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 missing labels needed, 468 the available part and 725 the target whole.
Id
B-first-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
An imaginary gallery needs 92 tiles, has 58.
Complete new source
A fictional poster plan needs 74 tiles, has 39.
Complete own invitation
A pretend maze needs 85 tiles, has 47.
Entry and teach
Use an empty known part/unknown part/whole bar; 35 joins 39 to 74.
Guided instruction
34 needed; 58+34=92. Invite each relationship before the answer; teach missing facts and name help.
Id
NEXT09
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 an empty known part/unknown part/whole bar; 35 joins 39 to 74.
-
Model on separate adult paper. 39+□=74; box counts needed tiles, not whole 74. Count up 35.
-
Guide a different complete source. An imaginary gallery needs 92 tiles, has 58. 34 needed; 58+34=92.
-
Receive one own attempt. A pretend maze needs 85 tiles, has 47. Staff reference only: 38 needed; 47+38=85.
-
Compare available work with: Labels distinguish known part, target whole and missing part. Choose one follow-up offer; never infer independence from a copied model.
What to look for
Labels distinguish known part, target whole and missing part.
Staff own possibility
38 needed; 47+38=85.
Teacher model
39+□=74; box counts needed tiles, not whole 74. Count up 35.
Timing
An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.
Title
A part and a whole
Own initial value
Prompt
What does the box count? Describe the known part and the whole.
After own work: adult practice possibility
Missing refill, not the target 725 or existing 468.
Criterion
A valid difference/count-up method gives 257.
Id
B-first-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 game target is 920, 456 available.
Complete new source
A fictional print target is 810 cards, 347 available.
Complete own invitation
A fictional clue target is 730, 286 available.
Entry and teach
Teach 47→50(+3)→80(+30)→81(+1)first.
Guided instruction
464: 44 to 500+420. Invite each relationship before the answer; teach missing facts and name help.
Id
NEXT10
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 47→50(+3)→80(+30)→81(+1)first.
-
Model on separate adult paper. 347→350(+3)→800(+450)→810(+10); 463 needed.
-
Guide a different complete source. An imaginary game target is 920, 456 available. 464: 44 to 500+420.
-
Receive one own attempt. A fictional clue target is 730, 286 available. Staff reference only: 444: 14 to 300+430.
-
Compare available work with: Count-up increments total the exact unknown addend. Choose one follow-up offer; never infer independence from a copied model.
What to look for
Count-up increments total the exact unknown addend.
Staff own possibility
444: 14 to 300+430.
Teacher model
347→350(+3)→800(+450)→810(+10); 463 needed.
Timing
An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.
Title
Stepping to a target
Own initial value
Prompt
Find a value for the box with a useful strategy.
After own work: adult practice possibility
468→500(+32)→725(+225); 32+225=257.
Criterion
Substitution retains 468+□=725 and yields 468+257=725.
Id
B-first-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
An invented reading plan has 378+□=650 cards.
Complete new source
A pretend puppet plan has 246+□=580 labels.
Complete own invitation
A fictional toy-map target is 720 with 459 available.
Entry and teach
Teach substitution with 9+□=14→5.
Guided instruction
272; 378+272=650. Invite each relationship before the answer; teach missing facts and name help.
Id
NEXT11
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 substitution with 9+□=14→5.
-
Model on separate adult paper. □=334; 246+334=580. Keep original known part and whole.
-
Guide a different complete source. An invented reading plan has 378+□=650 cards. 272; 378+272=650.
-
Receive one own attempt. A fictional toy-map target is 720 with 459 available. Staff reference only: 261; 459+261=720.
-
Compare available work with: The substitute makes the original equation true. Choose one follow-up offer; never infer independence from a copied model.
What to look for
The substitute makes the original equation true.
Staff own possibility
261; 459+261=720.
Teacher model
□=334; 246+334=580. Keep original known part and whole.
Timing
An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.
Title
Put the number back
Own initial value
Prompt
Put your value into the original equation and check it.
After own work: adult practice possibility
468+257=725; both sides 725. A different equation alone is not this requested substitution.
Criterion
Explains equality of the two sides and the unknown’s part role; rejects 725 as this missing part.
Id
B-first-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 story puzzle says 38+□=72.
Complete new source
A fictional code puzzle says 27+□=64.
Complete own invitation
A pretend rocket puzzle says 46+□=83.
Entry and teach
Show two equal amounts for 12+3=10+5.
Guided instruction
34; 38+34=72. Invite each relationship before the answer; teach missing facts and name help.
Id
NEXT12
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. Show two equal amounts for 12+3=10+5.
-
Model on separate adult paper. □=37 because 27+37=64; using 64 gives 91, not 64.
-
Guide a different complete source. An imaginary story puzzle says 38+□=72. 34; 38+34=72.
-
Receive one own attempt. A pretend rocket puzzle says 46+□=83. Staff reference only: 37; 46+37=83.
-
Compare available work with: The missing part is distinguished from the whole-side value and equality is interpreted relationally. Choose one follow-up offer; never infer independence from a copied model.
What to look for
The missing part is distinguished from the whole-side value and equality is interpreted relationally.
Staff own possibility
37; 46+37=83.
Teacher model
□=37 because 27+37=64; using 64 gives 91, not 64.
Timing
An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.
Title
Equal does not mean next
Own initial value
Prompt
A fictional note says “the box is 725 because that is the answer after the equals sign”. Keep or repair it with a reason.
After own work: adult practice possibility
468+725=1193, not 725. The missing part is 257; = relates two equal amounts, not a direction to copy the total.
Eligibility
After unknown addend, part/whole and substitution have been taught, e.g. Day 56. No assumed mastery from resource-week labels.
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-first
Complete neutral source
A fictional kit needs 725 labels in total. It has 468 labels available. Find the further labels needed: 468+□=725. The box stands for a whole-number value. No real refill is supplied.
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
The missing refill