# Staff · complete source-specific keys and next teaching

Open after keeping the actual first response. These original component criteria are teaching aids, not official A–E judgments. Full question/source context stays with each response. Accept usual communication and exact adult-directed records. Correct answer alone is less informative than a traceable method and meaning; no handwriting/speed/decoration criterion.

## a-first · Paper-window motifs

**Complete source (staff reference):** Original pretend question: which ONE paper-window motifs option would you choose? Options, in order: arch, square, wave. Available replies in order: arch, square, arch, wave, arch, square. Eight fictional invitations; six available choices; two no available replies, reason and preference unknown. Each available reply is one choice. No actual survey, visit or child result is supplied.

**Question:** Make or direct a complete list of the available replies. Keep the unavailable replies separate.

**Complete key and accepted variations:** Exact available list: arch, square, arch, wave, arch, square; keep two no-response records separate. Source order is useful for tracing but grouping order can differ if all six records are retained exactly once. No invented missing preference/reason.

**Component criterion:** Retains each available reply exactly once and marks unavailable status; categories have intelligible meaning.

**Specific unrelated next teaching:** If a repeated name is counted only once, trace unrelated circle,circle,triangle,square records with broad separate IDs. If category meaning unclear, revise a different pencil/crayon question before another list.

**Question:** Make or direct a table showing each named option and its recorded count.

**Complete key and accepted variations:** Full named table: arch: 3; square: 2; wave: 1. Check category sum6;6 available+2 unavailable=8 invited. Category labels name choices; frequencies count those replies.

**Component criterion:** Correct option names/frequencies, explicit count check, zero versus missing distinction where relevant.

**Specific unrelated next teaching:** If counts mismatch, map unrelated cloud,sun,cloud,cloud to one mark per record, then total rows against list. Do not hand over this stage's solved table.

**Question:** Which option has most recorded choices? Compare it with the second option in the source option order. How many more? What do the unavailable replies tell us?

**Complete key and accepted variations:** arch has most recorded choices, 3; square has 2, so 1 more. Two unavailable replies establish only unavailable preference/reason, not dislike or support. No claim about everyone/other populations.

**Component criterion:** Supported comparison with correct difference and unknowns kept unknown.

**Specific unrelated next teaching:** If unknowns become a preference, contrast unrelated bird2/fish1/no reply2. If difference confused, pair two versus four named tokens and describe unmatched count.

**Question:** Make, describe or direct one useful statement or sign for this pretend choice. Explain what it helps and what stays unknown.

**Complete key and accepted variations:** Open useful statement/sign: e.g. “arch had most of these six recorded choices; two invited replies are unavailable.” It names the question/source scope and can support a tentative pretend recommendation. No single wording/layout; an actual child decision/direction must be observed rather than inferred from a copied model.

**Component criterion:** Useful contextual statement with actual own choice and bounded scope.

**Specific unrelated next teaching:** If statement says everyone/best, use a different fictional stripe/spot table and name source-limited choice versus value judgment. If useful, invite a new ordinary reader question without inventing actual use.

**Record honestly:** full source familiarity/exposure; question and actual first response/method; reading/scribing/handling access; mathematical hints/device answers; observed child choices versus adult operations; actual teaching/source/date; interval before next source; initial versus supported revision; unattempted/uncaptured fields. No hypothetical learner score or attained level.

## a-later · Puppet-stage backdrops

**Complete source (staff reference):** Original pretend question: which ONE puppet-stage backdrops option would you choose? Options, in order: river, hill, cloud. Available replies in order: hill, river, river, hill, river, cloud. Eight fictional invitations; six available choices; two no available replies, reason and preference unknown. Each available reply is one choice. No actual survey, visit or child result is supplied.

**Question:** Make or direct a complete list of the available replies. Keep the unavailable replies separate.

**Complete key and accepted variations:** Exact available list: hill, river, river, hill, river, cloud; keep two no-response records separate. Source order is useful for tracing but grouping order can differ if all six records are retained exactly once. No invented missing preference/reason.

**Component criterion:** Retains each available reply exactly once and marks unavailable status; categories have intelligible meaning.

**Specific unrelated next teaching:** If a repeated name is counted only once, trace unrelated circle,circle,triangle,square records with broad separate IDs. If category meaning unclear, revise a different pencil/crayon question before another list.

**Question:** Make or direct a table showing each named option and its recorded count.

**Complete key and accepted variations:** Full named table: river: 3; hill: 2; cloud: 1. Check category sum6;6 available+2 unavailable=8 invited. Category labels name choices; frequencies count those replies.

**Component criterion:** Correct option names/frequencies, explicit count check, zero versus missing distinction where relevant.

**Specific unrelated next teaching:** If counts mismatch, map unrelated cloud,sun,cloud,cloud to one mark per record, then total rows against list. Do not hand over this stage's solved table.

**Question:** Which option has most recorded choices? Compare it with the second option in the source option order. How many more? What do the unavailable replies tell us?

**Complete key and accepted variations:** river has most recorded choices, 3; hill has 2, so 1 more. Two unavailable replies establish only unavailable preference/reason, not dislike or support. No claim about everyone/other populations.

**Component criterion:** Supported comparison with correct difference and unknowns kept unknown.

**Specific unrelated next teaching:** If unknowns become a preference, contrast unrelated bird2/fish1/no reply2. If difference confused, pair two versus four named tokens and describe unmatched count.

**Question:** Make, describe or direct one useful statement or sign for this pretend choice. Explain what it helps and what stays unknown.

**Complete key and accepted variations:** Open useful statement/sign: e.g. “river had most of these six recorded choices; two invited replies are unavailable.” It names the question/source scope and can support a tentative pretend recommendation. No single wording/layout; an actual child decision/direction must be observed rather than inferred from a copied model.

**Component criterion:** Useful contextual statement with actual own choice and bounded scope.

**Specific unrelated next teaching:** If statement says everyone/best, use a different fictional stripe/spot table and name source-limited choice versus value judgment. If useful, invite a new ordinary reader question without inventing actual use.

**Record honestly:** full source familiarity/exposure; question and actual first response/method; reading/scribing/handling access; mathematical hints/device answers; observed child choices versus adult operations; actual teaching/source/date; interval before next source; initial versus supported revision; unattempted/uncaptured fields. No hypothetical learner score or attained level.

## b-first · Reserve park-map icons

**Complete source (staff reference):** Original pretend question: which ONE reserve park-map icons option would you choose? Options, in order: bench, gate, tree. Available replies in order: bench, gate, bench, tree, gate, bench. Eight fictional invitations; six available choices; two no available replies, reason and preference unknown. Each available reply is one choice. No actual survey, visit or child result is supplied.

**Question:** Make or direct a complete list of the available replies. Keep the unavailable replies separate.

**Complete key and accepted variations:** Exact available list: bench, gate, bench, tree, gate, bench; keep two no-response records separate. Source order is useful for tracing but grouping order can differ if all six records are retained exactly once. No invented missing preference/reason.

**Component criterion:** Retains each available reply exactly once and marks unavailable status; categories have intelligible meaning.

**Specific unrelated next teaching:** If a repeated name is counted only once, trace unrelated circle,circle,triangle,square records with broad separate IDs. If category meaning unclear, revise a different pencil/crayon question before another list.

**Question:** Make or direct a table showing each named option and its recorded count.

**Complete key and accepted variations:** Full named table: bench: 3; gate: 2; tree: 1. Check category sum6;6 available+2 unavailable=8 invited. Category labels name choices; frequencies count those replies.

**Component criterion:** Correct option names/frequencies, explicit count check, zero versus missing distinction where relevant.

**Specific unrelated next teaching:** If counts mismatch, map unrelated cloud,sun,cloud,cloud to one mark per record, then total rows against list. Do not hand over this stage's solved table.

**Question:** Which option has most recorded choices? Compare it with the second option in the source option order. How many more? What do the unavailable replies tell us?

**Complete key and accepted variations:** bench has most recorded choices, 3; gate has 2, so 1 more. Two unavailable replies establish only unavailable preference/reason, not dislike or support. No claim about everyone/other populations.

**Component criterion:** Supported comparison with correct difference and unknowns kept unknown.

**Specific unrelated next teaching:** If unknowns become a preference, contrast unrelated bird2/fish1/no reply2. If difference confused, pair two versus four named tokens and describe unmatched count.

**Question:** Make, describe or direct one useful statement or sign for this pretend choice. Explain what it helps and what stays unknown.

**Complete key and accepted variations:** Open useful statement/sign: e.g. “bench had most of these six recorded choices; two invited replies are unavailable.” It names the question/source scope and can support a tentative pretend recommendation. No single wording/layout; an actual child decision/direction must be observed rather than inferred from a copied model.

**Component criterion:** Useful contextual statement with actual own choice and bounded scope.

**Specific unrelated next teaching:** If statement says everyone/best, use a different fictional stripe/spot table and name source-limited choice versus value judgment. If useful, invite a new ordinary reader question without inventing actual use.

**Record honestly:** full source familiarity/exposure; question and actual first response/method; reading/scribing/handling access; mathematical hints/device answers; observed child choices versus adult operations; actual teaching/source/date; interval before next source; initial versus supported revision; unattempted/uncaptured fields. No hypothetical learner score or attained level.

## b-later · Reserve seaside-book icons

**Complete source (staff reference):** Original pretend question: which ONE reserve seaside-book icons option would you choose? Options, in order: shell, boat, bird. Available replies in order: shell, boat, shell, bird, boat, shell. Eight fictional invitations; six available choices; two no available replies, reason and preference unknown. Each available reply is one choice. No actual survey, visit or child result is supplied.

**Question:** Make or direct a complete list of the available replies. Keep the unavailable replies separate.

**Complete key and accepted variations:** Exact available list: shell, boat, shell, bird, boat, shell; keep two no-response records separate. Source order is useful for tracing but grouping order can differ if all six records are retained exactly once. No invented missing preference/reason.

**Component criterion:** Retains each available reply exactly once and marks unavailable status; categories have intelligible meaning.

**Specific unrelated next teaching:** If a repeated name is counted only once, trace unrelated circle,circle,triangle,square records with broad separate IDs. If category meaning unclear, revise a different pencil/crayon question before another list.

**Question:** Make or direct a table showing each named option and its recorded count.

**Complete key and accepted variations:** Full named table: shell: 3; boat: 2; bird: 1. Check category sum6;6 available+2 unavailable=8 invited. Category labels name choices; frequencies count those replies.

**Component criterion:** Correct option names/frequencies, explicit count check, zero versus missing distinction where relevant.

**Specific unrelated next teaching:** If counts mismatch, map unrelated cloud,sun,cloud,cloud to one mark per record, then total rows against list. Do not hand over this stage's solved table.

**Question:** Which option has most recorded choices? Compare it with the second option in the source option order. How many more? What do the unavailable replies tell us?

**Complete key and accepted variations:** shell has most recorded choices, 3; boat has 2, so 1 more. Two unavailable replies establish only unavailable preference/reason, not dislike or support. No claim about everyone/other populations.

**Component criterion:** Supported comparison with correct difference and unknowns kept unknown.

**Specific unrelated next teaching:** If unknowns become a preference, contrast unrelated bird2/fish1/no reply2. If difference confused, pair two versus four named tokens and describe unmatched count.

**Question:** Make, describe or direct one useful statement or sign for this pretend choice. Explain what it helps and what stays unknown.

**Complete key and accepted variations:** Open useful statement/sign: e.g. “shell had most of these six recorded choices; two invited replies are unavailable.” It names the question/source scope and can support a tentative pretend recommendation. No single wording/layout; an actual child decision/direction must be observed rather than inferred from a copied model.

**Component criterion:** Useful contextual statement with actual own choice and bounded scope.

**Specific unrelated next teaching:** If statement says everyone/best, use a different fictional stripe/spot table and name source-limited choice versus value judgment. If useful, invite a new ordinary reader question without inventing actual use.

**Record honestly:** full source familiarity/exposure; question and actual first response/method; reading/scribing/handling access; mathematical hints/device answers; observed child choices versus adult operations; actual teaching/source/date; interval before next source; initial versus supported revision; unattempted/uncaptured fields. No hypothetical learner score or attained level.

## n-first · Paper-puzzle order

**Complete source (staff reference):** Original fictional label numbers: 507, 570, 750. Chosen amount to represent: 507. Two pretend card groups contain 38 and 27 cards. A separate pretend project needs 73 labels and has 29 ready. These are supplied mathematical quantities, not actual stock, price, creation or a child result. All quantities can be read aloud; no object handling is required.

**Question:** Put 507, 570, 750 in numerical order. Show or direct a labelled number line and explain one comparison.

**Complete key and accepted variations:** Order: 507 < 570 < 750. A labelled line with relevant hundred reference points and consistent equal intervals can show this order; exact pixel position is not a compulsory measurement. Explain comparison by hundreds then tens/ones, not digit width.

**Component criterion:** Orders all numerals by magnitude, supports a comparison and uses a meaningful labelled line.

**Specific unrelated next teaching:** If highest digit decides order, use unrelated192/219 with named hundreds. If line positions unlabelled, make a new200→300 scale before another placement.

**Question:** Show 507 using hundreds, tens and ones. Show a different valid partition and explain the zero in its standard form.

**Complete key and accepted variations:** 507 = 5 hundreds0 tens7 ones = 4 hundreds10 tens7 ones. Check 500+0+7 = 400+100+7. Other nonnegative whole-unit partitions summing507 accepted. Zero is no tens in standard form, not no total value.

**Component criterion:** Names standard places, keeps zero meaning and preserves value in a distinct alternate partition.

**Specific unrelated next teaching:** If exchange changes value, use unrelated34:3 tens4 ones↔2 tens14 ones and recount. If zero removed, compare204/240; do not teach by revealing this held amount.

**Question:** How many cards are in the two groups together? Show your chosen number sentence and strategy. Check it.

**Complete key and accepted variations:** 38+27=65 cards. Example partition 30+20+8+7=65; regroup the ones where useful. Counted marks, bridge or another valid own strategy accepted. Inverse check 65−27=38.

**Component criterion:** Chooses join/addition model and a valid conserved strategy/check, with card meaning.

**Specific unrelated next teaching:** If a bridge double-counts, split unrelated18+5 as+2 then+3; if concatenation occurs, recombine20+10+7+6. Ask for a new inverse check after teaching.

**Question:** How many more labels does the separate project need? Choose a representation and strategy; explain and check what your answer means.

**Complete key and accepted variations:** 29+?=73, or73−29=44. Count up 29→30(+1)→73(+43); parts sum44. A correctly represented other strategy is accepted. Answer44 more labels, checked by29+44=73, not need+ready. No actual supplies/delivery.

**Component criterion:** Selects the missing part, represents/solves/checks it and communicates contextual meaning.

**Specific unrelated next teaching:** If need+ready is used, model unrelated25 needed/17 ready with a missing portion. If no units, ask what8 would count in that new model; choose a fresh ordinary problem afterwards.

**Record honestly:** full source familiarity/exposure; question and actual first response/method; reading/scribing/handling access; mathematical hints/device answers; observed child choices versus adult operations; actual teaching/source/date; interval before next source; initial versus supported revision; unattempted/uncaptured fields. No hypothetical learner score or attained level.

## n-later · Toy-city label order

**Complete source (staff reference):** Original fictional label numbers: 604, 640, 460. Chosen amount to represent: 604. Two pretend card groups contain 46 and 28 cards. A separate pretend project needs 82 labels and has 37 ready. These are supplied mathematical quantities, not actual stock, price, creation or a child result. All quantities can be read aloud; no object handling is required.

**Question:** Put 604, 640, 460 in numerical order. Show or direct a labelled number line and explain one comparison.

**Complete key and accepted variations:** Order: 460 < 604 < 640. A labelled line with relevant hundred reference points and consistent equal intervals can show this order; exact pixel position is not a compulsory measurement. Explain comparison by hundreds then tens/ones, not digit width.

**Component criterion:** Orders all numerals by magnitude, supports a comparison and uses a meaningful labelled line.

**Specific unrelated next teaching:** If highest digit decides order, use unrelated192/219 with named hundreds. If line positions unlabelled, make a new200→300 scale before another placement.

**Question:** Show 604 using hundreds, tens and ones. Show a different valid partition and explain the zero in its standard form.

**Complete key and accepted variations:** 604 = 6 hundreds0 tens4 ones = 5 hundreds10 tens4 ones. Check 600+0+4 = 500+100+4. Other nonnegative whole-unit partitions summing604 accepted. Zero is no tens in standard form, not no total value.

**Component criterion:** Names standard places, keeps zero meaning and preserves value in a distinct alternate partition.

**Specific unrelated next teaching:** If exchange changes value, use unrelated34:3 tens4 ones↔2 tens14 ones and recount. If zero removed, compare204/240; do not teach by revealing this held amount.

**Question:** How many cards are in the two groups together? Show your chosen number sentence and strategy. Check it.

**Complete key and accepted variations:** 46+28=74 cards. Example partition 40+20+6+8=74; regroup the ones where useful. Counted marks, bridge or another valid own strategy accepted. Inverse check 74−28=46.

**Component criterion:** Chooses join/addition model and a valid conserved strategy/check, with card meaning.

**Specific unrelated next teaching:** If a bridge double-counts, split unrelated18+5 as+2 then+3; if concatenation occurs, recombine20+10+7+6. Ask for a new inverse check after teaching.

**Question:** How many more labels does the separate project need? Choose a representation and strategy; explain and check what your answer means.

**Complete key and accepted variations:** 37+?=82, or82−37=45. Count up 37→40(+3)→82(+42); parts sum45. A correctly represented other strategy is accepted. Answer45 more labels, checked by37+45=82, not need+ready. No actual supplies/delivery.

**Component criterion:** Selects the missing part, represents/solves/checks it and communicates contextual meaning.

**Specific unrelated next teaching:** If need+ready is used, model unrelated25 needed/17 ready with a missing portion. If no units, ask what8 would count in that new model; choose a fresh ordinary problem afterwards.

**Record honestly:** full source familiarity/exposure; question and actual first response/method; reading/scribing/handling access; mathematical hints/device answers; observed child choices versus adult operations; actual teaching/source/date; interval before next source; initial versus supported revision; unattempted/uncaptured fields. No hypothetical learner score or attained level.

## r-first · Reserve story-card order

**Complete source (staff reference):** Original fictional label numbers: 709, 790, 970. Chosen amount to represent: 709. Two pretend card groups contain 47 and 26 cards. A separate pretend project needs 84 labels and has 38 ready. These are supplied mathematical quantities, not actual stock, price, creation or a child result. All quantities can be read aloud; no object handling is required.

**Question:** Put 709, 790, 970 in numerical order. Show or direct a labelled number line and explain one comparison.

**Complete key and accepted variations:** Order: 709 < 790 < 970. A labelled line with relevant hundred reference points and consistent equal intervals can show this order; exact pixel position is not a compulsory measurement. Explain comparison by hundreds then tens/ones, not digit width.

**Component criterion:** Orders all numerals by magnitude, supports a comparison and uses a meaningful labelled line.

**Specific unrelated next teaching:** If highest digit decides order, use unrelated192/219 with named hundreds. If line positions unlabelled, make a new200→300 scale before another placement.

**Question:** Show 709 using hundreds, tens and ones. Show a different valid partition and explain the zero in its standard form.

**Complete key and accepted variations:** 709 = 7 hundreds0 tens9 ones = 6 hundreds10 tens9 ones. Check 700+0+9 = 600+100+9. Other nonnegative whole-unit partitions summing709 accepted. Zero is no tens in standard form, not no total value.

**Component criterion:** Names standard places, keeps zero meaning and preserves value in a distinct alternate partition.

**Specific unrelated next teaching:** If exchange changes value, use unrelated34:3 tens4 ones↔2 tens14 ones and recount. If zero removed, compare204/240; do not teach by revealing this held amount.

**Question:** How many cards are in the two groups together? Show your chosen number sentence and strategy. Check it.

**Complete key and accepted variations:** 47+26=73 cards. Example partition 40+20+7+6=73; regroup the ones where useful. Counted marks, bridge or another valid own strategy accepted. Inverse check 73−26=47.

**Component criterion:** Chooses join/addition model and a valid conserved strategy/check, with card meaning.

**Specific unrelated next teaching:** If a bridge double-counts, split unrelated18+5 as+2 then+3; if concatenation occurs, recombine20+10+7+6. Ask for a new inverse check after teaching.

**Question:** How many more labels does the separate project need? Choose a representation and strategy; explain and check what your answer means.

**Complete key and accepted variations:** 38+?=84, or84−38=46. Count up 38→40(+2)→84(+44); parts sum46. A correctly represented other strategy is accepted. Answer46 more labels, checked by38+46=84, not need+ready. No actual supplies/delivery.

**Component criterion:** Selects the missing part, represents/solves/checks it and communicates contextual meaning.

**Specific unrelated next teaching:** If need+ready is used, model unrelated25 needed/17 ready with a missing portion. If no units, ask what8 would count in that new model; choose a fresh ordinary problem afterwards.

**Record honestly:** full source familiarity/exposure; question and actual first response/method; reading/scribing/handling access; mathematical hints/device answers; observed child choices versus adult operations; actual teaching/source/date; interval before next source; initial versus supported revision; unattempted/uncaptured fields. No hypothetical learner score or attained level.

## r-later · Reserve paper-gallery order

**Complete source (staff reference):** Original fictional label numbers: 806, 860, 680. Chosen amount to represent: 806. Two pretend card groups contain 57 and 25 cards. A separate pretend project needs 91 labels and has 46 ready. These are supplied mathematical quantities, not actual stock, price, creation or a child result. All quantities can be read aloud; no object handling is required.

**Question:** Put 806, 860, 680 in numerical order. Show or direct a labelled number line and explain one comparison.

**Complete key and accepted variations:** Order: 680 < 806 < 860. A labelled line with relevant hundred reference points and consistent equal intervals can show this order; exact pixel position is not a compulsory measurement. Explain comparison by hundreds then tens/ones, not digit width.

**Component criterion:** Orders all numerals by magnitude, supports a comparison and uses a meaningful labelled line.

**Specific unrelated next teaching:** If highest digit decides order, use unrelated192/219 with named hundreds. If line positions unlabelled, make a new200→300 scale before another placement.

**Question:** Show 806 using hundreds, tens and ones. Show a different valid partition and explain the zero in its standard form.

**Complete key and accepted variations:** 806 = 8 hundreds0 tens6 ones = 7 hundreds10 tens6 ones. Check 800+0+6 = 700+100+6. Other nonnegative whole-unit partitions summing806 accepted. Zero is no tens in standard form, not no total value.

**Component criterion:** Names standard places, keeps zero meaning and preserves value in a distinct alternate partition.

**Specific unrelated next teaching:** If exchange changes value, use unrelated34:3 tens4 ones↔2 tens14 ones and recount. If zero removed, compare204/240; do not teach by revealing this held amount.

**Question:** How many cards are in the two groups together? Show your chosen number sentence and strategy. Check it.

**Complete key and accepted variations:** 57+25=82 cards. Example partition 50+20+7+5=82; regroup the ones where useful. Counted marks, bridge or another valid own strategy accepted. Inverse check 82−25=57.

**Component criterion:** Chooses join/addition model and a valid conserved strategy/check, with card meaning.

**Specific unrelated next teaching:** If a bridge double-counts, split unrelated18+5 as+2 then+3; if concatenation occurs, recombine20+10+7+6. Ask for a new inverse check after teaching.

**Question:** How many more labels does the separate project need? Choose a representation and strategy; explain and check what your answer means.

**Complete key and accepted variations:** 46+?=91, or91−46=45. Count up 46→50(+4)→91(+41); parts sum45. A correctly represented other strategy is accepted. Answer45 more labels, checked by46+45=91, not need+ready. No actual supplies/delivery.

**Component criterion:** Selects the missing part, represents/solves/checks it and communicates contextual meaning.

**Specific unrelated next teaching:** If need+ready is used, model unrelated25 needed/17 ready with a missing portion. If no units, ask what8 would count in that new model; choose a fresh ordinary problem afterwards.

**Record honestly:** full source familiarity/exposure; question and actual first response/method; reading/scribing/handling access; mathematical hints/device answers; observed child choices versus adult operations; actual teaching/source/date; interval before next source; initial versus supported revision; unattempted/uncaptured fields. No hypothetical learner score or attained level.

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