Acronyms
LFIN
The Learning Framework in Number
What is subitizing?
Instantly naming the number of items in a collection without counting
What kind of assessment task could you give to determine if a child is at least Construct 1?
Tasks that involve having the child form a collection of a specified size and count collections involving visible items
Why would asking a child to locate a given number on a 100’s chart not be the way to assess numeral identification?
The hundreds chart provides support for locating the number.
What is facile?
Easily Acheived
AVMR
Add+Vantage Math Recovery
What visual models are used to aid students in developing structuring knowledge?
5,10, & 20 Frames
Bead Rack
Fingers, dots & cubes precede the frames and bead rack
The development of a “Numerical Composite” is associated with which Construct?
Construct 3 – Initial Number Sequence
What Level does the student stop dropping back to produce a given number?
BONUS - This student is facile up to what number?
FNWS and BNWS Level 3
BONUS - this means the student is Facile to "10"
What type of questioning helps clarify student strategies?
Open-ended questions
Count From 1
What structuring knowledge to demonstrate how a child could solve 8+7.
One way could be:
8+2=10
5 left over
10+5=15
or 7+714+1=15
Use the problem 9 + 4 to demonstrate the difference between unitary and composite strategies.
Unitary: 9… 10, 11, 12, 13 (or any example of Constructs 1 – 3)
Composite: 9+1 is 10 and 3 more makes 13 (or any example of Construct 5)
Give an example of a classroom activity that is working on a Number Words and Numerals skill?
One example:
Teacher says a number and students say the three numbers that come before.
A child with will have all 3 aspects of number.
number sense
NWA
Number Word After
How does structuring numbers support addition and subtraction strategies?
Structuring numbers tools and teaching promotes composite thinking and helps students move from a construct 3 to a construct 5.
However, structuring numbers is still a skill so teachers need to link to addition and subtraction situations.
Demonstrate a solution to the problem 13 – 9 that would indicate Construct 4 thinking.
Count-down-to: 13…12, 11, 10, 9 “4”
WHAT IS THE DIFFERENCE BETWEEN “COUNTING” AND “FORWARD NUMBER WORD SEQUENCE”?
Counting involves the enumeration of a collection of objects (in a Steffe sense) - Forward Number Word Sequence refers to saying the words in order
The LFIN allows teachers to...
BONUS - How do you decide when to move a student across/down the LFIN?
Plan instruction
BONUS - Teacher discretion on student use of wait time and/or finger use
Classroom Instructional Framework for Early Number
Why is structuring number so important within mathematics?
BONUS - What other areas does it help with?
Lays a foundation
BONUS - multiplication, addition & subtraction to 100, and fractions
List the following in order of arithmetic sophistication starting with the lowest.
figurative counter, count on child, non count by ones child, perceptual counter
Perceptual counter
Figurative counter
Counting on child
Non count by ones child
In what ways does Number Words and Numerals instruction support addition and subtraction?
It gives students the verbal and written sequences to apply to addition & subtraction situations.
A child that counts the items that go away is a counter.
Bonus - Give an example
Discrete
BONUS - 12-4
12, 11, 10, 9, "so there are 8 left"