Can You Count Like the Maya?

Oct 9, 2026 · Dustin Purdy | @MrPurdyMath | Original blog post

Overview

The Maya are Indigenous peoples of southern Mexico and Central America, and millions of Maya people still live there today. More than 1,500 years ago, Maya mathematicians used a base-20 place-value system with a symbol for zero, one of the earliest zeros in the world. Students decode Maya numerals, write the year 2026 the Maya way, and compare base 20 with our base 10. The big idea: place value works in any base, and each place is a power of that base.

Grade level: 6–12 (grades 9–12 add the challenge tasks)

Time frame: 45 minutes

(Short on time? Run it as a 20-minute warm-up: read the hook, project the key, and do Rounds 1 and 2 only.)

Resources: Google Slides; the Maya number key and Mystery Numerals A–D (in Plan step 2), projected or printed; scratch paper

CCLS alignment

• 5.NBT.A.1–2: Place value and powers of ten (review for grade 6)

• 6.EE.A.1: Write and evaluate expressions with whole-number exponents

• 6.NS.B.4: Factors and multiples

• 8.EE.A.1: Properties of integer exponents

• HSA-SSE.A.1: Interpret the parts of an expression

• HSA-APR.A.1: Polynomials form a system like the integers

• MP7, MP8: Look for and use structure; reason from repeated patterns

Math topics

• Place value

• Number bases (base 10 and base 20)

• Exponents and powers

• Expanded form

• Multiples and divisibility

• Polynomial expressions (grades 9–12)

Key vocabulary

• Base (number base)

• Base 20 (vigesimal)

• Place value

• Positional system

• Numeral

• Zero as a placeholder

• Power (exponent)

• Expanded form

• Regroup (carry)

• Multiple

• Divisible

Plan

1. Hook (3 min). Read aloud: "The Maya are Indigenous peoples of southern Mexico and Central America. Millions of Maya people live there today and speak around 30 Mayan languages. Over 1,500 years ago, Maya mathematicians used a number system with a symbol for zero, something Europe didn't adopt for centuries. Instead of counting in 10s, they counted in 20s. Think fingers and toes." Speak about the Maya in the present tense where it fits.

2. Introduce the key (5 min). Project the key below. A dot is 1, a bar is 5 and a shell is 0. Within a level, bars sit at the bottom and dots on top. Levels stack: the bottom counts 1s, the next counts 20s, the next counts 400s. Ask: "Why might a culture count in 20s?" Expect: fingers and toes.

Maya number key 0–19 and Mystery Numerals A–D

3. Round 1: Write it (5 min). In pairs, students draw 7, 13 and 19, then answer: "What's the largest number one level can hold? Why can't a level have four bars?" Answers: 7 = 1 bar + 2 dots; 13 = 2 bars + 3 dots; 19 = 3 bars + 4 dots. The largest is 19, because four bars make 20, which carries up as one dot in the next level. Misconception: drawing 20 as four bars. Ask, "What happens in base 10 when you reach 10 ones?"

4. Round 2: Crack the code (7 min). Students decode Mystery Numerals A–D. Answers: A = 22 (1 × 20 + 2), B = 100 (5 × 20 + 0), C = 59 (2 × 20 + 19), D = 400 (1 × 400). Misconception: adding the levels instead of multiplying, such as reading B as 5. Ask, "What is each level worth?"

5. Challenge (10 min; grades 9–12 and early finishers). (a) Write 2026 as a Maya numeral. Answer: top level 1 bar, middle level 1 dot, bottom level 1 bar + 1 dot, because 5 × 400 + 1 × 20 + 6 = 2026. (b) What happens when you slide a shell in under a numeral? Answer: every level moves up a place, so the value is multiplied by 20. (c) What do you know about a numeral whose bottom level is one bar? Answer: it's 5 more than a multiple of 20, so it's divisible by 5, never by 20, and always odd. Key question: "How is this like putting a 0 at the end of a base-10 number?"

6. Calendar twist (5 min). In the Long Count calendar, Maya scribes made the third level worth 360 (18 × 20) instead of 400, close to the length of a year. Students recompute Mystery Numeral D under that rule. Answer: 360.

7. Secret numbers game (7 min). Each student writes a secret number from 20 to 399 as a Maya numeral, trades with a partner, decodes it, and checks the answer together.

Closing (3 min): Ask: "Why might counting in 20s make sense, and where do we still use bases other than 10?" Look for: fingers and toes; 60 seconds and minutes; 12 in a dozen; 2 in computer binary. French says 80 as quatre-vingts, "four twenties."

Assessment

Observation look-fors: students multiply each level by its place value, and they use the shell as a placeholder rather than skipping a level.

Exit ticket:

1. Write 45 as a Maya numeral. Answer: top level 2 dots, bottom level 1 bar (2 × 20 + 5 = 45).

2. A numeral has 3 dots in the 20s place and a shell in the 1s place. What number is it? Answer: 60.

3. Grades 9–12: Write 2026 as an expression using powers of 20. Answer: 5 · 20² + 1 · 20 + 6.

Extensions

• Write numbers in base 2 and base 60 and compare them with base 10 and base 20.

• Grades 9–12: build a spreadsheet that converts any number up to 7,999 into its three Maya levels.

• Research the Maya calendar and why the Long Count uses 360 in its third place.

• Local connection: look up the Indigenous nations whose homelands include your school's location, and whether their languages have their own counting words.

Does Every Diamond in a Star Quilt Have the Same Angle?

Oct 9, 2026 · Dustin Purdy | @MrPurdyMath | Original blog post

Overview

Star quilts are a living art form of Lakota, Dakota and Nakota quilters and other Plains nations. They are given as honoring gifts at graduations, memorials and powwows. Every star is built from eight diamonds that must meet perfectly in the center. Students uncover the angles, symmetry and counting patterns inside the star, construct their own, and write a rule for any size of star. The big idea: angles around a point add to 360°, and a visual pattern can be described with an algebraic rule.

Grade level: 6–12 (grades 9–12 add trigonometry and area)

Time frame: 50 minutes

(Short on time? Run steps 1, 3 and 4 plus the closing question as an 18-minute warm-up.)

Resources: Google Slides; the projected star (in Plan step 2); photos of contemporary star quilts by named Native quilters, from a museum collection or the artists' own sites; protractors, rulers, colored pencils and calculators

CCLS alignment

• 6.EE.A.2: Write and evaluate expressions with variables

• 7.G.A.2: Draw geometric shapes with given conditions

• 7.G.B.5: Supplementary, vertical and adjacent angles

• 7.G.B.6: Area of two-dimensional figures

• 8.G.A.1–3: Rotations, reflections and translations

• HSG-CO.A.3: Rotations and reflections that carry a polygon onto itself

• HSG-CO.D.12: Geometric constructions

• HSG-SRT.C.8: Use trigonometry to solve for lengths

• HSG-SRT.D.9 (+): Area of a triangle = ½ab sin C

• HSA-SSE.A.1: Interpret the parts of an expression

• MP5, MP6, MP7: Use tools, attend to precision, look for structure

Math topics

• Angles around a point

• Properties of rhombi

• Line and rotational symmetry

• Transformations

• Patterns and algebraic rules

• Area

• Scale

• Right-triangle trigonometry (grades 9–12)

Key vocabulary

• Polygon

• Rhombus

• Vertex

• Acute and obtuse angles

• Supplementary angles

• Angles around a point

• Diagonal

• Line of symmetry

• Rotational symmetry

• Order of rotational symmetry

• Translation, reflection, rotation

• Tessellation

• Frieze pattern

• Scale factor

• Sine and cosine

Plan

1. Hook (3 min). Read aloud: "Star quilts are a living art form of the Lakota, Dakota and Nakota peoples and other Plains nations. Starting in the late 1800s, they took the place of buffalo robes as honoring gifts. Today they are given at graduations, memorials, powwows and other important moments, wrapped around the person being honored. The design is often called a morning star, and it's built entirely from diamonds. Quilters have to get the geometry exactly right, or the points won't meet in the center. Let's find out why."

2. Notice and wonder (4 min). Show two or three photos of real star quilts, naming the quilter or nation for each, then project the star below. Students list what they notice (bands, points, colors) and wonder.

Eight-pointed star of 8 diamonds, 128 small diamonds

3. Angles (5 min). No protractors; reason it out. Ask: "How many big diamonds meet at the center? What angle does each make there? What are the diamond's other three angles?" Answers: 8 diamonds; 360° ÷ 8 = 45°; the other angles are 45°, 135° and 135°, because opposite angles of a rhombus are equal and neighboring angles add to 180°. Misconception: assuming every angle of the diamond is 45°. Ask, "What do all four angles of any quadrilateral add to?"

4. Counting (5 min). Ask: "How many small diamonds are in one big diamond? In the whole star? Count the small diamonds in each color band from the center out." Answers: 16; 128; bands of 1, 2, 3, 4, 3, 2, 1, which add up to 16.

5. Construct a star (13 min). Students mark a center point and draw 8 rays 45° apart. On two neighboring rays they mark 8 cm from the center, then draw an 8 cm segment from each mark parallel to the other ray; the segments meet at the tip of a rhombus. They repeat around the circle, split each side into 4 parts of 2 cm to make the 4 × 4 grid, and color the bands. Grades 6–8 can trace the projected star instead. Look for: rays measured from the same baseline, so errors don't build up around the circle.

6. Find the rule (8 min). Students fill in a table for stars with n small diamonds along each side: n = 2 gives 4 per big diamond, 32 in the star and 3 bands; n = 3 gives 9, 72 and 5; n = 4 gives 16, 128 and 7. They predict n = 5 (25, 200, 9) and write the rules: n² per diamond, 8n² in the star, 2n − 1 bands. Grades 9–12: band k from the center holds 8 · min(k, 2n − k) small diamonds; prove that 1 + 2 + … + n + … + 2 + 1 = n².

7. Scale it to a real quilt (7 min; grades 9–12). A 45° rhombus with side a has a long diagonal of 2a · cos 22.5° ≈ 1.848a, the distance from the star's center to a tip. Worked example: n = 8 with 3-inch small diamonds gives 24-inch big diamonds, about 88.7 inches tip to tip, and an area of 8 × 24² × sin 45° ≈ 3,258 in², about 22.6 square feet. Task: choose n and a side length so the star fits a 66-inch-wide quilt top (n × side ≤ 17.8; for example, n = 6 with 2.5-inch diamonds gives about 55 inches).

Closing (5 min): Ask: "Why must every center angle be exactly 45°? What would happen to the quilt if each were 46°?" Answer: 8 × 46° = 368°, 8° more than a full turn, so the pieces won't lie flat and the center buckles. Small errors add up across eight diamonds, which is why quilters' precision matters.

Assessment

Observation look-fors: students justify 45° with 360° ÷ 8 rather than measuring, and they connect the counting table to the rule.

Exit ticket:

1. How many small diamonds are in a star with n = 10? Answer: 8 × 10² = 800.

2. Explain in one sentence why each center angle must be 45°. Answer: eight equal angles fill a full 360° turn, and 360° ÷ 8 = 45°.

3. How many lines of symmetry does the star have, and what is its smallest rotation? Answer: 8 lines (through each tip and each gap); 45°.

4. Grades 9–12: each small diamond has 2-inch sides. Find the star's area. Answer: one diamond is 2 × 2 × sin 45° ≈ 2.83 in², so 128 diamonds ≈ 362 in².

Extensions

• Design and count: students design their own star with a chosen n and color scheme, then list how many small diamonds of each color a quilter would need to cut.

• Geometry in Indigenous art: each student picks one work by a named Indigenous artist or nation, from a museum collection or the artist's or nation's own site (not mass-produced souvenirs). Starting points include star quilts (Lakota, Dakota, Nakota and other Plains nations), woven rugs (Diné weavers), dream catchers (Ojibwe and other Anishinaabe makers), patchwork clothing (Seminole and Miccosukee sewers), pottery (Pueblo potters such as Acoma, Hopi and Zuni) and beadwork (Haudenosaunee, Plains and Great Lakes nations). Students report the work's maker, date and story (cited), a marked-up diagram, and three geometry findings with evidence: shapes, angles, symmetry, transformations or patterns.

• Grades 9–12: use a museum record's real dimensions to find the scale factor of a printout, or classify a repeating border as one of the seven frieze patterns.

• Invite a local Native artist or educator to speak about their work, and pay them for their time.

Whose Land Are We On?

Oct 9, 2026 · Dustin Purdy | @MrPurdyMath | Original blog post

Overview

Every place in the Americas is the homeland of Indigenous peoples, and many of those nations are still here today. Students use the free Native Land Digital map to find the nations connected to the land under their school, analyze what the class finds, and put history on a 24-hour clock. They finish by writing their own one-sentence land acknowledgment. The big idea: statistics summarize real data, and ratios and scale make huge numbers easier to understand.

Grade level: 6–12 (grades 9–12 add the challenge questions)

Time frame: 40 minutes

(Short on time? Run it as a 15-minute warm-up: do steps 1 and 2, skip to step 6, and use the acknowledgment sentence as the exit slip.)

Resources: Google Slides; the Native Land Classic Map; one device per pair or a projected map; board space for a class tally; sticky notes or exit slips

CCLS alignment

• 6.SP.B.4: Display numerical data in dot plots

• 6.SP.B.5: Summarize data with measures of center and spread

• 6.RP.A.1, 6.RP.A.3: Ratios, rates and percents

• 7.RP.A.3: Solve percent problems

• 6.NS.A.1: Work with fractions

• HSN-Q.A.1: Use units to guide problem solving

• HSS-ID.A.2–3: Compare center and spread; explain outliers

• MP2, MP4: Reason quantitatively; model with mathematics

Math topics

• Data collection

• Mean, median and range

• Dot plots

• Percents

• Ratios and fractions

• Scale and unit conversion

• Estimation

Key vocabulary

• Data

• Tally

• Mean

• Median

• Range

• Dot plot

• Outlier

• Ratio

• Fraction

• Percent

• Scale

• Unit conversion

• Estimate

Plan

1. Hook (2 min). Read aloud: "Every place in the Americas is the homeland of Indigenous peoples, and many of those nations are still here today. A land acknowledgment is a short statement that names the people whose land you're on. It's a way of telling the truth about history and showing respect to the people who live here now. But a good acknowledgment starts with knowing the facts. Today you'll be detectives: find out whose land our school is on."

2. Explore the map (8 min). In pairs, students check the school plus one other local place you assign (a park, the library, the town center). They search the Classic Map, list every nation whose territory covers the spot, switch to the Languages and Treaties layers, and open one nation's entry to find one fact. Students search public places only, never home addresses. Remind them the map is a starting point: Native Land Digital says its maps are not official or legal boundaries.

3. Build the class tally (5 min). Pairs record their counts on the board in a table with columns for place, territories, languages and treaties.

4. Part A: Analyze the data (8 min). Students find the mean, median and range of the territory counts, make a dot plot, and find the percent of places that overlap 3 or more territories. Key questions: "Which measure best describes a typical place?" and "Did every pair checking the school get the same count? Why might that be?" Grades 9–12: "Most places show overlapping territories. What does that tell you about drawing fixed borders around peoples who moved with the seasons, shared land, or were forced to relocate?"

5. Part B: History on a 24-hour clock (9 min). Indigenous peoples have lived in the Americas for at least 15,000 years, a commonly cited, approximate archaeological figure. The United States declared independence 250 years ago, in 1776. (a) Squeeze 15,000 years into one day, starting at midnight. When does 1776 arrive? Answer: 250 ÷ 15,000 = 1/60 of a day, or 24 minutes before midnight, so 11:36 p.m. (b) What fraction and percent of that history comes after 1776? Answer: 1/60, about 1.7%. (c) Grades 9–12: on a 100-yard football field timeline, how far from the end zone is 1776? Answer: 1/60 × 300 ft = 5 feet. (d) Grades 9–12: some evidence suggests people were here more than 20,000 years ago. Redo (a). Answer: 250 ÷ 20,000 × 1,440 minutes = 18 minutes, so 11:42 p.m. Misconception: dividing 15,000 by 250 and stopping at 60 without connecting it to minutes in a day.

6. Write it (5 min). Each student completes this frame: "We are learning and working on the homelands of the ______, who have cared for this land for generations and are still part of this community today." Then they add one sentence naming an action they could take to learn more or show respect.

Closing (3 min): A few volunteers read their acknowledgments aloud. Ask: "An acknowledgment is a first step. What could come next?" Look for: learning a nation's history, supporting a local Native organization, or checking the class acknowledgment with a local tribe.

Assessment

Observation look-fors: students use the mean or median to describe the class data and explain their choice; they set up Part B as a ratio before converting units.

Exit slip:

1. The completed acknowledgment sentence, naming at least one nation from the map.

2. Five places overlap 3, 4, 2, 5 and 3 territories. Find the mean, median and range. Answer: mean 3.4, median 3, range 3.

3. If 20,000 years were squeezed into one day, at what time would 1776 arrive? Answer: 11:42 p.m.

Extensions

• Combine the strongest sentences into a class acknowledgment, and check it with a local tribe, Native organization or cultural center before using it.

• Explore Native Land's own land acknowledgment guide and teacher's guide.

• Research one nation from the tally: where its government is today, its language, and a current event or leader.

• Grades 9–12: graph the time 1776 arrives for estimates from 12,000 to 25,000 years, and describe how sensitive the answer is to the estimate.

Source (optional)

• Native Land Digital: How It Works

• The 15,000-year figure is a commonly cited estimate, not drawn from a source checked for this plan.