First Steps Diagnostic Math Assessment
Administered ***
May 12, 2008
for
XXX Elementary – XXX (Grade 2)
Levels:
Phase / Age Typically EnteredEmergent
Matching / 3 - 5 years of age
Quantifying / 5 - 6 years of age
Partitioning / 6 - 9 years of age
Factoring / 9 - 11 years of age
Operating / 11 - 13 years of age
Name / Description / Level
XXX / · When asked to get a number of items, used counting to figure it out rather than just grabbing some.
· When counting items, includes each item once (good one to one correspondence).
· Says the number names in the correct order and is able to keep track of his starting point.
· Understands that the last number said indicates “how many”.
· Does not trust the count – does not understand that the arrangement of the objects does not affect how many there are.
· When items are placed in a line and is asked to start counting from the middle, includes all items.
· When asked to get some items to give to everyone, just grabbed a handful and handed them out one at a time with no counting.
· Can count by 2s (rote) to 10; counting sequence = 2, 4, 6, 8, 10, 20, 21, 22…...
· Does not understand what it means to count by 2s.
· Does not understand that skip counting a collection gives the same result as counting by 1s.
· Understands the oral pattern of counting.
· Knows the written pattern of counting up to 109; wrote 110 as 1010, 111 as 1011, etc.
· Is able to subitize (recognizes what numbers look like without counting the items).
· Has difficulty partitioning numbers into its various parts.
· Does not understand that the position (or place) of a digit tells us the quantity it represents.
· Had difficulty determining which operation to use in a word problem.
· Unable to make a semantic number sentence from a word problem. / Quantifying
XXX has a good understanding of the following Key Understandings:
· We can count a collection to find out how many are in it.
o Each item is included only once.
o The numbers must be said once and in the conventional order.
o The last number said tells “how many” are in the whole collection.
o The starting point and order in which objects are counted does not affect how many there are.
· The whole numbers are in a particular order and there are patterns in the way we say them that help us to remember the order.
o Has memorized the words for numbers from 1 to 13.
o Hears the 4 to 9 part of the sequence in 14 to 19.
o Repeats the 1 to 9 sequence within each decade (up to 109).
o Repeats the decade sequence and 1 to 9 sequence within each of the hundreds.
· We often see how many are in a collection just by looking and also by thinking of it in parts.
o It’s easier to see how many there are when collections are in special arrangements.
XXX does not have a good understanding of the following Key Understandings:
· We can count a collection to find out how many are in it.
o The arrangement of the objects does not affect how many there are.
o Does not realize that skip counting a collection gives the same answer as counting by ones.
· We can often see how many are in a collection just by looking and also by thinking of it in parts.
o You can break up a quantity and move parts from one group to another without changing the overall quantity (partitioning numbers).
o Any collection can be separated into parts and each part can be represented by a number.
o A number can be thought of in parts in different ways.
o A number can be thought of in more than two parts.
· There are patterns in the way we write whole numbers that help us to remember their order.
o The position of a digit tells us the quantity it represents.
o The order of the digits makes a difference to the number.
· Thinking of a problem as a number sentence often helps us solve it. Sometimes we need to rewrite the number sentence in a different but equivalent way.
o It is important to represent problems in ways that can be dealt with mathematically.
Activities to try:
Number Trains Grouping Skip Counting a Large Collection
Skip Counting Money Separating Collections Die Combinations
Flash Cards Snap Five Little Monkeys
Number Scatters Ten Frames Combining Groups
Playing Cards Wipeout Identifying Operations
Inverse Relationships
**Have XXX use the constant function on the calculator to check his written counting sequence. He predicts what comes next then checks it on the calculator. Have XXX start at 107. Into his calculator he would key in 107 + 1. He would predict the answer, write it down, and then check by pressing =. He predicts again, then checks by pressing =. When he gets to 110, ask him why his written answer is different than the calculator. What pattern do you see?
**The constant function on the calculator can also be used for skip counting. For skip counting by 2s, press 0 + 2 =. Each time you press =, the answer will go up by 2.
XXX:
The learning activities that I have given to you for XXX are on trusting the count (different arrangements of items still gives you the same amount - including skip counting items), becoming more confident in the written counting sequence and partitioning numbers. Being able to partition numbers is a very important skill as it is this concept that really holds students back. Kids need to be able to partition successfully in order to learn their basic facts and have a good understanding of place value.
I hope that this is helpful for you. Please do not hesitate to contact me if you have any further questions.
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