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How To Number Talk: Estimation 180

This particular number talk holds nostalgia for me. When I was in elementary school, there was a jar by the principal's office that would be filled with various objects, such as candy or other food items. We’d each get an opportunity to take a guess and “win” the jar. What I didn’t realize at the time was that, all the while, I was practicing:

• Number sense
• Spatial reasoning
• Attuning my brain to what was reasonable
• An appreciation for mathematics

Estimation 180, from Andrew Stadel, takes this nostalgic math activity a step farther by providing estimation visuals that tackle a variety of areas, such as money, fractions and measurement. Images range from single shots to a series of photos that can be built on daily.

How to do it

There are a few ways to approach Estimation 180:

1. Make your own visual. Grab a jar, fill it with a large amount of small objects and get your students to make their best, reasonable guess
2. Take a single picture from Estimation180 that relates to your topic. Do this from time to time.
3. Use a series of Estimation 180 photos that build on each other to help support a unit or lesson series.

Once you have chosen your path, Stadel recommends you do three things, using an open number line:

1. Have students pick a “too high” estimate.
2. Have students pick a “too low” estimate.
3. Have students pick a “just right” estimate.

Allow students time to chat with those around them before sharing their estimates with the whole class. Once it’s time to share, record as many answers as possible. At first, students might act a little silly, but with consistency and acknowledgement they’ll begin to buy in, and you’ll be surprised by how many students get close to the precise number. I highly recommend you check out , which includes handouts to support student thinking as they estimate.

Now, grab a pencil and let’s try it out (remember, no counting!):

About how many staples in this single strip?

Now, draw an open number line. Put your “too high” estimate on the line, and then add your “too low” estimate. Next, add your “just right” estimate on; however, when you place this number instead of putting it right in the middle, challenge yourself to estimate where it belongs between the two numbers (you can try this with students too). If you’d like to check your estimate click the link in the caption.

Questions to ask:

As you work through the process in class, ask your students:

• What do you notice? What do you wonder?
• What is a “too high” estimate? What is “too low”? What is “just right”? How do you know?
• What do you notice when you compare your estimate to the final answer? What do you wonder? How far apart were they?
• How did you arrive at the estimate?

Links to Standards of Mathematical Practice

Number talks provide a great opportunity to link back to the Standards of Mathematical Practice (SMP’s), particularly the following:

1. SMP 7: Look for and make use of structure
   Here we’re asking students to use what they know about spatial reasoning and general number sense to make a reasonable guess. They have to know how items chunked together might look.
2. SMP 3: Construct viable arguments and critique the reasoning of others
   Students participating in these estimations need to be able to use a “logical progression of statements” to support their own estimate. They must also be able to logically support or challenge the reasoning of their peers.

Where to find visuals

• Create your own — make it a math “project” or invite families to participate.

Note: If you’d like to try a visual challenge that builds from day to day try which all deal with staples.

from Math for Teachers by ŷ��AV.