# Ten daily plans · complete teacher sources

One route is enough; show the ordinary source before your separate model. Session suggestions are flexible and unpiloted. Learner ownership concerns the mathematics and choices, not a required physical action.

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

## Lessons

### A total worth checking

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Adult model:** 612 + 243 = (600 + 200) + (10 + 40) + (2 + 3) = 800 + 50 + 5 = 855 badges. Say what each part counts. This is joining two collections, not 612 groups of 243.

**Child direction:** Can we make a stock note that someone else can trust? Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

**Common tangle:** columns are mixed; check the roles and equivalent quantities, rather than memorising a printed answer.

**Day:** 51

**Different guided practice:** An invented drawing archive has 421 cards plus 136 new cards. Invite the partition before the total: 400 + 100, 20 + 30, 1 + 6, then 557 cards. Ask why units can be joined.

**Entry check and teach:** Ask for 42 + 15 and a representation of 42 as four tens and two ones. If either is unavailable, count labelled tens/ones, join 2 + 5 ones then 4 + 1 tens. Teach 57 before increasing the number. Earlier fraction, parity or multiplication packs are not an entry guarantee.

**Hook:** Can we make a stock note that someone else can trust?

**Materials:** Broad paper, labelled place-value/part-whole/number-line alternatives as suitable; optional familiar safe counters; usual communication. No hundreds of loose marks, purchases or physical handling required. Keep adult model and own work separate.

**Next teaching:** If columns are mixed, label hundreds/tens/ones on 203 + 124, build 327, then invite 302 + 113 = 415 with labels faded.

**Ordinary source:** Fictional badge studio: 612 blank badges arrive in one parcel and 243 in another. Every badge is counted once. How many badges are available?

**Own exit:** For 304 + 152, give a total and one way to check its parts.

#### Partial codes

1. AC9M4N06

**Purpose:** Join like whole counts using place-value partitioning.

#### Routes

##### A

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** A fictional game has 42 clue cards, then 15 arrive. Make a total note using tens and ones.

**Entry or access:** Return to two broad tens and three ones plus one ten if needed.

**Id:** A

**Title:** Small card repair

**Worked staff:** 42 + 15 = 57 cards: 40 + 10 = 50, 2 + 5 = 7.

##### B

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Use the 612 and 243 badge parcels. Compare partitioning with adding 200, then 40, then 3 to 612.

**Entry or access:** Use labels rather than 855 loose marks.

**Id:** B

**Title:** Badge maker

**Worked staff:** 855 badges; 612→812→852→855 keeps the complete second quantity.

##### C

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** A fictional archive joins 2436 and 1523 cards. Show two compatible partitions.

**Entry or access:** Check thousands/hundreds entry before this larger route.

**Id:** C

**Title:** Archive upgrade

**Worked staff:** 3959 cards: 2000 + 1000, 400 + 500, 30 + 20, 6 + 3. Or 2436 + 1500 + 23.

#### Session stages

##### Meet the job

**Instruction:** Can we make a stock note that someone else can trust? Read the source. Ask what the numbers count and the wanted quantity. Ask for 42 + 15 and a representation of 42 as four tens and two ones. If either is unavailable, count labelled tens/ones, join 2 + 5 ones then 4 + 1 tens. Teach 57 before increasing the number. Earlier fraction, parity or multiplication packs are not an entry guarantee.

**Minutes suggestion:** 5

**Stage:** Meet the job

##### Teach one relationship

**Instruction:** 612 + 243 = (600 + 200) + (10 + 40) + (2 + 3) = 800 + 50 + 5 = 855 badges. Say what each part counts. This is joining two collections, not 612 groups of 243. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

**Minutes suggestion:** 10

**Stage:** Teach one relationship

##### Guide then choose

**Instruction:** An invented drawing archive has 421 cards plus 136 new cards. Invite the partition before the total: 400 + 100, 20 + 30, 1 + 6, then 557 cards. Ask why units can be joined. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

**Minutes suggestion:** 15

**Stage:** Guide then choose

##### Receive and choose tomorrow

**Instruction:** For 304 + 152, give a total and one way to check its parts. Receive an available response before staff key. If columns are mixed, label hundreds/tens/ones on 203 + 124, build 327, then invite 302 + 113 = 415 with labels faded.

**Minutes suggestion:** 5

**Stage:** Receive and choose tomorrow

**Specific criterion:** The result and a valid like-unit partition agree; a copied total alone is insufficient for the explanation.

**Staff key:** 456; 300 + 100, 0 + 50, 4 + 2. Check 456 − 152 = 304 or recombine the parts.

**Status:** Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

**Title:** A total worth checking

### Ten ones can travel together

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Adult model:** 364 + 278 = 500 + 130 + 12 = 642. Rename 12 ones as 1 ten 2 ones; 14 tens as 1 hundred 4 tens, with 6 hundreds altogether. Equivalently 364 + 200 = 564, +70 = 634, +8 = 642. No item disappears when regrouped.

**Child direction:** Make a plan for a collection that crosses a ten or a hundred. Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

**Common tangle:** a carried ten disappears; check the roles and equivalent quantities, rather than memorising a printed answer.

**Day:** 52

**Different guided practice:** A fictional picture station joins 527 cards and 186 cards: 527 + 100 = 627, +80 = 707, +6 = 713. Ask the learner to show where a hundred boundary was crossed.

**Entry check and teach:** Check 8 + 7 and explain ten ones = one ten. If needed, show 8 plus 2 fills ten and 5 remains; use 28 + 7 = 35 before hundreds.

**Hook:** Make a plan for a collection that crosses a ten or a hundred.

**Materials:** Broad paper, labelled place-value/part-whole/number-line alternatives as suitable; optional familiar safe counters; usual communication. No hundreds of loose marks, purchases or physical handling required. Keep adult model and own work separate.

**Next teaching:** If a carried ten disappears, teach 48 + 16 with ten-unit labels: 40 + 10 + 8 + 6 = 64. Then offer 57 + 18 = 75.

**Ordinary source:** An invented costume cupboard has 364 tags, then receives 278 tags of the same kind. Find the new count.

**Own exit:** Try 258 + 167. Show the regroup or describe it exactly.

#### Partial codes

1. AC9M4N06

**Purpose:** Regroup an addition without changing its value.

#### Routes

##### A

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** There are 28 fictional counters and 17 more. Show what happens to fifteen ones.

**Entry or access:** Build one ten from ten labelled ones if needed.

**Id:** A

**Title:** Game counters

**Worked staff:** 45 counters: 30 + 15 = 45.

##### B

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Use 527 and 186 cards. Make a checkable regrouping note.

**Entry or access:** Keep each place-value amount visible.

**Id:** B

**Title:** Picture station

**Worked staff:** 713 cards; 600 + 100 + 13 = 713.

##### C

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Join 2687 and 1756 imagined sheets. Compare adding chunks with place-value regrouping.

**Entry or access:** Use this only after thousands can be renamed.

**Id:** C

**Title:** Print store

**Worked staff:** 4443: 3000 + 1300 + 130 + 13 = 4443; chunks +1000,+700,+50,+6.

#### Session stages

##### Meet the job

**Instruction:** Make a plan for a collection that crosses a ten or a hundred. Read the source. Ask what the numbers count and the wanted quantity. Check 8 + 7 and explain ten ones = one ten. If needed, show 8 plus 2 fills ten and 5 remains; use 28 + 7 = 35 before hundreds.

**Minutes suggestion:** 5

**Stage:** Meet the job

##### Teach one relationship

**Instruction:** 364 + 278 = 500 + 130 + 12 = 642. Rename 12 ones as 1 ten 2 ones; 14 tens as 1 hundred 4 tens, with 6 hundreds altogether. Equivalently 364 + 200 = 564, +70 = 634, +8 = 642. No item disappears when regrouped. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

**Minutes suggestion:** 10

**Stage:** Teach one relationship

##### Guide then choose

**Instruction:** A fictional picture station joins 527 cards and 186 cards: 527 + 100 = 627, +80 = 707, +6 = 713. Ask the learner to show where a hundred boundary was crossed. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

**Minutes suggestion:** 15

**Stage:** Guide then choose

##### Receive and choose tomorrow

**Instruction:** Try 258 + 167. Show the regroup or describe it exactly. Receive an available response before staff key. If a carried ten disappears, teach 48 + 16 with ten-unit labels: 40 + 10 + 8 + 6 = 64. Then offer 57 + 18 = 75.

**Minutes suggestion:** 5

**Stage:** Receive and choose tomorrow

**Specific criterion:** Each regroup keeps the quantity, including both parts of the added amount, and yields 425.

**Staff key:** 425: 300 + 110 + 15 = 425, or 258 + 100 + 60 + 7.

**Status:** Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

**Title:** Ten ones can travel together

### Borrow a friendly number, then put it back

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Adult model:** 398 + 267 = 400 + 267 − 2 = 665. We added two extra in the friendly-number step, so remove two from 667. About 400 + 300 = 700 is an estimate, not this exact calculation.

**Child direction:** Would moving to a nearby round number make this job easier? Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

**Common tangle:** the adjustment goes the wrong way; check the roles and equivalent quantities, rather than memorising a printed answer.

**Day:** 53

**Different guided practice:** For fictional prompt cards, 497 + 186 = 500 + 186 − 3 = 683. Contrast the wrong 686: it counts the three extra cards. Invite a different check: 497 + 180 + 6.

**Entry check and teach:** Ask why 39 + 12 can be worked as 40 + 12 − 1. Model with a labelled extra mark if needed. Teach the compensation before rounding two large inputs.

**Hook:** Would moving to a nearby round number make this job easier?

**Materials:** Broad paper, labelled place-value/part-whole/number-line alternatives as suitable; optional familiar safe counters; usual communication. No hundreds of loose marks, purchases or physical handling required. Keep adult model and own work separate.

**Next teaching:** If the adjustment goes the wrong way, compare 19 + 6 with 20 + 6 − 1 using marks. Guide 29 + 14, then invite 49 + 17 = 66.

**Ordinary source:** An invented sticker design has 398 blue stickers and 267 plain stickers. Find the exact total.

**Own exit:** Work 299 + 146 exactly using a friendly number, and name the adjustment.

#### Partial codes

1. AC9M4N06
2. AC9M4N07 partial

**Purpose:** Use exact compensation and distinguish it from estimation.

#### Routes

##### A

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** An invented puzzle tray joins 49 and 27 pieces. Use fifty carefully.

**Entry or access:** Draw the one added extra separately.

**Id:** A

**Title:** Puzzle pieces

**Worked staff:** 76: 50 + 27 − 1.

##### B

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Find 398 + 267 and compare compensation with chunks.

**Entry or access:** Explain which quantity was changed.

**Id:** B

**Title:** Sticker plan

**Worked staff:** 665 exactly; 700 is a coarse estimate.

##### C

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** An imaginary exhibit game counts 1998 + 367 slips. Compare exact compensation and a nearest-hundred estimate.

**Entry or access:** This fictional game is not a museum programme or attendance fact.

**Id:** C

**Title:** Museum-copy game

**Worked staff:** 2365 exact; 2000 + 400 ≈ 2400, 35 above exact.

#### Session stages

##### Meet the job

**Instruction:** Would moving to a nearby round number make this job easier? Read the source. Ask what the numbers count and the wanted quantity. Ask why 39 + 12 can be worked as 40 + 12 − 1. Model with a labelled extra mark if needed. Teach the compensation before rounding two large inputs.

**Minutes suggestion:** 5

**Stage:** Meet the job

##### Teach one relationship

**Instruction:** 398 + 267 = 400 + 267 − 2 = 665. We added two extra in the friendly-number step, so remove two from 667. About 400 + 300 = 700 is an estimate, not this exact calculation. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

**Minutes suggestion:** 10

**Stage:** Teach one relationship

##### Guide then choose

**Instruction:** For fictional prompt cards, 497 + 186 = 500 + 186 − 3 = 683. Contrast the wrong 686: it counts the three extra cards. Invite a different check: 497 + 180 + 6. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

**Minutes suggestion:** 15

**Stage:** Guide then choose

##### Receive and choose tomorrow

**Instruction:** Work 299 + 146 exactly using a friendly number, and name the adjustment. Receive an available response before staff key. If the adjustment goes the wrong way, compare 19 + 6 with 20 + 6 − 1 using marks. Guide 29 + 14, then invite 49 + 17 = 66.

**Minutes suggestion:** 5

**Stage:** Receive and choose tomorrow

**Specific criterion:** The nearby number, compensating adjustment and exact result are linked; rounding alone is not an exact proof.

**Staff key:** 445: 300 + 146 − 1; the added extra one is removed.

**Status:** Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

**Title:** Borrow a friendly number, then put it back

### Take away without losing the place values

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Adult model:** 806 = 7 hundreds + 9 tens + 16 ones. Subtract 2 hundreds, 4 tens, 7 ones to leave 5 hundreds 5 tens 9 ones = 559. Check 247 + 559 = 806. A count-up check is 247→250 (+3)→800 (+550)→806 (+6), total 559.

**Child direction:** Can a repair drawer show what is left clearly? Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

**Common tangle:** 0 tens blocks the subtraction; check the roles and equivalent quantities, rather than memorising a printed answer.

**Day:** 54

**Different guided practice:** A made-up card store has 704 cards, uses 168. Guide 6 hundreds 9 tens 14 ones minus 1 hundred 6 tens 8 ones = 536. Or subtract 100, 60, 8 in chunks.

**Entry check and teach:** Ask for 52 − 17 and whether one ten can become ten ones. If not, teach 30 − 8 as 2 tens 10 ones minus 8 = 22; return to 52 − 17 = 35.

**Hook:** Can a repair drawer show what is left clearly?

**Materials:** Broad paper, labelled place-value/part-whole/number-line alternatives as suitable; optional familiar safe counters; usual communication. No hundreds of loose marks, purchases or physical handling required. Keep adult model and own work separate.

**Next teaching:** If 0 tens blocks the subtraction, teach 102 − 38 by trading one hundred for tens, then one ten for ones. Guide 64; invite 201 − 46 = 155.

**Ordinary source:** A fictional repair drawer starts with 806 labels. It uses 247 labels once. Find labels left.

**Own exit:** For 603 − 157, show what remains and a connected check.

#### Partial codes

1. AC9M4N06

**Purpose:** Subtract through regrouping or a connected count-up check.

#### Routes

##### A

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** A fictional drawer has 63 labels and uses 28. Find what remains with regrouping.

**Entry or access:** No actual paint or material handling is needed.

**Id:** A

**Title:** Small paint labels

**Worked staff:** 35 labels; 28 + 35 = 63.

##### B

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Use 806 − 247. Make a left-count record with a check.

**Entry or access:** Describe bundles instead of drawing hundreds of marks.

**Id:** B

**Title:** Repair drawer

**Worked staff:** 559 labels; 247 + 559 = 806.

##### C

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** An invented archive has 2004 cards and retires 786. Find remaining cards using two approaches.

**Entry or access:** Check thousands entry and the meaning of retiring a count.

**Id:** C

**Title:** Archive use

**Worked staff:** 1218; 786→800(+14)→2000(+1200)→2004(+4).

#### Session stages

##### Meet the job

**Instruction:** Can a repair drawer show what is left clearly? Read the source. Ask what the numbers count and the wanted quantity. Ask for 52 − 17 and whether one ten can become ten ones. If not, teach 30 − 8 as 2 tens 10 ones minus 8 = 22; return to 52 − 17 = 35.

**Minutes suggestion:** 5

**Stage:** Meet the job

##### Teach one relationship

**Instruction:** 806 = 7 hundreds + 9 tens + 16 ones. Subtract 2 hundreds, 4 tens, 7 ones to leave 5 hundreds 5 tens 9 ones = 559. Check 247 + 559 = 806. A count-up check is 247→250 (+3)→800 (+550)→806 (+6), total 559. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

**Minutes suggestion:** 10

**Stage:** Teach one relationship

##### Guide then choose

**Instruction:** A made-up card store has 704 cards, uses 168. Guide 6 hundreds 9 tens 14 ones minus 1 hundred 6 tens 8 ones = 536. Or subtract 100, 60, 8 in chunks. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

**Minutes suggestion:** 15

**Stage:** Guide then choose

##### Receive and choose tomorrow

**Instruction:** For 603 − 157, show what remains and a connected check. Receive an available response before staff key. If 0 tens blocks the subtraction, teach 102 − 38 by trading one hundred for tens, then one ten for ones. Guide 64; invite 201 − 46 = 155.

**Minutes suggestion:** 5

**Stage:** Receive and choose tomorrow

**Specific criterion:** Renamed values conserve 603; subtraction and inverse agree with 446 labels/items left.

**Staff key:** 446; 157 + 446 = 603. Regroup 603 as 5 hundreds 9 tens 13 ones.

**Status:** Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

**Title:** Take away without losing the place values

### How much more?

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Adult model:** 987→1000 adds 13; 1000→1200 adds 200; 1200→1203 adds 3. The gap is 216 labels: 987 + 216 = 1203. The difference is a count comparison, not evidence the larger design is preferable.

**Child direction:** Help two made-up teams compare their counts without calling one better. Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

**Common tangle:** the difference is added to both counts; check the roles and equivalent quantities, rather than memorising a printed answer.

**Day:** 55

**Different guided practice:** Two invented folders contain 1501 and 1297 cards. Guide +3 to 1300,+200 to 1500,+1 to 1501 =204. Ask whether taking 1297 away from 1501 gives the same difference.

**Entry check and teach:** Ask how many more 37 is than 29; count 29→30(+1)→37(+7)=8. Both original collections still exist. If comparison is unclear, use 7 and 4 labels side by side.

**Hook:** Help two made-up teams compare their counts without calling one better.

**Materials:** Broad paper, labelled place-value/part-whole/number-line alternatives as suitable; optional familiar safe counters; usual communication. No hundreds of loose marks, purchases or physical handling required. Keep adult model and own work separate.

**Next teaching:** If the difference is added to both counts, keep a bar for each whole. Teach 46 compared with 39 gives 7, check 39+7=46; invite 81 compared with 68 gives 13.

**Ordinary source:** Two fictional poster designs require 1203 labels and 987 labels. What is the difference in their requirements? No labels have been removed.

**Own exit:** A fictional score sheet lists 1002 and 875 points. Find the difference and explain its meaning.

#### Partial codes

1. AC9M4N06

**Purpose:** Find a difference by counting up; distinguish comparison from a removal event.

#### Routes

##### A

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Compare fictional 52 and 38 game points. Show the gap, keeping both scores.

**Entry or access:** Use a marked line or exact spoken steps.

**Id:** A

**Title:** Small score comparison

**Worked staff:** 14 points; 38 + 14 = 52.

##### B

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Compare 1203 and 987 labels needed. Give a gap note that avoids a value judgement.

**Entry or access:** Use friendly stepping stones.

**Id:** B

**Title:** Poster designs

**Worked staff:** 216 more labels for the first design.

##### C

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Two invented game routes are 3502 and 2789 step-cards long. Find the difference, not a real walking distance.

**Entry or access:** The counts are fictional game units, not travel or fitness advice.

**Id:** C

**Title:** Fictional trail game

**Worked staff:** 713 step-cards; +11 to 2800,+700 to 3500,+2.

#### Session stages

##### Meet the job

**Instruction:** Help two made-up teams compare their counts without calling one better. Read the source. Ask what the numbers count and the wanted quantity. Ask how many more 37 is than 29; count 29→30(+1)→37(+7)=8. Both original collections still exist. If comparison is unclear, use 7 and 4 labels side by side.

**Minutes suggestion:** 5

**Stage:** Meet the job

##### Teach one relationship

**Instruction:** 987→1000 adds 13; 1000→1200 adds 200; 1200→1203 adds 3. The gap is 216 labels: 987 + 216 = 1203. The difference is a count comparison, not evidence the larger design is preferable. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

**Minutes suggestion:** 10

**Stage:** Teach one relationship

##### Guide then choose

**Instruction:** Two invented folders contain 1501 and 1297 cards. Guide +3 to 1300,+200 to 1500,+1 to 1501 =204. Ask whether taking 1297 away from 1501 gives the same difference. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

**Minutes suggestion:** 15

**Stage:** Guide then choose

##### Receive and choose tomorrow

**Instruction:** A fictional score sheet lists 1002 and 875 points. Find the difference and explain its meaning. Receive an available response before staff key. If the difference is added to both counts, keep a bar for each whole. Teach 46 compared with 39 gives 7, check 39+7=46; invite 81 compared with 68 gives 13.

**Minutes suggestion:** 5

**Stage:** Receive and choose tomorrow

**Specific criterion:** The difference and count-up bridge are correct and interpreted as comparison, not a performed removal.

**Staff key:** 127 points: +25 to 900,+100 to 1000,+2. No claim about real players.

**Status:** Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

**Title:** How much more?

### Find the missing part

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Adult model:** 468→500 adds 32; 500→725 adds 225; missing part 257. Check 468+257=725. The box is a number value, not the total 725; the equation has two equal sides.

**Child direction:** What needs to join a collection to reach the target? Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

**Common tangle:** the total is placed in the box; check the roles and equivalent quantities, rather than memorising a printed answer.

**Day:** 56

**Different guided practice:** A fictional badge target is 630 with 275 available. Guide 275+□=630; 275→300(+25)→630(+330)=355. Check 275+355.

**Entry check and teach:** Check 18 + □ = 31. Show 18 and the target 31, count up 13, then check 18+13. If the box is treated as a decoration, put a temporary question card over one part of a small 4+3=7 model.

**Hook:** What needs to join a collection to reach the target?

**Materials:** Broad paper, labelled place-value/part-whole/number-line alternatives as suitable; optional familiar safe counters; usual communication. No hundreds of loose marks, purchases or physical handling required. Keep adult model and own work separate.

**Next teaching:** If the total is placed in the box, label whole 54, known part 28, unknown part 26. Guide 28+26=54, then invite 37+□=65. Staff reference: □=28; check 37+28=65.

**Ordinary source:** An invented card kit needs 725 cards in total. It already has 468. How many more are needed? 468 + □ = 725.

**Own exit:** Solve 386 + □ = 540, and show the check in the original equation.

#### Partial codes

1. AC9M4A01
2. AC9M4N06

**Purpose:** Use addition/subtraction relationships for an unknown addend.

#### Routes

##### A

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** A made-up game target is 65 points, with 37 already recorded. Find the missing part.

**Entry or access:** Use two bars for known part and unknown part.

**Id:** A

**Title:** Small game target

**Worked staff:** 28; 37+28=65.

##### B

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Use 468+□=725. Tell the next maker how many more cards would be needed.

**Entry or access:** The future requirement is not a completed supply event.

**Id:** B

**Title:** Card kit

**Worked staff:** 257 cards.

##### C

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** An invented print target is 2400 sheets; 1587 are already counted. Find the missing part and an exact check.

**Entry or access:** Choose a thousands representation only if available.

**Id:** C

**Title:** Print target

**Worked staff:** 813; 1587+813=2400.

#### Session stages

##### Meet the job

**Instruction:** What needs to join a collection to reach the target? Read the source. Ask what the numbers count and the wanted quantity. Check 18 + □ = 31. Show 18 and the target 31, count up 13, then check 18+13. If the box is treated as a decoration, put a temporary question card over one part of a small 4+3=7 model.

**Minutes suggestion:** 5

**Stage:** Meet the job

##### Teach one relationship

**Instruction:** 468→500 adds 32; 500→725 adds 225; missing part 257. Check 468+257=725. The box is a number value, not the total 725; the equation has two equal sides. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

**Minutes suggestion:** 10

**Stage:** Teach one relationship

##### Guide then choose

**Instruction:** A fictional badge target is 630 with 275 available. Guide 275+□=630; 275→300(+25)→630(+330)=355. Check 275+355. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

**Minutes suggestion:** 15

**Stage:** Guide then choose

##### Receive and choose tomorrow

**Instruction:** Solve 386 + □ = 540, and show the check in the original equation. Receive an available response before staff key. If the total is placed in the box, label whole 54, known part 28, unknown part 26. Guide 28+26=54, then invite 37+□=65. Staff reference: □=28; check 37+28=65.

**Minutes suggestion:** 5

**Stage:** Receive and choose tomorrow

**Specific criterion:** The missing part 154 and original equality are supported by an inverse or count-up relationship.

**Staff key:** 154; 386+154=540.

**Status:** Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

**Title:** Find the missing part

### Which part is missing?

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Adult model:** Used tags 930−586=344, check 930−344=586. Starting cards 428+175=603, check 603−175=428. Addition or subtraction is chosen by the unknown role, not by spotting the word left.

**Child direction:** A missing count can sit at the start or in the amount used. Can your note make that clear? Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

**Common tangle:** all left stories trigger subtraction; check the roles and equivalent quantities, rather than memorising a printed answer.

**Day:** 57

**Different guided practice:** A fictional game starts with 702 tokens and ends with 459: used 243. A different game uses 126 and ends with 387: start 513. Guide both original-equation checks, one case at a time.

**Entry check and teach:** Contrast □ − 7 =12 with 19 − □ =12 using an empty part/whole bar. First means start 19; second means used 7. Teach small connected addition if the roles are swapped.

**Hook:** A missing count can sit at the start or in the amount used. Can your note make that clear?

**Materials:** Broad paper, labelled place-value/part-whole/number-line alternatives as suitable; optional familiar safe counters; usual communication. No hundreds of loose marks, purchases or physical handling required. Keep adult model and own work separate.

**Next teaching:** If all left stories trigger subtraction, teach □−4=9 by joining used 4 and left 9 into 13. Then invite □−8=15. Staff reference: starting value □=23; check 23−8=15.

**Ordinary source:** A fictional store starts with 930 tags and finishes with 586. How many were used?930−□=586. Separately, a fictional box uses 175 cards and has 428 left. How many did it start with?□−175=428.

**Own exit:** Solve □ − 148 =367 and explain what the box counts.

#### Partial codes

1. AC9M4A01
2. AC9M4N06

**Purpose:** Distinguish unknown starting quantity from unknown subtraction amount.

#### Routes

##### A

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** A pretend tray starts with 61 cards and ends with 38. Find how many were used.

**Entry or access:** Keep start/use/left labels visible.

**Id:** A

**Title:** Small stock story

**Worked staff:** 23 used; 61−23=38.

##### B

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Work the 930/586 tags and 175/428 cards cases separately. Name each unknown role.

**Entry or access:** Do not join card and tag quantities.

**Id:** B

**Title:** Two store notes

**Worked staff:** 344 used tags; 603 starting cards.

##### C

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** A fictional archive has 2001−□=1278; another has□−586=1447. Explain and check both.

**Entry or access:** Offer just one equation if two cases overload the purpose.

**Id:** C

**Title:** Archive puzzles

**Worked staff:** 723 removed; 2033 starting.

#### Session stages

##### Meet the job

**Instruction:** A missing count can sit at the start or in the amount used. Can your note make that clear? Read the source. Ask what the numbers count and the wanted quantity. Contrast □ − 7 =12 with 19 − □ =12 using an empty part/whole bar. First means start 19; second means used 7. Teach small connected addition if the roles are swapped.

**Minutes suggestion:** 5

**Stage:** Meet the job

##### Teach one relationship

**Instruction:** Used tags 930−586=344, check 930−344=586. Starting cards 428+175=603, check 603−175=428. Addition or subtraction is chosen by the unknown role, not by spotting the word left. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

**Minutes suggestion:** 10

**Stage:** Teach one relationship

##### Guide then choose

**Instruction:** A fictional game starts with 702 tokens and ends with 459: used 243. A different game uses 126 and ends with 387: start 513. Guide both original-equation checks, one case at a time. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

**Minutes suggestion:** 15

**Stage:** Guide then choose

##### Receive and choose tomorrow

**Instruction:** Solve □ − 148 =367 and explain what the box counts. Receive an available response before staff key. If all left stories trigger subtraction, teach □−4=9 by joining used 4 and left 9 into 13. Then invite □−8=15. Staff reference: starting value □=23; check 23−8=15.

**Minutes suggestion:** 5

**Stage:** Receive and choose tomorrow

**Specific criterion:** The box is the starting quantity 515; rebuilding from used 148 and left 367 supports the original equality.

**Staff key:** 515 starting items; 515−148=367.

**Status:** Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

**Title:** Which part is missing?

### Both sides mean the same amount

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Adult model:** Right side 390+75=465;□=465−245=220. Substitution 245+220=465 and 390+75=465. The box is 220, not 465. Keep each original side intact.

**Child direction:** Make a puzzle another person can check without guessing what the equals sign means. Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

**Common tangle:** If 465 is entered in the box; check the roles and equivalent quantities, rather than memorising a printed answer.

**Day:** 58

**Different guided practice:** For a fictional drawer 620−185=□+240: left 435, unknown 195, check 195+240=435. Invite the learner to compute the known side before undoing the other part.

**Entry check and teach:** Check 12+3=10+5 as equal 15, then 12+□=10+5 gives 3. If = means next answer, use two named equal 15 bars and vary one decomposition.

**Hook:** Make a puzzle another person can check without guessing what the equals sign means.

**Materials:** Broad paper, labelled place-value/part-whole/number-line alternatives as suitable; optional familiar safe counters; usual communication. No hundreds of loose marks, purchases or physical handling required. Keep adult model and own work separate.

**Next teaching:** If 465 is entered in the box, use 20+□=30+7: known side 37, missing 17. Guide 20+17=37; then invite 14+□=20+8 gives 14.

**Ordinary source:** An invented display equation is 245+□=390+75. Find the box value and check both sides.

**Own exit:** Solve 128+□=200+47 and check the two sides.

#### Partial codes

1. AC9M4A01
2. AC9M4N06

**Purpose:** Find an unknown when each side contains a calculation.

#### Routes

##### A

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Solve 18+□=25+7, preserving both sides.

**Entry or access:** Represent each entire side as a whole.

**Id:** A

**Title:** Small equality puzzle

**Worked staff:** 14; 18+14=32=25+7.

##### B

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Use 245+□=390+75. Create a readable substitution check.

**Entry or access:** No balance-scale physical claim is needed.

**Id:** B

**Title:** Display equation

**Worked staff:** 220; both sides 465.

##### C

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Solve 2000−675=□+486. Show what is known first.

**Entry or access:** Use a broad labelled two-side diagram.

**Id:** C

**Title:** Archive equality

**Worked staff:** 839; 1325=839+486.

#### Session stages

##### Meet the job

**Instruction:** Make a puzzle another person can check without guessing what the equals sign means. Read the source. Ask what the numbers count and the wanted quantity. Check 12+3=10+5 as equal 15, then 12+□=10+5 gives 3. If = means next answer, use two named equal 15 bars and vary one decomposition.

**Minutes suggestion:** 5

**Stage:** Meet the job

##### Teach one relationship

**Instruction:** Right side 390+75=465;□=465−245=220. Substitution 245+220=465 and 390+75=465. The box is 220, not 465. Keep each original side intact. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

**Minutes suggestion:** 10

**Stage:** Teach one relationship

##### Guide then choose

**Instruction:** For a fictional drawer 620−185=□+240: left 435, unknown 195, check 195+240=435. Invite the learner to compute the known side before undoing the other part. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

**Minutes suggestion:** 15

**Stage:** Guide then choose

##### Receive and choose tomorrow

**Instruction:** Solve 128+□=200+47 and check the two sides. Receive an available response before staff key. If 465 is entered in the box, use 20+□=30+7: known side 37, missing 17. Guide 20+17=37; then invite 14+□=20+8 gives 14.

**Minutes suggestion:** 5

**Stage:** Receive and choose tomorrow

**Specific criterion:** Unknown 119 makes both full sides equal 247; explanation distinguishes box value from whole-side value.

**Staff key:** 119; 128+119=247 and 200+47=247.

**Status:** Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

**Title:** Both sides mean the same amount

### An estimate helps. An exact check decides.

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Adult model:** Handouts 268+124=392; 485−392=93 more needed. Budget 265+148=413 cost; 450−413=37 left. Nearest-ten estimate 270+150≈420 checks scale but is not the exact 413 or 37. Keep handouts and dollars separate.

**Child direction:** Pick a made-up supply or budget job. What decision does the arithmetic need to answer? Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

**Common tangle:** an estimate is treated as exact; check the roles and equivalent quantities, rather than memorising a printed answer.

**Day:** 59

**Different guided practice:** An imaginary card plan needs 600 cards; 328+195=523 available, gap 77. A separate invented budget $380 costs $197+$186=$383, $3 over. A rough $200+$190≈$390 suggests close but exact arithmetic settles it.

**Entry check and teach:** Check sum/difference role and nearest-ten rounding. Show 265 rounds 270 and 148 rounds 150; nearest-ten rough cost 420 differs from exact 413. No cents, retail price or family-finance knowledge assumed.

**Hook:** Pick a made-up supply or budget job. What decision does the arithmetic need to answer?

**Materials:** Broad paper, labelled place-value/part-whole/number-line alternatives as suitable; optional familiar safe counters; usual communication. No hundreds of loose marks, purchases or physical handling required. Keep adult model and own work separate.

**Next teaching:** If an estimate is treated as exact, compare 49+52≈50+50=100 with exact 101 and target 100. Guide it is 1 over; then invite 98+103 with target 200. Staff reference: 98+103=201, which is 1 over 200.

**Ordinary source:** A fictional print stand needs 485 handouts. It has 268 in one pile and 124 in another. Is there enough? Separately a pretend art plan has costs $265 and $148, within an invented AUD450 budget.

**Own exit:** Budget $300, fictional costs $148 and $153. Does it fit? Give an exact reason.

#### Partial codes

1. AC9M4N08 additive partial
2. AC9M4N07
3. AC9M4N06

**Purpose:** Formulate additive practical problems and interpret exact comparisons.

#### Routes

##### A

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** An invented set needs 90 cards; there are 47 and 36. Find whether more are needed.

**Entry or access:** Use whole counts rather than a purchase.

**Id:** A

**Title:** Small card order

**Worked staff:** 83 available, 7 more.

##### B

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Use fictional $265+$148 and $450 budget. State total cost and money left.

**Entry or access:** No real cash handling or spending follows.

**Id:** B

**Title:** Art budget

**Worked staff:** 413 cost, 37 left; about 420 checks scale.

##### C

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** An invented print target is 2000 sheets, with 987+1018 available. Estimate then decide exactly.

**Entry or access:** Compare a rough equality with exact five-extra.

**Id:** C

**Title:** Close print decision

**Worked staff:** 2005 available, 5 surplus; about 1000+1000=2000 is inconclusive.

#### Session stages

##### Meet the job

**Instruction:** Pick a made-up supply or budget job. What decision does the arithmetic need to answer? Read the source. Ask what the numbers count and the wanted quantity. Check sum/difference role and nearest-ten rounding. Show 265 rounds 270 and 148 rounds 150; nearest-ten rough cost 420 differs from exact 413. No cents, retail price or family-finance knowledge assumed.

**Minutes suggestion:** 5

**Stage:** Meet the job

##### Teach one relationship

**Instruction:** Handouts 268+124=392; 485−392=93 more needed. Budget 265+148=413 cost; 450−413=37 left. Nearest-ten estimate 270+150≈420 checks scale but is not the exact 413 or 37. Keep handouts and dollars separate. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

**Minutes suggestion:** 10

**Stage:** Teach one relationship

##### Guide then choose

**Instruction:** An imaginary card plan needs 600 cards; 328+195=523 available, gap 77. A separate invented budget $380 costs $197+$186=$383, $3 over. A rough $200+$190≈$390 suggests close but exact arithmetic settles it. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

**Minutes suggestion:** 15

**Stage:** Guide then choose

##### Receive and choose tomorrow

**Instruction:** Budget $300, fictional costs $148 and $153. Does it fit? Give an exact reason. Receive an available response before staff key. If an estimate is treated as exact, compare 49+52≈50+50=100 with exact 101 and target 100. Guide it is 1 over; then invite 98+103 with target 200. Staff reference: 98+103=201, which is 1 over 200.

**Minutes suggestion:** 5

**Stage:** Receive and choose tomorrow

**Specific criterion:** A correct additive model, exact 301 and interpretation of $1 over agree; approximate 300 is not affordability proof.

**Staff key:** 301 cost, $1 over. A nearest-ten estimate 150+150≈300 cannot settle the tight decision.

**Status:** Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

**Title:** An estimate helps. An exact check decides.

### Make a useful note of your own

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Adult model:** 675+148=823; 823−236=587 labels left. Check 587+236=823 and 823−148=675. A plan to use 236 is a model condition; only an actual authorised observation could establish real use.

**Child direction:** Choose a small planning problem you care about: a game, a collection, a pretend budget or a number puzzle. Make one note useful to someone else. Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

**Common tangle:** the plan lacks given counts; check the roles and equivalent quantities, rather than memorising a printed answer.

**Day:** 60

**Different guided practice:** Guide a different fictional game: 508 cards, 176 arrive, 245 used; 684−245=439 left. Ask the learner to select addition then subtraction from roles, not follow a hiddenpreset. Receive one useful step if the whole chain is too much.

**Entry check and teach:** Review actual work. If partitioning, unknown roles or comparison remain unclear, choose that teaching instead of an open project. For a new problem teach identifying given counts/unit/wanted quantity with small 12+8=20 first.

**Hook:** Choose a small planning problem you care about: a game, a collection, a pretend budget or a number puzzle. Make one note useful to someone else.

**Materials:** Broad paper, labelled place-value/part-whole/number-line alternatives as suitable; optional familiar safe counters; usual communication. No hundreds of loose marks, purchases or physical handling required. Keep adult model and own work separate.

**Next teaching:** If the plan lacks given counts, offer empty start/change/question headings and neutral scribing. Teach one missing relationship using fictional 35 plus 18 then 12 used=41. Invite a new own small problem later.

**Ordinary source:** Adult example: a fictional making station has 675 labels, receives 148 more and uses 236. How many remain? No real making or stock count is claimed.

**Own exit:** Choose one result from your own problem. What does it count and what check supports it?

#### Partial codes

1. AC9M4N08 additive partial
2. AC9M4N06
3. AC9M4A01 optional

**Purpose:** Formulate a complete additive situation, solve and check it for a reader.

#### Routes

##### A

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Choose imaginary starting cards 20–60, an arrival 10–30 and use 0–20. State all values and find cards left.

**Entry or access:** Values are choices, not pupil possessions.

**Id:** A

**Title:** Small game note

**Worked staff:** Adult possibility 35+18−12=41. Other valid selected values accepted.

##### B

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Use 675+148−236. Prepare a short source/strategy/check note for another maker.

**Entry or access:** A handover note is not proof real use.

**Id:** B

**Title:** Maker handover

**Worked staff:** 587 labels left; inverse checks above.

##### C

**Access:** Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

**Complete task:** Choose whole a, b, c from 100–2000 with a+b≥c; write a+□=b+c and find the unknown only if b+c≥a. Or choose a nonnegative starting/use story.

**Entry or access:** Teach the role and eligibility before selecting this open equality.

**Id:** C

**Title:** Own puzzle card

**Worked staff:** Adult possibility 480+□=600+125→245; both sides 725.

#### Session stages

##### Meet the job

**Instruction:** Choose a small planning problem you care about: a game, a collection, a pretend budget or a number puzzle. Make one note useful to someone else. Read the source. Ask what the numbers count and the wanted quantity. Review actual work. If partitioning, unknown roles or comparison remain unclear, choose that teaching instead of an open project. For a new problem teach identifying given counts/unit/wanted quantity with small 12+8=20 first.

**Minutes suggestion:** 5

**Stage:** Meet the job

##### Teach one relationship

**Instruction:** 675+148=823; 823−236=587 labels left. Check 587+236=823 and 823−148=675. A plan to use 236 is a model condition; only an actual authorised observation could establish real use. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

**Minutes suggestion:** 10

**Stage:** Teach one relationship

##### Guide then choose

**Instruction:** Guide a different fictional game: 508 cards, 176 arrive, 245 used; 684−245=439 left. Ask the learner to select addition then subtraction from roles, not follow a hiddenpreset. Receive one useful step if the whole chain is too much. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

**Minutes suggestion:** 15

**Stage:** Guide then choose

##### Receive and choose tomorrow

**Instruction:** Choose one result from your own problem. What does it count and what check supports it? Receive an available response before staff key. If the plan lacks given counts, offer empty start/change/question headings and neutral scribing. Teach one missing relationship using fictional 35 plus 18 then 12 used=41. Invite a new own small problem later.

**Minutes suggestion:** 5

**Stage:** Receive and choose tomorrow

**Specific criterion:** Available own formulation, strategy, result, units and check agree; unsupported or unfinished steps remain visible.

**Staff key:** No prescribed own numbers. Fixed routes below have separate staff possibilities. Check against the learner actual stated conditions; do not fill missing choices from adult work.

**Status:** Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

**Title:** Make a useful note of your own


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