1. Imagine you are a first grade teacher. You want to begin instruction to help the children understand place value. How might you asses what the children already know? What would you include in that assessment?
2. A) Why is im important for your students to be able to represent numbers in more than one way? B) How might your students’ understanding of number help him or her start to develop some beginning mental computational skills?
Numbers and operations in the base ten are important concepts for first graders to understand. They must grasp the idea of number sequences and patterns in order to understand place value and strategies for addition and subtraction within 10 (20 before entering the second grade). Counting by ones and tens, as well as backwards are critical for a first grader to succeed.
Introducing place value is dependent on ensuring the students are capable of counting to at least 120. With use of a number chart, teachers can have their students show their understanding by having them write the numbers in order in a 10 x 10 chart. To further the lesson, I would provide each student with a blank calendar. The students may decorate their month however they wish, perhaps bringing to life an important holiday within the month, but most importantly they must glue down number cut outs according to the days of the month. One last activity I might use to ensure an understanding of numbers and begin to dive into place value is with the use of coins, pennies and dimes specifically. This way I am introducing the concept of money, as well as emphasizing the idea of tens.
Word problems are a brilliant way for first graders to creatively show their understanding of counting and place value. Using pictures, words, and numbers to prove their math thinking, students should be able to respond to a variety of questions.
One activity I specifically thought was helpful in assessing students was called “Putting Numbers in their Place”. Each child will pick a number out of a hat between 1 and 120. Construction paper divided into three categories (ones, tens, hundreds), would be provided for each student. Using cut out squares to represent unifix cubes, students must represent their number exemplifying their knowledge of numbers and place value.
Finally, to make assessment fun and further introduce the idea of place value, I recently learned of the game “I Have, Who Has” which I thought would be a great group activity to get a grasp on how much the students know as well as emphasizing the importance of a helpful and noncritical environment should a student need assistance from classmates. In order to play, each student will stand by their desk and receive a card with a number between 1 and 120. I decided to change the rules a little bit; instead of having a student with a “Start” card, I (teacher) will begin. Say for example I have the number 67. I would say I have “6 tens and 7 ones”. Whichever student has the number 67 written on their card will say “I have 6 tens and 7 ones” followed by the second number they have written on their card, say 32. The game will go on until each student has their number called out, and have in response addressed another number.
Through this sequence of activities I will be able to understand where my first graders are in terms of counting and further their knowledge with place value. I have recognized that many students fail to see ten things as one ten or have problems with the concept of greater and less than, so it is important to consistently assess in clever ways to make sure you are moving in the correct direction with your students’ understanding.
Emphasizing that math is prominent in the real world is important for students who don’t understand why they must understand mathematical concepts. Numbers are represented in a variety of ways and used in everyday activities. Numbers are the main factor of mental computational skills, something that progresses as students excel through their schooling.
Websites I came across with helpful worksheets for assessment:
 http://www.nclack.k12.or.us/cms/lib6/OR01000992/Centricity/Domain/115/Grade_1_Units_1and3_revised_6_11.pdf

http://www.nsa.gov/academia/_files/collected_learning/elementary/arithmetic/place_for_everything.pdf