Download - Assessing Mathematical Understanding
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BALLANTYNE ELEMENTARY
N O V E M B E R 2 0 1 2
A M Y L E H E W, E L E M E N TA RY M AT H S P E C I A L I S T
Assessing Mathematical Understanding
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Counting is as easy as 1,2,3…
… right?
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a = b= c= d=
Let’s Count…
b + g=
c + e =
d+ f =
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a = b= c= d=
POP QUIZ! Keep UP
c + e =
b + g =
d + f =
How did you figure these
out?
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a = b= c= d=
c + e =
b + g =
d + f =
Now tryd + e =
How did you figure this one out? Did you use a relationship, or revert to counting?
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a = b= c= d=
e + g d + b
g – c h – e
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How fast are you?
What would you have to do to get faster?
Could you memorize the facts if you needed to?
Would memorizing help you develop a sense of quantity?
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a = b= c= d=
Let’s Try it in Context:
How many more is “i" than “c”?
Which is more (c+f) or (b+h)?
If you have “g” people at a party, will “s” cookies be enough for everyone
to get 3 cookies?
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a = b= c= d=
What’s the difference between memorizing facts
and conceptualizing combinations?
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What’s The Difference?
3 + 4 7
5 + 4 9
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Parent Teacher Conference
Nikolai should be moved to ___ grade! He is smart in math!
He knew all of his addition and
subtraction facts at age 2. And all of his multiplication
facts in kindergarten!
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Counting; More than 1,2,3
Rote CountingOne-to-One CorrespondenceKeeping TrackConnecting Numbers to QuantitiesConservationCounting by Groups
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Watch Corey
When presentedwith 21
-what does he estimate?
-how does he count?
When presentedwith 21
-what does he estimate?
-how does he count?
Do you just want to reach out and organize the counters for him?
When presentedwith 12
-what does he
estimate?
-how does he count?
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Strategies for Part 1, Task 1
Tips for “Tells How Many”
Remembers: Are able to tell you the number they counted.
Recounts to find out: If they recount, this means they know they have a way of answering, but didn’t keep the number in their head the first time they counted.
Doesn’t remember: They can’t remember because their attention wasn’t on quantity, but on the act of counting; the number they landed on has no meaning to them and they can’t remember it.
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Strategies for Part 1, Task 1
Tips for “Counting Method” Strategies
Moves – the child moves each counter as he or she counts it.
Lines up first – lines counters up first, before they begin to count.
Points – the child points at the objects without moving them. It may mean they don’t have a way of keeping track, or they could be able to keep track without moving anything.
Looks – the child counts without touching counters; this may mean they don’t realize touching helps; or they are more sophisticated and can accurately count without touching or moving the counters.
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Strategies for Part 1, Task 1
Tips for “Keeping Track Strategies”
Keeps track with ease – keeps track confidently and is accurate.
Keeps track with difficulty – student might recount to be sure they are correct.
Loses track – may count correctly at first, and then lose track.
Can’t keep track – doesn’t always touch each object; doesn’t have a system for keeping track; may count some more than once.
Lacks one-to-one – doesn’t touch one object for each number word.
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Assessment Results
Summarized at end of assessment as:
A – Ready to Apply
P – Needs Practice
I – Needs Instruction
Complete descriptions included in assessment guide.
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ByKathy Richardson
Assessment #5Combination Trains
Overview & Description of
Strategies
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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.
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Common Core Alignment
KindergartenOperations & Algebraic Thinking
Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
K.OA.5. Fluently add and subtract within 5
Grade 1Operations & Algebraic ThinkingUnderstand and apply properties of operations and the relationship between addition and subtraction.
1.OA.3. Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
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Common Core Alignment continued
Grade 1Operations & Algebraic Thinking
Add and subtract within 20.
1.OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
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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.
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What will my students be asked to do during the Combination Train assessment?
• 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.
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Break Time
Meet in the Computer Lab in Ten Minutes
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