
This book was created and published on StoryJumper™
©2014 StoryJumper, Inc. All rights reserved.
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Text Reflection
Chapters 14, 15, 16, 17




My teacher wants me to read this book and show what I learned. I
could do this on a simple word document, but everyone knows a
ballerina always has to sparkle and go above and beyond. So,
today I'm going to outline four chapters for you in a creative and fun
way. I hope your ready!!!!





Chapter 14
Algebraic Thinking:
Generalizations,
Patterns, and
Functions

The Big Idea of Algebra:
o Algebra is a useful tool for generalizing arithmetic and representing patterns
and regularities in our world
o Symbolism, especially involving equality and variables, must be well understood
conceptually for students to be successful in mathematics, particularly algebra
o Methods we use to compute and the structure in our number system can and
should be generalized. For example, the generalization that a + b= b + a tells us that
83 + 27 = 27 + 83 without computing the sums on each side of the equal sign.
o Patterns, both repeating and growing, can be recognized, extended, and generalized.
o Functions in K-8 mathematics describe in concrete ways the notion that for every
input there is a unique output
o Understanding of functions is strengthened when they are explored across
representation, as each representation provides a different view of the same
relationship


said that Algebraic thinking begins in prekindergarten
and continues through high school.
The book states algebraic thinking happens in
prekindergarten, because students recognize
and duplicate simple sequential patterns.
(triangle, square,circle, triangle, square circle)



The Meaning of the Equal Sign
The equal sign is one of the most important symbols in
elementary arithmetic, in algebra and in all mathematics
using numbers and operations. So why is it so important
that students correctly understand the equal sign?
First, it is important for students to understand and
symbolize relationships in our number systems. The equal
sign is a principal method of representing these
relationships.
A second reason is that when students fail to understand
the equal sign, they typically have difficulty with algebraic
expression.


Odd and Even Relationships
I found the section in the book about odd and even
numbers interesting. What I never really realized
was that:
The sum of two even numbers is even,
The sum of two odd numbers is even
but.....
The sum of an even and an odd number is always
odd!!!
I found this very fascinating.




Formative Assessment
I love how the book gives ways to assess students learning. The
one assessment I liked was on graphs. The book states:
Being able to make connections across representations is
important for understanding functions, and the only way to know
if a student is seeing the connections is to ask. In a diagnostic
interview, ask students the following question and see whether
students are able to link the graph to the context, to the table,
and to the formula.
1. How does each graph represent each of the string
patterns?
2. Why is there not a line connecting the dots?
3. Why is one line steeper than the others?
4. What does this particular point on the graph match
up to in the mood and the table?

Patterns
Through geometric patterns and motions like clapping are
good ways to introduce patterns, it is important that
students see patterns in the world around them. I like how
the book relates patterns to everyday life like seasons,
days of the week, months of the year. Once students make
these connections they can then make other patterns in
their daily activities such as going to school, going home
from school, or setting the table before eating.



The textbook gives three examples of books that are
excellent beginnings for patterns and chart building.
Anno's Magic Seed- This book has several patterns in
it. It's a good book to develop charts and extend the current
patterns into the future. Can be used for 6th and 7th
graders.
Bats on Parade- This story includes the patterns of bats
walking 1 by 1, then 2 by 2, and so on. It's a good book to
determine growing patterns of the number of bats given the
array length.
Two of Everything: A Chinese Folktale- This book
is good for input- output idea. Whatever goes in doubles.
Good for grades 2nd- 8th.





Chapter 15
Developing Fractions
Concepts


The Big Ideas
1. For students to really understand fractions, they
must experience fractions across many constructs,
including part of a whole, ratios, and division.
2. Three categories of modes exist for working with
fractions- area, length, and set or quantity.
3. Partitioning and iterating are ways for students to the
meaning of fractions, especially numerators and
denominators.
4. Students need many experiences estimating with
fractions.
5. Understanding equivalent fractions is critical. Two
equivalent fractions are two ways of describing the
same amount by using different- sized fractional parts.

Why Are Fractions So Difficult?
Based on research, there are a number of reasons students
struggle with fractions. They include:
1. There are many meanings of fractions
2. Fractions are written in an unusual way.
3. Instruction does not focus on a conceptual
understanding of fractions.
4. Students overgeneralize their whole- number
knowledge.



I think its great that the book gave an entire list of area models. The
ones most people are familiar with are circular "pie"pieces. These area
models emphasize the part-whole concept fractions and the meaning of
the relative size of a part to the whole. My favorite area model to use as
a student were pattern blocks. I remember my teachers having us
create cool designs with these blocks to teach us about shapes.



One thing that I learned and is going to help me out is to
not call fractions improper fractions. Improper fractions
describe a fraction such as 5/ 2 or a fraction that is
greater than one. Using improper can be a misconception
and can confuse students. Instead of saying improper
fraction it can be termed as a "fraction greater than 1."
Explain to students that they should change there
fractions greater than 1 into mixed number.



Fun with Fractions is an excellent set of three units. Each unit uses
one of the model types: area, length, or set. The units focuses on
comparing and ordering fractions and equivalences. The five to six
lessons in each unit incorporate a range of manipulatives and
engaging activities to support students learning.
Area Model Unit:
http://illuminations.nctm.org/LessonDetail. aspx?id=U113
Set Model Unit:
http: //illuminations.nctm.org/LessonDetail.aspx?id=U112
Lenght Model Unit:
http://illuminations.nctm.org/LessonDetail.aspx?id=U152



Chapter 16
Developing Strategies for
Fraction Computation

Big Ideas
1. The meanings of each operation with fractions are the same as the
meanings for the operations with whole numbers. Operations with
fractions should begin by applying these same meanings to fractional
parts.
*For addition and subtraction, the numerators tells the number of
parts and the denominator the unit. The parts are added or
subtracted.
*Repeated addition and area models support development of
concepts and algorithms for multiplication of fractions.
*Partition and measurements models lead to two different thought
processes for division of fractions
2. Estimation should be an integral part of computation development
to keep student's attention on the meanings of the operations and the
expected sizes of the results.
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This book was created and published on StoryJumper™
©2014 StoryJumper, Inc. All rights reserved.
Publish your own children's book:
www.storyjumper.com


Text Reflection
Chapters 14, 15, 16, 17




My teacher wants me to read this book and show what I learned. I
could do this on a simple word document, but everyone knows a
ballerina always has to sparkle and go above and beyond. So,
today I'm going to outline four chapters for you in a creative and fun
way. I hope your ready!!!!





Chapter 14
Algebraic Thinking:
Generalizations,
Patterns, and
Functions
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