About this curriculum
Children share groups of large matching blocks between two mats, check every block has a partner and distinguish a complete equal split from an unmatched remainder.
What children learn
By the end of this curriculum a child can split a group of up to ten into two equal parts and check both sides match.
Ages and rhythm
around 2 to around 6. 5 sessions per week, 6 minutes per session. 10 weeks.
Scope
Does not cover doubling, sharing between three, fractions.
What the scope means
The unit divides whole objects into two equal groups, checks one to one matches and recognises an unmatched block. There is no doubling task, third recipient, fractional notation or cutting a whole object into parts.
The learning space
A stable low table or clear indoor floor holding two flat sharing mats at least fifty centimetres square, a central starting space and a clear view for up to four children. Enlarge either mat if six chosen blocks cannot fit in a column with clear gaps. Keep access around the edges so the active child can reach both mats by changing position without leaning over blocks.
Materials
Use ten matching age appropriate solid one piece blocks at least six centimetres in every dimension, two large flat sharing mats and the setting’s ordinary adult storage box. All arithmetic uses the same durable objects indoors; no consumable, purchased specialist kit, local material or found object is required.
How we use the sharing space
- Stay beside the sharing surface with up to four children. Give individual turns. Keep unused blocks in your box outside the display.
- Use matching large, solid, single piece blocks suitable for the children. Check for smooth surfaces, sound edges and no cracks, splinters, residue, loose fittings or detachable parts. No small counters, coins, beads, seeds, food or broken pieces. Keep blocks out of mouths.
- Use a stable low table or clear floor and two flat sharing mats. Leave room for six blocks in each column with clear gaps and a starting group between the mats. Let children move around to reach, without leaning over blocks.
- Place one block gently at a time. Keep fingers clear. No throwing, stacking, standing on blocks or carrying piles.
- Keep blocks whole. No cutting, tearing, breaking or food sharing. The centre holds the starting group; it is not a third share.
- Use every starting block and check every partner. Never add, hide or remove one to make the groups look equal. Keep any unmatched block visible and name the limit.
- If anything unfamiliar enters, stop and move back without touching it. Continue in another clear place after the usual response.
How the term develops
- Weeks 1 to 3: Share two, four and six blocks and match one group against the other.
- Weeks 4 to 5: Extend equal sharing to eight and ten with all starting blocks used.
- Weeks 6 to 8: Check spread out arrangements, repair unequal groups and recognise an unmatched block in odd totals.
- Weeks 9 to 10: Independently split even groups up to ten and check both groups and the original total.
The Two Equal Groups Reference
Fixed totals, exact equal splits, one to one checking, unequal group repairs and the limits of odd whole block groups.
Use of this curriculum
Free to read. Licensed for use in any setting by holders of an Empathy Global account, free or paid. Not licensed for reproduction, redistribution, resale or use in a setting by anyone else.
Complete original curriculum source
curriculum_id: "halving"
name: "Halving"
slug: "halving"
code_prefix: "HALV"
family: "Early Maths"
strand_line: "TWO EQUAL GROUPS WITH WHOLE BLOCKS"
shape: "MINI"
outcome_sentence: "By the end of this curriculum a child can split a group of up to ten into two equal parts and check both sides match."
scope_boundary: "Does not cover doubling, sharing between three, fractions."
scope_boundary_notes: "The unit divides whole objects into two equal groups, checks one to one matches and recognises an unmatched block. There is no doubling task, third recipient, fractional notation or cutting a whole object into parts."
description: "Children share groups of large matching blocks between two mats, check every block has a partner and distinguish a complete equal split from an unmatched remainder."
tradition: "none"
non_affiliation: "Produced by Empathy Global. Not affiliated with, endorsed by or connected to any external organisation."
age_band: "around 2 to around 6"
levels: [{"level_id":"L1","level_name":"All Ages","age_line":"around 2 to around 6"}]
terms: 1
weeks_per_term: 10
lessons: 10
blocks_per_week: 5
minutes_per_block: 6
weekly_minutes: 30
weekly_minutes_min: 30
weekly_minutes_max: 30
space: "A stable low table or clear indoor floor holding two flat sharing mats at least fifty centimetres square, a central starting space and a clear view for up to four children. Enlarge either mat if six chosen blocks cannot fit in a column with clear gaps. Keep access around the edges so the active child can reach both mats by changing position without leaning over blocks."
season_dependent: false
weeks_reorderable: false
materials_philosophy: "Use ten matching age appropriate solid one piece blocks at least six centimetres in every dimension, two large flat sharing mats and the setting’s ordinary adult storage box. All arithmetic uses the same durable objects indoors; no consumable, purchased specialist kit, local material or found object is required."
domain_tags: [{"tag":"M","meaning":"Mathematics"},{"tag":"CL","meaning":"Communication and Language"},{"tag":"PD","meaning":"Physical Development"}]
headings: {"teacher_note":"Before the two mat turns","standing_rules":"How we use the sharing space","session_word":"Five Short Sharing Turns","take_home":"A small sharing conversation","signs":"Look for a complete match"}
standing_rules_block: "1. Stay beside the sharing surface with up to four children. Give individual turns. Keep unused blocks in your box outside the display.\n2. Use matching large, solid, single piece blocks suitable for the children. Check for smooth surfaces, sound edges and no cracks, splinters, residue, loose fittings or detachable parts. No small counters, coins, beads, seeds, food or broken pieces. Keep blocks out of mouths.\n3. Use a stable low table or clear floor and two flat sharing mats. Leave room for six blocks in each column with clear gaps and a starting group between the mats. Let children move around to reach, without leaning over blocks.\n4. Place one block gently at a time. Keep fingers clear. No throwing, stacking, standing on blocks or carrying piles.\n5. Keep blocks whole. No cutting, tearing, breaking or food sharing. The centre holds the starting group; it is not a third share.\n6. Use every starting block and check every partner. Never add, hide or remove one to make the groups look equal. Keep any unmatched block visible and name the limit.\n7. If anything unfamiliar enters, stop and move back without touching it. Continue in another clear place after the usual response."
asset_title: "The Two Equal Groups Reference"
asset_file: "halving_two_equal_groups_reference.md"
asset_summary: "Fixed totals, exact equal splits, one to one checking, unequal group repairs and the limits of odd whole block groups."
supplied_factual_pattern: {"even_splits":[{"total":2,"left":1,"right":1,"leftover":0},{"total":4,"left":2,"right":2,"leftover":0},{"total":6,"left":3,"right":3,"leftover":0},{"total":8,"left":4,"right":4,"leftover":0},{"total":10,"left":5,"right":5,"leftover":0}],"odd_groups":[{"total":1,"left":0,"right":0,"leftover":1},{"total":3,"left":1,"right":1,"leftover":1},{"total":5,"left":2,"right":2,"leftover":1},{"total":7,"left":3,"right":3,"leftover":1},{"total":9,"left":4,"right":4,"leftover":1}],"zero":"An empty starting group can form two empty groups, zero and zero. This is background arithmetic, not a required early lesson turn.","equal_check":"Place one group in a column on its mat and align one block from the other group opposite each one on the second mat. Every block needs a partner, all starting blocks must be used and the central starting space must be empty. Counting can confirm the match, but visual spread alone cannot.","repair_examples":[{"total":4,"start":[3,1],"move":"Move one from the group of three to the group of one.","finish":[2,2]},{"total":6,"start":[4,2],"move":"Move one from the group of four to the group of two.","finish":[3,3]},{"total":8,"start":[5,3],"move":"Move one from the group of five to the group of three.","finish":[4,4]},{"total":10,"start":[6,4],"move":"Move one from the group of six to the group of four.","finish":[5,5]}],"odd_limit":"A group of 1, 3, 5, 7 or 9 whole blocks cannot be split into two equal groups using all the blocks. Equal smaller groups plus one block in the middle are incomplete for the original total. Naming that fact is a correct response. Do not divide the block or change the total.","outcome_interpretation":"Successful whole block splits use even starting totals 2, 4, 6, 8 and 10. The up to ten wording includes an explicit limit for odd totals: identify the unmatched block instead of claiming an impossible equal whole object split. Fractions remain outside scope.","place_independence":"All turns use durable indoor blocks and mats, independent of climate, shops, food or outdoor space.","finding_nothing":"No found material is needed. The prepared block set and mats supply every task.","unknown_appears":"If an unfamiliar object or living thing enters, stop, move children back and do not touch it."}
term_arc_note: "Four phases within one ten week term."
term_arc: [{"weeks":"1 to 3","phase":"Share two, four and six blocks and match one group against the other."},{"weeks":"4 to 5","phase":"Extend equal sharing to eight and ten with all starting blocks used."},{"weeks":"6 to 8","phase":"Check spread out arrangements, repair unequal groups and recognise an unmatched block in odd totals."},{"weeks":"9 to 10","phase":"Independently split even groups up to ten and check both groups and the original total."}]
search_terms: "halving activities preschool, sharing equally eyfs"
version: 1
date: "2026-09-09"
access: "Free"
published: false
publisher: "Empathy Global"
author: "Eric Gonzalez-Payne"
author_url: "https://www.linkedin.com/in/eric-gp/"
copyright: "© 2026 Empathy Global. All rights reserved."
licence: "Free to read. Licensed for use in any setting by holders of an Empathy Global account, free or paid. Not licensed for reproduction, redistribution, resale or use in a setting by anyone else."
source_url: "https://empathy.global/curriculum/halving/"