Critical Learning Phases
Understanding Whole Numbers
Use this chart to connect students’ skills to assessments in AMC. Numbers in parentheses correlate to assessment #.
Counting Objects / Number Relationships / Number Composition and Decomposition to 20 / Place Value: Numbers as 10's and 1's / Numbers as 100's, 10's, 1's / Equal Groups· (1) Gets a particular quantity
· (1) Keeps track when counting objects
· (1) Remembers how many after counting
· (8) Counts objects by groups (2's, 5's, 10's, 25's, 100's) / · (1) Knows one more/one less without counting
(2) When changing one number to another:
· tells whether they need to take some away or get some more
· adds on or take away by counting on or removing extras
· knows how many to add or take away
(1) When estimating a number of objects:
· reacts to number estimated while counting
· adjusts estimate while counting and makes a closer estimate
(3) When comparing two different groups:
· uses what is known about one amount to determine another
· adds or takes away from one group to make it the same as another group
· tells how many more
· tells how many less / (4) When working with number arrangements:
· recognizes groups of numbers to 5 in a variety of configurations
· recognizes and describes the smaller parts contained in larger numbers
· identifies one or more parts and counts the rest (counting on)
· combines parts of arrangements by knowing
(5) Uses relationships to combine numbers, such as:
· rearranges (ex: 4+2, moves 1 from the 4 to make 3+3)
· uses doubles plus one/minus one
· uses commutative property
· uses one more or one less for related combinations
· combines numbers by knowing
(6) When decomposing numbers:
· figures out the missing part
· knows the missing part without figuring out
· relates +/-
(7) When organizing numbers into one ten and leftovers:
· tells how many needed to make 10
· knows 10 plus any number up to 10
· tells how many leftovers when removing ten in numbers from 11-20
· uses knowledge of plus 10 to add 9
· combines quantities by reorganizing them into one ten and leftovers
· Breaks apart tens when necessary and reorganizes what is left into a ten and leftovers / · (8) Forms and counts groups of 10
· (8) Instantly knows total when number of tens and ones is known
· (8) Knows 10 more/10 less for any two-digit number
· (9) Uses what is known about numbers to 10 to solve problems using larger numbers
· (9) Combines quantities by forming new tens when necessary
· (9) Rearranges (ex: for 29+31, moves the 1 to get 30+30)
· (9) Can determine the difference between numbers by counting up by tens and ones
· (9) Can subtract by using what is known about addition
· (9) Subtracts by breaking up tens when necessary
· (9) Uses compensation (ex: 42-18 is the same as 44-20)
· (9) Uses related combinations (ex: 75-25 is 50 so 75-26 is 49) / · Instantly knows total when 100's, 10's, 1's are known
· Knows 100 more/less
· Knows all the ways that 100 can be decomposed into groups of 10
· Instantly knows he total when the number of tens is greater than 10 (ex: 17 tens is 170)
· Can decompose 100 into groups of tens and ones
· Tells how many needed to make the next hundred
· Combines quantities by forming new 10's and 100's when necessary
· Uses what is known about numbers to ten to solve problems using large numbers (ex: 2+8=10 so 200+800=1000)
· Combines quantities into minimal groups of 100's, 10's, 1's (ex: 19 tens and 43 ones is 233)
· Computes by rearranging
· Can determine the different by counting up from one number to another by 100's, 10's, 1's
· Separates numbers by breaking up tens and hundreds and reorganizing what is left
· Can use compensation to subtract / · Forms and counts equal groups
· Partitions an amount into equal groups and leftovers
· Analyzes arrays in terms of equal groups
· Recognizes relationship between groups such as 3 groups of 4 and 4 groups of 3
· Uses relationships such as doubling to use what is known to solve what is not known (ex: if 2x3 is 6 then 4x3 must be 12)
· Relates multiplication and division
From Assessing Math Concepts series by Kathy Richardson