1 Breakout 2 Patterning and Algebra Building Learning Goals and Consolidating Questions

Curious Actions … or is there? Identify a recorder. Brainstorm “goals” that may have motivated each “Curious Action”. Recorder be ready to report. 2

Curious Actions Goals and Actions Learning goals ensure we: engage students in significant mathematical thinking know what to look for in student work can identify the mathematical thinking know what questions to pose to focus student thinking 3

4 Multiple Representations and Generalization Breakout 2 Patterning and Algebra

Session Goals Study and re-present growing patterns Practice instructional sequence – copy, extend, translate, create Appreciate the use of building mats and position cards to identify patterning concepts Write growing pattern rules (additive, iterative def’n) Write position pattern rules (multiplicative thinking, explicit def’n) Matching thinking to generalizations strategies chart 5

6 You will need building mats position cards square tiles How many “animals, fish or insects” at the pond at each stage? Represent the pattern.

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99 Heather’s Notebook page is on the wiki as a separate file.

Pattern Rules Growing pattern rule additive iterative Position pattern rule multiplicative explicit 10

And, how will we re-present this pattern graphically? 11

But for children… Building a snake that grows Copy growing patterns Extending growing patterns Translating to a different representation Creating growing patterns 12

Growing Patterns copy – extend – represent – create Note: We discussed in Breakout how these patterns should have started at zero and too the ones on the next slide

Your Turn – pick 1, copy, extend A B write 2 kinds of Pattern Rules and graph it

Growing Pattern Rules the starting number? the value by which the pattern changes? 15 Tiles = pattern starts at and grows by

Position Number Pattern Rules the constant? the multiplicative? 16 Tiles = position number x +

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NSN Expectations Kindergarten quantity relationships; counting; operational sense Grade 1 demonstrate, using concrete materials, the concept of one-to-one correspondence between number and objects when counting Grade 2 count forward by 1’s, 2’s, 5’s, 10’s, and 25’s to 200, using number lines and hundreds charts represent and explain, through investigation using concrete materials and drawings, multiplication as the combining of equal groups Grade 3 count forward by 1’s, 2’s, 5’s, 10’s, and 100’s to 1000 from various starting points, and by 25’s to 1000 starting from multiples of 25, using a variety of tools and strategies Grade 4 connect each term in a growing or shrinking pattern with its term number, and record the patterns in a table of values that shows the term number and the term create a number pattern involving addition, subtraction, or multiplication, given a pattern rule expressed in words 18

Create your Own Think of a linear growing pattern. Show the second term of your pattern on building mat 2. Ask your partner… –What rule describes this pattern? –Build the term for position 1 and position 3? 19

H pattern additions to chart 20 Repeating Patterns Growing Patterns connections Developing knowledge