# Ontario Grade 7 Mathematics — 27 October 2026

The Grade 7 pass audits **64 retained expectations: 52 specific and 12 overall**. The source catalogue and hierarchy are unchanged. [Official Ontario curriculum](https://www.dcp.edu.gov.on.ca/en/curriculum/elementary-mathematics/grades/g7-math).

It adds **252 topic–expectation pairs on 173 topics**, reusing **171 existing topics** and adding **two**. Fifty-four codes have direct associations; ten overall expectations roll up their stored children. The verified graph and staging DB contain **1,852 topics / 3,979 dependencies / 5,455 known pairs**, plus the same 41 legacy graph pairs. Every earlier pair remains, including Grades 1–6 Mathematics counts of 152 / 124 / 156 / 186 / 190 / 244.

## Two additions after challenging reuse

- **Symmetry of 3-D solids** distinguishes reflection planes from rotation axes, tests the actual solid's symmetries and distinguishes finite rotational orders from the continuous axial symmetry of an ideal right circular cylinder. Existing 2-D symmetry and solid face/cross-section claims do not themselves assess these operations. No separate vertex is created for each solid or symmetry order.
- **Drawing perspective views** creates a suitable parallel projection, such as an isometric or cabinet view, at a stated scale. Reading an isometric picture and drawing orthographic views are existing skills; neither alone establishes creating the perspective representation. The source examples do not require every drawing style or vanishing-point perspective. Projected depth and axis units follow the chosen convention.

The proposed perfect-square/root extraction was withdrawn: the existing powers-and-roots claim explicitly finds square roots of perfect squares. It contributes that component without certifying cube/higher roots or approximations. Its existing prerequisite remains; the operation-order claim has a genuine Grade 7 source contribution. No difficulty, grade, numerical-range or country copies are added. All old topic content and other non-alignment graph attributes remain unchanged; no merges, retirements, scope expansions or learner resets occur.

## Worked reuse with explicit limits

The mapping retains explicit composition limits. Fraction/decimal density uses progressively finer units, equivalent fractions or averaging rather than a fixed decimal-place cap. Decimal multiplication uses fraction/place-value scaling and decimal division uses common units. Integer counters and like-term tiles give contextual representations without certifying every facet of broader claims.

Counted-loop coding follows the expectation's and/or route; it does not claim mastery of defining or calling subprograms. Joint dependent-event tasks update the second-draw sample space, reset the experiment between full trials and compare observed with theoretical probabilities. More trials reduce typical sampling variability without guaranteeing that each next estimate is closer.

Existing mean, median, mode and distribution skills support adding/removing data. For example, 12, 14, 15, 15 has mean 14, median 14.5 and mode 15; adding 48 changes the mean to 20.8 and median to 15. Adding another 2 to 1, 1, 2 changes the mode set. No false rule says that changing a non-modal value cannot affect the mode.

Compass-circle construction composes the existing fixed-radius arc operation with circle relationships and inverse arithmetic. Circle-area explanation uses sectors rearranged towards a rectangle as the sectors become finer; a few curved sectors are not an exact parallelogram. Right-cylinder nets combine unrolling, circumference, circle/rectangle areas and additivity, including which ends are present. The older prism/pyramid net claim retains its explicit scope; the transfer is documented rather than silently broadening it. General oblique-cylinder geometry is not asserted.

Fictional currency rates, budgets and account/loan terms support financial tasks. Source reliability uses general credibility and multiple-source skills, with source-specific health or research-writing applications kept distinct. Budget tracking records actual amounts and adjusts the plan against its goal. Rate/fee comparison preserves given balances and periods; no current bank products, compulsory compound-interest machinery or guaranteed investment growth are introduced.

All 64 rows have a Full contextual authoring judgment. Component tasks do not establish whole-topic learner mastery. A1 remains a learning-support/process association without permission to assess, evaluate or report SEL; C4 keeps its modelling-process contributions. Deferred corroboration and macroeconomics links remain documented; no earlier country ages are invented to clear prerequisites.

## Prerequisites, preservation and validation

Two broad gates become soft supports: tree diagrams to set/Venn notation, and general source reliability to health-message interpretation. Basic theoretical probability and advertising/purpose awareness become the respective hard foundations. Existing source-variety knowledge remains hard and has a genuine Grade 7 contribution. The unrelated history-to-reading chain is unchanged.

Canadian closure contains **173 holders / 346 topics / 467 hard edges / zero issues**. New hard edges pass all applicable source countries; no country context or flag category is newly affected. The entire hard/soft graph is acyclic. Earlier baseline flags remain visible.

Independent checks compare the exact authorized topic fields, source contexts and dependencies; complete source identities/hierarchy and pairs; derived ages and centralities; embedding presence; and protected learner/assessment/research fingerprints. All **17 catalogues / 7,743 source rows**, including **nine Ontario documents / 3,862 expectations**, are preserved. Ontario publication contains codes and official links only.

The public projection preserves all **1,049 exact teaching-research records** and the historical archive. Only the two additions increase explicitly missing research from 801 to **803 topics**. Schema, references and checksums pass, as do the 14 existing data-validator tests. Private replay checks cover relocated inputs and deliberate incomplete/tampered evidence failures.

## 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_HLUqHJ9Y7n`, `mt_JwP9QFv6gQ`, `mt_PsylzZ9lHW`, `mt_x8TshvbbQT` |
| B1.2 | Full | `mt_gxCIASSezX`, `mt_hCVPYlF-7Y` |
| B1.3 | Full | `mt_933BohS9BH`, `mt_9QzSnn8m80`, `mt_Ac7oMWhyPw`, `mt_PL9VkDwXfh`, `mt_PsylzZ9lHW`, `mt_uDJY0X0hgo` |
| B1.4 | Full | `mt_b7T-CjOYUR`, `mt_ebPelt-qAl` |
| B1.5 | Full | `mt_Cg8VPguS_V`, `mt_PsylzZ9lHW`, `mt_ebPelt-qAl`, `mt_kdWoAel3Zl` |
| B1.6 | Full | `mt_Ii1hV4V5ql`, `mt__casygEB85` |
| B1.7 | Full | `mt_4K1dr204Hi`, `mt_4Km38F4L-6`, `mt_ALUrJpY0cZ`, `mt_W17Kbwm0-u`, `mt_ZM9mhHsyYZ` |
| B2 | Full | Stored-child expectation rollup |
| B2.1 | Full | `mt_8jFSnXxqQD`, `mt_GDG9_SZmsO`, `mt_Lb2ZnMdkYR`, `mt_PNSyfH56eQ`, `mt_Qe2PsFmSAH`, `mt_X5cypSGoGU`, `mt_anAe11HAEH`, `mt_e7filQgayF`, `mt_ehGS_uVSJv`, `mt_h0gJcSuwdL`, `mt_jHgRQ4hR0g`, `mt_p-nbe0w_lf` |
| B2.2 | Full | `mt_4K1dr204Hi`, `mt_4ubP_RMg9o`, `mt_W17Kbwm0-u` |
| B2.3 | Full | `mt_4ubP_RMg9o`, `mt_ALUrJpY0cZ`, `mt_LlMl2PbaZe`, `mt_PNSyfH56eQ`, `mt_kJ5wYzO8qC` |
| B2.4 | Full | `mt_1KkvzwYxbR`, `mt_9QzSnn8m80`, `mt_PgsHGYJMH-` |
| B2.5 | Full | `mt_-V7EnqU7gG`, `mt_14T5yPXUq_`, `mt_CBHwluE6Lp`, `mt_VgOePicFYK`, `mt_e7filQgayF` |
| B2.6 | Full | `mt_FHIAv6dfhU`, `mt_xhoOWnhtHq` |
| B2.7 | Full | `mt_HLUqHJ9Y7n`, `mt_gxCIASSezX` |
| B2.8 | Full | `mt_9Y96vxG_LH`, `mt_AabJisinfi`, `mt_ifPDOYvUqm` |
| B2.9 | Full | `mt_AabJisinfi`, `mt_SoDP1fSQEB`, `mt_TqDq6jyOmL`, `mt_WsM4EmdOLe`, `mt_iNdrM2-oJf`, `mt_wPgpMJ0-PA` |
| B2.10 | Full | `mt_EmR5n58jZt`, `mt_FnUJMXPUZX`, `mt_FspV_imUGK`, `mt_HRKzwEQJgO`, `mt_Qe2PsFmSAH`, `mt_XWSGuFW7It`, `mt_h0gJcSuwdL`, `mt_xAf2bu9wYK`, `mt_yK51ZnKA8m` |
| C1 | Full | Stored-child expectation rollup |
| C1.1 | Full | `mt_HRKzwEQJgO`, `mt_W3VOAuFwVw`, `mt_ZjIFGc6zPW`, `mt_yXO7lQ9Yn7` |
| C1.2 | Full | `mt_Cqm8iy48UI`, `mt_HRKzwEQJgO`, `mt_W3VOAuFwVw`, `mt_ZjIFGc6zPW`, `mt_hBZwbst0ow`, `mt_i5_HnoFOYw`, `mt_yXO7lQ9Yn7` |
| C1.3 | Full | `mt_HRKzwEQJgO`, `mt_W3VOAuFwVw`, `mt_ZjIFGc6zPW`, `mt_anAe11HAEH`, `mt_fZTn0W_iZR`, `mt_hBZwbst0ow` |
| C1.4 | Full | `mt_9QzSnn8m80`, `mt_hBZwbst0ow` |
| C2 | Full | Stored-child expectation rollup |
| C2.1 | Full | `mt_AQo4u7O4sM`, `mt_AR-K72OIIO`, `mt_KwdjWEmMNo`, `mt_g_fkAqmz72`, `mt_nNNVrLqPW3` |
| C2.2 | Full | `mt_8jFSnXxqQD`, `mt_JH_6RpNWjr`, `mt_Jvg8X0N5u0`, `mt_KwdjWEmMNo`, `mt_SoDP1fSQEB`, `mt_jHgRQ4hR0g` |
| C2.3 | Full | `mt_JH_6RpNWjr`, `mt_anAe11HAEH`, `mt_nNNVrLqPW3`, `mt_oIzycTBeE4` |
| C2.4 | Full | `mt_MHaiUd2FLA`, `mt_i2F1nWxJjv`, `mt_nNNVrLqPW3` |
| C3 | Full | Stored-child expectation rollup |
| C3.1 | Full | `mt_6XbAmdmjDb`, `mt_JTuhd-cPiV`, `mt_XXpEz9tyu6`, `mt_YZOjP8KHsM`, `mt_nfGAtwqSvP`, `mt_sPV503BQnI` |
| C3.2 | Full | `mt_5UtPmgdoQ9`, `mt_6XbAmdmjDb`, `mt_JTuhd-cPiV`, `mt_XXpEz9tyu6`, `mt_YZOjP8KHsM`, `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_4zgPzc6yu5`, `mt_ALUrJpY0cZ`, `mt_Y3ZnDGGmln`, `mt_sHJqh6UUya`, `mt_xAf2bu9wYK` |
| D1.2 | Full | `mt_4zgPzc6yu5`, `mt_ALUrJpY0cZ`, `mt_ChjMU2GDJa`, `mt_ebQURBOsM5`, `mt_iykH2P5oFq`, `mt_oderfUBZPw`, `mt_sHJqh6UUya` |
| D1.3 | Full | `mt_ChjMU2GDJa`, `mt_HlNSurPVDp`, `mt_QpJydot2Kh`, `mt_TiFjjvBMaY`, `mt_bESTSBB0wK`, `mt_c29FaCTNsx`, `mt_oderfUBZPw`, `mt_r8XnXwRA6g` |
| D1.4 | Full | `mt_QpJydot2Kh`, `mt_bESTSBB0wK`, `mt_ebQURBOsM5`, `mt_kxeuXm6EyC` |
| D1.5 | Full | `mt_Cg8VPguS_V`, `mt_OwYms2tB1L`, `mt_XSXnTQoQ4l`, `mt_qwFJvRRucu`, `mt_ryyJWULiP5` |
| D1.6 | Full | `mt_1VSfm9yiLn`, `mt_6gpryAnpoZ`, `mt_8IsaoMPvod`, `mt_OwYms2tB1L`, `mt_bESTSBB0wK`, `mt_gTI7MuS-y8`, `mt_kxeuXm6EyC` |
| D2 | Full | Stored-child expectation rollup |
| D2.1 | Full | `mt_Zt30Gxi-qp`, `mt_dlg6i-Lw0I` |
| D2.2 | Full | `mt_-bMnJcPJy8`, `mt_GDtFU5fyUv`, `mt_Zt30Gxi-qp`, `mt_dlg6i-Lw0I`, `mt_gu0NPDvlhY`, `mt_sHJqh6UUya` |
| E1 | Full | Stored-child expectation rollup |
| E1.1 | Full | `mt_Mnodea7mG_`, `mt_REwgr0d_ss`, `mt_nRksLqt-iR`, `mt_qMu1oc7ZHd` |
| E1.2 | Full | `mt_1badik7iKJ`, `mt_T3bTU2aet-`, `mt_r8bOJtofM7` |
| E1.3 | Full | `mt_2OtRUM_0zW`, `mt_y-BuQAfw4B` |
| E1.4 | Full | `mt_K0Y15w48SY`, `mt_R4AY0LKxfl`, `mt_SH7QgFl8-v`, `mt_efOeaGFyGM`, `mt_hVpGOEz2kG`, `mt_lxaM6iVpdr` |
| E2 | Full | Stored-child expectation rollup |
| E2.1 | Full | `mt_4lp_b5Pzik`, `mt_IuHa5UI5od`, `mt_d7XktBQPxm`, `mt_tpT9brpI6D` |
| E2.2 | Full | `mt_2VpdPjvewx`, `mt_d8al9JcajP`, `mt_eiB3-6pu6a`, `mt_nTL-owFJTF`, `mt_tpT9brpI6D` |
| E2.3 | Full | `mt_svFa6_mjO_`, `mt_xq3YHZ2zeR` |
| E2.4 | Full | `mt_Jf8xcX4UTq`, `mt_svFa6_mjO_`, `mt_xq3YHZ2zeR` |
| E2.5 | Full | `mt_ML5t7n2-U8`, `mt_svFa6_mjO_`, `mt_xq3YHZ2zeR` |
| E2.6 | Full | `mt_eiB3-6pu6a`, `mt_nRksLqt-iR`, `mt_svFa6_mjO_`, `mt_tegkuJA5gM` |
| E2.7 | Full | `mt_GDG9_SZmsO`, `mt_nTL-owFJTF`, `mt_tAJH5BrpOx` |
| F1 | Full | Stored-child expectation rollup |
| F1.1 | Full | `mt_0Rx1ISxXFE`, `mt_EmR5n58jZt`, `mt_Qe2PsFmSAH`, `mt_tpT9brpI6D` |
| F1.2 | Full | `mt_Amojd_oviu`, `mt_JVVKT-_AD9`, `mt_W5euSyU2sO`, `mt_r1hw-KenpK` |
| F1.3 | Full | `mt_Qzbh-_v0Gq`, `mt_r1hw-KenpK`, `mt_zrCyqhngYm` |
| F1.4 | Full | `mt_JivEBTD_KV`, `mt_My0OL6fhGL`, `mt__ab4knIaSL`, `mt_bAy4dmP1-A`, `mt_sDT1M0z7c3`, `mt_uP9faJlnRq` |
| F1.5 | Full | `mt_PNSyfH56eQ`, `mt_UXMNnis3v3`, `mt_bAy4dmP1-A`, `mt_uSUqTjOl8m` |
| F1.6 | Full | `mt_PNSyfH56eQ`, `mt_UXMNnis3v3` |

The [machine-readable mapping](ontario-grade7-mathematics-mapping-2026-10-27.json) uses codes and official links without verbatim expectations. Detailed clauses and preservation evidence remain private.