Hat Lab: Hat Sizes and Pi
A US hat size like 7 1/8 is not a length you can find anywhere on the hat. Students discover that it is the head's circumference in inches divided by pi: the width the head would have if it were a perfect circle. They measure, convert centimeters to inches, divide by pi and round to the nearest eighth, then check each answer in Hat Lab, and find why every centimeter around the head adds one eighth to the size.
At a glance
Essential question
What does a hat size measure, and how can pi tell you yours?
Objectives
Students will be able to:
- measure a circumference and convert it from centimeters to inches
- use the relationship between circumference and diameter to find a US hat size from a head measurement
- round a measurement to the nearest eighth of an inch and check it against the app
- explain why each centimeter around the head adds about one eighth to the US size
Vocabulary
circumference, diameter, pi, convert, hat size, eighth
Standards
6.RP.A.3d, 7.G.B.4, 7.EE.B.3
Time and materials
45 minutes, grades 6-8.
- One computer or Chromebook per student or pair
- A projector
- A cloth tape measure, or a piece of string and a ruler, per student
- A calculator, or the one on the computer
- The worksheet and exit ticket, one copy each per student
- The rubric, one copy per student if you grade the worksheet
Prep
Make copies of the worksheet and exit ticket, and set out tape measures or string and rulers. Before class, open mytekdev.com/try/hatlab?lesson=hat-sizes-and-pi&ref=tpt-hatlab-2 once on a student computer and open Shape to see the Size readout, and to check that your school's filter allows it. No account is needed. Some students may not want their head measured: the worksheet has a set of measurements to use instead.
Assessment
- Formative: the questions under What to look for, asked while students work, and the exit ticket (answer key included).
- Summative: the completed worksheet, scored with the rubric out of 12.
Technology and privacy
Runs in any browser, Chromebooks included, with nothing to install. Students need no account and no email: the link works signed out, and nothing they make is stored on our server unless they choose to save it to an account. If your school blocks new sites, ask IT to allow mytekdev.com.
What’s included
- A one-page overview: objectives, essential question, vocabulary, standards and assessment
- A ten-minute walkthrough to rehearse before class, and background in plain words for the teacher
- A 45-minute lesson sequence: warm-up, direct instruction, guided practice, independent practice, closure
- Slides for the board: a PowerPoint file that also opens in Google Slides
- A student worksheet with a QR code and a data table
- A 3-question exit ticket, two to a page, with an answer key
- A rubric: 3 criteria, 4 levels, scored out of 12
- Differentiation for English learners, students with IEPs or 504 plans, and students who need more support or more challenge
- Cross-curricular extensions, and notes for teaching it in grades 4-5 and 9-12
- Standards: Common Core math
Standards
These Common Core standards are the center of the lesson: students use the circumference of a circle to solve a real problem, and convert units with ratio reasoning.
| Framework | Code | Grades | Standard | How the lesson meets it |
|---|---|---|---|---|
| Common Core Math | 6.RP.A.3d | 6 | Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. | Students convert head measurements from centimeters to inches, dividing by 2.54. |
| Common Core Math | 7.G.B.4 | 7 | Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. | Students use C = pi x d to find the diameter a head would have as a circle, which is its US hat size. |
| Common Core Math | 7.EE.B.3 | 7 | Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. | Students solve a multi-step problem (divide by 2.54, divide by 3.14, round to the nearest eighth), convert decimals such as 6.77 to 6 3/4, and check reasonableness against Hat Lab. |
Checked October 2026 against: Common Core State Standards, Grade 6 Ratios and Proportional Relationships, Common Core State Standards, Grade 7 Geometry, Common Core State Standards, Grade 7 Expressions and Equations.