🏴☠️ The fair-shares case — division and fractions
The Sunken Share is the fractions case, and it is built on the one idea that makes fractions make sense: fair sharing. A chest of gold was sworn to be split into equal parts, one greedy pirate took more than their share, and every round of the investigation asks the cadet to work out what 'equal' actually means. That progression is the spine of the curriculum — sharing counters into equal piles in Kindergarten becomes halves and fourths in Grade 1, equal-area fractions in Grade 3, and by Grade 5 the realisation that a fraction was a division all along. Fractions are where a lot of children quietly fall off the maths, and they usually fall off because nobody ever tied them back to sharing. This case never lets go of the rope.
A chest of gold was sworn to be split into fair, equal shares — but one greedy pirate grabbed more than their share and re-buried the treasure! Split the plunder into equal shares, weigh the doubloons, crack the captain's log and fire the cannons to unmask the pirate who broke the code of fair shares.
Each round is a different interactive mechanic — not the same question in a new coat. Crack all four to unmask the culprit.
The same story, re-levelled for each grade against its own Common Core standards. Pick your child's grade:
| Grade | Skill focus | Standards | XP | |
|---|---|---|---|---|
| Kindergarten | Count & share equal piles, +/− within 10 | K.OA.A.2 K.CC.B.5 K.OA.A.5 | ⚡ 100 XP | Launch → |
| Grade 1 | Halves & fourths, +/− within 20 | 1.G.A.3 1.OA.D.7 1.OA.A.1 1.OA.C.6 | ⚡ 110 XP | Launch → |
| Grade 2 | Fractions, +/− within 1000, word problems | 2.G.A.3 2.NBT.B.7 2.OA.A.1 2.OA.B.2 | ⚡ 130 XP | Launch → |
| Grade 3 | Equal-area fractions, ×, two-step problems | 3.G.A.2 3.NBT.A.2 3.OA.D.8 3.OA.C.7 | ⚡ 140 XP | Launch → |
| Grade 4 | Decompose fractions, multi-digit ×/+ | 4.NF.B.3.b 4.NBT.B.4 4.OA.A.3 4.NBT.B.5 | ⚡ 150 XP | Launch → |
| Grade 5 | Fractions as division, decimals & division | 5.NF.B.3 5.NBT.B.7 5.NBT.B.5 5.NBT.B.6 | ⚡ 160 XP | Launch → |
Earns the 🏅 Fair-Share Sleuth badge.
Across K–5, The Sunken Share covers these 23 standards. Mastery is tracked per standard for each agent. Official Common Core wording:
| 1.G.A.3 | Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. |
|---|---|
| 1.OA.A.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. |
| 1.OA.C.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums. |
| 1.OA.D.7 | Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. |
| 2.G.A.3 | Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. |
| 2.NBT.B.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. |
| 2.OA.A.1 | Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. |
| 2.OA.B.2 | Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. |
| 3.G.A.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. |
| 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. |
| 3.OA.C.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. |
| 3.OA.D.8 | Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. |
| 4.NBT.B.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. |
| 4.NBT.B.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. |
| 4.NF.B.3.b | Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. |
| 4.OA.A.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. |
| 5.NBT.B.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. |
| 5.NBT.B.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. |
| 5.NBT.B.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. |
| 5.NF.B.3 | Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. |
| K.CC.B.5 | Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1—20, count out that many objects. |
| K.OA.A.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. |
| K.OA.A.5 | Fluently add and subtract within 5. |
Earlier than most people expect. Equal sharing begins in Kindergarten, halves and fourths in Grade 1, and formal fraction comparison in Grade 3. This case follows that ladder rather than dropping fractions in suddenly.
Very common — it usually means the procedure was learned before the idea. This case leads with the idea (fair shares) and lets the procedure follow, which is the order the standards intend.
It's treasure and teamwork, not violence — the crime is a pirate taking more than their fair share, and the worst thing that happens is somebody gets found out.