Grade 5 Math Unit 1

Grade 5 Maths – Unit 1 Notes

📚 Grade 4 Maths

Unit 1: Place Value within 1,000,000

Lessons 1 – 8 | Complete Study Notes

✏️ Lesson 1: Roman Numerals
✏️ Lesson 2: Numbers to 10,000
✏️ Lesson 3: Numbers to 100,000
✏️ Lesson 4: Numbers to 1,000,000
✏️ Lesson 5: Read & Write 5- and 6-digit Numbers
✏️ Lesson 6: Powers of 10
✏️ Lesson 7: 10/100/1,000/10,000/100,000 More or Less
✏️ Lesson 8: Partition Numbers to 1,000,000

Cover

Lesson 1 — Roman Numerals

🔑 Key Roman Numeral Values (MEMORISE THESE!)

Number	1	5	10	50	100	500	1,000
Roman	I	V	X	L	C	D	M

📝 Rules for Writing Roman Numerals

Write symbols from largest to smallest (left → right)
Add values when a smaller symbol comes AFTER a larger one → VI = 6
Subtract when a smaller symbol comes BEFORE a larger one → IV = 4
Never repeat I, X, C, M more than 3 times in a row
Key subtractive pairs: IV=4, IX=9, XL=40, XC=90, CD=400, CM=900

Q1 — Write these numbers in Roman Numerals

12 = XII (10 + 1 + 1)
35 = XXXV (10+10+10+5)
43 = XLIII (50−10 + 1+1+1)
90 = XC (100−10)
114 = CXIV (100 + 10 + (5−1))

Q2 — Multiples of 100 in Roman Numerals

100 = C
200 = CC
300 = CCC
400 = CD (500−100)
500 = D

600 = DC
700 = DCC
800 = DCCC
900 = CM (1000−100)
1,000 = M

Q3 — Fill in missing numbers

MMCXI = 1000 + 1000 + 100 + 10 + 1 = 2,111
DCCL = 500 + 100 + 100 + 50 = 750
CXCV = 100 + 100 − 10 + 5 = 195

Q4 — Part-Whole Models

a) CDLXX = 470

CD = 400
LXX = 70
400 + 70 = 470 ✓

b) MXLVII = 1047

M = 1,000
XL = 40
VII = 7
1000+40+7 = 1,047 ✓

Q5 — Match Coins to Years

MCCXI → 1211
MDXLV → 1545
MCDLXI → 1461
MCMI → 1901

How to decode MCMI:

M=1000, CM=900, I=1 → 1000+900+1 = 1901

Q6 — Is Lexi correct? (MCX vs CMX)

MCX = 1000 + 100 + 10 = 1,110
CMX = 1000 − 100 + 10 = 910

❌ Lexi is NOT correct. The ORDER of letters matters! MCX ≠ CMX even though they use the same letters.

Q7 — Complete using Roman Numerals

10 years earlier than 1985 → 1975 = MCMLXXV
100 years later than 1480 → 1580 = MDLXXX
50 years later than 1962 → 2012 = MMXII

Working out MCMLXXV (1975):

M(1000) + CM(900) + L(50) + XX(20) + V(5) = 1975 ✓

🏆 Challenge Q8 — Descending order using V, X, L, C, D

The column must go in descending order. Work out each value:

MDCLIX → L=50 → 1659
MCDVI → D=500 → 1506
DCCLX → X=10 → 760
CDXXI → C=100 → 521
CCCXV → V=5 → 395

Cards used in order: L, D, X, C, V

📌 Reflect — Key facts to remember

M = 1,000 | D = 500 | L = 50
MDXL = 1000+500+40 = 1,540 (because XL = 50−10 = 40)

Page 1 — Roman Numerals

Lesson 2 — Numbers to 10,000

🔑 Place Value Columns (4-digit numbers)

Thousands

Hundreds

Tens

Ones

1,000s

100s

10s

Q1 — Read the place value counters

a) 1 Th + 2 H + 5 T + 3 O = 1,253
b) 3 Th + 2 H + 2 T + 6 O = 3,226 (Note: 7 ones shown → 6 ones written, slight mark in book, answer is 3,226)
c) 2 Th + 6 H + 0 T + 5 O = 2,605
d) 3 Th + 0 H + 0 T + 5 O = 3,005
e) Part-whole: 2,000 + 800 + 20 + 4 = 2,824

💡 How to read place value counters

Count how many counters are in each column. Multiply by the column value.
E.g. 3 counters in the Hundreds column = 3 × 100 = 300

Q2 — Draw counters for 5,632 & partition

Th column: 5 counters (5 × 1,000)
H column: 6 counters (6 × 100)
T column: 3 counters (3 × 10)
O column: 2 counters (2 × 1)

5,632 = 5,000 + 600 + 30 + 2

Q3 — Value of each underlined digit

1,794 → 9 is in the Tens column → 90
6,480 → 4 is in the Hundreds column → 400
2,058 → 2 is in the Thousands column → 2,000

Q4 — Read the representations

a) Abacus (5 Th, 3 H, 5 T, 6 O) = 5,356
b) Part-whole: 2,000 + 100 + 0 + 5 = 2,105
c) Counter grid (1000+10+1000+1 / 1+10+100+10 / 1+100+1000 / 1+1000+1) = 4,235

For counter grids:

Add up ALL counters of each type across the whole grid, then put them in the right column.

🏆 Challenge Q5 — Digit cards 0, 2, 5, 8

a) A number with 5 hundreds → 2,508 or 8,502 etc.
b) A number that is odd (ends in odd digit: 5) → 2,805
c) Where 2 has value of 20 (2 in tens column) → 8,025
d) Largest possible even number (arrange largest first, must end in even) → 8,520

💡 For largest even: try 8,520 → ends in 0 (even) ✓ and is the largest possible arrangement!

📌 Reflect — Describe a 4-digit number

When you make a number from dice, describe it using:
→ How many thousands? How many hundreds? Tens? Ones?
→ What does each digit represent? (e.g. the 6 in 6,345 = 6,000)

Page 2 — Numbers to 10,000

Lesson 3 — Numbers to 100,000

🔑 5-Digit Place Value Columns

TTh

Ten Thous.

Thousands

Hundreds

Tens

Ones

10,000s

1,000s

100s

10s

Q1 — Number 85,013

TTh=8, Th=5, H=0, T=1, O=3

What does digit 5 represent? → 5 thousands = 5,000
What does digit 1 represent? → 1 ten = 10
What does digit 8 represent? → 8 ten thousands = 80,000
Digit in 100s position? → 0

b) Swap digits 5 and 8: New number = 58,013
In words: Fifty-eight thousand and thirteen

Q2 — Match the value of digit 4

43,250 → 4 is in TTh place → value = 40,000
32,409 → 4 is in H place → value = 400
34,250 → 4 is in Th place → value = 4,000
23,546 → 4 is in T place → value = 40

Q3 — Draw counters for 26,415

TTh: 2 counters (20,000)
Th: 6 counters (6,000)
H: 4 counters (400)
T: 1 counter (10)
O: 5 counters (5)

Q4 — Complete part-whole models

a) 55,327 = 50,000 + 5,000 + 300 + 20 + 7
b) 12,300 = 10,000 + 2,000 + 300
c) 20,090 = 20,000 + 90

💡 Tip for part-whole models:

Split the number by each place value. If a column is 0, you don’t need that branch!
E.g. 20,090 has 0 thousands, 0 hundreds, so only show 20,000 and 90.

Q5 — More/Less than 13,572

a) 1,000 more than 13,572 = 14,572
b) 100 more than 13,572 = 13,672
c) 200 less than 13,572 = 13,372
d) 50,000 more than 13,572 = 63,572

💡 Only the relevant digit changes! Adding 1,000 only changes the Thousands digit.
Adding 100 only changes the Hundreds digit (unless you need to regroup).

📌 Key vocabulary

Ten Thousands (TTh) — the 5th digit from the right
Example: In 85,013 → the 8 is worth eighty thousand = 80,000
Remember: Zero as a placeholder is essential! 20,090 ≠ 2,090

Page 3 — Numbers to 100,000

Lesson 4 — Numbers to 1,000,000

🔑 6-Digit Place Value Columns

HTh

TTh

Hundred
Thousands

Ten
Thousands

Thousands

Hundreds

Tens

Ones

100,000s

10,000s

1,000s

100s

10s

Q1 — Pencil boxes (each has 100,000)

6 boxes × 100,000 = 600,000
In words: Six hundred thousand

Q2 — What numbers are shown?

a) 5 × 100,000 counters = 500,000
b) 10 × 100,000 counters = 1,000,000
c) Grid: 1 HTh + 7 TTh + 2 Th + 3 H + 1 T + 5 O = 172,315

Q3 — Number of views on a video: 123,419

In words: One hundred and twenty-three thousand, four hundred and nineteen

How to say 6-digit numbers:

Split at the comma: “123” + “419”
→ Say “one hundred and twenty-three THOUSAND, four hundred and nineteen”

Q4 — Draw 126,300 in place value grid

HTh: 1 counter (100,000)
TTh: 2 counters (20,000)
Th: 6 counters (6,000)
H: 3 counters (300)
T: 0 counters
O: 0 counters

Q5 — Write in numerals

a) Three hundred and twenty-nine thousand and one hundred = 329,100
b) Six hundred thousand and forty = 600,040
c) Four hundred thousand, five hundred and ninety-six pounds = £400,596

Q6 — What does the 4 represent?

a) 314,912 → 4 is in Thousands → 4,000
b) 240 → 4 is in Tens → 40
c) 500,240 → 4 is in Tens → 40
d) 77,314 → 4 is in Ones → 4
e) Four hundred and eight thousand, three hundred and one = 408,301 → 4 is in HTh → 400,000

🏆 Challenge Q7 — Olivia’s number: 301,125

HTh=3, TTh=0, Th=1, H=1, T=2, O=5 (reading the counters)

She moves 2 counters so the number now has 1 thousand (Th column = 1).

The 2 moved counters can go to other columns. Five possible answers:

301,125 — move TTh counter → 311,025
311,025, 310,125, 301,215, 302,115, 300,225 (any where Th=1)

Page 4 — Numbers to 1,000,000

Lesson 5 — Read & Write 5- and 6-Digit Numbers

🔑 Commas in large numbers

We use a comma to separate thousands from hundreds:
→ 4-digit: 1,324 5-digit: 61,324 6-digit: 525,262
Count from the RIGHT — comma goes after 3rd digit from right.

Q1 — Read dice numbers (each die = one digit)

a) Dice show 1,3,2,4 → 1,324
b) Dice show 5,2,6,2 → 5,262
c) Dice show 6,1,3,2,4 → 61,324
d) Dice show 5,2,5,2,6,2 → 525,262

Q2 — Arrange digit cards 9, 0, 9, 0, 0, 0 into 6-digit numbers

Strategy: place the 9s in different positions each time

909,000 (9 in HTh, 9 in Th)
990,000 (9 in HTh, 9 in TTh)
900,900 (9 in HTh, 9 in H)
900,090 (9 in HTh, 9 in T)
900,009 (9 in HTh, 9 in O)
090,900 = 90,900 (9 in TTh, 9 in H)

⚠️ 0 cannot be the leading digit — a 6-digit number must start with 1–9!

Q3 — Match number pairs

“Twelve thousand, three hundred and twenty-four” → TTh=1, Th=2, H=3, T=2, O=4 = 12,324
“Twelve thousand and twenty-five” → TTh=1, Th=2, H=0, T=2, O=5 = 12,025
“Thirteen thousand, one hundred and thirty” → TTh=1, Th=3, H=1, T=3, O=0 = 13,130
“Thirty thousand, one hundred and three” → TTh=3, Th=0, H=1, T=0, O=3 = 30,103

Q4 — Rewrite with comma in correct place

32,15 → 3,215
203,21 → 20,321
42,3471 → 423,471
1,9999 → 19,999

2,1215 → 21,215
107,3 → 1,073
5,08017 → 508,017
90,9909 → 909,909

💡 Trick — count digits to fix comma:

Remove the comma, count ALL digits, then put comma after 3rd from right.
E.g. 203,21 → 20321 (5 digits) → comma after 2nd digit → 20,321

Page 5 — Read & Write 5- and 6-digit Numbers

Lesson 6 — Powers of 10

🔑 Key Idea — Exchange between columns

1 thousand = 10 hundreds = 100 tens = 1,000 ones
1 hundred thousand = 10 ten-thousands = 100 thousands
Moving LEFT in the place value table = × 10
Moving RIGHT = ÷ 10

Q1 — How many hundreds in each number?

a) 1,400 = 14 hundreds (1,400 ÷ 100 = 14)
b) 2,500 = 25 hundreds (2,500 ÷ 100 = 25)
c) 9,700 = 97 hundreds (9,700 ÷ 100 = 97)
d) 12,000 = 120 hundreds (12,000 ÷ 100 = 120)

Q2 — How many thousands?

a) 31,000 = 31 thousands
b) 73,000 = 73 thousands
c) 126,000 = 126 thousands

Q3 — Max exchanges 5,000 step by step

Start: 5 counters in Thousands column

a) Each 1,000 → ten 100s: 5 × 10 = 50 hundreds
b) Each 100 → ten 10s: 50 × 10 = 500 tens
c) Each 10 → ten 1s: 500 × 10 = 5,000 ones

💡 Pattern: Each exchange multiplies the count by 10!
5 thousands → 50 hundreds → 500 tens → 5,000 ones

Q4 — Complete the sentences

a) 24,000

= 24 thousands
= 240 hundreds
= 2,400 tens

b) 213,000

= 213 thousands
= 2,130 hundreds
= 21,300 tens

Q5 — 23 hundreds = what number?

23 hundreds = 23 × 100 = 2,300

📌 Powers of 10 — Quick Reference

10¹ = 10 | 10² = 100 | 10³ = 1,000 | 10⁴ = 10,000 | 10⁵ = 100,000 | 10⁶ = 1,000,000

To find how many 100s in a number: divide by 100
To find how many 10s in a number: divide by 10
To find how many 1,000s: divide by 1,000

Page 6 — Powers of 10

Lesson 7 — 10/100/1,000/10,000/100,000 More or Less

🔑 Key Rule

When adding/subtracting these amounts, only ONE digit changes (the one in that column).
All other digits stay the same!
Exception: if a column reaches 10 or drops below 0 → you must regroup.

Q1 — Bella’s number on the place value grid

Grid: HTh=2, TTh=3, Th=0, H=4, T=1, O=6 → 230,416

a) Bella’s number = 230,416
b) 10,000 more = 240,416 (TTh: 3→4)
c) Add one 100 counter = 230,516 (H: 4→5)
d) Remove one 10,000 counter = 220,516 (TTh: 3→2, using updated number from c)

Q2 — Complete the sequences

a) Counting in 10,000s: 140,000 → 150,000 → 160,000 → 170,000 → 180,000 → 190,000 → 200,000
b) Counting in 1,000s: 96,000 → 97,000 → 98,000 → 99,000 → 100,000 → 101,000 → 102,000
c) Counting in 100s: 760,400 → 760,500 → 760,600 → 760,700 → 760,800 → 760,900 → 761,000

💡 For sequence b: Notice 99,000 + 1,000 = 100,000. The TTh and HTh digits change — this is called regrouping!

Q3 — Table for 795,104

Less	Answer	More	Answer
100,000 less	695,104	100,000 more	895,104
10,000 less	785,104	10,000 more	805,104
1,000 less	794,104	1,000 more	796,104
100 less	795,004	100 more	795,204
10 less	795,094	10 more	795,114

Q4 — Complete the sentences

a) 100,000 more than 777,777 = 877,777
b) 10,000 less than 444,444 = 434,444
c) 1,000 more than 555,555 = 556,555

Q5 — Complete sequences

a) +100,000 each time: 108,150 → 208,150 → 308,150 → 408,150 → 508,150 → 608,150 → 708,150
b) +10,000 each time: 535,420 → 545,420 → 555,420 → 565,420 → 575,420 → 585,420
c) +10 each time: 751,087 → 751,097 → 751,107 → 751,117 → 751,127 → 751,137

Q6 — Complete sequence in 3 ways (the number in the middle is 720,000)

+100,000: 320,000 → 420,000 → 520,000 → 620,000 → 720,000 → 820,000
+10,000: 680,000 → 690,000 → 700,000 → 710,000 → 720,000 → 730,000
+1,000: 716,000 → 717,000 → 718,000 → 719,000 → 720,000 → 721,000

Q7 — Complete the following

a) 100,000 more than 725,007 = 825,007
b) 10,000 more than 174,512 = 184,512
c) 1,000 less than 870,300 = 869,300
d) 382,150 is 10,000 more than 372,150
e) 492,107 is 100,000 more than 392,107
f) 183,512 is 1,000 less than 184,512

🏆 Challenge Q8 — Find A, B and C

Given: C is 1,000 less than 37,928 → C = 36,928

C is 10,000 more than B → B = 36,928 − 10,000 = B = 26,928

A is 100,000 more than B → A = 26,928 + 100,000 = A = 126,928

✅ A = 126,928 B = 26,928 C = 36,928

📌 Reflect — Counting in 100s vs 10,000s from 100,000 to 200,000

Counting in 100s: 200,000 − 100,000 = 100,000 → 100,000 ÷ 100 = 1,000 steps
Counting in 10,000s: 100,000 ÷ 10,000 = 10 steps

Counting in 100s takes MUCH longer because 100 is smaller than 10,000!

Page 7 — More or Less

Lesson 8 — Partition Numbers to 1,000,000

🔑 What is Partitioning?

Breaking a number into its place value parts:
365,248 = 300,000 + 60,000 + 5,000 + 200 + 40 + 8
Each part represents the value of one digit in its column.

Q1 — How many counters?

Bags: 2×100,000 + 5×10,000 + 2×1,000 + 7×100 + 2×10 + 3 ones

= 200,000 + 50,000 + 2,000 + 700 + 20 + 3 = 252,723

💡 Count each type of bag separately, then add:

HTh bags: 2 → 200,000
TTh bags: 5 → 50,000
Th bags: 2 → 2,000
H bags: 7 → 700
T bags: 2 → 20
Ones (dots): 3 → 3

Q2 — How much money?

3 × £100,000 = £300,000
1 × £10,000 = £10,000
4 × £100 = £400
5 × £10 = £50

Total = 300,000 + 10,000 + 400 + 50 = £310,450

Q3 — Read the place value grid

HTh=1, TTh=6+1=7 (6 in top row, 1 in bottom), Th=8+3=11…

Reading the grid carefully:

HTh: 1 counter → 100,000
TTh: 6+1 = 7 counters → 70,000 (wait — book shows 168,032)
Working back: 168,032 = 100,000 + 60,000 + 8,000 + 0 + 30 + 2

Answer = 168,032

Q4 — Value of the underlined digit

a) 76,128 → 6 in Thousands → 6,000
b) 610,950 → 9 in Hundreds → 900
c) 7,318 → 1 in Tens → 10

Q5 — Complete the partitions

a) 218,492 = 200,000 + 10,000 + 8,000 + 400 + 90 + 2
b) 710,388 = 700,000 + 10,000 + 300 + 80 + 8
c) 39,448 = 30,000 + 9,000 + 400 + 40 + 8
d) 200,000 + 70,000 + 9,000 + 700 + 30 + 1 = 279,731
e) 500,000 + 2,000 + 900 + 80 + 1 = 502,981
f) 7,000 + 70 + 3 = 7,073
g) 600,000 + 50,000 + 100 + 3 = 650,103

⚠️ Watch out for missing place values! In (e), there are no ten-thousands → use 0 as placeholder: 502,981

Q6 — What are these partitioned numbers?

a) 5 hundred thousands + 4 ten thousands + 9 thousands + 5 hundreds + 2 tens + 7 ones
= 500,000 + 40,000 + 9,000 + 500 + 20 + 7 = 549,527
b) 7 ten thousands + 5 hundreds + 6 ones
= 70,000 + 500 + 6 = 70,506
c) 9 hundred thousands + 1 ten thousand + 2 tens + 8 ones
= 900,000 + 10,000 + 20 + 8 = 910,028

🏆 Challenge Q7 — Work out missing numbers

28,230 − 8,000 = 20,230
28,230 − 200 = 28,030
28,230 − 30 = 28,200

615,804 − 10,000 = 605,804
615,804 − 800 = 615,004
615,804 − 15,804 = 600,000

📌 Reflect — 5- and 6-digit numbers with 4 as hundreds digit

Any number where the hundreds column = 4:
5-digit: e.g. 12,400 or 73,421
6-digit: e.g. 521,487 or 304,100
The hundreds digit is always the 3rd digit from the right.

Page 8 — Partition Numbers to 1,000,000

Unit 1 — Quick Summary & Key Facts

🔑 Roman Numeral Cheat Sheet

I=1 V=5 X=10 L=50 C=100 D=500 M=1000
Subtract when smaller comes BEFORE larger: IV=4, IX=9, XL=40, XC=90, CD=400, CM=900

🔑 Place Value Columns

HTh TTh Th H T O

100,000s | 10,000s | 1,000s | 100s | 10s | 1s

Powers of 10

10 × 10 = 100
100 × 10 = 1,000
1,000 × 10 = 10,000
10,000 × 10 = 100,000
100,000 × 10 = 1,000,000

Partitioning Rule

Each digit × its column value
372,615 =
300,000 + 70,000 +
2,000 + 600 + 10 + 5

Common Mistakes to Avoid ⚠️

Roman numerals: order matters! MCX ≠ CMX
Zero IS a placeholder — 20,090 ≠ 2,090 ≠ 209
Commas go after every 3rd digit from RIGHT: 1,234,567
When adding/subtracting, only the relevant column changes (unless regrouping needed)
A 6-digit number CANNOT start with 0

Summary Page

Mountcrest Academy

Grade 5 Math Unit 1

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