September 24, 2010
Dear Families,
Here’s an update on what's been happening in first and second grade math. I have almost completed all of the beginning of year math assessments. We call this assessment the PNOA (Primary Number and Observation Assessment). It is an assessment that is used in grades K-2 throughout the elementary schools in the Washington West district, and in many other schools around the state. The PNOA is an interview-style assessment and requires the teacher and student to sit together for 30 to 45 minutes. It's a very special time to get to know and understand how a child thinks mathematically. This assessment is often broken up into smaller time frames, so as not to overwhelm or overtire the child. A great deal of information is gathered about a child's mathematical understandings, his/her knowledge of the base ten system, estimation and mathematical reasoning skills, the language of number words and other math terms, and how to use the operations of addition and subtraction.
In addition to assessing each child, we have been working on the operation of addition in first grade. Using dice, cards, counters, pennies, balances and other manipulatives, including our own bodies, we've been acting out the operation or ACTION of putting two and three numbers together, known as addition. I wrote the following for all of the first graders: six plus one equals seven. Then I showed them the shortcut that mathematicians made up many years ago. Rather than write out all of the words and have to think about spelling and all that goes with writing words, mathematicians came up with symbols that we all could agree mean the same thing. They use symbols like 6 + 1 = 7. We discussed how the plus sign means “plus,” which is the same as "add," "put with," or "and." Equals means to balance each side of the sign or "is the same as." We have been using balances to help us determine missing addends and how we might find a way to use two numbers to equal or balance with one number on the other side. For example, if we put a blue weight on the number 8, what numbers could we put the other two blue weights on the OTHER side of the balance to create an equal or a balance. I do not use the word "even" because that has other implications later when we explore even and odd number properities. There are some photos attached to show the work using balances. Such mathematical balances are also being used to help second graders understand subtraction and the reciprocity of addition and subtraction. When children in first or second grade are creating addition or subtraction equations, they are asked to verbally state the equation each time. After a period of time, they are then expected to write, while verbalizing, these equations on paper before they take their next turn.
Many math concepts and skills, such as addition and subtraction, learning what one or two more or less than a number is, counting backwards or forwards, skip counting by twos, fives or tens beginning with any number, etc, are rehearsed with games so that they are internalized and learned or mastered by your child.
Second graders have been reviewing addition facts up to 10 and also up to 20 using what they know about the "tens" partners. For example, 3+7 is 10, so 13+7 or 17 +3 must equal 20. This comes quickly for some students, and other students need daily practice with this at school and at home.
We have also begun exploring the concept of subtraction, which means to take away, pull apart, minus, or find the difference between two amounts. There have been many subtraction stories we've acted out in a large group to see what is actually happening and how we begin with a greater amount and end up with a lesser amount when subtracting. We've been using the number balances to explore this concept and several of us have discovered that addition (reciprocal of subtraction) can help us solve these computation problems. For example, 10-4 is 6 because I know that 4+6 more is 10. We've been playing several different guessing games using the large balances these past couple of weeks to help learn subtraction facts, in addition to polishing up on our addition facts up to 10 and up to 20.
Another skills we've been practicing in school is counting by 25's. We've rehearsed the rhythmic sound pattern of 25, 50, 75..100. We've also discussed out this skip counting pattern begins to almost repeat itself with 125, 150, 175, 200, 225, 250, 275, 300, 325, etc. One of our favorite games is "POP," which helps us practice forward and counting skills like this one. It's a game your child knows well and is easily played at home with family members or friends.
When we first learned how to use the balance (in both the first and second grade groups), we spent a lot of time pretending our bodies were the balance by holding out our arms horizontally and being "in balance," or a place of "equal," with our arms at the same height. We also found ways to bend to one side or the other with our arms outstretched to show being unbalanced or unequal. In essence, our outstretched arms were acting like the arms of the number balance.
The work we began at the end of this week included a discussion in both groups about problem solving. We are defining what a problem is, how it feels when a problem is faced, and what it feels like when a problem is solved. We're also discovering that some things aren't problems just yet, but might become one if something isn't done. Your children helped me identify that some problems are people (family or friend) problems and some problems are with things (like a machine not working or getting stuck), and other problems are about something you face in school or a learning situation like writing or mathematics. We will be continuing this conversation in both first and second grade mathematics next week. We will come up with suggestions for "What do you do when you discover or approach a problem?" and "How do you deal with a problem?" The next math update will include what we come up with as a mathematics learning community that can help us when we find ourselves faced with a problem.
A Word About Math Homework: Math homework has not begun yet, but it will arrive shortly. If children are assigned homework, they will receive it on Thursdays, and I will send out an email to parents letting you know to be on the lookout for it in backpacks. Homework is always due on the following Monday from the Thursday it is sent home. If this poses a problem for your family on some weeks, please email me when it does and we can discuss alternatives.
Homework is often a game to be played at home with a parent, sibling or other family relative or friend. The games are rehearsed in the classroom and help to review a math concept or skill your child has been introduced to and expected to master according to grade level expectations. I ask that the game sheet or score sheet be signed by the person playing with the first or second grader and then return it to me during math class on the following Monday. Returning completed homework in this manner is part of your child's report card each trimester.
I hope this math update has been helpful. If you have any comments or questions, please email me at bhart@madriver.com
Sincerely,
Brenda
PS: Please check out the photos that are attached.
