1 breakout 2 patterning and algebra building learning goals and consolidating questions
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Breakout 2Patterning and AlgebraBuilding
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.
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Curious ActionsGoals 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
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Multiple Representations
and Generalization
Breakout 2Patterning 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
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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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1 2
3 4 5
• Photos of our work
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So how would a student describe this pattern?
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Growing pattern rule
• additive• iterative
And again…
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Number of blocks = position number x +
Position pattern rule • multiplicative• explicit
Pattern Rules
Growing pattern rule
• additive• iterative
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And, how will we re-present this pattern graphically?
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But for children…• Building a snake that grows
• Copy growing patterns• Extending growing patterns• Translating to a different representation• Creating growing patterns
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Growing Patterns
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1 2 3
1 2 3
copy – extend – represent – create
Your Turn – pick 1, copy, extend
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1 2 3
1 2 3
A
B
write 2 kinds of Pattern Rules and graph it
Growing Pattern Rules
• the starting number?• the value by which the pattern changes?
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Tiles = pattern starts at and grows by
Position Number Pattern Rules
• the constant?• the multiplicative?
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Tiles = position number x +
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NSN ExpectationsKindergarten
•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
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H pattern additions to chart
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Repeating Patterns
Growing Patterns
connections
Developing know
ledge