Transcript RTI K.Richardson PD October 2011

August 2011
RTI Kathy Richardson
Assessment Pilot
Memorized knowledge is knowledge that can be forgotten.
Internalized knowledge can’t be forgotten because it is a part of
the way we see the world.
Amy LeHew
Family
Teaching
(Iowa)
Math
Ocean
How many?
How many more to make ten?
What does a student need to know before they can engage in
this type of activity?
By
Kathy Richardson
Assessment #5
Combination Trains
Overview &
Description of Strategies
Learning Number Combinations
• Children need to see the basic facts as a set of interrelated
concepts.
• Children need to be able to look for relationships between
the facts they know and other larger, more complex numbers
or problems.
• Emphasis needs to be on learning number composition and
decomposition and number relationships – not just on
getting the right answers.
What are we trying to determine with this assessment?
To determine what number combinations the student knows and to find out
if they can use the answer to a combination they know to figure out one
they don't know.
Does student know the parts of numbers to 10?
Can student use efficient strategies to solve
problems to 20.
• Students will be presented with connecting cube trains of
different lengths – they will be asked to add a variety of
number combinations.
• Will assess their fluency with numbers to 6, to 10, and to
20.
Select Downloads
Select Linking Assessment
By
Kathy Richardson
Assessment #6
Hiding Assessment
Overview &
Description of Strategies
Learning to Decompose Numbers
• To subtract children need to know the
parts of numbers and see the relationship
between composition and decomposition.
• Children must recognize that one number
is contained within another number.
• Children must understand that the number
stays the same even when it is broken
apart and recombined in various ways.
What are we trying to determine with
this assessment?
Does the student…
-know parts of numbers to 10 quickly, without
counting to figure them out.
Can the student…
-use what they know about parts of numbers to solve
subtraction problems.
What Strategies do Students Use?
Knows Quickly: Does not hesitate or count
to figure out.
Related Combinations: Uses what they
already know to figure out what they don't
know. Ex: I see 2. 4 and 2 is 6 so 4 are hiding.
Counts On or back: Starts with what they see
and counts on or starts with the whole
number and counts back for each counter
they see. "I see 4...So, 5...6 are hiding. Two
are hiding."
Counts All: Uses fingers or visualizes the
whole number.
Counts On or back: Starts with what they see
and counts on or starts with the whole
number and counts back for each counter
they see. "I see 4...So, 5...6 are hiding. Two
are hiding."
I’ve Assessed, Now What?
Assessment book
Page 52 – 54
2:2-5
Book 2
Chapter 2
Activity 5
Look in Developing
Book 2 – page v
By
Kathy Richardson
Assessment #6
Hiding Assessment
What questions do you
have?
By
Kathy Richardson
Should we go back?
(to assessment #5)
Or Forward?
(to assessment #6)
By
Kathy Richardson
Assessment #5
Combination Trains
Overview &
Description of Strategies
Learning Number Combinations
• Children need to see the basic facts as a set of interrelated
concepts.
• Children need to be able to look for relationships between
the facts they know and other larger, more complex numbers
or problems.
• Emphasis needs to be on learning number composition and
decomposition and number relationships – not just on
getting the right answers.
What are we trying to determine with this assessment?
To determine what number combinations the student knows and to find out
if they can use the answer to a combination they know to figure out one
they don't know.
Does student know the parts of numbers to 10?
Can student use efficient strategies to solve
problems to 20.
• Students will be presented with connecting cube trains of
different lengths – they will be asked to add a variety of
number combinations.
• Will assess their fluency with numbers to 6, to 10, and to
20.
How is this different from the
Hiding Assessment? .
By
Kathy Richardson
Assessment #7
Ten Frames
Overview &
Description of Strategies
Learning about Numbers as One Ten
and Some More
• Understanding that numbers are made up of “ten and some
ones” is a foundational skill students must learn to work
with larger numbers.
• To solve more challenging problems student must move
beyond counting on strategies and be able to solve
problems by using relationships and understanding the
underlying structure of numbers to 20.
What are we trying to determine with this assessment?
To determine if the student can combine single digit
numbers by reorganizing them into a 10 and leftovers.
To determine if the student can use their knowledge
of the parts of numbers to 10 to subtract numbers up
to 20.
Using ten frames, students answer a series of addition and
subtraction questions.
Assesses whether students know parts of numbers and can
break numbers apart to complete the ten to solve the
problem.
To complete assessment, students solve “what if” questions
without the support of the ten frame.
Adding Ones to a Ten (10 +9 and 6 +10):
Trying to assess if student can easily add the ones
to the ten without counting on or counting all.
These strategies are self-explanatory.
If “N” assessment will end.
Part 1, Addition continued
Knows Parts of Numbers
Making a Ten and Adding Ones
8 + 7, 7 + 6, 8 + 5
Recognizes Ten More
18 + 5
• To determine if the student can decompose a
teen number into a ten and leftovers.
• To determine if the student can subtract by
breaking up a number in order to get to ten
and then subtracting what is left from 10.
• Practice Problem: 12-3
By
Kathy Richardson
Assessment #8
Grouping Tens
Overview &
Description of Strategies
Learning about Numbers as
Tens and Ones
Children need to learn that numbers to 100 are composed of
groups of tens and ones.
Children must do more than label the digits in a number – they
must understand that numbers are organized into groups of
tens and ones.
Children must recognize that a ten is both one ten and ten ones.
This level of thinking is difficult for young children.
What are we trying to determine with this assessment?
Do students understand that numbers to 100 are
organized into groups of tens and ones.
Can they add tens without counting.
Can they take away tens without counting.
Do they understand that counting by groups doesn’t
change the total quantity?
• Students will be asked to identify tens and ones when presented
with number cards. Note: Number cards available under downloads
of www.amcanywhere.com.
• Using counters, student will identify groups of ten and leftovers.
• Student will use what they know about tens to find out how many
altogether.
• Students will be asked to add and take away tens without counters.
• Video: 33:20
• First Grader and Second Grader: 33:50 – 37:10
• 40:12 Tad Second Grader
•
By
Kathy Richardson
Assessment #9
Two-Digit Addition
& Subtraction
Overview &
Description of Strategies
Learning to Add & Subtract Two-Digit Numbers
• Students must understand the underlying math to solve
two-digit addition & subtraction problems – otherwise
they will simply be following a procedure.
• They must have a solid understanding of number
relationships, number combinations to ten and numbers
as tens and ones for two-digit addition & subtraction to
have meaning for them.
• Children must have repeated practice combining,
separating, and regrouping numbers.
What are we trying to determine with this assessment?
To determine if the student can use the concept of tens and ones to add
two-digit numbers, by mentally breaking them apart and reorganizing them
into a total number of tens and ones, when the problem is presented
1) using models
2) with the model covered and
3) symbolically
Students will be asked to solve a series of two-digit addition and
subtraction problems.
They will be asked to solve the problems by
grouping/regrouping the numbers into tens and leftovers.
They will be asked to use models appropriately to show their
thinking, and they will be asked to solve the problems
without models.
Present a variety of two-digit problems to student:
•
•
•
Solves Problem with Model – showing trains of cubes
Solves Problem w/out Model – cover cubes with paper
Solving Symbolic Problems – use equation cards
Assessment is capturing student’s answers, their strategies for
solving the problems and their use of the models.
Equation Cards available in the Downloads section of
www.amcanywhere.com
Knows parts to make/adds ten:
Student easily forms tens; knows
parts of numbers without having to
figure anything out.
Counts to make/add ten: Student
can form tens and leftovers, but not
automatically and still needs to figure
them out.
Visualizes written problem: Trying to
solve problem using standard
algorithm.
Strategy Unknown: Prompts teacher to ask
“How did you think about that?”
Counts all or on: Student still thinks
of numbers as a collection of units
(rather than tens & ones) and counts
all or on to get answer.