GRADE-LEVEL MILESTONES-OPERATIONS on WHOLE NUMBERS

Operations on Whole Number Progression

Addition and Kinderg 1st Grade 2nd Grade 3rd Grade 4th Grade Subtraction arten Represe Add and subtract within 20 Add and subtract within 1000 nts addition  Counting on  Concrete models or drawings and Making 10 Strategies based on place value, properties subtracti   on with: of operations, and/or the relationship  Decomposing a number leading between addition and subtraction  to a 10 Object  Using relationships between Represent whole-number sums and differences s addition and subtraction. within 100 on a number line diagram   Creating equivalent but easier Finger or known sums. s

 Add within 100 Mental Imag Add two-digit numbers and a one es digit numbers  Drawi Add two-digit numbers and a multiple ngs of 10   Concrete models or drawings Sound s  Strategies based on place value, properties of operations,  and/or the relationship between Acting addition and subtraction out situat  Introduce 100’s Chart ions  Verbal expla natio ns  Expre ssion s  Equati on

Decomp ose numbers less than or equal Handout 4 to 10 into pairs in more than one way.

For any number from 1 to 9, find the number that makes 10 when added to the given number.

Compos e and decomp ose numbers from 11 to19 into ten ones and some further ones. Fluently Fluently add and subtract within 10 Fluently add and subtract within 100 Fluently add and Fluently add and subtract multi-digit add and subtract within 1,000 whole numbers using the standard  Strategies based on place value, subtract Mentally find 10 more or 10 less algorithm within 5 properties of operations, and/or the  Strategies and without having to count relationship between addition and subtraction algorithms based on place value, Mentally add and subtract within 20 properties of operations, and/or the Mentally add/subtract 10 or 100 to/from any relationship between number 100-900 addition and Know from memory all sums of two one-digit subtraction numbers (by the end of the 2nd grade) Solve Solve addition and subtraction word Solve one-and two-step addition and subtraction Solve two-step problems Solve multi-step word problems addition problems within 20 word problems within 100 using the four operations posed with whole numbers and and having whole –number answers  Situations involving adding  Situations involving adding to, taking  Assess subtracti reasonableness of using the four operations to taking apart, and comparing from, putting together, taking apart, and on word answers using mental  Assess reasonableness of problem comparing Use objects, drawings, and computation answers using mental s within  Situations involving lengths that are strategies computation and estimation 10 equations with a symbol for the  unknown number to represent the given in the same units strategies  problem Use  Unknowns in all positions objec ts or  Use drawings and equations with a drawi symbol for the unknown number to represent ngs the problem to repre sent the probl em.

Multiplication and 2nd 3rd Grade 4th Grade 5th grade 6th Grade Division Grade Use Multiply one-digit whole numbers by Multiply a whole number of up to four digits by a Find whole-number addition multiples of 10 in the range 10-90 one-digit whole number quotients of whole to find  Use strategies based on numbers with up to four- the total place value and properties of Multiply two two-digit numbers digit dividends and two- number operations digit divisors of objects Find whole—number quotients and remainders  Use strategies arranged Understand division as an unknown- with up to four-digit dividends and one-digit based on place value, in factor problem divisors properties of rectangu operations, and/or the relationship between lar Relate area to the operations of For all of the above: arrays multiplication and addition multiplication and with up  Use strategies based on place value, division to 5 rows properties of operations, and/or the Illustrate and and up relationship between multiplication and  to 5 division explain the calculation columns  Illustrate and explain the calculation by using by using  Equa  Equations tions  Rectangular arrays  Rect angular arrays  Area models  Area models Fluently multiply and divide within Fluently multiply multi- Fluently divide multi-digit whole 100 digit whole numbers numbers using the standard  Use strategies based on using the standard algorithm properties of operations, and/or algorithm the relationship between multiplication and division Know from memory all products of two one-digit numbers by the end of 3rd grade Solve multiplication and division Solve multiplication and division word problems word problems within 100, involving: involving:  Equal groups  Multiplicative comparison  Arrays  Measurement quantities Solve multi-step word problems posed with Solve two-step problems using the whole numbers and having whole-number four operations answers using the four operations

Handout 4  Assess reasonableness of  Assess reasonableness of answers answers using mental using mental computation and estimation computation and estimation strategies strategies Find all factor pairs for a whole number in the Find the greatest common factor of range 1-100 two whole numbers less than or Determine whether a given whole number in the equal to 100 range 1-100 is a multiple of a given one-digit number Find the least common multiple of Determine whether a given whole number in the two whole numbers less than or range 1-100 is prime or composites equal to 12