# Ten optional free family offers

Choose any single offer for 5–15 minutes, stop or skip freely. No return, photo, bought kit, real household/money inventory, device, sound, fine motor skill or writing is required. Reused drawn marks, large suitable materials, tactile forms or adult marks at child direction are alternatives. Follow actual individual safety/access arrangements; small loose pieces are unnecessary. The adult records child decisions separately from their own reading/movement, if making a local note. These are invitations, not a home attainment check.

## Home 1 · Pair and unpair

**Time:** Optional 5–15 minutes, with no completion deadline.

**Start/material swaps:** Eight large drawn dots, eight suitable existing objects, or eight tactile marks an adult places at the child’s direction.

**Child choice and action:** Spread the eight without a fixed grouping. Invite: “Could we make a pretend small game set easy to check?” Child chooses pairs or another arrangement, counts it, then changes the layout.

**One adult prompt:** “What does your last number include?”

**Observed mathematics:** Look for every object included once, four real pairs and 8 objects if pairs are used; a count of 4 names groups only.

**Optional next step:** Try a different six-mark layout, or stop after the first count. The child can point/direct instead of touching.

You may end here, keep work private or simply leave the idea for another day. No mandatory audience or returned task.

## Home 2 · Quiet two-step trail

**Time:** Optional 5–15 minutes, with no completion deadline.

**Start/material swaps:** A reused surface with a six-mark starting stage; two sets of two large marks, or directed adult drawing. No moving bodies or sound needed.

**Child choice and action:** Keep the six base. Invite the child to add one pair, then another, choosing where to put them; match 6,8,10 to the stages by selection or explanation.

**One adult prompt:** “Which two marks are new in this step?”

**Observed mathematics:** Observe whether the base remains included and the two-object change is connected to 8/10; labels alone are not a made stage.

**Optional next step:** Make one further pair-stage or another start only if wanted; no completed sheet needs returning.

You may end here, keep work private or simply leave the idea for another day. No mandatory audience or returned task.

## Home 3 · A growing pretend badge

**Time:** Optional 5–15 minutes, with no completion deadline.

**Start/material swaps:** Large shapes/marks on scrap paper, reusable board, or safe existing pieces; an adult may mark at the child’s direction.

**Child choice and action:** Child chooses a symbol and makes stages 2,4,6,8, saying/showing the change. The badge is a pretend count picture, not a craft-quality task.

**One adult prompt:** “How could your next stage keep the same change?”

**Observed mathematics:** See a quantitative two-object increase and a supported next 10. A repeating decoration can be enjoyable but is different evidence.

**Optional next step:** Change the picture layout while keeping the same stage amounts, or leave it unfinished without penalty.

You may end here, keep work private or simply leave the idea for another day. No mandatory audience or returned task.

## Home 4 · A pair needs fixing

**Time:** Optional 5–15 minutes, with no completion deadline.

**Start/material swaps:** Six marks in groups 2,3,1, drawn large or placed by an adult; no small loose items required.

**Child choice and action:** Say the claim is “each group is a pair”. Child chooses a group to audit and directs a repair. Moving one from 3 to 1 makes three real pairs without changing 6.

**One adult prompt:** “What would you change in the objects or the claim?”

**Observed mathematics:** Notice actual membership reasoning. Six may be counted correctly even before equal groups are established; keep those observations separate.

**Optional next step:** Offer a new eight-mark arrangement with a different uneven grouping, or simply recount the repaired set.

You may end here, keep work private or simply leave the idea for another day. No mandatory audience or returned task.

## Home 5 · Tell me your count

**Time:** Optional 5–15 minutes, with no completion deadline.

**Start/material swaps:** Twelve large marks or suitable materials; a waiting/counted space can be two areas on a board.

**Child choice and action:** Child chooses a way to organise the pretend collection and count it. A child may count one by one first, then decide whether pairs help. Adult moves/draws only under direction.

**One adult prompt:** “Which things have you included so far?”

**Observed mathematics:** Look for coverage, a verified unit and a total 12. A full model supplied by the adult is adult grouping, even when the child reads its numeral.

**Optional next step:** Choose a different layout for ten marks or ask the child to make a short own twos sequence; both are optional.

You may end here, keep work private or simply leave the idea for another day. No mandatory audience or returned task.

## Home 6 · Five has to be full

**Time:** Optional 5–15 minutes, with no completion deadline.

**Start/material swaps:** Ten large marks and two five-space areas, or two directed adult-drawn panels. Frames can be imagined on a reusable surface.

**Child choice and action:** Invite a pretend bookmark plan: fill two verified groups of five, then count 5,10. Remove one mark from a panel and ask the child to inspect the new actual quantity.

**One adult prompt:** “Does that panel still have five objects?”

**Observed mathematics:** Observe full-unit checking: ten becomes nine when a mark is actually removed. Frame capacity alone does not prove the count.

**Optional next step:** Restore the mark for 10 or relabel the actual 9; child chooses the purpose. No real bookmark manufacture is required.

You may end here, keep work private or simply leave the idea for another day. No mandatory audience or returned task.

## Home 7 · Five more in a picture

**Time:** Optional 5–15 minutes, with no completion deadline.

**Start/material swaps:** Five large marks for a starting picture plus two groups of five, or an adult following directions.

**Child choice and action:** Child chooses a mark and makes 5,10,15-object stages, adding an actual five each time. Numerals may be pointed to, selected or scribed.

**One adult prompt:** “Show what you added, then what the whole stage contains.”

**Observed mathematics:** Look for the added five and cumulative totals rather than restarting at 5 for every whole picture.

**Optional next step:** Make a fourth 20 stage or begin from a different known amount if useful; speed and appearance do not matter.

You may end here, keep work private or simply leave the idea for another day. No mandatory audience or returned task.

## Home 8 · Two fives can become a ten

**Time:** Optional 5–15 minutes, with no completion deadline.

**Start/material swaps:** Ten large marks arranged as two fives, with a new blank boundary area; no cutting needed.

**Child choice and action:** Count 5,10. Child changes the grouping into one full ten using the same marks. Keep the old drawing only as another representation of the same set.

**One adult prompt:** “Which objects stayed the same?”

**Observed mathematics:** Observe ten retained and replacement of groups, not twenty because both representations are counted as new objects.

**Optional next step:** Use twenty marks as four fives/two tens, or stop after the single conversion. Adult execution is separately named.

You may end here, keep work private or simply leave the idea for another day. No mandatory audience or returned task.

## Home 9 · Choose your steps

**Time:** Optional 5–15 minutes, with no completion deadline.

**Start/material swaps:** Twenty large marks or existing suitable materials; no family inventory, real money or bought set.

**Child choice and action:** Child chooses pairs/fives/tens, audits a unit and counts the whole pretend kit. Another grouping is optional. All approaches can work when each object is included once.

**One adult prompt:** “How much does one of your groups stand for?”

**Observed mathematics:** Valid accounts include ten pairs→20, four fives→20, two tens→20. Group count alone is not the object total.

**Optional next step:** Try a new smaller set in another layout if coverage needs support; no homework return or viewer is expected.

You may end here, keep work private or simply leave the idea for another day. No mandatory audience or returned task.

## Home 10 · A note someone could check

**Time:** Optional 5–15 minutes, with no completion deadline.

**Start/material swaps:** A reused surface and a child-chosen manageable number of large marks, normally at most 20 here; tactile/directed adult marks are equal choices.

**Child choice and action:** Child chooses a pretend purpose, groups/counts actual marks and makes a small own increasing sequence with a stated 2/5/10 change. A willing viewer is optional; the child can check it privately.

**One adult prompt:** “What would help someone see that your count or next step makes sense?”

**Observed mathematics:** Observe the child’s selected unit, coverage, last object count and created rule. Planned/imagined stages remain predictions until actually made or represented.

**Optional next step:** Try a different start or leave a question for later. None of this requires a photo, recording, polished writing, identified data or completed product.

You may end here, keep work private or simply leave the idea for another day. No mandatory audience or returned task.

Original SubjectNest teaching expression © NeuroForgeIO Pty Ltd 2026, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). Credit creator/source/licence and note changes. National/QCAA source expression and exclusions remain separate; no endorsement or human efficacy claim.