Grade 5 Maths · Division · siSwati/English

Week 1 — Foundations

Division concepts and mental-maths patterns. Build fluency with breaking numbers apart.

Week 1 · Classwork 1 · §5.1, p.82

Emaprophathi etinombolo

Number properties (distributive property)

CAPS strand: Numbers, Operations & Relationships · Whole numbers: division

Warmup (siSwati)

Bhala 96 = 60 + 36. Bhala 123 = 90 + 33.

Warmup (English)

Rewrite each number as two tens-friendly chunks. (96 = 60+36, 123 = 90+33)

Core idea (siSwati)

Uma uhlukanisa usebentisa idistributhivu prophathi, awukwati kuhlahlela idivayisa. Usebenta kuphela nawuhlahlela idividenthi.

Core idea (English)

When dividing with the distributive property, you CANNOT split the divisor. You can only split the dividend (the number being divided).

Worked examples

96 ÷ 6

= (60 + 36) ÷ 6 = 10 + 6

= 16

123 ÷ 3

= (90 + 33) ÷ 3 = 30 + 11

= 41

248 ÷ 4

= (200 + 48) ÷ 4 = 50 + 12

= 62

189 ÷ 7

= (140 + 49) ÷ 7 = 20 + 9

= 29

Key vocabulary (siSwati ↔ English)

siSwati	English	Note
idividenthi	dividend	the number being divided
idivayisa	divisor	the number we divide by
ngekhoshiyenti	quotient	the answer
kuhlahlela	to split / break down	split the dividend into parts that divide cleanly
idistributhivu prophathi	distributive property	(a + b) ÷ c = a÷c + b÷c

Chalkboard prompt — write this on the board

216 ÷ 4 (hlahlela 216 abe 200 + 16)

216 ÷ 4 (split 216 into 200 + 16)

Week 1 · Classwork 2 · §5.2, p.83

Kubutsanisa nekwabelana

Grouping vs sharing — the two meanings of ÷

CAPS strand: Numbers, Operations & Relationships · Whole numbers: division

Warmup (siSwati)

Tsatsa 12 emaswidi. (1) Yabelana ebantfwaneni la-3. (2) Butsanisa emacembu la-4.

Warmup (English)

Take 12 sweets. (1) SHARE them among 3 children. (2) GROUP them into piles of 4. Both are ÷, but feel different.

Core idea (siSwati)

Kubutsanisa = ungatsi mangaki emacembu? Kwabelana = ungatsi munye nawabelana?

Core idea (English)

GROUPING asks 'how many groups fit?'. SHARING asks 'how much does each person get?'. Both are division but the word-problem cue differs.

Worked examples

882 emahembe, 42 kulibhokisi. Mangaki emabhokisi?

kubutsanisa: 882 ÷ 42

= 21 emabhokisi

462 emakhasi, 21 ngemalanga. Mangaki emakhasi ngelilanga?

kwabelana: 462 ÷ 21

= 22 emakhasi/lilanga

528 emathoyi, 24 ngelibhokisi. Mangaki emabhokisi?

kubutsanisa: 528 ÷ 24

= 22 emabhokisi

Key vocabulary (siSwati ↔ English)

siSwati	English	Note
kubutsanisa	grouping / pooling	'how many groups of N fit?'
kwabelana	sharing	'each one gets how much?'
inambasentensi	number sentence	e.g. 882 ÷ 42 = 21
i-invesi ophareshini	inverse operation	multiplication undoes division

Chalkboard prompt — write this on the board

Ikhilasi la-720 bafundzi, bahlukanisiwe emakamelweni la-24. Bangakhi ebantfwaneni ekamelweni? (kwabelana)

720 learners split into 24 rooms. How many per room? (sharing)

Week 1 · Classwork 3 · §5.3, p.84

Kuhlukanisa nemaphethini (ekhanda)

Dividing with patterns (mental — dividing by tens)

CAPS strand: Numbers, Operations & Relationships · Mental calculation strategies

Warmup (siSwati)

30 ÷ 30 = ? 60 ÷ 30 = ? 300 ÷ 30 = ? 3 000 ÷ 30 = ?

Warmup (English)

Chain: when the divisor has a trailing zero and the dividend does too, the zeros 'cancel'. Use to build up mentally.

Core idea (siSwati)

Nxa udivayisa une-0, susa li-0 eludondolweni lwedivayisa kanye nesikhalenweni sedividenthi. Loku kwenta bala libe lula.

Core idea (English)

When the divisor ends in 0, cancel one zero from divisor AND dividend. The answer is the same but easier. (e.g. 300÷30 = 30÷3 = 10)

Worked examples

270 ÷ 30

= 27 ÷ 3

= 9

2 700 ÷ 30

= 270 ÷ 3

= 90

4 500 ÷ 50

= 450 ÷ 5

= 90

9 900 ÷ 90

= 990 ÷ 9

= 110

Key vocabulary (siSwati ↔ English)

siSwati	English	Note
maphethini	patterns	the regularity in these answers
susa li-0	cancel the zero	shortcut

Chalkboard prompt — write this on the board

Tfola bala ekhanda: 6 300 ÷ 70 = ?

Mental only: 6 300 ÷ 70 = ? (hint: cancel a zero → 630 ÷ 7)

Week 1 · Classwork 4 · §5.4, p.85

Kuhlukanisa nemaphethini (kuchumana)

Dividing with patterns (matching pairs)

CAPS strand: Numbers, Operations & Relationships · Mental calculation strategies

Warmup (siSwati)

Chumanisa: 300 ÷ 30 = 10 nalo 240 ÷ 80 = ?

Warmup (English)

Pair up division facts that give the same answer. Colour-code matches (the guide uses red / orange / yellow / green).

Core idea (siSwati)

Sebentisa bala lotemembulile ecebhweni lokucala kutolula bala lesibili. Buka kuchumana.

Core idea (English)

Use a division fact you already know to solve one you don't. Look for the pattern.

Worked examples

300 ÷ 30 matches 150 ÷ 15

both give 10

= colour same

150 ÷ 50 matches 120 ÷ 40

both give 3

= colour same

1 080 ÷ 36 matches 840 ÷ 56

both give 30 / 15 — pair carefully

= check before colouring

Key vocabulary (siSwati ↔ English)

siSwati	English	Note
kuchumana	matching / connecting	pairing facts
ibhlokhi	block / column	the two columns in the matching table
umbala	colour	used to mark matched pairs

Chalkboard prompt — write this on the board

Chumanisa: 400 ÷ 100 no 360 ÷ 12. Yini kuchumana?

Match: 400 ÷ 100 = ?, 360 ÷ 12 = ?. Which pairs share an answer?

Week 2 — Procedures

Clue-list scaffold → breaking-down method → long division. Each method formalises the one before.

Week 2 · Classwork 1 · §5.5, p.86

Kuhlukanisa tinombolo letinemadijithi la-3 ngeledijithi la-2 (iklubhodi)

Three-digit ÷ two-digit using the clue list (times-table scaffold)

CAPS strand: Numbers, Operations & Relationships · Long-division preparation

Warmup (siSwati)

Bhala i-klubhodi ye-13: 13×1, 13×2, 13×5, 13×10, 13×20, 13×25.

Warmup (English)

Build a 'clue list' (times-table mini) before dividing. This is the scaffold the guide uses before long division.

Core idea (siSwati)

Emacembu la-25 e-13 atawuba nge-325. Kusho kutsi 327 ÷ 13 = 25 insalela 2.

Core idea (English)

Build up with 13×20=260, 13×25=325. Since 327 is 2 more than 325, the answer is 25 remainder 2.

Worked examples

728 ÷ 26

26×20 = 520; 26×5 = 130; 25 groups of 26 = 650; 728-650 = 78 = 3 more groups

= 28 (no remainder)

520 ÷ 35

35×10 = 350; 35×5 = 175; 35×14 = 490; 35×15 = 525 (too big)

= 14 rem 30

684 ÷ 57

57×10 = 570; 57×2 = 114; 10+2 = 12 groups

= 12 exactly

Key vocabulary (siSwati ↔ English)

siSwati	English	Note
iklubhodi	clue list	mini times-table written before dividing
lithebula	table	multiplication table
insalela	remainder	what's left after dividing
∴	therefore	maths symbol, from Greek — read as 'ngako-ke'

Chalkboard prompt — write this on the board

Kwenta iklubhodi ye-18 (×1,×2,×5,×10,×20). Besibale 594 ÷ 18.

Build a clue list for 18 (×1, ×2, ×5, ×10, ×20). Then do 594 ÷ 18.

Week 2 · Classwork 2 · §5.6, p.87

Kuhlukanisa usebentisa indlela yekuhlahlela tinombolo

Dividing by breaking down the dividend

CAPS strand: Numbers, Operations & Relationships · Decomposition strategies

Warmup (siSwati)

Ku 450 ÷ 25: 450 ubitwa ngedivaydendi, 25 ubitwa ngedivayiza, li-18 libitwa ngekhoshiyenti.

Warmup (English)

Name the parts. 450 is dividend, 25 is divisor, 18 is quotient. Vocabulary consolidation before method.

Core idea (siSwati)

Kuhlahlela idivaydendi ibe ngemamaltipuli edivayisa. Buka uma ingangeni impela, beke insalela.

Core idea (English)

Break the dividend into MULTIPLES of the divisor. If a remainder is left, keep it separate.

Worked examples

240 ÷ 12

= (120 + 120) ÷ 12 = 10 + 10

= 20

438 ÷ 25

= (250 + 175) ÷ 25 + rem 13 = 10 + 7 rem 13

= 17 rem 13

805 ÷ 32

= (640 + 160 + 5) ÷ 32 = 20 + 5 rem 5

= 25 rem 5

Key vocabulary (siSwati ↔ English)

siSwati	English	Note
idivaydendi	dividend (alt spelling in guide)	the number being divided
idivayiza	divisor (alt spelling in guide)	the number we divide by
emamaltipuli	multiples	12, 24, 36, … are multiples of 12
insalela	remainder	leftover after dividing

Chalkboard prompt — write this on the board

324 ÷ 18. Hlahlela: (180 + 144) ÷ 18 = 10 + 8 = 18.

324 ÷ 18. Break: (180 + 144) ÷ 18 = 10 + 8 = 18.

Week 2 · Classwork 3 · §5.7, pp.88-89

Usebentisa i-long divishini

Long division (standard vertical algorithm)

CAPS strand: Numbers, Operations & Relationships · Formal algorithm

Warmup (siSwati)

Chaza: 54 × 10 = 540, 54 × 2 = 108. Lamapheyimenti atawusetjentiswa ku 648 ÷ 54.

Warmup (English)

Build the clue list first (54×1, ×2, ×5, ×10). The long-division steps then just pick multiples from this list.

Core idea (siSwati)

Setla phansi ngamabitha: khipha lelikhudlwana linagakulandzelayo, phindza.

Core idea (English)

Subtract the largest chunk that fits, bring down, repeat. The clue list tells you what chunks are available.

Worked examples

648 ÷ 54

−540 (54×10), leaves 108 −108 (54×2), leaves 0

= 12 exactly

479 ÷ 23

−460 (23×20), leaves 19

= 20 rem 19

748 ÷ 52

−520 (52×10), leaves 228; −208 (52×4), leaves 20

= 14 rem 20

Key vocabulary (siSwati ↔ English)

siSwati	English	Note
i-long divishini	long division	the standard vertical algorithm
khipha	subtract / take away	the subtraction step
setla phansi	bring down	pull the next digit into the working number

Chalkboard prompt — write this on the board

Sebentisa i-long divishini: 812 ÷ 29. Yakha i-klubhodi kucala.

Long-divide 812 ÷ 29. Build the clue list for 29 first.

Week 2 · Classwork 4 · §5.8, p.90

Kusombulula tinkinga: kupaka

Word problems: packing / boxing contexts

CAPS strand: Numbers, Operations & Relationships · Problem solving with division

Warmup (siSwati)

Kufanele upake 432 emahembe. Libhokisi ngalinye linela 36. Mangaki emabhokisi?

Warmup (English)

Packing problem. 432 shirts, 36 fit per box. Number of boxes = 432 ÷ 36.

Core idea (siSwati)

Shono inambasentensi kucala. Phendvula kancane. Khuluma ngekufulathetayo: 'Batawudzinga emabhokisi la-12.'

Core idea (English)

Write the number sentence first. Solve. Then answer in a FULL sentence referring to the objects (boxes, shirts).

Worked examples

432 shirts ÷ 36/box

432 ÷ 36 = 12

= Batawudzinga emabhokisi la-12 (They need 12 boxes.)

782 eggs ÷ 32/tray

782 ÷ 32 = 24 rem 14

= Kudzingeka emabhokisi la-25 kufaka itreyi le-14 (Need 25, the 25th holds only 14.)

Key vocabulary (siSwati ↔ English)

siSwati	English	Note
libhokisi / emabhokisi	box / boxes
emahembe	shirts
itreyi	tray
emacandza	eggs
ngalinye	each / per

Chalkboard prompt — write this on the board

Emabhotela la-560, ngalinye linela 14 emasumo. Mangaki emabhotela ladvingekako?

560 bottles, 14 fit per crate. How many crates? (560 ÷ 14 = 40)

Week 3 — Applications

Word problems across money, measurement, rate, and ratio. Every problem is still just division.

Week 3 · Classwork 1 · §5.9, pp.91-92

Tinkinga tetimali

Money problems

CAPS strand: Numbers, Operations & Relationships · Financial problem-solving

Warmup (siSwati)

Ngisebentise R600 kutsenga imidlalo le-6 lefanako. R ngamunye?

Warmup (English)

Spent R600 on 6 identical games. Cost per game = R600 ÷ 6 = R100.

Core idea (siSwati)

Tinkinga tetimali tivamile kusebentisa 'total ÷ count = unit price'. Khuluma nge-R esicabucabu seletsola.

Core idea (English)

Money problems follow the pattern: total cost ÷ quantity = price per item. Always state answer with R (rand).

Worked examples

R864 for 24 identical books

864 ÷ 24 = 36

= Libhuku ngalinye libita R36.

R990 for 18 soccer balls

990 ÷ 18 = 55

= Ibhola linye nge-R55.

R768 for 32 identical pencil cases

768 ÷ 32 = 24

= Sikhwama ngasinye sibita R24.

Budget R912, juice R38/bottle, R5 off

912 ÷ 33 = 27 rem 21

= Angatsenga ti-27 wasale ne-R21.

Key vocabulary (siSwati ↔ English)

siSwati	English	Note
imali	money
intsengo	price
ibhajethi	budget
-bita	to cost (verb root)	'ibita R36' = 'it costs R36'
ngalinye	each

Chalkboard prompt — write this on the board

Ibhajethi R540, ilokwe linye R45. Mangaki malokwe?

Budget R540, each dress R45. How many dresses? (540 ÷ 45 = 12)

Week 3 · Classwork 2 · §5.10, p.93

Tinkinga tekukala (emalitha, makilo, mimithala)

Measurement problems (litres, kilograms, metres)

CAPS strand: Measurement · Division in measurement contexts

Warmup (siSwati)

Lisaka leflawa le-750 kg. Babhaki bapake emasaka la-25 kg ngalinye. Masaka lamangaki?

Warmup (English)

750 kg flour repacked into 25 kg bags. Number of bags = 750 ÷ 25 = 30.

Core idea (siSwati)

Yiwacinise emayunithi: kg, m, ℓ. Uma likula idivaydendi lemetha (m), iphendvulo iyakuba ngetinkambu, hhayi ngemethengeni.

Core idea (English)

Watch the UNITS. If the dividend is in metres and the divisor is metres-per-panel, the answer is PANELS (a count), not metres. Always label the answer.

Worked examples

750 kg ÷ 25 kg/bag

= 30

= 30 emasaka

Fence 864 m, panels 3×5 = 15 m each

864 ÷ 15 = 57 rem 9

= Kutawudzingeka emaphanela la-58.

Tank 960 ℓ into 25 ℓ containers

960 ÷ 25 = 38 rem 10

= 38 emakhontheyna lamancane lagcwele.

Key vocabulary (siSwati ↔ English)

siSwati	English	Note
kg / makilo	kilograms
ℓ / emalitha	litres
m / metha	metres
iphaneli / emaphaneli	panel / panels	fence panel
ikhontheyina	container

Chalkboard prompt — write this on the board

Itangi le-1 440 ℓ. Emabhodlela la-12 ℓ. Mangaki emabhodlela?

Tank holds 1 440 ℓ. Bottles are 12 ℓ. How many bottles? (1 440 ÷ 12 = 120)

Week 3 · Classwork 3 · §5.11, p.94

Tinkinga teireythi (lelilodvwa ngemunye)

Rate problems (one-per-another)

CAPS strand: Numbers, Operations & Relationships · Rate as a division concept

Warmup (siSwati)

R975 kutsenga timoto le-25. Intsengo yemoto ngayinye?

Warmup (English)

R975 for 25 toy cars. Price-per-car rate = 975 ÷ 25 = R39 each.

Core idea (siSwati)

Ireythi itjengisa bala ngemunye. '_______ ngamunye' kuyiphendvula yakho. Umela tiketsetse ngekuhlukanisa toni tone.

Core idea (English)

A rate tells you a 'per-one' amount: price per car, litres per day, km per hour. The division does exactly this — total ÷ count.

Worked examples

R816 for 24 identical chairs

816 ÷ 24 = 34

= R34 ngesitulo ngasinye (R34 per chair).

480 ℓ water used over 30 days

480 ÷ 30 = 16

= 16 ℓ ngelilanga (16 ℓ per day).

144 km in 12 hours (warmup, not in guide)

144 ÷ 12 = 12

= 12 km/h — typical speed rate

Key vocabulary (siSwati ↔ English)

siSwati	English	Note
ireythi	rate	e.g. ngelilanga, ngemoto, ngestulo
ngamunye / ngayinye	per / each	follow with the noun: 'ngemoto' = per car
ngelilanga	per day

Chalkboard prompt — write this on the board

Umuntfu uphutsa kilomitha le-60 emahoreni la-3. Liboma lakhe ngehora ngayinye?

Runs 60 km in 3 hours. Pace per hour? (60 ÷ 3 = 20 km/h)

Week 3 · Classwork 4 · §5.12, p.95

Tinkinga teireyshyo (kuhlukanisa ngebulongozelo)

Ratio / proportion problems (splitting in a ratio)

CAPS strand: Numbers, Operations & Relationships · Ratio and proportion

Warmup (siSwati)

Ependi: 180 ℓ lelihlata kwesibhakabhaka + 60 ℓ lephuti. Ireyshyo yini?

Warmup (English)

Paint mix: 180 ℓ turquoise + 60 ℓ yellow. Ratio = 180:60 = simplify by 60 → 3:1.

Core idea (siSwati)

Ireyshyo itjengisa buningi lobubili kanye. Hlukanisa tonkhe tinombolo ngelnombolo lenkhulu lehlanganako (GCD).

Core idea (English)

Ratio shows two quantities together. Simplify by dividing BOTH numbers by the largest common factor. '3:1 turquoise-to-yellow' means for every 3 ℓ turquoise you need 1 ℓ yellow.

Worked examples

180 ℓ : 60 ℓ

÷60 both sides

= 3 : 1 (turquoise : yellow)

480 apples across 12 oranges-per-basket

480 ÷ 12 = 40

= 40 baskets total

720 learners : 20 teachers

÷20 both sides = 36 : 1

= 36 learners per teacher

Key vocabulary (siSwati ↔ English)

siSwati	English	Note
ireyshyo	ratio	written as 3:1 or 'three to one'
kuhlukanisa ngetinombolo letifanako	divide by a common number	simplifying
lelihlata kwesibhakabhaka	turquoise (sky-green)	literally 'blue-green-sky'
lephuti	yellow

Chalkboard prompt — write this on the board

Libhokisi line 120 t'gamu telhlata ne 30 telphuti. Ireyshyo?

Box has 120 green sweets and 30 yellow. Ratio? (120:30 = 4:1)

Glossary — siSwati / English maths terms (this unit)

Every key term introduced across the 12 lessons, alphabetical. Useful as a wall chart or take-home sheet. Print with Ctrl+P.

siSwati	English	Note
-bita	to cost (verb root)	'ibita R36' = 'it costs R36'
emacandza	eggs
emahembe	shirts
emamaltipuli	multiples	12, 24, 36, … are multiples of 12
i-invesi ophareshini	inverse operation	multiplication undoes division
i-long divishini	long division	the standard vertical algorithm
ibhajethi	budget
ibhlokhi	block / column	the two columns in the matching table
idistributhivu prophathi	distributive property	(a + b) ÷ c = a÷c + b÷c
idivaydendi	dividend (alt spelling in guide)	the number being divided
idivayisa	divisor	the number we divide by
idivayiza	divisor (alt spelling in guide)	the number we divide by
idividenthi	dividend	the number being divided
ikhontheyina	container
iklubhodi	clue list	mini times-table written before dividing
imali	money
inambasentensi	number sentence	e.g. 882 ÷ 42 = 21
insalela	remainder	what's left after dividing
intsengo	price
iphaneli / emaphaneli	panel / panels	fence panel
ireyshyo	ratio	written as 3:1 or 'three to one'
ireythi	rate	e.g. ngelilanga, ngemoto, ngestulo
itreyi	tray
kg / makilo	kilograms
khipha	subtract / take away	the subtraction step
kubutsanisa	grouping / pooling	'how many groups of N fit?'
kuchumana	matching / connecting	pairing facts
kuhlahlela	to split / break down	split the dividend into parts that divide cleanly
kuhlukanisa ngetinombolo letifanako	divide by a common number	simplifying
kwabelana	sharing	'each one gets how much?'
lelihlata kwesibhakabhaka	turquoise (sky-green)	literally 'blue-green-sky'
lephuti	yellow
libhokisi / emabhokisi	box / boxes
lithebula	table	multiplication table
m / metha	metres
maphethini	patterns	the regularity in these answers
ngalinye	each / per
ngamunye / ngayinye	per / each	follow with the noun: 'ngemoto' = per car
ngekhoshiyenti	quotient	the answer
ngelilanga	per day
setla phansi	bring down	pull the next digit into the working number
susa li-0	cancel the zero	shortcut
umbala	colour	used to mark matched pairs
ℓ / emalitha	litres
∴	therefore	maths symbol, from Greek — read as 'ngako-ke'

About this site · scope and caveats

Read this before using in class.

What this is

A 3-week teaching reference for Grade 5 Division (ITHEMU 2, IYUNITHI 5) — 12 lessons × 4 per week, lined up exactly with the 2026 Siswati Grade 5 Mathematics Teacher Guide, pp. 82–95. Each lesson gives: a CAPS strand tag, a one-line warmup, a one-line core idea (both siSwati and English), three worked examples with solutions, a siSwati ↔ English vocabulary block, and a chalkboard prompt designed to be written verbatim on the board.

How to use it

On phone/tablet: tabs collapse, layout stacks single-column. Low-bandwidth: no images, no JS beyond tab switching.
On a projector: click 'Toggle board/projector mode' (bottom-right) — switches to white background, black text, large font.
Printing: Ctrl+P. Each week fits roughly 4 A4 pages; the glossary fits one.

Caveats and known gaps

siSwati content is adapted from the official teacher guide. Spelling or tone should still be sanity-checked by a native speaker before print.
'Year 5' terminology in the brief — interpreted as 'Grade 5' per SA CAPS. Intermediate phase.
Only this unit is content-filled. Other terms and strands (Measurement, Space & Shape, Data) are scaffolded in CAPS for future weeks but not yet populated.
The chalkboard prompts are NEW questions (not from the guide) — gives learners exam practice beyond the textbook.

Coming next

Remaining Term 2 units (6+)
Terms 1, 3, 4 outlines
Optional: a 'learner view' without the teacher notes

Restricted

Grade 5 Mathematics — Division (kuhlukanisa) · Weeks 1–3

Week 1 — Foundations

Emaprophathi etinombolo

Kubutsanisa nekwabelana

Kuhlukanisa nemaphethini (ekhanda)

Kuhlukanisa nemaphethini (kuchumana)

Week 2 — Procedures

Kuhlukanisa tinombolo letinemadijithi la-3 ngeledijithi la-2 (iklubhodi)

Kuhlukanisa usebentisa indlela yekuhlahlela tinombolo

Usebentisa i-long divishini

Kusombulula tinkinga: kupaka

Week 3 — Applications

Tinkinga tetimali

Tinkinga tekukala (emalitha, makilo, mimithala)

Tinkinga teireythi (lelilodvwa ngemunye)

Tinkinga teireyshyo (kuhlukanisa ngebulongozelo)

Glossary — siSwati / English maths terms (this unit)

About this site · scope and caveats

What this is

How to use it

Caveats and known gaps

Coming next