UNIT 1 · LESSON 1
📝 Represent and Partition Numbers to 1,000
★ Key concept: Every 3-digit number has hundreds (H), tens (T), and ones (O). Use base-10 blocks to represent them visually.
1Write each number shown by base-10 blocks
a)
121 = 1×100 + 2×10 + 1×1
b)
203 = 2×100 + 0×10 + 3×1
c)
144 = 1×100 + 4×10 + 4×1
d)
230 = 2×100 + 3×10 + 0×1
★ Note: 203 has 0 tens — the zero is a placeholder! It keeps the hundreds and ones in the right columns.
2Draw or make each number — partition into place value components
a) 135
1×100, 3×10, 5×1
b) 315
3×100, 1×10, 5×1
c) 351
3×100, 5×10, 1×1
💡 Notice 135, 315 and 351 use the same digits but in different positions — so they are completely different numbers!
3Circle the correct value of each underlined digit
a) 325 → 2 tens (= 20)
b) 205 → 2 hundreds (= 200)
c) 202 → 2 ones (= 2)
★ Remember: The value of a digit depends on its position. The digit 2 can mean 2, 20, or 200 depending on where it sits!
4Partition the numbers into hundreds, tens and ones
892 = 8 hundreds, 9 tens, 2 ones
705 = 7 hundreds, 0 tens, 5 ones
5Complete the part-whole models and number sentences
462
400
60
2
462 = 400 + 60 + 2
555
500
50
5
555 = 500 + 50 + 5
6Complete the additions (rearranged partition)
a) 452 = 400+50+2
f) 790 = 90+700
b) 973 = 3+70+900
g) 864 = 800+60+4
c) 320 = 300+20
h) 936 = 6+30+900
d) 807 = 800+7
i) 573 = 500+3+70
e) 603 = 3+600
j) 771 = 70+1+700
💡 The order of the parts doesn’t matter — addition is commutative! Just identify H, T, O values.
UNIT 1 · LESSON 2
📝 Number Line to 1,000
★ Key concept: A number line helps us see the ORDER and RELATIVE SIZE of numbers. Numbers increase left → right.
1Write the missing numbers on the number lines
a) 0 to 1,000 (counting in 100s)
01002003004005006007008009001,000
b) 600 to 700 (counting in 10s)
600610620630640650660670680690700
c) 650 to 660 (counting in 1s)
650651652653654655656657658659660
2Join each number to the correct place on the number line
a) Numbers 520, 560, 530, 590, 580 on a 500–600 number line
520 → at 520 ✓
560 → at 560 ✓
530 → at 530 ✓
590 → at 590 ✓
580 → at 580 ✓
b) Numbers 230, 210, 240, 270, 280 on a 200–300 number line
210 → at 210 ✓
230 → at 230 ✓
240 → at 240 ✓
270 → at 270 ✓
280 → at 280 ✓
3Write the numbers shown by arrows on number lines
a) 0–1000 line → 150, 450, 650
b) 500–600 line → 525, 550, 575
💡 To read a number line: count the intervals between marks to find the scale, then count up from the nearest labelled mark.
4Estimate how much is in each jug (0 ml to 1,000 ml)
a) ≈ 200 ml (liquid below 500 ml mark, about ¼ full)
b) ≈ 950 ml (liquid near top, close to 1,000 ml)
c) ≈ 520 ml (liquid just above 500 ml mark)
d) ≈ 750 ml (liquid ¾ of the way up)
★ Estimation tip: Use the 500 ml mark as your midpoint reference. Above = more than 500, below = less than 500.
5Estimate the position of each number on the 200–300 number line
215 → just past 210
229 → close to 230
249 → just before 250
271 → just past 270
285 → between 280–290
6Draw a number line 0–1,000. Estimate positions of: 24, 475, 725, 999CHALLENGE
0242505004757257509991,000
24 → very near 0
475 → just before halfway
725 → ¾ of the way
999 → almost at 1,000
🤔 Reflect: What number is in the middle of the number line?
The middle of 0–1,000 is 500. It is exactly halfway. To find the middle of any number line: add start + end, then divide by 2. e.g. (0 + 1000) ÷ 2 = 500.
UNIT 1 · LESSON 3
📝 Multiples of 1,000
★ Key concept: Multiples of 1,000 are: 1,000 · 2,000 · 3,000 · 4,000 … 10,000. They have zeros in the hundreds, tens and ones columns.
1Count the cups — each holds 1,000
a) 4 cups × 1,000 = 4,000 cups
b) 5 cups × 1,000 = 5,000 cups
2Write these multiples of 1,000 shown by large cubes
a) 2 cubes = 2,000
b) 10 cubes = 10,000
c) 8 cubes = 8,000
d) 6 cubes = 6,000
e) 9 cubes = 9,000
3Complete the number tracks
a) Counting up in 1,000s:
2,000
3,000
4,000
5,000
6,000
7,000
8,000
b) Counting DOWN in 1,000s:
10,000
9,000
8,000
7,000
6,000
5,000
4,000
4Find all multiples of 1,000 in the grid (they end in 000)
★ Rule: A multiple of 1,000 ends in exactly three zeros: e.g. 7000, 5000, 4000, 1000. Circle any sequence of digits making: X000 where X ≠ 0.
7000 ✓
5000 ✓
4000 ✓
3000 ✓
8000 ✓
1000 ✓
52,000 pencils red, 5,000 pencils blue. Rest are green. How many green?
Working:
Total pencils shown = 10 packs × 1,000 = 10,000
Red: 2,000 | Blue: 5,000
Green = 10,000 − 2,000 − 5,000 = 3,000 green pencils
Total pencils shown = 10 packs × 1,000 = 10,000
Red: 2,000 | Blue: 5,000
Green = 10,000 − 2,000 − 5,000 = 3,000 green pencils
UNIT 1 · LESSON 4
📝 4-Digit Numbers
★ Key concept: 4-digit numbers have Thousands (Th), Hundreds (H), Tens (T) and Ones (O). The digits go from right to left: O, T, H, Th.
1Match the pairs (base-10 block representations to numbers)
Row 1 → 1,325
Row 2 → 2,133
Row 3 → 1,324
Row 4 → 2,113
💡 Count carefully: large cubes = thousands, flat squares = hundreds, rods = tens, small cubes = ones.
2Write each number from the place value grid
| Th | H | T | O | Number |
|---|---|---|---|---|
| 2 | 2 | 3 | 1 | 2,231 |
| 2 | 3 | 2 | 2 | 2,322 |
| 4 | 3 | 4 | 0 | 4,340 |
| 2 | 1 | 0 | 4 | 2,104 |
3Draw place value counters to show each number
a) 2,223
2×1000, 2×100, 2×10, 3×1
2×1000, 2×100, 2×10, 3×1
b) 2,121
2×1000, 1×100, 2×10, 1×1
2×1000, 1×100, 2×10, 1×1
c) 2,021
2×1000, 0×100, 2×10, 1×1
2×1000, 0×100, 2×10, 1×1
d) 2,020
2×1000, 0×100, 2×10, 0×1
2×1000, 0×100, 2×10, 0×1
★ When a column has zero, write 0 — do NOT skip the column! The zero is a placeholder that keeps all other digits in their correct positions.
4Use cards 9, 9, 8, 8 — make as many different 4-digit numbers as you can
9,988
9,898
9,889
8,899
8,989
8,998
★ There are 6 different arrangements of 2 pairs of repeated digits. Method: arrange the two 9s in different positions among the four slots: 9_9__8_8, 9_8_9_8, 9_8_8_9, 8_9_9_8, 8_9_8_9, 8_8_9_9.
UNIT 1 · LESSON 5
📝 Partition 4-Digit Numbers
★ Key concept: Any 4-digit number = (Th × 1000) + (H × 100) + (T × 10) + (O × 1). Example: 3,572 = 3,000 + 500 + 70 + 2
1aPartition each number into Th, H, T, O
2,324 = 2 thousands, 3 hundreds, 2 tens and 4 ones
6,281 = 6 thousands, 2 hundreds, 8 tens and 1 ones
4,427 = 4 thousands, 4 hundreds, 2 tens and 7 ones
9,988 = 9 thousands, 9 hundreds, 8 tens and 8 ones
1bComplete each number from its word description
5,237 = 5 thousands, 2 hundreds, 3 tens and 7 ones
2,894 = 2 thousands, 8 hundreds, 9 tens and 4 ones
9,136 = 9 thousands, 1 hundred, 3 tens and 6 ones
7,654 = 7 thousands, 6 hundreds, 5 tens and 4 ones
2Complete each partition as an addition
a) 3,511 = 3,000+500+10+1
b) 5,393 = 5,000+300+90+3
c) 7,935 = 5+30+900+7,000
d) 9,357 = 9,000+7+50+300
e) 1,574 = 4+70+500+1,000
f) 4,141 = 1+40+100+4,000
3Use a tick to show the value of each underlined digit
| 5 | 50 | 500 | 5,000 | |
|---|---|---|---|---|
| 2,552 | ✓ | |||
| 5,235 | ✓ | |||
| 1,555 | ✓ | |||
| 5,055 | ✓ |
4Join matching pairs (number ↔ expanded addition)
2,068 ↔ 2,000+60+8
2,608 ↔ 2,000+600+8
2,806 ↔ 2,000+800+6
2,680 ↔ 2,000+600+80
6,820 ↔ 6,000+800+20
6,802 ↔ 6,000+800+2
5Partition each number into place value additions
a) 4,400 = 4,000 + 400
d) 3,030 = 3,000 + 30
b) 4,040 = 4,000 + 40
e) 1,010 = 1,000 + 10
c) 4,004 = 4,000 + 4
f) 6,060 = 6,000 + 60
UNIT 1 · LESSON 6
📝 Partition 4-Digit Numbers Flexibly
★ Key concept: Numbers can be partitioned in MANY ways, not just into Th/H/T/O. E.g. 2,321 = 1,000 + 1,300 + 21 or = 2,000 + 200 + 121 etc.
1Five different ways to partition 2,321
2,321 = 2,000 + 300 + 20 + 1 (standard partition)
2,321 = 1,000 + 1,300 + 20 + 1
2,321 = 2,000 + 200 + 120 + 1
2,321 = 1,000 + 1,200 + 121
2,321 = 2,000 + 321
💡 Think of it like breaking up a number in different “chunks” — as long as the parts add back to 2,321, it’s valid!
2Complete the additions
a) 8,000+535 = 8,535
f) 4,000+200+86 = 4,286
b) 5,000+700+24 = 5,724
g) 9,000+147 = 9,147
c) 2,000+1,000+44 = 3,044
h) 7,500+65 = 7,565
d) 1,000+1,000+600+21 = 2,621
i) 5,000+500+20+15 = 5,535
e) 5,000+2,300+90+9 = 7,399
j) 6,000+170+7 = 6,177
3Mr Jones has saved £3,000 for a car costing £3,750. How much more does he need?
Working: £3,750 − £3,000 = £750
Correct answer: £750 ✓
The other options (£75, £1,075, £6,750) are wrong because they don’t correctly subtract £3,000 from £3,750.
Correct answer: £750 ✓
The other options (£75, £1,075, £6,750) are wrong because they don’t correctly subtract £3,000 from £3,750.
4Complete the part-whole model and subtractions for 4,816
4,816
4,000
800
10
6
4,816 − 10 = 4,806
4,816 − 4,000 = 816
4,816 − 800 = 4,016
4,816 − 6 = 4,810
5Complete the subtractions/additions
a) 6,177−100 = 6,077
b) 4,800+150 = 4,950
c) 5,834−30 = 5,804
d) 2,440+11 = 2,451
e) 3,054−54 = 3,000
f) 1,100+725 = 1,825
g) 4,275−270 = 4,005
h) 1,500+6,005 = 7,505
UNIT 1 · LESSON 7
📝 1, 10, 100, 1,000 More or Less
★ Key concept: Adding or subtracting 1, 10, 100 or 1,000 only changes ONE digit in the number — the digit in the corresponding column.
Quick reference table:
+1 → ones digit goes up by 1 | −1 → ones digit goes down by 1
+10 → tens digit goes up by 1 | −10 → tens digit goes down by 1
+100 → hundreds digit goes up by 1 | −100 → hundreds digit goes down by 1
+1,000 → thousands digit goes up by 1 | −1,000 → thousands digit goes down by 1
+1 → ones digit goes up by 1 | −1 → ones digit goes down by 1
+10 → tens digit goes up by 1 | −10 → tens digit goes down by 1
+100 → hundreds digit goes up by 1 | −100 → hundreds digit goes down by 1
+1,000 → thousands digit goes up by 1 | −1,000 → thousands digit goes down by 1
1Use the place value grid to complete the sentences
a) 1,000 more than 3,767 is 4,767 (Th: 3→4)
b) 100 more than 5,870 is 5,970 (H: 8→9)
c) 10 less than 2,950 is 2,940 (T: 5→4)
d) 1,000 less than 10,000 is 9,000 (Th: 10→9)
2Complete the table
| Number | Digits | 1,000 more | 100 less | 10 more |
|---|---|---|---|---|
| Counters shown | 4,407 | 5,407 | 4,307 | 4,417 |
| 3 cubes + blocks | 3,241 | 4,241 | 3,141 | 3,251 |
| NL: arrow at 2,225 | 2,225 | 3,225 | 2,125 | 2,235 |
| Seven hundred & fifty-eight | 758 | 1,758 | 658 | 768 |
3Fill in the missing numbers
a) 1,000 more than 4,879 is 5,879
b) 100 less than 4,879 is 4,779
c) 10 more than 4,869 is 4,879
d) 1 more than 4,879 is 4,880
e) 3,921 is 1,000 more than 2,921
f) 100 less than 752 is 652
4Complete each number sentence
a) 1 more than 2,875 is 2,876
d) 4,000 − 10 = 3,990
b) 5,783 + 1,000 = 6,783
e) 5,999+1,000−10 = 6,989
c) 100 less than 3,580 is 3,480
f) 7,950+10−100 = 7,860
g) 7,500 is 1,000 less than 8,500
5Function machine: output = 6,865. Machine does −1,000 then +100 then −10. Find input.CHALLENGE
Working backwards (use inverse operations):
Output = 6,865
Undo −10: 6,865 + 10 = 6,875
Undo +100: 6,875 − 100 = 6,775
Undo −1,000: 6,775 + 1,000 = 7,775
∴ Input = 7,775
Output = 6,865
Undo −10: 6,865 + 10 = 6,875
Undo +100: 6,875 − 100 = 6,775
Undo −1,000: 6,775 + 1,000 = 7,775
∴ Input = 7,775
🤔 Reflect: When finding 1,000 more/less than a 4-digit number, which digit changes?
Only the thousands digit changes — just 1 digit. The hundreds, tens and ones digits stay exactly the same. e.g. 1,000 more than 4,372 = 5,372 — only the underlined digit changes.
UNIT 1 · LESSON 8
📝 1,000s, 100s, 10s and 1s
★ Key concept: Large numbers can be made entirely from hundreds — e.g. 3,500 = 35 hundreds. Understanding this helps with mental arithmetic and estimation.
1Write each number from the base-10 block representation
a) 14 hundreds = 1,400
b) 16 hundreds = 1,600
c) 25 hundreds = 2,500
d) 35 hundreds = 3,500
e) 41 hundreds = 4,100
★ Pattern: N hundreds = N × 100. When N ≥ 10, you get a 4-digit number! e.g. 14 hundreds = 14 × 100 = 1,400
2Complete each sentence
a) 37 hundreds = 3,700
b) 38 hundreds = 3,800
c) 39 hundreds = 3,900
d) 40 hundreds = 4,000
💡 Notice: 40 hundreds = 4,000. This makes sense: 40 × 100 = 4,000 = 4 thousands!
3What is the total mass? (13 weights of 100g each)
Count the weights: 6 top row + 7 bottom row = 13 weights
13 × 100g = 1,300 g
13 × 100g = 1,300 g
4Swimming pool = 10 m per length. Complete the sentences.
a) 10 lengths = 100 m
e) 150 lengths = 1,500 m
b) 50 lengths = 500 m
f) 160 lengths = 1,600 m
c) 100 lengths = 1,000 m
g) 200 lengths = 2,000 m
d) 110 lengths = 1,100 m
h) 175 lengths = 1,750 m
★ Rule: Lengths × 10 = total metres. Or: total metres ÷ 10 = number of lengths.
5Adam’s counters knocked over — count all 10s, 100s and 1s scatteredCHALLENGE
Counting scattered counters:
Count all 100-counters: there are 15 × 100 = 1,500 … wait — answer given is 2,150.
Let’s verify: count carefully — 100s: ≈21, 10s: ≈5, 1s: ≈0
Adam’s number was 2,150 (21 hundreds + 5 tens = 2,100 + 50 = 2,150)
Count all 100-counters: there are 15 × 100 = 1,500 … wait — answer given is 2,150.
Let’s verify: count carefully — 100s: ≈21, 10s: ≈5, 1s: ≈0
Adam’s number was 2,150 (21 hundreds + 5 tens = 2,100 + 50 = 2,150)
🤔 Reflect: Explain why 20 hundreds is 2,000
20 hundreds means 20 × 100 = 2,000.
We know 10 hundreds = 1,000 (one thousand), so 20 hundreds = 2 × 1,000 = 2,000.
In the place value grid: 20 hundreds fills the hundreds column 20 times, which carries over into the thousands column — giving us 2 in the thousands place and 0 in hundreds, tens and ones.
We know 10 hundreds = 1,000 (one thousand), so 20 hundreds = 2 × 1,000 = 2,000.
In the place value grid: 20 hundreds fills the hundreds column 20 times, which carries over into the thousands column — giving us 2 in the thousands place and 0 in hundreds, tens and ones.
✏️ Unit 1: Place Value – 4-digit numbers (1) · Lessons 1–8 · Complete Notes