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Assessing Mathematical Understanding . BaLLA NTYNE ELEMENTARY NOVEMBER 2012 Amy LeHew, Elementary Math Specialist. Counting is as easy as 1,2,3…. … right?. a = b= c= d= Let’s Count…. c + e = .
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Assessing Mathematical Understanding BaLLANTYNE ELEMENTARY NOVEMBER 2012 Amy LeHew, Elementary Math Specialist
Counting is as easy as 1,2,3… … right?
a = b= c= d= Let’s Count… c + e = b + g= d+ f =
a = b= c= d= POP QUIZ! Keep UP c + e = b + g = d + f = How did you figure these out?
a = b= c= d= c + e = b + g = d + f = Now try d + e = How did you figure this one out? Did you use a relationship, or revert to counting?
a = b= c= d= e + g d + b g – c h – e
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?
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?
a = b= c= d= What’s the difference between memorizing facts and conceptualizing combinations?
What’s The Difference? 3 + 4 7 5 + 4 9
Parent Teacher Conference He knew all of his addition and subtraction facts at age 2. And all of his multiplication facts in kindergarten! Nikolai should be moved to ___ grade! He is smart in math!
Counting; More than 1,2,3 Rote Counting One-to-One Correspondence Keeping Track Connecting Numbers to Quantities Conservation Counting by Groups
Watch Corey When presented with 21 -what does he estimate? -how does he count? When presented with 21 -what does he estimate? -how does he count? Do you just want to reach out and organize the counters for him? • When presented • with 12 • -what does he estimate? • -how does he count?
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.
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.
Strategies for Part 1, Task 1 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. Tips for “Keeping Track Strategies”
Assessment Results Summarized at end of assessment as: A – Ready to Apply P – Needs Practice I – Needs Instruction Complete descriptions included in assessment guide.
ByKathy 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.
Common Core Alignment Kindergarten Operations & 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 1 Operations & Algebraic Thinking Understand 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.2Examples: 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.)
Common Core Alignment continued Grade 1 Operations & 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).
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.
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.
Break Time Meet in the Computer Lab in Ten Minutes
