{
  "format": "viable.course-package",
  "version": 1,
  "exported_at": "2026-10-30T19:00:00.000Z",
  "title": "Equivalent fractions, grade 5",
  "description": "Practice adding and subtracting fractions with a tutor that gives hints but never the answer, then a short check with the AI gone.",
  "guide": "For a grade 5 math teacher. A Questions panel sits beside a VETTING tutor that checks every hint against the question’s answer key before a learner sees it. How the AI helps is set to hints only, tied to standard 5.NF.A.1, with four common misconceptions from Eedi for the tutor to listen for. A post-test without the AI follows. Change the practice questions to your own first; the check stays hidden until you open it.",
  "agents": [
    {
      "ref": "tutor",
      "name": "Fractions tutor",
      "description": "Gives hints and guiding questions, checked against the answer key; never the answer.",
      "graph": {
        "version": 1,
        "name": "Fractions tutor",
        "entry": "input",
        "variables": {},
        "nodes": [
          {
            "id": "input",
            "type": "input",
            "config": {
              "guidance": "In a course, the Questions panel gives this tutor the question the learner is on and its answer key. To try it here, open Reference data → JSON and enter {\"question\":\"1/2 + 1/3 = ?\",\"answer_key\":\"Accepted answers: 5/6\"}.",
              "example": "I don’t get how to add these. Can you help?"
            },
            "next": "on_question",
            "x": 40,
            "y": 220
          },
          {
            "id": "on_question",
            "type": "condition",
            "config": {
              "field": "context.question",
              "op": "truthy"
            },
            "branches": {
              "true": "vet_question",
              "false": "vet_general"
            },
            "x": 280,
            "y": 220
          },
          {
            "id": "vet_question",
            "type": "vetting",
            "config": {
              "mode": "full",
              "model": "gpt-oss-120b",
              "question": "{{context.question}}",
              "answer_key": "{{context.answer_key}}",
              "max_attempts": 3,
              "includeHistory": true,
              "verification_model": "gpt-oss-120b"
            },
            "branches": {
              "passed": "reply_question",
              "unverified": "unverified",
              "attention": "attention_question"
            },
            "x": 540,
            "y": 100
          },
          {
            "id": "vet_general",
            "type": "vetting",
            "config": {
              "mode": "simple",
              "model": "gpt-oss-120b",
              "max_attempts": 3,
              "includeHistory": true,
              "guideline": "You are a patient math tutor for a ten-year-old practicing equivalent fractions and adding and subtracting fractions with unlike denominators. Give one hint or one guiding question at a time, with small numbers and short sentences. Never give the answer to a practice question or do the work for them. If they ask about something other than fractions, kindly bring them back to the practice.",
              "verification_model": "gpt-oss-120b"
            },
            "branches": {
              "passed": "reply_general",
              "unverified": "unverified",
              "attention": "attention_general"
            },
            "x": 540,
            "y": 360
          },
          {
            "id": "reply_question",
            "type": "output",
            "config": {
              "text": "{{vet_question.content}}"
            },
            "x": 820,
            "y": 40
          },
          {
            "id": "attention_question",
            "type": "output",
            "config": {
              "text": "{{vet_question.content}}"
            },
            "x": 820,
            "y": 160
          },
          {
            "id": "unverified",
            "type": "output",
            "config": {
              "text": "I couldn’t get a hint ready that I was sure about. Try asking in a different way, or ask your teacher."
            },
            "x": 820,
            "y": 280
          },
          {
            "id": "reply_general",
            "type": "output",
            "config": {
              "text": "{{vet_general.content}}"
            },
            "x": 820,
            "y": 400
          },
          {
            "id": "attention_general",
            "type": "output",
            "config": {
              "text": "{{vet_general.content}}"
            },
            "x": 820,
            "y": 520
          },
          {
            "id": "about",
            "type": "note",
            "config": {
              "text": "Each reply is drafted, then checked by a second model: against the answer key when a question is open, and against the guideline otherwise. A reply that gives the answer away is rewritten, up to three times; if none passes, the learner gets the “unverified” message instead."
            },
            "x": 280,
            "y": 440
          }
        ]
      }
    }
  ],
  "question_sets": [
    {
      "ref": "practice",
      "title": "Equivalent fractions: practice",
      "description": "Eight questions on equivalent fractions and adding and subtracting with unlike denominators, with hints and explanations.",
      "items": [
        {
          "id": "eq-2-3",
          "type": "single",
          "prompt": "Which fraction is equivalent to 2/3?",
          "answer": {
            "choice": "a"
          },
          "points": 1,
          "choices": [
            {
              "id": "a",
              "text": "4/6"
            },
            {
              "id": "b",
              "text": "3/4"
            },
            {
              "id": "c",
              "text": "2/6"
            },
            {
              "id": "d",
              "text": "4/3"
            }
          ],
          "skill": "equivalent fractions",
          "hints": [
            "Multiply the top and the bottom by the same number.",
            "Try multiplying the top and the bottom of 2/3 by 2."
          ],
          "explanation": "Multiply the top and the bottom of 2/3 by 2: 2 × 2 = 4 and 3 × 2 = 6, so 2/3 = 4/6."
        },
        {
          "id": "missing-top",
          "type": "fill",
          "prompt": "Fill in the missing number: 3/4 = ?/12",
          "answer": {
            "accept": [
              "9"
            ]
          },
          "points": 1,
          "skill": "equivalent fractions",
          "hints": [
            "What do you multiply 4 by to get 12?",
            "Multiply the top by that same number."
          ],
          "explanation": "4 × 3 = 12, so multiply the top by 3 too: 3 × 3 = 9. So 3/4 = 9/12."
        },
        {
          "id": "common-denominator",
          "type": "single",
          "prompt": "Which denominator could you use to add 1/2 and 1/3?",
          "answer": {
            "choice": "b"
          },
          "points": 1,
          "choices": [
            {
              "id": "a",
              "text": "5"
            },
            {
              "id": "b",
              "text": "6"
            },
            {
              "id": "c",
              "text": "3"
            },
            {
              "id": "d",
              "text": "2"
            }
          ],
          "skill": "common denominators",
          "hints": [
            "Look for a number that both 2 and 3 go into.",
            "Count by 2s and by 3s. Which number is in both lists first?"
          ],
          "explanation": "6 is a multiple of both 2 and 3, so both fractions can be written in sixths: 1/2 = 3/6 and 1/3 = 2/6. (Adding the denominators, 2 + 3 = 5, doesn’t give a common denominator.)"
        },
        {
          "id": "add-halves-thirds",
          "type": "fill",
          "prompt": "1/2 + 1/3 = ?",
          "answer": {
            "accept": [
              "5/6"
            ]
          },
          "points": 1,
          "skill": "adding unlike denominators",
          "hints": [
            "Write both fractions in sixths first.",
            "1/2 = 3/6. What is 1/3 in sixths?"
          ],
          "explanation": "1/2 = 3/6 and 1/3 = 2/6, so 3/6 + 2/6 = 5/6."
        },
        {
          "id": "subtract-eighths",
          "type": "fill",
          "prompt": "3/4 − 1/8 = ?",
          "answer": {
            "accept": [
              "5/8"
            ]
          },
          "points": 1,
          "skill": "subtracting unlike denominators",
          "hints": [
            "Write 3/4 in eighths.",
            "3/4 = 6/8. Now take away 1/8."
          ],
          "explanation": "3/4 = 6/8, and 6/8 − 1/8 = 5/8."
        },
        {
          "id": "spot-the-mistake",
          "type": "single",
          "prompt": "Sam says 1/3 + 1/4 = 2/7. What went wrong?",
          "answer": {
            "choice": "a"
          },
          "points": 1,
          "choices": [
            {
              "id": "a",
              "text": "He added the tops and added the bottoms, instead of writing both fractions with the same denominator first."
            },
            {
              "id": "b",
              "text": "He should have multiplied the tops."
            },
            {
              "id": "c",
              "text": "Nothing: 2/7 is right."
            },
            {
              "id": "d",
              "text": "He should have subtracted instead."
            }
          ],
          "skill": "adding unlike denominators",
          "hints": [
            "Is 2/7 bigger or smaller than 1/3 on its own? What does that tell you?",
            "Try writing both fractions in twelfths."
          ],
          "explanation": "The denominators can’t just be added. In twelfths, 1/3 = 4/12 and 1/4 = 3/12, so 1/3 + 1/4 = 7/12. Notice 2/7 is even smaller than 1/3, which can’t be right for a sum."
        },
        {
          "id": "mixed-sum",
          "type": "fill",
          "prompt": "2 1/2 + 1 1/3 = ? Write it as a mixed number, like 3 1/4.",
          "answer": {
            "accept": [
              "3 5/6",
              "23/6"
            ]
          },
          "points": 1,
          "skill": "mixed numbers",
          "hints": [
            "Add the whole numbers first.",
            "Then add 1/2 and 1/3, using sixths."
          ],
          "explanation": "Add the whole numbers: 2 + 1 = 3. Add the fractions: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. So the sum is 3 5/6."
        },
        {
          "id": "subtract-twelfths",
          "type": "fill",
          "prompt": "5/6 − 1/4 = ?",
          "answer": {
            "accept": [
              "7/12"
            ]
          },
          "points": 1,
          "skill": "subtracting unlike denominators",
          "hints": [
            "Find a number that both 6 and 4 go into.",
            "Use twelfths: 5/6 = 10/12. What is 1/4 in twelfths?"
          ],
          "explanation": "12 is a multiple of both 6 and 4: 5/6 = 10/12 and 1/4 = 3/12, so 10/12 − 3/12 = 7/12."
        }
      ]
    },
    {
      "ref": "check",
      "title": "Equivalent fractions: check",
      "description": "Five questions for the post-test.",
      "items": [
        {
          "id": "check-equivalent",
          "type": "single",
          "prompt": "Which fraction is equivalent to 3/5?",
          "answer": {
            "choice": "c"
          },
          "points": 1,
          "choices": [
            {
              "id": "a",
              "text": "3/10"
            },
            {
              "id": "b",
              "text": "5/3"
            },
            {
              "id": "c",
              "text": "6/10"
            },
            {
              "id": "d",
              "text": "6/5"
            }
          ],
          "skill": "equivalent fractions",
          "explanation": "Multiply the top and the bottom by 2: 3/5 = 6/10."
        },
        {
          "id": "check-missing",
          "type": "fill",
          "prompt": "Fill in the missing number: 2/3 = ?/9",
          "answer": {
            "accept": [
              "6"
            ]
          },
          "points": 1,
          "skill": "equivalent fractions",
          "explanation": "3 × 3 = 9, so 2 × 3 = 6: 2/3 = 6/9."
        },
        {
          "id": "check-add",
          "type": "fill",
          "prompt": "1/4 + 2/3 = ?",
          "answer": {
            "accept": [
              "11/12"
            ]
          },
          "points": 1,
          "skill": "adding unlike denominators",
          "explanation": "1/4 = 3/12 and 2/3 = 8/12, so the sum is 11/12."
        },
        {
          "id": "check-subtract",
          "type": "fill",
          "prompt": "7/8 − 1/2 = ?",
          "answer": {
            "accept": [
              "3/8"
            ]
          },
          "points": 1,
          "skill": "subtracting unlike denominators",
          "explanation": "1/2 = 4/8, and 7/8 − 4/8 = 3/8."
        },
        {
          "id": "check-mixed",
          "type": "fill",
          "prompt": "1 1/4 + 2 1/2 = ? Write it as a mixed number.",
          "answer": {
            "accept": [
              "3 3/4",
              "15/4"
            ]
          },
          "points": 1,
          "skill": "mixed numbers",
          "explanation": "1 + 2 = 3, and 1/4 + 1/2 = 1/4 + 2/4 = 3/4, so the sum is 3 3/4."
        }
      ]
    }
  ],
  "course": {
    "title": "Equivalent fractions",
    "description": "Practice adding and subtracting fractions by first making equivalent fractions. A tutor beside the questions gives hints and asks questions, but never gives the answer. Then try a short check on your own.",
    "appearance": {
      "theme": "playground",
      "color": null
    },
    "audience": "children",
    "identify": "code",
    "sections_from": "none",
    "data_level": "minimal",
    "keep_recordings": false,
    "units": [
      {
        "ref": "practice",
        "title": "Practice with a tutor"
      },
      {
        "ref": "check",
        "title": "Check on your own"
      }
    ],
    "activities": [
      {
        "unit_ref": "practice",
        "title": "Practice: equivalent fractions",
        "summary": "Eight questions with a tutor beside you. It gives hints, never the answer.",
        "role": "instruction",
        "agent_ref": "tutor",
        "workspace": {
          "ai": "right",
          "title": null,
          "layout": {
            "ai_width": 36,
            "resizable": true,
            "collapsible": true
          },
          "panels": [
            {
              "id": "practice",
              "type": "questions",
              "title": "Practice",
              "set_ref": "practice",
              "feedback": "each",
              "tries": 3,
              "hints": true,
              "ai_sees": "question",
              "starters": [
                "Can you give me a hint?",
                "Why do I need the same denominator?",
                "How do I find a common denominator?"
              ]
            }
          ]
        },
        "minutes": 20,
        "voice": null,
        "attachments": null,
        "teaching": {
          "goal": "Learners rewrite fractions with a common denominator before adding or subtracting, and can say why the denominators can’t just be added.",
          "help": "hint",
          "watch_for": "Adding the denominators (1/2 + 1/3 = 2/5), or asking for the answer again and again.",
          "standard": {
            "object": "standard",
            "uuid": "6b9c1a30-d7cc-11e8-824f-0242ac160002",
            "code": "5.NF.A.1",
            "description": "Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.",
            "jurisdiction": "Multi-State",
            "subject": "Mathematics",
            "grades": [
              "5"
            ],
            "learning_components": [
              {
                "id": "d022d8d2-37f6-5ce9-bb02-e000d731aba0",
                "description": "Add fractions with different denominators by using equivalent fractions"
              },
              {
                "id": "089c550e-f3a4-5ea2-959a-34e267c3e374",
                "description": "Subtract fractions with different denominators by using equivalent fractions"
              },
              {
                "id": "d2565c2d-3930-54d3-864e-e532fd65cf6c",
                "description": "Add mixed numbers with different denominators by using equivalent fractions"
              },
              {
                "id": "3f8f80e7-a5c3-56e5-bf2d-90c5bb5f4f08",
                "description": "Subtract mixed numbers with different denominators by using equivalent fractions"
              }
            ],
            "prior": [
              {
                "uuid": "6ba1136b-d7cc-11e8-824f-0242ac160002",
                "code": "4.NF.B.3.a",
                "description": "Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.",
                "jurisdiction": "Multi-State",
                "subject": "Mathematics",
                "grades": [
                  "4"
                ]
              },
              {
                "uuid": "6ba18d83-d7cc-11e8-824f-0242ac160002",
                "code": "4.NF.B.3.b",
                "description": "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.",
                "jurisdiction": "Multi-State",
                "subject": "Mathematics",
                "grades": [
                  "4"
                ]
              },
              {
                "uuid": "6ba208b6-d7cc-11e8-824f-0242ac160002",
                "code": "4.NF.B.3.c",
                "description": "Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.",
                "jurisdiction": "Multi-State",
                "subject": "Mathematics",
                "grades": [
                  "4"
                ]
              },
              {
                "uuid": "6ba25f3e-d7cc-11e8-824f-0242ac160002",
                "code": "4.NF.B.3.d",
                "description": "Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.",
                "jurisdiction": "Multi-State",
                "subject": "Mathematics",
                "grades": [
                  "4"
                ]
              }
            ],
            "source": {
              "name": "Learning Commons Knowledge Graph",
              "license": "https://creativecommons.org/licenses/by/4.0/",
              "attribution": [
                "Knowledge Graph is provided by Learning Commons under the CC BY-4.0 license. Common Core Mathematics standards provided by Common Good Learning Tools available at https://corestandards.org/wp-content/uploads/2023/09/Math_Standards1.pdf.",
                "Knowledge Graph is provided by Learning Commons under the CC BY-4.0 license. Learning Commons received learning components under CC BY-4.0 from Achievement Network.",
                "Knowledge Graph is provided by Learning Commons under the CC BY-4.0 license. Learning Commons received learning progressions under CC0 from Student Achievement Partners."
              ],
              "modified": "2025-02-06",
              "retrieved_at": "2026-10-21T00:00:00.000Z"
            }
          },
          "misconceptions": [
            {
              "id": "b59fa4bd-e452-595e-a292-933ed0ddb1ab",
              "description": "Believes that fractions are added by summing numerators and denominators as if they are separate whole numbers",
              "construct": {
                "id": "77e855a4-7e41-56fc-9a0c-c865ce1768c0",
                "description": "Add proper fractions with different denominators which do not share a common factor"
              },
              "source": {
                "name": "Eedi Misconceptions Graph v1.0",
                "license": "https://creativecommons.org/licenses/by/4.0/",
                "attribution": [
                  "Knowledge Graph is provided by Learning Commons under the CC BY-4.0 license, available at https://creativecommons.org/licenses/by/4.0. \"Eedi Misconceptions Graph v1.0\" (c) 2026 Eedi Ltd., licensed under CC BY 4.0 and available at https://www.eedi.com."
                ],
                "modified": "2026-06-15"
              }
            },
            {
              "id": "cd93583c-468a-5da0-a24f-9753f1b2fe1d",
              "description": "Believes adding the denominators gives a common denominator",
              "construct": {
                "id": "7bfdef9d-758a-5650-9581-c2cbf6b79e0c",
                "description": "Add proper fractions with different denominators where one is a multiple of the other"
              },
              "source": {
                "name": "Eedi Misconceptions Graph v1.0",
                "license": "https://creativecommons.org/licenses/by/4.0/",
                "attribution": [
                  "Knowledge Graph is provided by Learning Commons under the CC BY-4.0 license, available at https://creativecommons.org/licenses/by/4.0. \"Eedi Misconceptions Graph v1.0\" (c) 2026 Eedi Ltd., licensed under CC BY 4.0 and available at https://www.eedi.com."
                ],
                "modified": "2026-06-15"
              }
            },
            {
              "id": "cd0a50b7-672b-5a8b-ab98-46a7545e7af0",
              "description": "Believes numerators stay the same when finding common denominators",
              "construct": {
                "id": "77e855a4-7e41-56fc-9a0c-c865ce1768c0",
                "description": "Add proper fractions with different denominators which do not share a common factor"
              },
              "source": {
                "name": "Eedi Misconceptions Graph v1.0",
                "license": "https://creativecommons.org/licenses/by/4.0/",
                "attribution": [
                  "Knowledge Graph is provided by Learning Commons under the CC BY-4.0 license, available at https://creativecommons.org/licenses/by/4.0. \"Eedi Misconceptions Graph v1.0\" (c) 2026 Eedi Ltd., licensed under CC BY 4.0 and available at https://www.eedi.com."
                ],
                "modified": "2026-06-15"
              }
            },
            {
              "id": "173be8a9-26dc-597d-b9d1-6d608fe70e0d",
              "description": "Believes when making an equivalent fraction you can multiply the numerator and denominator by different values",
              "construct": {
                "id": "77e855a4-7e41-56fc-9a0c-c865ce1768c0",
                "description": "Add proper fractions with different denominators which do not share a common factor"
              },
              "source": {
                "name": "Eedi Misconceptions Graph v1.0",
                "license": "https://creativecommons.org/licenses/by/4.0/",
                "attribution": [
                  "Knowledge Graph is provided by Learning Commons under the CC BY-4.0 license, available at https://creativecommons.org/licenses/by/4.0. \"Eedi Misconceptions Graph v1.0\" (c) 2026 Eedi Ltd., licensed under CC BY 4.0 and available at https://www.eedi.com."
                ],
                "modified": "2026-06-15"
              }
            }
          ]
        },
        "release": "open",
        "done_when": "auto"
      },
      {
        "unit_ref": "check",
        "title": "Check: equivalent fractions",
        "summary": "Five questions, one try each, no tutor. You see how you did at the end.",
        "role": "posttest",
        "agent_ref": null,
        "workspace": {
          "ai": "off",
          "title": null,
          "layout": {
            "ai_width": 36,
            "resizable": true,
            "collapsible": true
          },
          "panels": [
            {
              "id": "check",
              "type": "questions",
              "title": "Check",
              "set_ref": "check",
              "feedback": "end",
              "tries": 1,
              "hints": false,
              "ai_sees": "nothing"
            }
          ]
        },
        "minutes": 10,
        "release": "hidden",
        "done_when": "auto"
      }
    ]
  },
  "attribution": [
    "Knowledge Graph is provided by Learning Commons under the CC BY-4.0 license. Common Core Mathematics standards provided by Common Good Learning Tools available at https://corestandards.org/wp-content/uploads/2023/09/Math_Standards1.pdf.",
    "Knowledge Graph is provided by Learning Commons under the CC BY-4.0 license. Learning Commons received learning components under CC BY-4.0 from Achievement Network.",
    "Knowledge Graph is provided by Learning Commons under the CC BY-4.0 license. Learning Commons received learning progressions under CC0 from Student Achievement Partners.",
    "Knowledge Graph is provided by Learning Commons under the CC BY-4.0 license, available at https://creativecommons.org/licenses/by/4.0. \"Eedi Misconceptions Graph v1.0\" (c) 2026 Eedi Ltd., licensed under CC BY 4.0 and available at https://www.eedi.com."
  ],
  "notes": []
}