Educ 325 Developing Whole Number Operations and Reading
Fluency
October 4Educ 325 Developing Whole Number Operations and Reading
FluencyDeveloping Operation Sense Recognizing real-world settings
for each operationDeveloping an awareness of models and properties
of each operationRecognizing relationships among the
operationsUnderstanding the effects of an operationCurriculum Focal
PointDevelop strategies for adding and subtracting whole numbers on
the basis of earlier work with small numbers (digits 0-9)Use a
variety of models, including discrete objects, length-based models
(e. g., lengths of connecting cubes), and number lines, to model
part-whole, adding to, taking away from, and comparing situations
to develop an understanding of the meanings of addition and
subtraction and strategies to solve such arithmetic
problemsIntroduce Operations with Word Problems Learning about
operations should be based on meaning and understandingThis begins
with an exploration of real world settings or story
problemsChildren have already constructed meaning for mathematical
operations before they enter school through real-life, informal
experiences such as sharing cookies or combining collections of
cars or BarbiesReal Life Word ProblemsAllow students to see more
personal relevance which enables them to more easily analyze the
problem and its component parts Routine, opening activities like
the calendar can provide problem contextsChildrens literature,
classroom events, and sharing materials all provide meaningful,
engaging problem contextsModel for introducing word
problemsUnderstanding Addition and Subtraction Types of Problems
(pp. 132-133)Join Problems items are added or joined to a setthe
starting amount, the change amount, and the resulting
amountSeparate Problems items are removed from a setthe starting
amount, the change amount, and the resulting amount
More problem typesPart-Part-Whole problems there is no action
but rather a relationship between a set and its two subsetsInvolves
three quantities, the whole and two partsCompare Problems there is
no action, instead they involve comparisons between two different
setsThree quantities are two wholes and a differenceUsing models to
solve addition and subtraction problemsDirect Modeling using real
world materials or concrete manipulatives
Using Measurement Models (p. 136) - lengths are used to
represent quantities in the problemAFTER MUCH MODELING Writing
Number Sentences p. 137Understanding Multiplication and
DivisionFundamentally different from addition and subtraction due
to the different types of quantities represented
Problem 1: Peter has 2 cookies Amy gives him 3 more. How many
cookies does Peter have now?
Problem 2: Peter has 2 bags with 3 cookies in each bag. How many
cookies does Peter have?
How are problems similar and different?Both have numbers 2 and 3
but what do the numbers 2 and 3 represent in each problem?
Multiplication is more complex because there are more factors to
pay attention to
Multiplication also requires a different type of countingMaking
transition from Adding to MultiplyingEncourage children to use the
phrase groups of to indicate creating a number of EQUAL GROUPSHelp
children understand the meaning of each quantity
2 x 3 is two groups of 3 objects3 x 2 is three groups of 2
objectsTypes of Multiplication ProblemsEqual groups problem based
on making a certain number of equal-sized groupsThe three numbers
in the problem represent the number of groups, the size of groups,
and the total number of objectsArea and Array problems finding the
area of a rectangular region or finding the total number of objects
in a rectangular displayArea can be found by counting OR by
multiplying the length by the widthMultiplicative Comparison
Problem involves comparing two quantities multiplicativelyDescribe
how many times as much one quantity is compared to another
Combination problems involves different combinations that can be
made from sets of objects Most difficult type of multiplication or
division problem to modelIntroducing children to divisionClarity
and familiarity of language used in division problems is very
importantChildren experience division throughout their everyday
life but they might not recognize it when they are sharing food or
toys with othersUse familiar language such as shared by or equal
groups to make sense in children before ever introducing term
divided byDivision with RemaindersChildren experience real life
situations with remainders in sharing cookies and having some left
over engage in discussion about what to do with the cookie that is
left overThis can lead to discussions about what to do with
leftovers in divisionSometimes leftovers will just be set aside and
sometimes it may be appropriate to make unequal groups (put 5
children in one car and 4 children in the other)Types of Division
ProblemsEqual Groups Problems splitting a larger group into several
smaller groupsThe three numbers represent the number of groups, the
size of the groups, and the total number of objects
PARTITIVE division problems total number of objects is
partitioned into a specific number of groups also known as fair
sharing
MEASUREMENT division problems total number of objects is
measured out into groups of a certain size also known as repeated
additionArea and Area problems- involve finding one of the
dimensions of a rectangular region or rectangular array when the
total number of objects in the arrangement is given Multiplicative
Comparison problems how many times as much one quantity is compared
to another quantity, is known, as is one of the quantities being
comparedEric ate twice as many cookies as Patrick did. If Eric ate
twice 18 cookies, how many cookies did Patrick eat?Combination
problems involve different combinations that can be made from sets
of objects, such as the number of outfits that can be made from 2
shirts and 3 pairs of pants. In division, the total number of
combinations is known, as the number of one of the objects being
combinedHow many pairs of pants are needed to make 6 different
outfits by using 2 shirts?Modeling to Solve Multiplication and
Division problemsPp. 143-144
Key Language Terms pp. 146
