---
code: "EMP-HALV-L1-T1-WK6"
curriculum_id: "halving"
curriculum_name: "Halving"
level_id: "L1"
level_name: "All Ages"
age_line: "around 2 to around 6"
term: 1
week: 6
title: "Match Even When the Spaces Change"
slug: "week-6"
aim: "Check two groups by matching blocks rather than judging how spread out they look."
blocks_this_week: 5
minutes_per_block: 6
weekly_minutes: 30
blocks: [{"n":1,"title":"Compare Close and Spread Out Twos","minutes":6,"aim":"Notice two groups of two with visibly different spacing.","staging":"Place two blocks on each mat, one close pair and one spread pair. Ask whether either group has more, accepting an initial judgement before inviting checking. Read \"Space can change while the number stays the same.\" Close by keeping all four blocks visible.","say":"One group is spread out. The other is close together. How could we check whether their numbers match?"},{"n":2,"title":"Move Within a Mat to Find Partners","minutes":6,"aim":"Restore opposite partners by changing positions within groups only.","staging":"Use the same four blocks and invite the child to slide blocks within their own mats to make two opposite pairs. Check that no block crosses to the other group. Close by confirming that each original group still has two.","say":"Slide blocks on their own mats to see the partners. Keep each block in its group. Do the numbers match now?"},{"n":3,"title":"Test Spacing With Three on Each Side","minutes":6,"aim":"Check two groups of three when one is arranged more widely.","staging":"Place three on each mat, spreading one group and clustering the other. Invite a one to one check after rearranging within the mats. Close by counting three on each side if useful and confirming all six remain.","say":"These groups look different in their spaces. Give each block an opposite partner. What do you notice about the numbers?"},{"n":4,"title":"Rearrange After an Eight Block Split","minutes":6,"aim":"Preserve equal groups when positions within the mats change.","staging":"Invite an equal split of eight, then ask the child to move blocks within one mat so its group looks wider. Recheck all four partners without adding, removing or transferring a block. Close by naming the unchanged equal counts.","say":"You shared eight blocks equally. Now change the spaces on one mat. Check whether every block still has a partner."},{"n":5,"title":"Use Matching to Judge the Groups","minutes":6,"aim":"Check two groups by matching blocks rather than judging how spread out they look.","staging":"Offer a four or six block equal split, then vary spacing on one mat with the child watching. Ask for a complete match check and a reason based on partners, not row length. Leave the matched partners still while the child explains, then return the same total to the centre.","say":"These rows look different. Show me one partner for every block. Do their numbers match?"}]
domains: ["M","PD","CL"]
objectives: [{"domain":"M","text":"Check two groups by matching blocks rather than judging how spread out they look."},{"domain":"PD","text":"Rearrange blocks within their own mat without transferring them to the other group."},{"domain":"CL","text":"Explain that spacing can change without changing the number."}]
materials: ["Ten matching large solid blocks from smooth untreated wood offcuts freely given and prepared by someone with suitable tools before the lesson, or an existing borrowed set; each must be safe for the children to handle and free of splinters, residue and loose parts","Two flat pieces of clean reclaimed cardboard, each roomy enough for six chosen blocks in a column with gaps","An old box kept by you for blocks outside the chosen total","The supplied Two Equal Groups Reference on an existing screen or copied onto used paper"]
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."
differentiation: {"younger":"Begin with two on each mat and restore opposite partners after one group is spread out.","older":"Check groups of three or four on each side after different spacing, confirming the same original total."}
watching_for: "Whether a longer looking row is called larger before the child checks one to one partners."
resources: []
version: 1
date: "2026-09-09"
access: "Free"
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/"
---

**HALVING · TWO EQUAL GROUPS WITH WHOLE BLOCKS**

# Match Even When the Spaces Change

**ALL AGES · around 2 to around 6 · TERM 1, WEEK 6 · 5 × 6**

|  |
| :-: |
| **DOMAINS:** M, PD, CL |
| **CODE:** EMP-HALV-L1-T1-WK6 |
| **DAY & DATE:** |

## Objectives
1. **M** Check two groups by matching blocks rather than judging how spread out they look.
2. **PD** Rearrange blocks within their own mat without transferring them to the other group.
3. **CL** Explain that spacing can change without changing the number.

## Before the two mat turns

You will want to say same number before the child calls the long row bigger. Let the first answer come. You can then offer a partner check that makes the number clear.

Two children will call the spread out group more. Invite them to move blocks only within that mat until opposite partners are clear, then ask again. No block needs to cross the central gap for this correction.

One child will transfer a block to make the row lengths match. Return to the original two and two groups and show the difference between sliding within a mat and moving between mats. The first changes spacing; the second changes the numbers.

## How we use the sharing space

1. Stay beside the sharing surface with up to four children. Give individual turns. Keep unused blocks in your box outside the display.
2. 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.
3. 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.
4. Place one block gently at a time. Keep fingers clear. No throwing, stacking, standing on blocks or carrying piles.
5. Keep blocks whole. No cutting, tearing, breaking or food sharing. The centre holds the starting group; it is not a third share.
6. 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.
7. If anything unfamiliar enters, stop and move back without touching it. Continue in another clear place after the usual response.

## Five Short Sharing Turns

### Compare Close and Spread Out Twos · 6 minutes

AIM: Notice two groups of two with visibly different spacing.

Place two blocks on each mat, one close pair and one spread pair. Ask whether either group has more, accepting an initial judgement before inviting checking. Read "Space can change while the number stays the same." Close by keeping all four blocks visible.

> SAY: "One group is spread out. The other is close together. How could we check whether their numbers match?"

### Move Within a Mat to Find Partners · 6 minutes

AIM: Restore opposite partners by changing positions within groups only.

Use one minute to introduce the turn, four minutes for individual attempts with a reset between children, and one minute for the closing check. Use the same four blocks and invite the child to slide blocks within their own mats to make two opposite pairs. Check that no block crosses to the other group. Close by confirming that each original group still has two.

> SAY: "Slide blocks on their own mats to see the partners. Keep each block in its group. Do the numbers match now?"

### Test Spacing With Three on Each Side · 6 minutes

AIM: Check two groups of three when one is arranged more widely.

Use one minute to introduce the turn, four minutes for individual attempts with a reset between children, and one minute for the closing check. Place three on each mat, spreading one group and clustering the other. Invite a one to one check after rearranging within the mats. Close by counting three on each side if useful and confirming all six remain.

> SAY: "These groups look different in their spaces. Give each block an opposite partner. What do you notice about the numbers?"

### Rearrange After an Eight Block Split · 6 minutes

AIM: Preserve equal groups when positions within the mats change.

Use one minute to introduce the turn, four minutes for individual attempts with a reset between children, and one minute for the closing check. Invite an equal split of eight, then ask the child to move blocks within one mat so its group looks wider. Recheck all four partners without adding, removing or transferring a block. Close by naming the unchanged equal counts.

> SAY: "You shared eight blocks equally. Now change the spaces on one mat. Check whether every block still has a partner."

### Use Matching to Judge the Groups · 6 minutes

AIM: Check two groups by matching blocks rather than judging how spread out they look.

Use one minute to introduce the turn, four minutes for individual attempts with a reset between children, and one minute for the closing check. Offer a four or six block equal split, then vary spacing on one mat with the child watching. Ask for a complete match check and a reason based on partners, not row length. Record the starting total and any help used.

> SAY: "These rows look different. Show me one partner for every block. Do their numbers match?"

## If you have more time
1. After block five’s match check, add two minutes to rearrange the other group and repeat the check without changing its number.

## A small sharing conversation
Ask your child whether spreading blocks farther apart changes how many there are. Linking spacing with an unchanged count supports a careful equality check.

## Look for a complete match
The child matches partners despite different spacing, moving blocks only within their own groups.

**Notes:**



Halving · Curriculum system designed by Eric Gonzalez-Payne · © 2026 Empathy Global · Free with an Empathy Global account