A leftover is information · complete teacher lesson
Purpose
Share whole pieces equally and leave the agreed leftover aside without adding/splitting.
Time and choice
About 20–30 minutes, unpiloted. Choose one route; shorten, split or pause. Days 71–80 are flexible sequence slots, not attendance or a claim about 195/200 calendar days.
Materials
Plain paper, a pencil or child-directed marks, safe large pieces and named places. A place can be a drawn box or spoken label. No food, real money, purchase, printer, account or device required. A helper moves only the piece/place the child chooses.
Entry
Use a fresh seven-card collection and three places. Make two complete rounds and name the one still aside. State that this job uses whole cards; we are not teaching fractions or saying all real-world fairness must leave a spare.
When a confusion appears
If the spare is given to one place, compare all shares after that move. Use a different ten-card/three-place model to show why 3/3/4 is unequal for this exact job. Record a new agreed purpose separately if the child wants a different arrangement.
Access choices
Let the child mix objects, a drawing, speech, signing, AAC, tactile marks or an exact directed helper. Read the whole source and allow processing time. Offer a quiet seated route and a pause. Record reading/motor access separately from hints that choose a mathematical step. These are choices, not fixed learning styles or neurotype assignments.
Choose a job and check entry · 0–3
Use a fresh seven-card collection and three places. Make two complete rounds and name the one still aside. State that this job uses whole cards; we are not teaching fractions or saying all real-world fairness must leave a spare.
Teach a whole different example · 3–9
Eleven whole sample cards are shared equally between three pretend sample trays. Give each tray as many whole cards as possible while keeping the shares equal. Leave any whole cards left over aside. How many go in each tray, and how many stay aside? After the first chosen attempt, demonstrate: Name 11 as the whole collection and 3 as the known number of recipients. Deal one sample card to each recipient in a complete round, or make a different equal-allocation model the child can explain. After 3 complete rounds each recipient has 3 sample cards; 2 whole sample cards remain aside. Check every recipient has the same amount and that every member of the original collection is in exactly one recipient place or the leftover place. The collection check is 3 + 3 + 3=9, then 9+2=11. The requested answer names an amount per recipient, not the total or number of recipients. Do not split a whole card or invent more members; another fairness arrangement would need a different agreed job. Then introduce the complete different source Fourteen whole drawing cards are shared equally between four pretend displays. Give each display as many whole cards as possible, keep shares equal and leave any leftovers aside. How many does each display get, and how many stay aside? Discuss the change in purpose/quantities rather than presenting a shortcut answer.
Try a new source together · 9–15
Thirteen new pattern cards shared equally between three kits, whole pieces with leftovers aside; guided 4 each/1 aside. Read this whole new job. Let the child identify what is known and choose a representation before showing the worked possibility. Keep the original collection visible and ask what the useful answer names.
Choose a practical route · 15–22
Offer one complete route below, not all three as a workload. The child may change response mode or pause. Keep the full source visible, leave own-record spaces empty and retain the first model/words before any numerical hint.
Make a usable outcome · 22–25
Make an equal-share note with a separate spare line. Include the exact source identity, useful answer unit and any whole leftovers. Invite a willing helper to follow it; if no helper is available, the child can point through the instruction. A planned invitation is not evidence that another person used it.
Check evidence and choose next teaching · 25–29
Fresh eleven postcard marks among four equal places:2 each and 3 aside. Check the entire original 11. Record the particular component shown/not yet shown/not observed and actual support. Select the specific unrelated next lesson after the first record; do not turn a revised answer into a new independent sample.
D74-R1 · Share a collection with a spare
D74-R1
Ten whole leaf-picture cards go equally to three sketch kits, as many whole cards per kit as possible; leave leftovers aside. How many go to each kit and how many remain?
Useful outcome
An equal-share note with a separate spare line.
- Read the complete job; name the whole and the known recipient count, pack size or equal-kit structure.
- Choose large safe objects, a labelled drawing/tactile record or an exact child-directed helper; represent every stated member once.
- Try a taught sharing/grouping/equal-whole method. Keep your first thinking; label what your answer and any leftovers mean.
- Check the actual equality/pack-size condition and the whole collection. Make the practical note; copying a supplied adult model is supported practice.
Adult model · after the first attempt
Name 10 as the whole collection and 3 as the known number of recipients. Deal one leaf-picture card to each recipient in a complete round, or make a different equal-allocation model the child can explain. After 3 complete rounds each recipient has 3 leaf-picture cards; 1 whole leaf-picture card remains aside. Check every recipient has the same amount and that every member of the original collection is in exactly one recipient place or the leftover place. The collection check is 3 + 3 + 3=9, then 9+1=10. The requested answer names an amount per recipient, not the total or number of recipients. Do not split a whole card or invent more members; another fairness arrangement would need a different agreed job.
Let the child mix objects, a drawing, speech, signing, AAC, tactile marks or an exact directed helper. Read the whole source and allow processing time. Offer a quiet seated route and a pause. Record reading/motor access separately from hints that choose a mathematical step. These are choices, not fixed learning styles or neurotype assignments.
Matching neutral route and empty record
D74-R2 · Keep a story-kit spare record
D74-R2
Thirteen whole story cards go equally to four kits, as many whole cards per kit as possible, with leftovers aside. How many go to each and how many stay aside?
Useful outcome
An equal-share note with a separate spare line.
- Read the complete job; name the whole and the known recipient count, pack size or equal-kit structure.
- Choose large safe objects, a labelled drawing/tactile record or an exact child-directed helper; represent every stated member once.
- Try a taught sharing/grouping/equal-whole method. Keep your first thinking; label what your answer and any leftovers mean.
- Check the actual equality/pack-size condition and the whole collection. Make the practical note; copying a supplied adult model is supported practice.
Adult model · after the first attempt
Name 13 as the whole collection and 4 as the known number of recipients. Deal one story card to each recipient in a complete round, or make a different equal-allocation model the child can explain. After 3 complete rounds each recipient has 3 story cards; 1 whole story card remains aside. Check every recipient has the same amount and that every member of the original collection is in exactly one recipient place or the leftover place. The collection check is 3 + 3 + 3 + 3=12, then 12+1=13. The requested answer names an amount per recipient, not the total or number of recipients. Do not split a whole card or invent more members; another fairness arrangement would need a different agreed job.
Let the child mix objects, a drawing, speech, signing, AAC, tactile marks or an exact directed helper. Read the whole source and allow processing time. Offer a quiet seated route and a pause. Record reading/motor access separately from hints that choose a mathematical step. These are choices, not fixed learning styles or neurotype assignments.
Matching neutral route and empty record
D74-R3 · Share display marks and label the rest
D74-R3
Seventeen whole exhibition marks go equally to three displays, as many whole marks per display as possible, with leftovers aside. How many go to each and how many remain?
Useful outcome
An equal-share note with a separate spare line.
- Read the complete job; name the whole and the known recipient count, pack size or equal-kit structure.
- Choose large safe objects, a labelled drawing/tactile record or an exact child-directed helper; represent every stated member once.
- Try a taught sharing/grouping/equal-whole method. Keep your first thinking; label what your answer and any leftovers mean.
- Check the actual equality/pack-size condition and the whole collection. Make the practical note; copying a supplied adult model is supported practice.
Adult model · after the first attempt
Name 17 as the whole collection and 3 as the known number of recipients. Deal one exhibition mark to each recipient in a complete round, or make a different equal-allocation model the child can explain. After 5 complete rounds each recipient has 5 exhibition marks; 2 whole exhibition marks remain aside. Check every recipient has the same amount and that every member of the original collection is in exactly one recipient place or the leftover place. The collection check is 5 + 5 + 5=15, then 15+2=17. The requested answer names an amount per recipient, not the total or number of recipients. Do not split a whole card or invent more members; another fairness arrangement would need a different agreed job.
Let the child mix objects, a drawing, speech, signing, AAC, tactile marks or an exact directed helper. Read the whole source and allow processing time. Offer a quiet seated route and a pause. Record reading/motor access separately from hints that choose a mathematical step. These are choices, not fixed learning styles or neurotype assignments.
Matching neutral route and empty record
Whole introductory sources
C07 · Keep an honest leftover note