Estimation Challenge, a rich and relevant learning experience!

IMG_4085
I am sure you can all come up with a number of every day examples when you have used estimating skills, for example, checking the time and estimating how long you have to get ready and do what you need to do before heading out the door and getting to your destination on time, or shopping at the grocery store and estimating the cost of the items in your cart to be sure you brought enough money with you to pay for them.
First, let’s consider why we help children learn to estimate. Children’s abilities to estimate, along with their estimation strategies, can offer a window into their mathematical thinking and problem solving.  The acquisition of estimation skills is important and, some say, contributes to children’s mathematical understanding of numbers, measurement, and time.  At the same time, estimation is an important life skill.  When children learn how to estimate we are giving them essential and practical ways of operating within many mathematical and everyday situations.  We don’t always need to calculate the precise number or measurement; sometimes, it’s simply not necessary or it’s impossible.Based on my experience, students prefer to find the exact answer.  They quickly move to counting out the objects in a jar one by one to get a precise number.  They want to be right!   For many children, estimation is perceived as extra work.  As a teacher, I know estimating is a skill that needs practice and relevant application.  I also know, that developmentally for younger children estimation is a challenging task.text books 
I remember talking about and planning curriculum experiences to help children understand the importance of estimating and developing ways to help them become good estimators with Dr. John Van de Walle, a well-known mathematics educator and the author of Elementary and Middle School Mathematics: Teaching Developmentally. I was lucky enough many years ago to be invited to a two-day workshop with Dr. Van de Walle.  According to Dr. Van de Walle, “Estimation is a high-level skill that requires students to be able to conceptualize and mentally manipulate numbers”.  I agree. It isn’t easy and often it doesn’t make sense to children.  Why estimate the number of things in the jar when I can count them?   As a teacher, we have to thoughtfully find  ways to engage children in meaningful and relevant activities so that children can practice and learn how to make good estimations, and most importantly, help them to understand the “whys” behind learning how to estimate.
The Importance of Learning How to Estimatemarcus 2
Learning how to estimate is an important skill for children to learn: to be able to judge and determine the reasonableness of their answers in solving a mathematical problem or calculating a mathematical equation; to be able to use mental math to calculate more quickly a reasonable solution, and to understand when and where we need to estimate and how it makes our lives easier and better.  Estimation does not replace the need to come up with accurate answers, but teaching children to estimate helps them become critical thinkers and to understand what’s being asked of them.

Estimation Challenge, a Learning Story

Two important learning goals in my classroom are to help students become good mathematicians and good thinkers; learning how and why we estimate can help achieve these goals.  I share this learning story as one way to plan and implement curriculum activities that invite children to do just that.

I first planned and invited students to participate in a Mini Estimation Challenge and begin to learn about and practice their estimating strategies.  Students rotated through a number of estimating tasks, practicing their estimating skills and recording their estimations.

During our debriefs, children learned some new concepts words, for example, approximations, rounding, and referent.  They also learned and named some estimating strategies such as “clumping” and “box and count”.

Two wonderful picture books I shared that helped move our discussions and helped us explore the concept of estimating were Great Estimations and Greater Estimations by Bruce Goldstone.

After working through all the mini-estimating station tasks, students worked in small groups to count the items in the jars and then compare their estimations to the actual number of items, calculating whether their estimations were greater than or less than the actual count and by how much.  As they worked on this task there was lots of discussion and number work.

Every child was invited to bring a “see-through” container filled with “something” for our Estimation Challenge.  We all decided that this would be a “blind study” – no one would know, not even the student, the exact number of items in the container he/she brought until after the challenge when the items would be counted by the students.

Children then prepared their Estimation Challenge Station signs.  Their sign needed to include the following:IMG_4002

  • title: Estimation Challenge
  • title: name of collection
  • instruction words: estimate how many _____ are in the _____
  • a unique message
  • your name
  • a boarder

It was wonderful to watch and listen to the children as they worked on their station signs.  Every child was engaged and motivated as they prepared for our Estimation Challenge.  Materials were chosen, collected, gathered, made, and organized for our big day.

Along with a jar of items to estimate and their station sign, each child was given a bunch of small papers for station visitors to jot down their estimation, name, and division; they also had an envelope for their papers, and a tally/observation task sheet on which they would tally the number of guests who visited their stations and made an estimation, and on which they would record any observations. They were ready to set up and ‘man’ their stations.

Estimation Challenge

IMG_4008We invited student, teachers, and parents, kindergarten to grade 7, to test and practice making estimations. A schedule was made and posted in the staffroom so classes who wanted to participate would not all come at the same time. On the day of our big event, students set up their Estimation Challenge Stations in our classroom, the hallways, and common areas just outside our room.  The students were ready to welcome their visitors and collect their data. Students, teachers, and parents arrived and our Estimation Challenge began!

We were excited to also welcome some special guests from our school district.

After the Estimation Challenge . . . lots of number work and mathematical thinking.

IMG_4138Over the next few weeks, children shared and discussed their observations and worked through a number of tasks.  They counted the items in their containers, counted up their tallies, sorted out their estimation papers, and analyzed all their data.  It was amazing to see how many mathematical concepts came into play, concepts such as place value, repeated addition, multiplication (to name a few), were being practiced, reinforced, and learned. Children recorded all their estimations and some even found averages, and learned the differences between the mean, median, mode, and range.

At the end of our Estimation Challenge, children reflected on their experiences and shared what they had learned.  In summary, they all agreed – it was a rich, meaningful, and fun learning experience for all.

When I reflect on this learning story, the first thing that comes to mind is the energy and focus children demonstrated; it was palpable. When I think about the learning that went on, I am amazed at how many intellectual, personal, and social and emotional proficiencies the students were learning and practicing – the very skills they would need in order to engage in deep, life-long learning as successful citizens in today’s society. Students were learning to communicate their ideas and thinking; they were learning to plan, to carry out, and to accomplish a goal.  For some, this was not an easy task.  Students had to learn to persevere and use their struggles productively if they were to succeed.  And so they did! 

IMG_3668The power of rich, hands-on learning and children working together is a magical formula that makes learning relevant and fun.  Our Estimation Challenge was a big success, and, without question, the learning was far reaching.  A heart-felt, BRAVO, to all my students.

A great website with all kinds of estimation problems for you and your students to check out is Estimation 180.

Happy estimating!
Kelli

2 comments

  1. Another fabulous post, Kelli. It made me reflect on our estimation challenge at J.T. I will do this again soon at my school on Galiano.
    You continue to inspire me with your fine work and words!

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s