# Ontario Grade 6 Mathematics — 27 October 2026

The Grade 6 pass follows a reuse audit of all **63 retained expectations: 51 specific and 12 overall**. Source IDs, wording, hashes, types and stored hierarchy are unchanged. [Official Ontario source](https://www.dcp.edu.gov.on.ca/en/curriculum/elementary-mathematics/grades/g6-math).

The release adds **244 topic-code pairs on 178 topics: 173 existing and five new**. Fifty-three codes are directly linked; ten overall expectations roll up their stored children. The verified graph and staging DB contain **1,850 topics / 3,967 dependencies / 5,203 known pairs**, plus the same 41 legacy graph pairs. Every earlier pair remains, including Grade 1–5 Mathematics counts of 152 / 124 / 156 / 186 / 190.

## Five additions, with different meanings

- **Divisibility rules** fills an explicit procedure gap for the rule family (2, 3, 4, 5, 6, 8, 9, 10). Place value and known multiples support explanations. There is no separate topic per divisor and no million-range reading gate.
- **Building objects from views** fills the inverse spatial-construction procedure: satisfy and check given top/front/side constraints, including ambiguous views. It does not broaden the Grade 5 drawing/matching claim or promise a unique reconstruction or universal height algorithm.
- **Diagonals of quadrilaterals** extracts focused assessment from a broader existing geometry claim. This is existing mathematical knowledge, not an absent mathematical idea. Learners investigate equality, bisection and perpendicularity; inclusive shape classes and non-rhombus kite counterexamples prevent false universal statements. The older geometry claim is unchanged.
- **Comparing ways to pay** adds financial decision content beyond recognising payment methods. Given scenarios support different criteria and methods; credit knowledge is optional when another legitimate comparison route is used.
- **Interest rates and bank fees** adds financial content about rates, periods and charges on fictional account/loan information. Fees need not be flat; a monthly fee per month can stay fixed while total fees increase over more months. Current rates, compulsory compound-interest calculations and actual product recommendations are outside the claim.

No old topic description, evidence, question, title, type, subject, domain or other non-alignment attribute changed. No range, grade, difficulty or country clones, merges, retirements or learner resets were applied.

## Reuse and the source compositions

Existing histograms include intervals and boundary conventions; connected-line graphs already show time trends. Existing mean/median/mode/range, surface-area and polygon-decomposition claims are reused. The donating proposal was withdrawn: the official examples allow donated time, already represented by community contribution, combined with trade and lender/borrower perspectives. A barter contributor remains explicitly unlinked because a later first Canadian context would create strict age flags; no dummy earlier age is invented.

Several rows use worked combinations rather than asserting every source facet inside a single holder. Division by a decimal uses common units: 234 L ÷ 0.6 L = 2,340 tenths ÷ 6 tenths = 390 groups. In 235 L, 391 whole groups leave 0.4 L, or two-thirds of a group. Dividing by a proper fraction similarly uses thirds as common units. Factor trees record repeated factor-pair splits stopped at primes. Positive-coefficient like terms use distinct labelled tiles and distributivity (2x + 3x + 4y = 5x + 4y); unlike letters remain separate. Joint independent-event outcomes use systematic listing, favourable/total and experiments rather than requiring fraction multiplication along a tree.

Rounding consumes a given recurring expansion; generating it by long division is background. Surface-area transfer beyond the existing rectangular/triangular-base scope is explicit through face identification, polygon decomposition and summing areas. The older net claim is not silently reinterpreted as covering every base. Clockwise/counterclockwise vocabulary is attributed to the existing direction claim, combined with protractor measurement and full-turn relations. Efficient-code contexts reuse loops and execution counts. Seventeen composition rows retain worked tasks and limits; a component task does not certify an entire broader topic.

All 63 rows have a Full contextual authoring judgment. This is separate from learner attainment and school reporting. Ontario retains SEL learning support while excluding the SEL overall expectation from assessment, evaluation and reporting; A1 associations here preserve support/process content. [Official strand note](https://www.dcp.edu.gov.on.ca/en/curriculum/elementary-mathematics/grades/g6-math/strands).

## Verification

Three old hard gates become soft supports. Two hard foundations are added on existing topics; the new claims add nine hard and fourteen soft links plus one incoming soft extraction link. Actual Canadian closure contains **178 holders / 319 topics / 416 hard edges / zero issues**. All eleven new hard edges pass every applicable source country under minimum-country/UNIVERSAL and strict-country rules. No edge/country context is newly affected and the full hard/soft graph is acyclic. Two old flags resolve; the earlier US rounding/place-value issue remains unchanged.

Independent checks match every authorized field and dependency, exact source identities/hierarchy and pairs, derived ages and centralities, embedding presence, and protected learner/research fingerprints. No learner, assessment or canonical teaching-research records changed. The public research projection preserves all **1,049 exact records** and the historical archive. The five additions increase explicit missing-research coverage from 796 to **801 topics**. All **17 catalogues / 7,743 source rows**, including **nine Ontario documents / 3,862 expectations**, are preserved. Ontario is exported as codes and official links only.

## Code-by-code mapping

| Code | Coverage judgment | Mapped topics or rollup |
|---|---|---|
| A1 | Full | `mt_20WfHhnL39`, `mt_35-DhMh_Yr`, `mt_8dstvf-KKb`, `mt_EBYGhd8X3x`, `mt_IM1G_7QzTa`, `mt_Iwg2diBSyW`, `mt_LhkP_KKIRS`, `mt_QxsoqVUt6u`, `mt_S4G6GLKr1-`, `mt_TMoHjMhRS2`, `mt_UGf6jICEhs`, `mt_WkKkb7W9Qd`, `mt_YbX3LD0Eca`, `mt_f67qGDhyfi`, `mt_j8Pv3s7TZR`, `mt_kJ5wYzO8qC`, `mt_pAuo9Op89t` |
| B1 | Full | Stored-child expectation rollup |
| B1.1 | Full | `mt_Gag_h98jWP`, `mt_JwP9QFv6gQ`, `mt_x8TshvbbQT` |
| B1.2 | Full | `mt_1KkvzwYxbR`, `mt_PsylzZ9lHW`, `mt_RVK655t391`, `mt_vXRzMbiPff` |
| B1.3 | Full | `mt_4K1dr204Hi`, `mt_933BohS9BH`, `mt_PL9VkDwXfh`, `mt_PsylzZ9lHW`, `mt_uDJY0X0hgo` |
| B1.4 | Full | `mt_933BohS9BH`, `mt_Ac7oMWhyPw`, `mt_kdWoAel3Zl`, `mt_lNGpnILM5C` |
| B1.5 | Full | `mt_Ii1hV4V5ql`, `mt__casygEB85` |
| B1.6 | Full | `mt_4K1dr204Hi`, `mt_4Km38F4L-6`, `mt_Ac7oMWhyPw`, `mt_NaqEP8xDhZ`, `mt_TqDq6jyOmL`, `mt_W17Kbwm0-u`, `mt_kdWoAel3Zl` |
| B2 | Full | Stored-child expectation rollup |
| B2.1 | Full | `mt_AR-K72OIIO`, `mt_GDG9_SZmsO`, `mt_JH_6RpNWjr`, `mt_Lb2ZnMdkYR`, `mt_PNSyfH56eQ`, `mt_QCgbiVrwnp`, `mt_QaYfeVL-0C`, `mt_Qe2PsFmSAH`, `mt_anAe11HAEH`, `mt_e7filQgayF`, `mt_ehGS_uVSJv`, `mt_h0gJcSuwdL`, `mt_p-nbe0w_lf` |
| B2.2 | Full | `mt_48Bjqr7j04`, `mt_oxfxzbat3k`, `mt_w6MxaaoMXZ` |
| B2.3 | Full | `mt_4ubP_RMg9o`, `mt_LlMl2PbaZe`, `mt_PNSyfH56eQ`, `mt_ZM9mhHsyYZ`, `mt_kJ5wYzO8qC` |
| B2.4 | Full | `mt_JH_6RpNWjr`, `mt_QaYfeVL-0C`, `mt_Yw1_4Nfsql`, `mt_yTWxkzzoOZ` |
| B2.5 | Full | `mt_-V7EnqU7gG`, `mt_14T5yPXUq_`, `mt_CBHwluE6Lp`, `mt_VgOePicFYK`, `mt_e7filQgayF` |
| B2.6 | Full | `mt_FHIAv6dfhU`, `mt_nZkL5-XjRX`, `mt_y1XCVsIelg` |
| B2.7 | Full | `mt_Lb2ZnMdkYR`, `mt_SoDP1fSQEB`, `mt_XLP1IM3Qbb` |
| B2.8 | Full | `mt_SoDP1fSQEB`, `mt_TqDq6jyOmL`, `mt_WsM4EmdOLe`, `mt_iNdrM2-oJf`, `mt_wPgpMJ0-PA` |
| B2.9 | Full | `mt_HJA2Oz-Zh1`, `mt_TgHxujL81r` |
| B2.10 | Full | `mt_1PAWhRhpdg`, `mt_TgHxujL81r`, `mt_WsM4EmdOLe` |
| B2.11 | Full | `mt_kdWoAel3Zl`, `mt_lU-2aTRB9f` |
| B2.12 | Full | `mt_4ubP_RMg9o`, `mt_EmR5n58jZt`, `mt_PNSyfH56eQ`, `mt_Qe2PsFmSAH`, `mt_ePXg_XyCKU`, `mt_h0gJcSuwdL` |
| C1 | Full | Stored-child expectation rollup |
| C1.1 | Full | `mt_W3VOAuFwVw`, `mt_ZjIFGc6zPW`, `mt_yXO7lQ9Yn7` |
| C1.2 | Full | `mt_Cqm8iy48UI`, `mt_HRKzwEQJgO`, `mt_W3VOAuFwVw`, `mt_ZjIFGc6zPW`, `mt_i5_HnoFOYw`, `mt_yXO7lQ9Yn7` |
| C1.3 | Full | `mt_HRKzwEQJgO`, `mt_W3VOAuFwVw`, `mt_ZjIFGc6zPW`, `mt_anAe11HAEH`, `mt_fZTn0W_iZR` |
| C1.4 | Full | `mt_HLUqHJ9Y7n`, `mt_TqDq6jyOmL`, `mt_W3VOAuFwVw`, `mt_YzM5goBctT`, `mt_doX1BhmFgk`, `mt_hBZwbst0ow`, `mt_kDMKJ5Ztt6` |
| C2 | Full | Stored-child expectation rollup |
| C2.1 | Full | `mt_AQo4u7O4sM`, `mt_AR-K72OIIO`, `mt_wh3UqnWsa7` |
| C2.2 | Full | `mt_4WaKWECpcv`, `mt_8jFSnXxqQD`, `mt_JH_6RpNWjr`, `mt_Jvg8X0N5u0`, `mt_SoDP1fSQEB`, `mt_jHgRQ4hR0g` |
| C2.3 | Full | `mt_AR-K72OIIO`, `mt_anAe11HAEH`, `mt_oIzycTBeE4` |
| C2.4 | Full | `mt_MHaiUd2FLA`, `mt_i2F1nWxJjv` |
| C3 | Full | Stored-child expectation rollup |
| C3.1 | Full | `mt_6XbAmdmjDb`, `mt_JTuhd-cPiV`, `mt_XXpEz9tyu6`, `mt_nfGAtwqSvP`, `mt_sPV503BQnI` |
| C3.2 | Full | `mt_5UtPmgdoQ9`, `mt_6XbAmdmjDb`, `mt_JTuhd-cPiV`, `mt_XXpEz9tyu6`, `mt_nfGAtwqSvP` |
| C4 | Full | `mt_IM1G_7QzTa`, `mt_WkKkb7W9Qd`, `mt_f67qGDhyfi`, `mt_fLOkq-HfPB`, `mt_iQYPw8bMfN` |
| D1 | Full | Stored-child expectation rollup |
| D1.1 | Full | `mt_ChjMU2GDJa`, `mt_HlNSurPVDp` |
| D1.2 | Full | `mt_4zgPzc6yu5`, `mt_ChjMU2GDJa`, `mt_ebQURBOsM5`, `mt_iykH2P5oFq`, `mt_oderfUBZPw` |
| D1.3 | Full | `mt_ChjMU2GDJa`, `mt_HlNSurPVDp`, `mt_QpJydot2Kh`, `mt_TiFjjvBMaY`, `mt_c29FaCTNsx`, `mt_oderfUBZPw`, `mt_r8XnXwRA6g` |
| D1.4 | Full | `mt_HlNSurPVDp`, `mt_QpJydot2Kh`, `mt_ebQURBOsM5`, `mt_kxeuXm6EyC`, `mt_oderfUBZPw` |
| D1.5 | Full | `mt_Cg8VPguS_V`, `mt_XSXnTQoQ4l`, `mt_gTI7MuS-y8`, `mt_qwFJvRRucu`, `mt_ryyJWULiP5` |
| D1.6 | Full | `mt_1VSfm9yiLn`, `mt_6gpryAnpoZ`, `mt_8IsaoMPvod`, `mt_H6LlpWgEYS`, `mt_HlNSurPVDp`, `mt_OwYms2tB1L`, `mt_gTI7MuS-y8`, `mt_kxeuXm6EyC`, `mt_oderfUBZPw` |
| D2 | Full | Stored-child expectation rollup |
| D2.1 | Full | `mt_-c4Ca_nBzX`, `mt_4K1dr204Hi`, `mt_J4j7d3iAfg`, `mt_UcGn2hjhYU`, `mt_W17Kbwm0-u`, `mt_t0g2SlP404` |
| D2.2 | Full | `mt_-bMnJcPJy8`, `mt_Zt30Gxi-qp`, `mt_dlg6i-Lw0I`, `mt_gu0NPDvlhY`, `mt_sHJqh6UUya` |
| E1 | Full | Stored-child expectation rollup |
| E1.1 | Full | `mt_3sE6fcAvkl`, `mt_8H2kO4k2B9`, `mt_NM5I3yN-Q6`, `mt_QysgF57dxh`, `mt_Xt1cRqaBOW`, `mt_hRZyKvz1KN`, `mt_liIW336odh` |
| E1.2 | Full | `mt_jsXoDOyiSv` |
| E1.3 | Full | `mt_R4AY0LKxfl`, `mt_Uq5vYqboCR`, `mt_hVpGOEz2kG`, `mt_lxaM6iVpdr` |
| E1.4 | Full | `mt_61Nhj8W78f`, `mt_SH7QgFl8-v`, `mt_efOeaGFyGM`, `mt_lxaM6iVpdr`, `mt_oqziWKry-L` |
| E2 | Full | Stored-child expectation rollup |
| E2.1 | Full | `mt_DOe893F6gN`, `mt_Zks8xyInSG`, `mt_d8al9JcajP`, `mt_eiB3-6pu6a`, `mt_y1n0Zwhoca` |
| E2.2 | Full | `mt_4MFUAsbx_6`, `mt_LBT-9jz7kR`, `mt_TdV9YGJEoY`, `mt_oqziWKry-L`, `mt_qUGMyMYn9m` |
| E2.3 | Full | `mt_89riIKwGYp`, `mt_QDTO3GAgcq`, `mt_cdMlC7EpTJ`, `mt_oqziWKry-L` |
| E2.4 | Full | `mt_ML5t7n2-U8`, `mt_i2-QaXbyzB` |
| E2.5 | Full | `mt_Mnodea7mG_`, `mt_i2-QaXbyzB`, `mt_tegkuJA5gM` |
| E2.6 | Full | `mt_ML5t7n2-U8`, `mt_Mnodea7mG_`, `mt_i2-QaXbyzB`, `mt_tegkuJA5gM` |
| F1 | Full | Stored-child expectation rollup |
| F1.1 | Full | `mt_3BDMrubDH8` |
| F1.2 | Full | `mt_r1hw-KenpK`, `mt_uP9faJlnRq`, `mt_zrCyqhngYm` |
| F1.3 | Full | `mt_My0OL6fhGL`, `mt_Qzbh-_v0Gq`, `mt__ab4knIaSL`, `mt_bAy4dmP1-A`, `mt_r1hw-KenpK`, `mt_uP9faJlnRq` |
| F1.4 | Full | `mt_UXMNnis3v3` |
| F1.5 | Full | `mt_0Rx1ISxXFE`, `mt_bAy4dmP1-A`, `mt_tF6XuKIq8_` |

The [machine-readable mapping](ontario-grade6-mathematics-mapping-2026-10-27.json) contains codes and official links without verbatim Ontario expectations. Detailed source clauses and preservation proofs remain private.