Patterning & Algebra Transitioning through grades 7 to 9 Kerri Everhsed I’m thinking of a pattern…

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Presentation transcript:

Patterning & Algebra Transitioning through grades 7 to 9 Kerri Everhsed I’m thinking of a pattern… It starts like this 2, 6, … What am I thinking of?

Let’s Explore Vocabulary Changes across curriculum My Ah-ah moment: Deeper understanding: visuals to expressions to graphs Resources

Vocabulary of strands

What Vocabulary Do you use? ?? Term Number Term Value vn Output Input CostTime yx

What Vocabulary Do you use? Term number Term value Pattern rule Constant Vertical pattern First difference Iterative rule The number the pattern increases by Then this number becomes a …coefficient, multiplier, part of the horizontal pattern, slope, ‘m’ and rate of change Then… 3n – 1

The confusing use of the word ‘constant’ “Linear” in grade 1 and 3 it is in Measurement, then re- appears in grade 7 New to grade 8 balancing of equations, in grade 9 (1D) called rearrange Solving by Substitution (the formal use of term) New to grade 9 slope, direct/indirect variation, fractional or negative slopes, POI Distribution of monomial to polynomial Curriculum Grade 5,6,7 Grade 4

Painting Towers Suppose you build a tower of interlocking cubes. You must paint every square on all four sides of the tower, as well as the top. You don't have to paint the base of the tower How many squares do you have to paint? What is the relationship between the height of the tower and the number of squares to paint? Can you determine how many squares need to be painted on a tower that is: 10 cubes high? 50 cubes high? 99 cubes high?

What’s the pattern? Where is the 5 in your pattern? Where is the 2 in your pattern? Explain the pattern From: Lessons for Algebraic Thinking

Investigating all parts of a pattern Describe the pattern How does it relate to the pattern rule? *Modified from Patterns to Algebra Task 1 pg 64 4x + 2

Find the pattern… and identify all parts Video 1VideoVideo 2 First triangle has a side length of 4, then 6 and then 8. How many dots are Required for a 20-dot-sided triangle? 4-sided 6-sided 8-sided ImageImage 1 ImageImage 2

Negative Constants 2n – 1 Representing increasing linear patterns with visuals and identifying all components is easier when the constant is being added. How do you show the pattern 2n – 1 visually?

Word Problems Bowling Dilemma A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 Used in Grade 6,7,8 Using the graph to support solution