Saturday, August 3, 2013

Estimating and Counting Routines Part 1

One of the BIGGEST ideas in the common core for K and 1 is counting and cardinality.  I use whole group, small group, and partner estimating and counting routines to give kids lots of practice with these big mathematical ideas.

Here is a peak at the common core standards from Kindergarten addressed by these routines.  (There are quite a few!)
• CCSS.Math.Content.K.CC.A.1 Count to 100 by ones and by tens.
• CCSS.Math.Content.K.CC.A.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
• CCSS.Math.Content.K.CC.B.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
• CCSS.Math.Content.K.CC.B.4a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
• CCSS.Math.Content.K.CC.B.4b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
• CCSS.Math.Content.K.CC.B.4c Understand that each successive number name refers to a quantity that is one larger.
• CCSS.Math.Content.K.CC.B.5 Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.
We start with a container of items like glass gems, counters, bears or pretty much anything!

I show the students the container and ask a question such as "do you think there are more or less than 100 gems in here?"  I have kids turn and talk to a neighbor to share their answer and then dump the container out on the floor or table

I have a student take 10 out of the collection and put it off to the side a bit.  This gives them a frame of reference and gets them thinking in tens.

Then we talk about if this small pile is 10, about how many are here altogether.  I give kids about 10 seconds to look and then cover the collection with a cookie sheet or a large book.  If kids have an unlimited time to look at the collection, I will see them moving their eyes and counting to themselves.  My goal in this part is to get them to estimate, not count.  I have kids turn and share their answer with a partner and have a few partners share out their thinking.  Then I uncover the collection and ask students to help me figure out how many are here.  With a collection this size, a student will often suggest grouping by 10.

Once it is grouped into 10's, I have the student count by tens.  We then write the number (in this case 85).  We talk about what the 8 means and what the 5 means.

Then I often tell kids we are going to give out all the gems before we count them by ones and assure them that I want each kid to have the same amount.  In whole group instruction,  this results in each kid having less than 10 but this day I was doing small group and each kid ended up with quite a pile. They shared the tens first and knew each kid would get 2 tens and then they shared the ones.  This is great conceptual development and life experience that is important for them to have when they start learning about division.

Once each kid has a pile, I ask them to count how many they have.  Then we count by ones while we place each item back in the container.  Sometimes I will stop the counting to make a comment, and then say something like "how many were in here?"  A student will answer 27.  Then we will count on from that number.  This stop and start counting helps kids be able to count on from any number which is a very important skill.  There are many vaiations on this routine that I will be sharing as the new school year gets underway.  Make sure you are following my blog so you are kept up to date!

One of my favorite purchases for back to school is a few of these lidded paint cups that I am thinking about using for some estimating and counting math centers.  They are cute and come in different colors and have a lid that doesn't pop open when kids throw them in a tub.

How do you work on counting or estimating with your students?

Here are some other ways I work on numbers to 120.