Patterns and Algebra K-3 PowerPoint
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Patterns and
Algebra
KindergartenGrade 3
1
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Why Teach Patterns and Algebra?
Working with patterns enables students
to make connections both within and
beyond mathematics.
Through the study of patterns, students come to
interpret their world mathematically and value
mathematics as a useful tool.
3
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5
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Kindergarten actions, sound, colour, size, shape, orientation
Grade 1 diagrams and events
Grade 2 focus on attributes and numbers
Grade 3 expressed as concrete, pictorial, symbolic
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Pattern Puzzles
Select an attribute card
Make a core unit with 35 elements, using this attribute
(big, big, small)
(square, triangle, triangle)
(yellow, blue, red)
Repeat the pattern 2 more times
Ask your partner to describe your pattern
Learning Tasks
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Non-numerical patterns can be
translated into a letter code (ABBA)
and then extended to make predictions and solve problems.
A AB B
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Learning Tasks Translating Patterns
Mix and Match
Create a 2- to 4-element core, using your choice of materials; e.g., colour, orientation, size.
Extend your pattern 2 more times.
Find someone else in the room with the same pattern code.
These are both
AABB patterns.
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Patterns can be repeating and made up of a core set of elementsa core unit that is iterated.
Patterns can be increasing or decreasing and created by orderly change.
9 7 5 3
32 16 8 4 212
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Learning Tasks Repeating Patterns
The Stamping Machine
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Learning Tasks Repeating Patterns
Rows and ColumnsCyclical Patterns
http://standards.nctm.org/document/eexamples/chap4/4.1/index.htm
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Learning Tasks
Predicting Patterns
Making the link between repeating and increasing patterns
2 31
5 10 15
a) What would the 20th shape be?
b) What would the 30th shape be?
c) What would the 32nd shape be?
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Learning Tasks
5
2 31
10 15
30 31 322515105 20
2 322717127 22
30 32 33 34 352515105 20
What would the
32nd shape be?
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Learning Tasks
5
2 31
10 15
a) Create a pattern in which the 20th shape is a .
b) Create a pattern in which the 12th shape is a .
c) Create a pattern in which the 6th and 9th shapes are both .
Your Turn
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Learning Tasks Increasing/Decreasing Patterns
Critters That Grow
Frame 1 Frame 2 Frame 3 Frame 4
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Learning Tasks Increasing/Decreasing Patterns
Frame 1 Frame 2 Frame 3 Frame 4
legs 2 4 6 8 ?
body parts 1 2 3 4 5
Add 2 legs each time, skip count
by 2 (recursive), legs go up by
twos, bodies go up by ones.
Look at relationships across
categories (function), double
the body parts.
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Learning Tasks Increasing/Decreasing Patterns
Note: Caterpillars, Worms and Pattern Block Trees are adapted from Lessons for Algebraic Thinking: Grades K2, pp. 211, 8998, 157170, by Leyani von Rotz and Marilyn Burns. Copyright 2002 by Math Solutions Publications.
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A pattern rule must account for all elements of a pattern,
including the first one.
Body Parts 4 7 10 13 ? ? ?
Age 1 2 3 4 5 10 100
Body parts: Start at 4 and add 3 each time
Age: Start at 1 and add 1 each time
Relationship: Body parts3 times the age plus 125
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Two of Everything by Lily Toy HongIllustrations on slides 27 to 36 and text on slides 28 to 34 are reproduced from Two of Everything by Lily Toy Hong. Copyright 1993 by
Lily Toy Hong. Excerpts reprinted by permission of Albert Whitman & Company. All rights reserved. 27
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28
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29
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30
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31
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32
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33
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34
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35
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Would you rather have a doubling pot
and a loonie, if you could only use
the pot ten times, or$1 000?Note: Excerpted and reprinted with permission from National Council of
Teachers of Mathematics. (2003). Reflections. Retrieved November 20,
2006, from http://my.nctm.org/eresources/reflections, copyright 2003 by
the National Council of Teachers of Mathematics. All rights reserved.
Create your own magic pot. Make up
a pattern rule for your pot. Show
what happens on an in-out chart.Note: Adapted from Lessons for Algebraic Thinking: Grades K2, by
Leyani von Rotz and Marilyn Burns. Copyright 2002 by Math Solutions
Publications.
36
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3 + 2 = 5
Equality (=) expresses a relationship of balance between numbers.
Inequality () expresses a relationship of imbalance.
3 + 1 5
37
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What do
elementary
students think
the equal sign
means?
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Equality and inequality between quantities can be considered as:
whole to whole relationships (5 = 5) partpart to whole relationships (3 + 5 = 8) whole to partpart relationships (8 = 5 + 3) partpart to partpart relationships (4 + 4 = 3 + 5).
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4 + 5 = + 3
Note: From Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School, by T. P. Carpenter, M. L. Franke and
L. Levi, 2003, Portsmouth, NH: Heinemann. Copyright 2003 by the authors. Reprinted with permission. 43
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Learning Task Double Dominos
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Mini Lessons True/False
3 + 5 = 8
8 = 3 + 5
8 = 8
3 + 5 = 5 + 3
3 + 5 = 4 + 4
Developing an
understanding of
the equal sign
Note: From Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School (p. 4), by T. P. Carpenter, M. L. Franke
and L. Levi, 2003, Portsmouth, NH: Heinemann. Copyright 2003 by the authors. Reprinted with permission.
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Other True/False Contexts
9 + 5 = 14
9 + 5 = 14 + 0
9 + 5 = 0 + 14
9 + 5 = 14 + 1
9 + 5 = 13 + 1
Using zero to introduce
part-part = part-part
equations
How could you change the false statements so that they are true?
Place Value
56 = 50 + 6
87 = 7 + 80
93 = 9 + 30
94 = 80 + 14
94 = 70 + 24
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Challenge
Determine if these equations are
true or false without calculating the
actual sum or difference. Use
relational thinking!
37 + 56 = 39 + 54
33 27 = 34 26471 382 = 474 385674 389 = 664 379583 529 = 83 29
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Join
Result Unknown
Connie had 15
marbles. Juan gave
her 28 more
marbles. How many
marbles does
Connie have
altogether?
Change Unknown
Connie has 15
marbles. How many
more marbles does
she need to have 43
marbles altogether?
Start Unknown
Connie had some
marbles. Juan gave
her 15 more
marbles. Now she
has 43 marbles.
How many marbles
did Connie have to
start with?
Separate
Connie had 43
marbles. She gave
15 to Juan. How
many marbles does
Connie have left?
Connie had 43
marbles. She gave
some to Juan. Now
she has 15 marbles
left. How many
marbles did Connie
give to Juan?
Connie had some
marbles. She gave
15 to Juan. Now she
has 28 marbles left.
How many marbles
did Connie have to
start with?
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Learning Tasks Whats In the Bag?
50
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Equalization
and
Compare
Difference
Unknown
Connie has 43
marbles. Juan has
15 marbles. How
many more marbles
does Connie have
than Juan?
(Compare)
How many more
marbles does Juan
need to have as
many as Connie?
(Equalize)
Quantity Unknown
Juan has 15
marbles. Connie
has 28 more than
Juan. How many
marbles does
Connie have?
Referent Unknown
Connie has 43
marbles. She has
15 more marbles
than Juan. How
many marbles does
Juan have?
Part-Part-
Whole
Quantity Unknown
Connie has 15 red marbles and
28 blue marbles. How many
marbles does she have?
Part Unknown
Connie has 43 marbles. 15 are
red and the rest are blue. How
many blue marbles does Connie
have?
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Mini Lessons Open Number Sentences
The teacher writes an open-number sentence on the board and asks
the students how to make the statement true. Students can justify
their responses; e.g., using balance models, comparing distances on
a number line.
3 + 5 =
8 = 3 +
8 =
3 + 5 = + 3
3 + 5 = + 453
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Note: From Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School, by T. P. Carpenter, M. L. Franke and
L. Levi, 2003, Portsmouth, NH: Heinemann. Copyright 2003 by the authors. Reprinted with permission.
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Each problem that I solved
became a rule which served afterwards
to solve other problems.
RenDescartes
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