assessing mathematical understanding

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

Counting is as easy as 1,2,3…

… right?

a = b= c= d=

Let’s Count…

b + g=

c + e =

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 tryd + 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

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!

Counting; More than 1,2,3

Rote CountingOne-to-One CorrespondenceKeeping TrackConnecting Numbers to QuantitiesConservationCounting by Groups

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?

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

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.

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 #5Combination 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

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.)

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).

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

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