# Two missing roles · educator review ## Access and help Read or sign the exact source and prompts neutrally, enlarge them, or scribe the learner’s chosen words. A figure, operation, regrouping, equation role or check supplied by an adult is mathematical help and is recorded as such. Show, draw, type, sign or use usual communication. One component can be enough; pause/pass/finish are choices. Four own spaces are genuinely empty. Models, criteria and next lessons stay on separate staff pages. ## Components 1. ### Criterion Box is the starting count 603, formed by joining 175 used and 428 left. ### Id B-later-Q1 ### Next ordinary teaching #### Access Read or sign the exact source and prompts neutrally, enlarge them, or scribe the learner’s chosen words. A figure, operation, regrouping, equation role or check supplied by an adult is mathematical help and is recorded as such. Show, draw, type, sign or use usual communication. One component can be enough; pause/pass/finish are choices. Four own spaces are genuinely empty. Models, criteria and next lessons stay on separate staff pages. #### Complete different guided source A pretend theatre uses 248 tickets, has 356 left. #### Complete new source A fictional puzzle box uses 126 cards and has 387 left. #### Complete own invitation An invented mask box uses 175 labels, has 468 left. #### Entry and teach Teach□−4=9: used 4 joins left 9 to get 13. #### Guided instruction 604 start; 604−248=356. Invite each relationship before the answer; teach missing facts and name help. #### Id NEXT13 #### Materials Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase. #### Observe and follow up Receive one available own relationship before staff possibility. If it matches criterion, offer another small new context later; this is not automatic mastery. If not, return to the entry relationship and fade one hint. Record the actual mathematical help. If access/time is not available, change access or sitting rather than marking wrong. #### Relationship to check Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item. #### Session sequence 1. Read the new source and name units/wanted quantity. Teach□−4=9: used 4 joins left 9 to get 13. 2. Model on separate adult paper. Starting 513=126+387; 513−126=387. 3. Guide a different complete source. A pretend theatre uses 248 tickets, has 356 left. 604 start; 604−248=356. 4. Receive one own attempt. An invented mask box uses 175 labels, has 468 left. Staff reference only: 643 start; 643−175=468. 5. Compare available work with: Unknown start is rebuilt from used and left, with roles explained. Choose one follow-up offer; never infer independence from a copied model. #### What to look for Unknown start is rebuilt from used and left, with roles explained. #### Staff own possibility 643 start; 643−175=468. #### Teacher model Starting 513=126+387; 513−126=387. #### Timing An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part. #### Title Rebuild the beginning ### Own initial value ### Prompt For Record 1, say what the box counts and find it. ### After own work: adult practice possibility 428+175=603 starting cards. Selecting subtraction solely from the word remain would be wrong here. 2. ### Criterion 603−175=428 supports the unknown start. ### Id B-later-Q2 ### Next ordinary teaching #### Access Read or sign the exact source and prompts neutrally, enlarge them, or scribe the learner’s chosen words. A figure, operation, regrouping, equation role or check supplied by an adult is mathematical help and is recorded as such. Show, draw, type, sign or use usual communication. One component can be enough; pause/pass/finish are choices. Four own spaces are genuinely empty. Models, criteria and next lessons stay on separate staff pages. #### Complete different guided source An imaginary map record is□−247=386. #### Complete new source A fictional game record is□−138=275. #### Complete own invitation A pretend music record is□−156=428. #### Entry and teach Check a smaller□−7=12→19 in original form. #### Guided instruction 633; 633−247=386. Invite each relationship before the answer; teach missing facts and name help. #### Id NEXT14 #### Materials Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase. #### Observe and follow up Receive one available own relationship before staff possibility. If it matches criterion, offer another small new context later; this is not automatic mastery. If not, return to the entry relationship and fade one hint. Record the actual mathematical help. If access/time is not available, change access or sitting rather than marking wrong. #### Relationship to check Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item. #### Session sequence 1. Read the new source and name units/wanted quantity. Check a smaller□−7=12→19 in original form. 2. Model on separate adult paper. Starting 413=138+275; 413−138=275. 3. Guide a different complete source. An imaginary map record is□−247=386. 633; 633−247=386. 4. Receive one own attempt. A pretend music record is□−156=428. Staff reference only: 584; 584−156=428. 5. Compare available work with: A substitution check retains unknown start and original subtraction. Choose one follow-up offer; never infer independence from a copied model. #### What to look for A substitution check retains unknown start and original subtraction. #### Staff own possibility 584; 584−156=428. #### Teacher model Starting 413=138+275; 413−138=275. #### Timing An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part. #### Title Starting equation check ### Own initial value ### Prompt Substitute your Record 1 value into its original equation and check. ### After own work: adult practice possibility 603−175=428. The value 603 is not the used amount. 3. ### Criterion Known side 435; missing part 195 so 195+240=435. ### Id B-later-Q3 ### Next ordinary teaching #### Access Read or sign the exact source and prompts neutrally, enlarge them, or scribe the learner’s chosen words. A figure, operation, regrouping, equation role or check supplied by an adult is mathematical help and is recorded as such. Show, draw, type, sign or use usual communication. One component can be enough; pause/pass/finish are choices. Four own spaces are genuinely empty. Models, criteria and next lessons stay on separate staff pages. #### Complete different guided source A fictional card puzzle is 186+□=420+35. #### Complete new source An invented mural-count puzzle is 215+□=340+68. #### Complete own invitation A pretend tile puzzle is 237+□=500+46. #### Entry and teach Use 18+□=25+7 and name known side 32. #### Guided instruction Known 455, box 269. Invite each relationship before the answer; teach missing facts and name help. #### Id NEXT15 #### Materials Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase. #### Observe and follow up Receive one available own relationship before staff possibility. If it matches criterion, offer another small new context later; this is not automatic mastery. If not, return to the entry relationship and fade one hint. Record the actual mathematical help. If access/time is not available, change access or sitting rather than marking wrong. #### Relationship to check Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item. #### Session sequence 1. Read the new source and name units/wanted quantity. Use 18+□=25+7 and name known side 32. 2. Model on separate adult paper. Known side 408; box 193; 215+193=408. 3. Guide a different complete source. A fictional card puzzle is 186+□=420+35. Known 455, box 269. 4. Receive one own attempt. A pretend tile puzzle is 237+□=500+46. Staff reference only: Known 546, box 309. 5. Compare available work with: Known side value and box value are distinguished through inverse reasoning. Choose one follow-up offer; never infer independence from a copied model. #### What to look for Known side value and box value are distinguished through inverse reasoning. #### Staff own possibility Known 546, box 309. #### Teacher model Known side 408; box 193; 215+193=408. #### Timing An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part. #### Title Two complete sides ### Own initial value ### Prompt For Record 2, find the box value. Show what the complete known side is first. ### After own work: adult practice possibility 620−185=435;□=435−240=195. Do not put 435 directly in the box. 4. ### Criterion Original left and right sides both give 435 after inserting 195. ### Id B-later-Q4 ### Next ordinary teaching #### Access Read or sign the exact source and prompts neutrally, enlarge them, or scribe the learner’s chosen words. A figure, operation, regrouping, equation role or check supplied by an adult is mathematical help and is recorded as such. Show, draw, type, sign or use usual communication. One component can be enough; pause/pass/finish are choices. Four own spaces are genuinely empty. Models, criteria and next lessons stay on separate staff pages. #### Complete different guided source An imaginary display equation is 850−376=□+218. #### Complete new source A fictional archive equation is 700−268=□+195. #### Complete own invitation A pretend theatre-equation is 920−485=□+167. #### Entry and teach Teach 35−8=□+12: known 27, box 15. #### Guided instruction Left 474, box 256; both sides 474. Invite each relationship before the answer; teach missing facts and name help. #### Id NEXT16 #### Materials Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase. #### Observe and follow up Receive one available own relationship before staff possibility. If it matches criterion, offer another small new context later; this is not automatic mastery. If not, return to the entry relationship and fade one hint. Record the actual mathematical help. If access/time is not available, change access or sitting rather than marking wrong. #### Relationship to check Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item. #### Session sequence 1. Read the new source and name units/wanted quantity. Teach 35−8=□+12: known 27, box 15. 2. Model on separate adult paper. Left 432; box 237; 237+195=432. 3. Guide a different complete source. An imaginary display equation is 850−376=□+218. Left 474, box 256; both sides 474. 4. Receive one own attempt. A pretend theatre-equation is 920−485=□+167. Staff reference only: Left 435, box 268; both sides 435. 5. Compare available work with: Both complete original sides are computed and agree after substitution. Choose one follow-up offer; never infer independence from a copied model. #### What to look for Both complete original sides are computed and agree after substitution. #### Staff own possibility Left 435, box 268; both sides 435. #### Teacher model Left 432; box 237; 237+195=432. #### Timing An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part. #### Title Both sides after substitution ### Own initial value ### Prompt Check both full sides of Record 2 after substitution. ### After own work: adult practice possibility 620−185=435 and 195+240=435. The box 195 differs from each whole side 435. ## Eligibility After unknown start and two-sided equality have both been taught, e.g. Days 57–58. One record or one prompt may be enough; do not require all four for a useful observation. ## First later limit First/later are opportunity labels, not fixed order, matches, calibrated difficulty or learning gain. If source/answer exposed, record that rather than claim unseen. ## Id B-later ## Complete neutral source Two separate fictional records use cards. Record 1:□−175=428, where 175 cards are used and 428 remain. Record 2: 620−185=□+240. Keep the records separate. There is no supplied history of a learner’s earlier work. ## Own page Four labelled true empty text areas with literal blank initial values; kept draft not required for judgement; staff information behind separate link, not autofilled. ## Source disclosure Full neutral whole source is initially closed native same-page details on own response page; reading it never navigates away or loses typed work. No worked/criterion/next source inside its child disclosure. Staff index is separate. ## Title Two missing roles