Measuring with Confidence

By middle school students need to “understand, select, and use units of appropriate size” and “use common benchmarks to select appropriate methods for estimating measurements” (Common Core State Standards Initiative, p. 240). Oftentimes I find students lack the skills to reason with quantities and make sense of numbers. Occasionally students' answers in math do not make sense. This could be due to incorrect or missing units, incorrect calculations, or a lack of number sense. By focusing on real world units and approximations, students can improve their mathematical reasoning which can benefit them throughout their mathematics journey. 

Ish- The Math-ish Mascot

In my classroom I have been focusing on supporting and encouraging students to use approximate numbers to check if their answers make sense. To remind us to use these estimation strategies we use an “Ish” stuffed animal made by Jo Boaler. In her book Math-ish (2024) she examines real world applications and diversity within math. This can help give students an authentic context to apply the skills they are learning.

In order for students to correctly identify the units of a problem, students need to be able to picture what various units look like. To support students developing their content knowledge around units of measurement, I continue to strengthen my own Common Content Knowledge (Hill & Ball, 2009). I continually try to improve my measurement skills through hands-on explorations of measurement within construction, baking and other artistic expressions. As I continue to strengthen my Mathematical Knowledge for Teaching (Hill & Ball, 2009), I have discovered a variety of resources to incorporate into my teaching. By using these resources I can better help my students build their understanding of quantities and measurements they will use throughout their lives.  Often in math students are so focused on the right answer or numerical value,  they skip over mathematical reasonableness. My students struggle to picture what a quart, meter, or milliliter are. If they can not picture these quantities, how would they be able to know if their answer makes sense? While I have been using "Ish" to focus on numerical computations, I have the opportunity to use Ish with units of measurement. 

How many candy corn in 1/4 cup?

To help my students, I am going to use some of the resources in Estimation 180 by Andrew Stadel. This source has real-world quantities in which students use estimation strategies to solve problems, such as estimating how many pieces of candy corn are in ¼ cup. While these activities do have a “right” answer, the goal is not to find the correct answer. These activities encourage students to hone their estimation and reasoning skills with quantities and measurements in order to come up with an accurate estimate. I could extend these activities by asking students what unit they would use to measure the objects, besides just looking at the number of objects.

This activity challenges students' view of math and lets students experience the fluidity of math. While there is a time and place for the right answers in mathematics, students need to also have measurement and estimation - the Ish - skills that they will use and apply in the real world. Whether it is cooking, construction, or determining how much gas a car needs for a trip, there are many real world applications of measurement. My job is to help students make these connections and provide them opportunities to work with numbers in the real world - not just on a worksheet.

References 

Boaler, J. (2024). Math-Ish. HarperCollins books. https://www.mathish.org/ 

Common Core State Standards Initiative (CCSSI). (n.d.). Mathematics standards. Mathematics Standards | Common Core State Standards Initiative. http://www.corestandards.org/Math/

Hill, H., & Ball, D. L. (2009). The curious - and crucial - case of Mathematical Knowledge for Teaching. Phi Delta Kappan, 91(2), 68–71.