patterns and algebra k-3 powerpoint

Patterns and

Algebra

KindergartenGrade 3

1

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

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

7

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

9

Non-numerical patterns can be

translated into a letter code (ABBA)

and then extended to make predictions and solve problems.

A AB B

10

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.

11

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

Learning Tasks Repeating Patterns

The Stamping Machine

13

Learning Tasks Repeating Patterns

Rows and ColumnsCyclical Patterns

http://standards.nctm.org/document/eexamples/chap4/4.1/index.htm

14

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?

16

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?

17

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

18

Learning Tasks Increasing/Decreasing Patterns

Critters That Grow

Frame 1 Frame 2 Frame 3 Frame 4

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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.

20


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.

23

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

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

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

3 + 2 = 5

Equality (=) expresses a relationship of balance between numbers.

Inequality () expresses a relationship of imbalance.

3 + 1 5

37

What do

elementary

students think

the equal sign

means?

38

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).

40

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

Learning Task Double Dominos

44

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.

45

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

46

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

47

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?

49

Learning Tasks Whats In the Bag?

50

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?

52

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

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.

54

Each problem that I solved

became a rule which served afterwards

to solve other problems.

RenDescartes

55

patterns and algebra k-3 powerpoint

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