K-2+ Assessments

The nine assessments are:

Critical Learning Phases

3. MORE/LESS TRAINS

Instructional Goals

Children Need to Learn:

To compare two groups and determine which is more and which is less
To compare two groups in a variety of settings and determine how many more or less one number is than the other

Critical Learning Phases

Compare Two Groups: Lined Up

Uses what is known about one number to determine another when the groups are lined up
Compares two groups that are lined up and determines when is more, and which is less
When the groups are lined up, tells how many more or less, when the difference is 1 or 2
When the groups are lined up, tells how many more or less, when the difference is more than 2

Compares Two Groups: Not Lined Up

Compares two groups that are not lined up and tells which is more, and which is less
When the groups are not lined up, tells how many more or less, when the difference is 1 or 2
*When the groups are not lines up, tells how many more or less, when the difference is more than 2

Using Symbols

*Uses the greater than (>) and less than (<) symbols as a shortcut for the commonly used words (is more than, is less than) when comparing objects

6. HIDING ASSESSMENT

Instructional Goals

Children Need to Learn:

The parts of numbers to 10
To use what they know about the parts of numbers to solve subtraction problems

Critical Learning Phases

Identifies missing parts of numbers to 10 by using related combinations including:
--Using number combinations to solve subtraction (Ex: 5 + 3 = 8, so 8 - 5 = 3)
--Knowing taking away 1 part leaves the other part (Ex: 6 - 4 = 2, so 6 - 2 = 4)
Knows missing parts of numbers to 10

1. COUNTING OBJECTS

Instructional Goals

Children Need to Learn:

To use numbers to answer the question, "how many?"
To count objects with consistency, accuracy and confidence
To know one more and one less than a number
To interpret and write numerals to label quantities

Critical Learning Phases

Counting Objects:

Counts one item for each number (one-to-one)
Keeps track of an unorganized pile
Spontaneously checks by recounting to see if the result is the same
Knows "how many" after counting
Notices when recounting a group results in a different number
Is bothered when counting a group results in the same number after some have been added or taken away
Reacts to estimate while counting
Gets a particular number without counting past it

One More/One Less:

Knows "one more" in sequence without counting
Knows "one less" in sequence without counting
Notices if a counting pattern doesn't make sense
(Ex: saying 20, 30, 40 instead of 21, 22, 23, or 13, 14, 15 instead of 13, 12, 11)
Knows one more without counting when numbers are presented out of sequence
*Knows one less without counting when numbers are presented out of sequence

2. CHANGING NUMBERS

Instructional Goals

Children Need to Learn:

To change one quantity into another
That a smaller number is contained within a larger number
To count starting from a known amount (counting on)
To describe how one number is related to another number

Changing One Number to Another:

Changes a number to a larger number by counting on, or adding on a group
Changes a number to a smaller number by counting back, or removing a group

Describing the Relationship between the Numbers:

After changing one number to another, is aware of how many were added or taken away
Knows how many to add or take away from a number to make another number

4. NUMBER ARRANGEMENTS

Instructional Goals

Children Need to Learn:

To recognize the parts of numbers
To combine parts of numbers without counting all

Critical Learning Phases

Recognizes groups of numbers to 5 in a variety of configurations
Recognizes and describes parts contained in larger numbers
Describes parts of numbers; counts on to determine total
Combines parts by using related combinations including:
--Knowledge of commutative property (6 + 3 = 3 + 6)
--Rearranging parts to create known combinations (ex: adding 6 + 4 by moving 1 from the 6 to the 4, making 5 + 5)
*Knows totals when combining parts

8. GROUPING TENS

Instructional Goals

Children Need to Learn:

That numbers to 100 are organized into groups of tens and ones
To add tens without counting
To take away tens without counting
To interpret symbols for 2-digit numbers

Critical Learning Phases

Counts groups of ten
Knows total instantly when the number of tens and ones is known
Knows the number of tens that can be made from any group of ones and the number of ones left over
Knows the number of tens in any two-digit number
Knows ten more for any two-digit number
Knows ten less for any two-digit number

9. TWO-DIGIT ADDITION AND SUBTRACTION

Instructional Goals

Children Need to Learn:

To use what they know about single-digit numbers to add and subtract two-digit numbers
To add and subtract two-digit numbers using knowledge of tens and one
*To describe how they solve problems

Critical Learning Phases

Adding Numbers to 100

*Adds 2 numbers up to 100 by reorganizing them into tens and left over ones

Subtracting Numbers to 100

*Subtracts from numbers to 100 by breaking apart tens when necessary, and reorganizing what is left into the remaining tens and leftovers

5. COMBINATION TRAINS

Instructional Goals

Children Need to Learn:

To use known combinations to figure out unknown combinations
To describe how they solve problems
To know the parts of numbers to 10
To use efficient strategies to solve problems to 20
*To write equations

Critical Learning Phases

Combines parts by using related combinations including doubles plus or minus 1
Knows totals when combining parts

7. TEN FRAMES

Instructional Goals

Children Need to Learn:

To combine single-digit numbers by reorganizing them into a ten and leftover ones
To use their knowledge of the parts of numbers to 10 to subtract from numbers up to 20

Critical Learning Phases

Understanding Ten as a Unit

*Counts ten as a single unit

Understanding the Structure of One Ten and Some Ones

Combines 1 ten with any number of ones up to 9 without counting
Decomposes numbers from 10 to 19 into 1 ten and some ones

Adding Numbers to 20

*Adds 10 to any number of ones to 9, without counting

Subtracting Numbers to 20

Adds 2 single-digit numbers with sums larger than ten by reorganizing them into 1 ten and leftovers
When adding 2 single-digit numbers that result in a ten and some ones, knows what part of the number is needed to make a ten, and what part will be leftover
Subtracts 10 from any number from 11-20, without counting
When subtracting single-digit numbers, knows what part of the number needs to be taken away to get to ten, and what is still left to take away
*Subtracts from numbers to 19 by breaking up the ten when necessary, and knows how many left without counting

Assessing Math Concepts - All 9 Assessments

Assessing Math Concepts - 2012 Edition

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K-2+ Assessments

*To compare two groups and determine which is more and which is less *To compare two groups in a variety of settings and determine how many more or less one number is than the other

*Compares two groups that are not lined up and tells which is more, and which is less *When the groups are not lined up, tells how many more or less, when the difference is 1 or 2 *When the groups are not lines up, tells how many more or less, when the difference is more than 2

*Uses the greater than (>) and less than (<) symbols as a shortcut for the commonly used words (is more than, is less than) when comparing objects

*The parts of numbers to 10 *To use what they know about the parts of numbers to solve subtraction problems

*Identifies missing parts of numbers to 10 by using related combinations including: --Using number combinations to solve subtraction (Ex: 5 + 3 = 8, so 8 - 5 = 3) --Knowing taking away 1 part leaves the other part (Ex: 6 - 4 = 2, so 6 - 2 = 4) *Knows missing parts of numbers to 10

*To use numbers to answer the question, "how many?" *To count objects with consistency, accuracy and confidence *To know one more and one less than a number *To interpret and write numerals to label quantities

*To change one quantity into another *That a smaller number is contained within a larger number *To count starting from a known amount (counting on) *To describe how one number is related to another number

*Changes a number to a larger number by counting on, or adding on a group *Changes a number to a smaller number by counting back, or removing a group

*After changing one number to another, is aware of how many were added or taken away *Knows how many to add or take away from a number to make another number

*To recognize the parts of numbers *To combine parts of numbers without counting all

*That numbers to 100 are organized into groups of tens and ones *To add tens without counting *To take away tens without counting *To interpret symbols for 2-digit numbers

*To use what they know about single-digit numbers to add and subtract two-digit numbers *To add and subtract two-digit numbers using knowledge of tens and one *To describe how they solve problems

*Adds 2 numbers up to 100 by reorganizing them into tens and left over ones

*Subtracts from numbers to 100 by breaking apart tens when necessary, and reorganizing what is left into the remaining tens and leftovers

*To use known combinations to figure out unknown combinations *To describe how they solve problems *To know the parts of numbers to 10 *To use efficient strategies to solve problems to 20 *To write equations

*Combines parts by using related combinations including doubles plus or minus 1 *Knows totals when combining parts

*To combine single-digit numbers by reorganizing them into a ten and leftover ones *To use their knowledge of the parts of numbers to 10 to subtract from numbers up to 20

*Counts ten as a single unit

*Combines 1 ten with any number of ones up to 9 without counting *Decomposes numbers from 10 to 19 into 1 ten and some ones

*Adds 10 to any number of ones to 9, without counting

Assessing Math Concepts - All 9 Assessments

Assessing Math Concepts - 2012 Edition

To compare two groups and determine which is more and which is less
To compare two groups in a variety of settings and determine how many more or less one number is than the other

Compares two groups that are not lined up and tells which is more, and which is less
When the groups are not lined up, tells how many more or less, when the difference is 1 or 2
*When the groups are not lines up, tells how many more or less, when the difference is more than 2

The parts of numbers to 10
To use what they know about the parts of numbers to solve subtraction problems

Identifies missing parts of numbers to 10 by using related combinations including:
--Using number combinations to solve subtraction (Ex: 5 + 3 = 8, so 8 - 5 = 3)
--Knowing taking away 1 part leaves the other part (Ex: 6 - 4 = 2, so 6 - 2 = 4)
Knows missing parts of numbers to 10

To use numbers to answer the question, "how many?"
To count objects with consistency, accuracy and confidence
To know one more and one less than a number
To interpret and write numerals to label quantities

To change one quantity into another
That a smaller number is contained within a larger number
To count starting from a known amount (counting on)
To describe how one number is related to another number

Changes a number to a larger number by counting on, or adding on a group
Changes a number to a smaller number by counting back, or removing a group

After changing one number to another, is aware of how many were added or taken away
Knows how many to add or take away from a number to make another number

To recognize the parts of numbers
To combine parts of numbers without counting all

That numbers to 100 are organized into groups of tens and ones
To add tens without counting
To take away tens without counting
To interpret symbols for 2-digit numbers

To use what they know about single-digit numbers to add and subtract two-digit numbers
To add and subtract two-digit numbers using knowledge of tens and one
*To describe how they solve problems

To use known combinations to figure out unknown combinations
To describe how they solve problems
To know the parts of numbers to 10
To use efficient strategies to solve problems to 20
*To write equations

Combines parts by using related combinations including doubles plus or minus 1
Knows totals when combining parts

To combine single-digit numbers by reorganizing them into a ten and leftover ones
To use their knowledge of the parts of numbers to 10 to subtract from numbers up to 20

Combines 1 ten with any number of ones up to 9 without counting
Decomposes numbers from 10 to 19 into 1 ten and some ones