problem: For the pattern 5000, 4750, 4500, 4250, 4000, 3750, ..., find the 15th term. Explain your reasoning.);– extend and create repeating patterns that result from rotations, through investigation using a variety of tools (e.g., pattern blocks, dynamic geometry software, geoboards, dot paper).Lesson Plan:Review 3 types of patterns (growing, shrinking and repeating) - Do You Remember (Nelson Textbook)Do grade 4 question 1 (added feature: represent pattern in a graph)Question 1:(Consolidation for grade 5 - tables are most efficient – split grade)Consolidation for grade 6 - table represents coordinates on a graph (x,y); patterns are representations of graphs- *Need worksheets here*Patterning with Patty (go through interactive video as a class): 2 – Have grade 6’s graph both grade 4 student and 5 student questions (total tiles only) lines on same graphQuestion 2:Consolidation: Looking at both lines on one graph, with same x and y axis, see how the slope changes for both equations (this is why it is important that x and y axis are going up by same increments, so we can compare equations.Teacher Directed – As a class check out the interactive videos, then work on math sheets.Pattern rules a Graphic Representation Patrick (as a class): sheets – Charts to graphs (one step or two)Consolidation: Charts to graphs – difference between y = x + 1, and y = x + 3 (affects where line intersects with y-axis; and y = X x 2 and y = X x 3 (Affects the slope)Question 3 - Solve grade 5 problem using graph onlyQuestion 3:Question 4 – Handshake questionQuestion 4:Consolidation – graph can go up or down? Is there a straight line? Which graph is a better representation of the question (or the answer)Solve question - Question 5 – Coffee Question Question 5:Consolidation: common errors, using the “0” – does graph line always have to go to the zero? (no, you bring the line to the y-axis)review y=mx + b (m changes steepness, b changes position on graph) Question 6 – Can questionGuide question... (From: A Guide to Effective Instruction in Mathematics – Patterning and Algebra)Testing/EvaluationNotes to Myself:Note: I would like to have a “constant” question (change how we say the rule) to do as a classNote: Test :I would a graphing question specifically in “Application”.I would like a “Thinking” question (a student made the following graph – they decided the formula is this... Is the student correct? I would like a question turning t-charts into “y = “ formulas (added to Thinking) ................
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