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
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
-
Read the new source and name units/wanted quantity. Teach□−4=9: used 4 joins left 9 to get 13.
-
Model on separate adult paper. Starting 513=126+387; 513−126=387.
-
Guide a different complete source. A pretend theatre uses 248 tickets, has 356 left. 604 start; 604−248=356.
-
Receive one own attempt. An invented mask box uses 175 labels, has 468 left. Staff reference only: 643 start; 643−175=468.
-
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.
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
-
Read the new source and name units/wanted quantity. Check a smaller□−7=12→19 in original form.
-
Model on separate adult paper. Starting 413=138+275; 413−138=275.
-
Guide a different complete source. An imaginary map record is□−247=386. 633; 633−247=386.
-
Receive one own attempt. A pretend music record is□−156=428. Staff reference only: 584; 584−156=428.
-
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.
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
-
Read the new source and name units/wanted quantity. Use 18+□=25+7 and name known side 32.
-
Model on separate adult paper. Known side 408; box 193; 215+193=408.
-
Guide a different complete source. A fictional card puzzle is 186+□=420+35. Known 455, box 269.
-
Receive one own attempt. A pretend tile puzzle is 237+□=500+46. Staff reference only: Known 546, box 309.
-
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.
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
-
Read the new source and name units/wanted quantity. Teach 35−8=□+12: known 27, box 15.
-
Model on separate adult paper. Left 432; box 237; 237+195=432.
-
Guide a different complete source. An imaginary display equation is 850−376=□+218. Left 474, box 256; both sides 474.
-
Receive one own attempt. A pretend theatre-equation is 920−485=□+167. Staff reference only: Left 435, box 268; both sides 435.
-
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