# GRADE-LEVEL MILESTONES-OPERATIONS on WHOLE NUMBERS by qLq9rW

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```									                                                                                        Operations on Whole Number Progression
with:                                     Counting on                            Concrete models or drawings
 Objects                               Making 10                              Strategies based on place
 Fingers                               Decomposing a number leading            value, properties of operations,
 Mental Images                          to a 10                                 and/or the relationship between
 Drawings                              Using relationships between
 Creating equivalent but easier      Represent whole-number sums and
 Acting out situations                                                      differences within 100 on a number
or known sums.
 Verbal explanations                                                        line diagram
 Expressions
 Equation

Add two-digit numbers and a one
Decompose numbers less than or         digit numbers
equal to 10 into pairs in more than
one way.
Add two-digit numbers and a multiple
of 10
For any number from 1 to 9, find the
 Concrete models or drawings

number that makes 10 when added
to the given number.                       Strategies based on place
value, properties of operations,
and/or the relationship between
Compose and decompose numbers
from 11 to19 into ten ones and some
further ones.                              Introduce 100’s Chart

Fluently add and subtract within 5     Fluently add and subtract within 10     Fluently add and subtract within 100   Fluently add and subtract within       Fluently add and subtract multi-digit
 Strategies based on place value,     1,000                                  whole numbers using the standard
Mentally find 10 more or 10 less           properties of operations, and/or      Strategies and algorithms based     algorithm
without having to count                    the relationship between addition      on place value, properties of
and subtraction                        operations, and/or the
Mentally add and subtract within 20       subtraction
to/from any number 100-900
Know from memory all sums of two
one-digit numbers (by the end of the
Solve addition and subtraction word    Solve addition and subtraction word     Solve one-and two-step addition and    Solve two-step problems using the      Solve multi-step word problems
problems within 10                     problems within 20                      subtraction word problems within 100   four operations                        posed with whole numbers and
 Use objects or drawings to            Situations involving adding to          Situations involving adding to,       Assess reasonableness of            having whole –number answers
represent the problem.                taking apart, and comparing              taking from, putting together,          answers using mental               using the four operations
 Use objects, drawings, and               taking apart, and comparing             computation strategies               Assess reasonableness of
equations with a symbol for the         Situations involving lengths that                                              answers using mental
unknown number to represent the          are given in the same units                                                    computation and estimation
problem                                                                                                                 strategies
 Unknowns in all positions
 Use drawings and equations with
a symbol for the unknown number
to represent the problem

Handout 4
Use addition to find the total number   Multiply one-digit whole numbers by      Multiply a whole number of up to four   Find whole-number quotients of
of objects arranged in rectangular      multiples of 10 in the range 10-90       digits by a one-digit whole number      whole numbers with up to four-digit
arrays with up to 5 rows and up to 5      Use strategies based on place                                                 dividends and two-digit divisors
columns                                    value and properties of                                                         Use strategies based on place
Multiply two two-digit numbers
operations                                                                        value, properties of operations,
and/or the relationship between
Find whole—number quotients and             multiplication and division
Understand division as an unknown-       remainders with up to four-digit
factor problem                           dividends and one-digit divisors          Illustrate and explain the
calculation by using
Relate area to the operations of                                                       Equations
For all of the above:
multiplication and addition                                                            Rectangular arrays
 Use strategies based on place
value, properties of operations,         Area models
and/or the relationship between
multiplication and division
 Illustrate and explain the
calculation by using
 Equations
 Rectangular arrays
Multiplication and Division

 Area models
Fluently multiply and divide within                                              Fluently multiply multi-digit whole    Fluently divide multi-digit whole
100                                                                              numbers using the standard             numbers using the standard
 Use strategies based on                                                       algorithm                              algorithm
properties of operations, and/or
the relationship between
multiplication and division
two one-digit numbers by the end of
Solve multiplication and division        Solve multiplication and division
word problems within 100, involving:     word problems involving:
 Equal groups                            Multiplicative comparison
 Arrays
 Measurement quantities                Solve multi-step word problems
Solve two-step problems using the        posed with whole numbers and
four operations                          having whole-number answers using
the four operations
 Assess reasonableness of
answers using mental                 Assess reasonableness of
computation and estimation              answers using mental
strategies                              computation and estimation
strategies
Find all factor pairs for a whole                                              Find the greatest common factor of
number in the range 1-100                                                      two whole numbers less than or
Determine whether a given whole                                                equal to 100
number in the range 1-100 is a
multiple of a given one-digit number                                           Find the least common multiple of
Determine whether a given whole                                                two whole numbers less than or
number in the range 1-100 is prime                                             equal to 12
or composites

Handout 4

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