PAGE 2 - CONCEPT: 4-DIGIT NUMBERS INTRO
Context: Bindu went to a household exhibition cum sales center with her mother. Observe the items and their price tags from the given display to help her read the numbers.
★ Critical Thinking Question:
Q: What do we call the fourth place in a 4-digit number?
Answer: We call the fourth place from the right the Thousands place (వేల స్థానము).
Q: What do we call the fourth place in a 4-digit number?
Answer: We call the fourth place from the right the Thousands place (వేల స్థానము).
Answer the following based on the exhibition picture:
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1. Can you tell any 3 items that you observe in this sales center?
Answer: Refrigerator, Mixer, and Gas Stove. (రిఫ్రిజిరేటర్, మిక్సర్ మరియు గ్యాస్ స్టవ్).
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2. What is the price of Mixer?
Answer: The price of the Mixer is ₹ 795/-.
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3. What is the price of Kettle?
Answer: The price of the Kettle is ₹ 230/-.
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4. What are the prices of Gas Stoves?
Answer: The prices of the two available Gas Stoves are ₹ 800/- and ₹ 999/-.
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5. What is the price of Refrigerator?
Answer: The price of the Refrigerator is ₹ 8925/-.
Do These: Write the numbers in words
| S.No. | Item | Price (₹) | In Words |
|---|---|---|---|
| 1 | Mixer | 795 | Seven hundred ninety five |
| 2 | Gas Stove | 999 | Nine hundred ninety nine |
| 3 | Kettle | 230 | Two hundred thirty |
| 4 | Refrigerator | 8925 | Eight thousand nine hundred twenty five |
PAGE 4 - CONCEPT: HOW WE GET 1000
Recall Basis:
• By adding 1 to 9, we get 10 ($9 + 1 = 10$; 2-digit number)
• By adding 1 to 99, we get 100 ($99 + 1 = 100$; 3-digit number)
• By adding 1 to 999, we get 1000 ($999 + 1 = 1000$; 4-digit number)
• By adding 1 to 9, we get 10 ($9 + 1 = 10$; 2-digit number)
• By adding 1 to 99, we get 100 ($99 + 1 = 100$; 3-digit number)
• By adding 1 to 999, we get 1000 ($999 + 1 = 1000$; 4-digit number)
Q: How many hundreds are there in 1000?
Answer: There are exactly 10 hundreds in 1000.
Block Representation: 9 hundreds + 1 hundred = 10 hundreds = One thousand. We write one thousand as 1000.
Answer: There are exactly 10 hundreds in 1000.
Block Representation: 9 hundreds + 1 hundred = 10 hundreds = One thousand. We write one thousand as 1000.
PAGE 8 - THOUSANDS AROUND US
Exercise: Identify the range of numbers most suitable for situations
| Range | Suitable Situations from Environment |
|---|---|
| Only 1 | • Number of headmasters in your school. • Number of sachivalayams in a tiny locality. |
| 2 to 5 | • Number of blackboards in a standard classroom. • Number of ceiling fans in your classroom. |
| 10 to 50 | • Number of teachers in your school. • Number of students in your classroom. • Number of tables/benches in your classroom. |
| 50 to 100 | • Number of books in your classroom cupboard. • Number of pages in a small math textbook unit. |
| 500 to 1000 | • Number of children in your school. • Number of girls in your school. • Number of houses in your village area. |
| More than 1000 | • Number of bricks in a commercial brick kiln. • Number of books in the central school library. • Number of letters printed on a full textbook page. |
PAGE 10 - MAKING ONE THOUSAND (1000)
Number Line Target Activities:
a) We are at 900. How much more must be added to reach 1000?
Solution: 900 + 100 = 1000
b) Mark 800. How much more must be added to reach 1000?
Solution: 800 + 200 = 1000
c) Mark 850. How much more must be added to reach 1000?
Solution: 850 + 150 = 1000
d) Mark 760. How much more must be added to reach 1000?
Solution: 760 + 240 = 1000
e) Mark 400. How much less is 400 than 1000?
Solution: It is less by 600 (1000 - 400 = 600).
f) Orange Segment Challenge: Complete addition to make 1000
Solution:
Solution: 900 + 100 = 1000
b) Mark 800. How much more must be added to reach 1000?
Solution: 800 + 200 = 1000
c) Mark 850. How much more must be added to reach 1000?
Solution: 850 + 150 = 1000
d) Mark 760. How much more must be added to reach 1000?
Solution: 760 + 240 = 1000
e) Mark 400. How much less is 400 than 1000?
Solution: It is less by 600 (1000 - 400 = 600).
f) Orange Segment Challenge: Complete addition to make 1000
Solution:
- 497 + 503 = 1000
- 670 + 330 = 1000
- 830 + 170 = 1000
- 500 + 500 = 1000
- 920 + 80 = 1000
- 775 + 225 = 1000
- 895 + 105 = 1000
- 100 + 900 = 1000
PAGE 14 - REPRESENTATION OF FOUR DIGIT NUMBERS
Abacus Key Rule:
One Red Bead (Th) = 1000 |
One Green Bead (H) = 100 |
One Blue Bead (T) = 10 |
One Yellow Bead (O) = 1
Do These: 1. Write the correct digits based on blocks
Given Block Array Structure:
• 4 large thousands cubes, 4 hundreds grids, 6 tens columns, 5 single ones blocks.
Filled Solution Values:
• 4 large thousands cubes, 4 hundreds grids, 6 tens columns, 5 single ones blocks.
Filled Solution Values:
[ 4 ] thousands
[ 4 ] hundreds
[ 6 ] tens
[ 5 ] ones
Final Numeric Value In Box: 4465
PAGE 16 - Do These continue
2. Write the number and number name by observing beads:
a) Given Example: Th=4, H=2, T=5, O=3 ➲ 4253
In Words: Four thousand two hundred and fifty three.
b) Solved Abacus: Th=7, H=4, T=3, O=0 ➲ 7430
In Words: Seven thousand four hundred and thirty.
c) Solved Abacus: Th=3, H=5, T=2, O=1 ➲ 3521
In Words: Three thousand five hundred and twenty one.
In Words: Four thousand two hundred and fifty three.
b) Solved Abacus: Th=7, H=4, T=3, O=0 ➲ 7430
In Words: Seven thousand four hundred and thirty.
c) Solved Abacus: Th=3, H=5, T=2, O=1 ➲ 3521
In Words: Three thousand five hundred and twenty one.
3. Mr. Pradeep Check Fill Assistance:
Amount: ₹ 3456/-
Pay to the order of: Self
Rupees only: Three thousand four hundred and fifty six rupees only
PAGE 18 - Do These ➲ PLACE VALUE AND FACE VALUE
Golden Rule to Remember: No matter where '0' is located inside any number, its place value as well as its face value is always **0**.
a) Place & Face value breakdown for 6742:
| Digit | Place Value | Face Value |
|---|---|---|
| 6 (Thousands) | 6000 | 6 |
| 7 (Hundreds) | 700 | 7 |
| 4 (Tens) | 40 | 4 |
| 2 (Ones) | 2 | 2 |
b) Place & Face value breakdown for 5309:
| Digit | Place Value | Face Value |
|---|---|---|
| 5 (Thousands) | 5000 | 5 |
| 3 (Hundreds) | 300 | 3 |
| 0 (Tens) | 0 | 0 |
| 9 (Ones) | 9 | 9 |
PAGE 20 - VALUE SLIDER & ERROR CORRECTION
Place Value Slider Operations:
a) 1895 - increase the number by 1.
Solution: 1895 + 1 = 1896
b) 2785 - increase the number by 10.
Solution: 2785 + 10 = 2795
c) 5648 - decrease the number by 300.
Solution: 5648 - 300 = 5348
d) 6487 - increase the number by 2000.
Solution: 6487 + 2000 = 8487
Solution: 1895 + 1 = 1896
b) 2785 - increase the number by 10.
Solution: 2785 + 10 = 2795
c) 5648 - decrease the number by 300.
Solution: 5648 - 300 = 5348
d) 6487 - increase the number by 2000.
Solution: 6487 + 2000 = 8487
Think and Discuss (Student Misconceptions Checked):
1) Yashu wrote Seven thousand and twenty four as 724. Is this correct?
Answer: No, it is incorrect. 724 is a 3-digit number (Seven hundred twenty-four).
Correct Standard Form: 7024 (since there are 0 hundreds).
Answer: No, it is incorrect. 724 is a 3-digit number (Seven hundred twenty-four).
Correct Standard Form: 7024 (since there are 0 hundreds).
2) Padmaja wrote Five thousand six hundred and three as 563. Is this correct?
Answer: No, it is incorrect. 563 is Five hundred sixty-three.
Correct Standard Form: 5603 (since there are 0 tens).
Answer: No, it is incorrect. 563 is Five hundred sixty-three.
Correct Standard Form: 5603 (since there are 0 tens).
PAGE 22 - TOKEN SYSTEM AND EXPANDED FORMS
| Expanded Form | Th | H | T | O | Number | Number Name |
|---|---|---|---|---|---|---|
| 1000 + 1 | 1 | 0 | 0 | 1 | 1001 | One thousand and one |
| 1000 + 2 | 1 | 0 | 0 | 2 | 1002 | One thousand and two |
| 1000 + 3 | 1 | 0 | 0 | 3 | 1003 | One thousand and three |
| 1000 + 4 | 1 | 0 | 0 | 4 | 1004 | One thousand and four |
| 1000 + 10 | 1 | 0 | 1 | 0 | 1010 | One thousand and ten |
| 1000 + 100 | 1 | 1 | 0 | 0 | 1100 | One thousand one hundred |
| 1000 + 30 + 8 | 1 | 0 | 3 | 8 | 1038 | One thousand thirty eight |
| 1000 + 400 + 2 | 1 | 4 | 0 | 2 | 1402 | One thousand four hundred two |
| 1000 + 500 + 30 | 1 | 5 | 3 | 0 | 1530 | One thousand five hundred thirty |
| 3000 + 0 + 10 + 9 | 3 | 0 | 1 | 9 | 3019 | Three thousand and nineteen |
PAGE 24 - MATH LAB ACTIVITY
1. Token Composition Conversion Table:
| Given Composition | Th | H | T | O | Converted Number Name |
|---|---|---|---|---|---|
| a) 8 Tens and 2 Ones | 0 | 0 | 8 | 2 | Eighty Two |
| b) 4 Tens and 12 Ones (40+12) | 0 | 0 | 5 | 2 | Fifty Two |
| c) 3 Hundreds, 14 Tens, 8 Ones (300+140+8) | 0 | 4 | 4 | 8 | Four hundred forty eight |
| d) 12 Hundreds, 18 Tens, 2 Ones (1200+180+2) | 1 | 3 | 8 | 2 | One thousand three hundred eighty two |
| e) 1 Th, 5 H, 10 T, 17 O (1000+500+100+17) | 1 | 6 | 1 | 7 | One thousand six hundred seventeen |
2. Bigger Number Selected:
• 30 or 300
• 6000 or 600
• 2000 or 3000
• 5000 or 4000
• 7000 or 8000
• 6000 or 600
• 2000 or 3000
• 5000 or 4000
• 7000 or 8000
3. Smaller Number Selected:
• 2 Ones or 2 Hundreds
• 2 Tens or 5 Thousands
• 7 Hundreds or 2 Tens
• 9 Tens or 4 Hundreds
• 8 Hundreds or 30 Tens (300 < 800)
• 2 Tens or 5 Thousands
• 7 Hundreds or 2 Tens
• 9 Tens or 4 Hundreds
• 8 Hundreds or 30 Tens (300 < 800)
PAGE 26 - NUMBER LINE INTERPOLATION AND BOUNDARIES
1. Circle the numbers that lie strictly between 2226 and 3226:
Given list: [3316, 3236, 2236, 2216, 3126, 3216]
Solved Selections (In-Between): 2236, 3126, 3216.
Given list: [3316, 3236, 2236, 2216, 3126, 3216]
Solved Selections (In-Between): 2236, 3126, 3216.
2. Number Line Marking Target Coordinates:
a) Scale 1000 to 1100 (Interval=10):
• 1043 is located 3 small points past the 1040 line mark.
• 1069 is located exactly 1 small point before the 1070 line mark.
• 1084 is located 4 small points past the 1080 line mark.
b) Scale 2000 to 2500 (Interval=100):
• 2025 & 2080 are between 2000 and 2100.
• 2175 is between 2100 and 2200.
• 2245 & 2295 are between 2200 and 2300.
• 2310 & 2390 are between 2300 and 2400.
• 2430 & 2460 are between 2400 and 2500.
c) Scale 5500 to 5725 (Interval=25):
• 5512 (between 5500-5525) | 5548 (just before 5550) | 5590 (between 5575-5600) | 5636 (between 5625-5650) | 5673 (just before 5675) | 5695 (just before 5700).
d) Solved Empty Boxes on Abacus Scale:
From left to right, the missing sequence boxes point to: [ 8600 ], [ 8700 ], [ 8800 ], [ 8900 ] respectively.
• 1043 is located 3 small points past the 1040 line mark.
• 1069 is located exactly 1 small point before the 1070 line mark.
• 1084 is located 4 small points past the 1080 line mark.
b) Scale 2000 to 2500 (Interval=100):
• 2025 & 2080 are between 2000 and 2100.
• 2175 is between 2100 and 2200.
• 2245 & 2295 are between 2200 and 2300.
• 2310 & 2390 are between 2300 and 2400.
• 2430 & 2460 are between 2400 and 2500.
c) Scale 5500 to 5725 (Interval=25):
• 5512 (between 5500-5525) | 5548 (just before 5550) | 5590 (between 5575-5600) | 5636 (between 5625-5650) | 5673 (just before 5675) | 5695 (just before 5700).
d) Solved Empty Boxes on Abacus Scale:
From left to right, the missing sequence boxes point to: [ 8600 ], [ 8700 ], [ 8800 ], [ 8900 ] respectively.
PAGE 28 - ROUNDING OFF TO NEAREST 100's
Core Rounding Logic: Look carefully at the tens digit. If it is 0, 1, 2, 3, 4 $\rightarrow$ round down to previous hundred. If it is 5, 6, 7, 8, 9 $\rightarrow$ round up to next hundred. Middle values always round up.
Do These Solutions:
a) Round off 284:
• Tens digit is 8 (>=5).
• Rounds up to 300
• Tens digit is 8 (>=5).
• Rounds up to 300
b) Round off 354:
• Tens digit is 5 (>=5).
• Rounds up to 400
• Tens digit is 5 (>=5).
• Rounds up to 400
c) Round off 4324:
• Tens digit is 2 (<5 br=""> • Rounds down to 4300
• Tens digit is 2 (<5 br=""> • Rounds down to 4300
d) Round off 5568:
• Tens digit is 6 (>=5).
• Rounds up to 5600
• Tens digit is 6 (>=5).
• Rounds up to 5600
EXERCISE - 1
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1. Observe the series and fill the boxes with correct numbers:
a) 2001, 2002, 2003, 2004, 2005, 2006, 2007.
b) 4571, 4572, 4573, 4574, 4575, 4576, 4577. -
2. Read the numbers given in words below and write in numerals:
a) Three thousand five hundred and twenty-five = 3525
b) Seven thousand seven hundred and eight = 7708
c) Eight thousand and five = 8005 -
3. Write the place value of circled digits:
a) In 5937, the place value of 9 is = 900 (Hundreds position)
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4. Write the following numbers in words:
a) 5876 = Five thousand eight hundred and seventy six.
b) 7305 = Seven thousand three hundred and five.
c) 2089 = Two thousand and eighty nine. -
5. Write each of the following in expanded form:
a) 3870 = 3000 + 800 + 70 + 0
b) 7077 = 7000 + 0 + 70 + 7 -
6. Write the short form / standard form:
a) Five thousands + Two Hundreds + Forty + Three = 5243
b) Seven thousands + One Hundred + Sixty + Eight = 7168 -
7. Write the four digit number having 5 in thousands place, 8 in hundreds place, 3 in tens place and 2 in ones place:
Answer: 5832
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8. Which number lying between 5000 and 6000 that has 8 in its tens place can be formed using [2, 5, 6, 8]?
Correct Choice: d) 5682 (Lies between 5000-6000 and has 8 in the tens spot).
PAGE 32 - DIGIT CARDS CREATION WORKBENCH
Rule Framework: Take four cards from the pile, form distinct variations, and type out the complete phrase version verbatim.
| S. No | Number | Number In Words |
|---|---|---|
| 1 | 4592 | Four thousand five hundred and ninety two |
| 2 | 5942 | Five thousand nine hundred and forty two |
| 3 | 9524 | Nine thousand five hundred and twenty four |
| 4 | 2459 | Two thousand four hundred and fifty nine |
| 5 | 3678 | Three thousand six hundred and seventy eight |
| 6 | 8763 | Eight thousand seven hundred and sixty three |
PAGE 36 - LOGICAL SYMBOLS COMPARISON (<, =, >)
1. Fill boxes with symbols based on item contexts:
a) Price of Toy Car (₹ 250) [ < ] Price of Toy JCB (₹ 350)
b) Price of Pressure Cooker (₹ 2675) [ > ] Price of another variant (₹ 1675)
b) Price of Pressure Cooker (₹ 2675) [ > ] Price of another variant (₹ 1675)
2. Direct Numerical Comparison Exercise:
a) 6472 [ > ] 5306
b) 465 [ < ] 3079
c) 5780 [ < ] 5967
d) 6504 [ > ] 6079
e) 3281 [ < ] 3896
f) 4650 [ < ] 4698
g) 7856 [ > ] 7854
h) 6702 [ < ] 6923
i) 5063 [ = ] 5063
j) 5716 [ > ] 5186
PAGE 38 - MERCHANT INVESTMENTS ORDERING
Merchant Investment Ledger: Anwar = ₹ 5526 | Somu = ₹ 3480 | Gourayya = ₹ 4690 | Lakshmayya = ₹ 6370
- a) Who invested more money? How much?
Answer: Lakshmayya invested the highest amount of ₹ 6370. - b) Who invested less money? How much?
Answer: Somu invested the lowest amount of ₹ 3480. - c) Write the investments of the merchants from less to more (Ascending Order):
Answer: 3480 < 4690 < 5526 < 6370 (Somu < Gourayya < Anwar < Lakshmayya) - d) Write the investments of the merchants from more to less (Descending Order):
Answer: 6370 > 5526 > 4690 > 3480 (Lakshmayya > Anwar > Gourayya > Somu)
EXERCISE - 2
1. Write any five 4-digit numbers using the digits 1, 3, 7 and 9:
Answer variants: 1379, 3791, 7913, 9137, 9731.
2. Circle the correct boundary interval range:
• a) 250 lies inside interval 200 - 300
• b) 460 lies inside interval 400 - 500
• c) 884 lies inside interval 800 - 900
Answer variants: 1379, 3791, 7913, 9137, 9731.
2. Circle the correct boundary interval range:
• a) 250 lies inside interval 200 - 300
• b) 460 lies inside interval 400 - 500
• c) 884 lies inside interval 800 - 900
3. Write the biggest and smallest 4-digit numbers formed by given digits:
| Digits Set | Biggest 4-Digit Number | Smallest 4-Digit Number |
|---|---|---|
| 3, 7, 5, 9 | 9753 | 3579 |
| 6, 4, 9, 5 | 9654 | 4569 |
| 1, 0, 5, 2 | 5210 | 1025 (Note: 0 cannot lead) |
| 2, 9, 4, 6 | 9642 | 2469 |
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4. Fill in the blanks with single digit to satisfy inequality:a) $7\mathbf{5}3 < 768$ (Any digit from 0 to 5 works)
b) $853 > 8\mathbf{4}3$ (Any digit from 0 to 4 works) -
5. Which of the spike abacuses shows the number "One Thousand and Ten" (1010)? ( B )
IMPROVE YOUR LEARNING
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1. Which of these is as SAME as 67? ( A )Answer: A) sixty seven
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2. Three tens + two thousands + eight hundreds + seven ones $\rightarrow$ Which number matches? ( D )Answer: D) 2837 ($2000 + 800 + 30 + 7$)
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3. Who wrote the expanded form of 9329 correctly among Kareena, Sushma, and Rajesh? ( D )Answer: D) All three wrote it correctly in different mathematical valid forms.
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4. Raju [4,3,9,5] and Santi [3,9,1,6]. Who can form the largest number? ( A )Answer: A) Raju (Raju can form 9543 whereas Santi can only form 9631).
Short Explanatory Theory Questions:
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5. A student was asked to use [3, 0, 8, 5] to make the smallest number. He wrote 0358. Is it a true 4-digit number?
Answer: No, it is not a true 4-digit number because a leading zero has no value, making 0358 effectively a 3-digit number (358).
Correct Smallest 4-Digit Number: 3058 (put the smallest non-zero digit 3 first). -
6. Create a "Skip Counting" challenge sequence starting at 120 (adding a value between 5 and 10):
Answer Sequence: 120, 128, 136, 144, 152
Rule used: Skip counting by adding 8 successively ($+8$). -
7. Observe sequence: 250, 275, 300, 325, ... What are next three numbers? Explain rule.
Next Three Numbers: 350, 375, 400
Rule: The pattern is skip counting by adding twenty-five ($+25$) to the previous number. -
8. A farmer collected 463 eggs. Round this number to nearest hundred:
Answer: The number 463 rounded to the nearest hundred is 500.
Reason: The tens digit is 6, which is greater than 5, so we round up to the next hundred.
