About this Unit: This unit teaches children how to read, write, compare and evaluate arithmetic expressions like 13 + 2, 30 + 5 × 4, or 100 − (15 + 56). Students learn to use brackets and the idea of "terms" to avoid confusion when an expression has more than one operation. The chapter builds strong number sense through the commutative property (swapping terms), the associative property (grouping terms), and the distributive property (multiplying a bracket term-by-term) — all explained through simple stories (marbles, dosas, coins, mangoes) rather than abstract rules, so children discover why a rule works before they use it.
✏️ Figure It Out – 2.1 (Page 90)
1. Fill in the blanks to make the expressions equal on both sides of the '=' sign:
| (a) 13 + 4 = 11 + 6 | (b) 22 + 8 = 6 × 5 |
| (c) 8 × 4 = 64 ÷ 2 | (d) 34 − 9 = 25 |
2. Arrange the following expressions in ascending (increasing) order of their values:
(a) 67 − 19 = 48 (b) 67 − 20 = 47 (c) 35 + 25 = 60 (d) 5 × 11 = 55 (e) 120 ÷ 3 = 40
In-text question (Page 90): "Choose your favourite number and write as many expressions as you can having that value."
In-text question (Page 93): Use '>', '<' or '=' to compare (without complicated calculation):
| (a) 245 + 289 > 246 + 285 | 246 is 1 more, 285 is 4 less than the originals — net decrease of 3, so LHS is greater. |
| (b) 273 − 145 = 272 − 144 | First number is 1 less, and 1 less is subtracted — effects cancel. |
| (c) 364 + 587 < 363 + 589 | 363 is 1 less but 589 is 2 more — net increase of 1 on RHS. |
| (d) 124 + 245 < 129 + 245 | 129 is 5 more than 124. |
| (e) 213 − 77 < 214 − 76 | 214 is 1 more, and 1 less is subtracted — RHS gains 2 in total. |
In-text question (Page 98): "Check if replacing subtraction by addition does not change the value" — e.g., 20 − 7 = 13 and 20 + (−7) = 13. Both are equal, so the rule works.
"Can you explain why subtracting a number is the same as adding its inverse (Token Model)?" — Taking away 7 positive tokens has the same effect as putting in 7 negative tokens, because a positive and a negative token together make a zero-pair and cancel out.
In-text table (Page 100) — Complete the table:
| Expression | As sum of its terms | Terms |
|---|---|---|
| 13 − 2 + 6 | 13 + (−2) + 6 | 13, −2, 6 |
| 5 + 6 × 3 | 5 + (6 × 3) | 5, 6 × 3 |
| 4 + 15 − 9 | 4 + 15 + (−9) | 4, 15, −9 |
| 23 − 2 × 4 + 16 | 23 + (−2 × 4) + 16 | 23, −2 × 4, 16 |
| 28 + 19 − 8 | 28 + 19 + (−8) | 28, 19, −8 |
Does changing the order of adding terms give a different value? — No. Addition is commutative; the order never changes the sum.
✏️ Figure It Out – 2.2 (Page 112)
1. Find the values of the following expressions by writing the terms in each case.
| (a) 28 − 7 + 8 | = 28 + (−7) + 8 = 29 |
| (b) 39 − 2 × 6 + 11 | = 39 + (−2 × 6) + 11 = 39 − 12 + 11 = 38 |
| (c) 40 − 10 + 10 + 10 | = 40 − 10 + 10 + 10 = 50 |
| (d) 48 − 10 × 2 + 16 ÷ 2 | = 48 − 20 + 8 = 36 |
| (e) 6 × 3 − 4 × 8 × 5 | = 18 − 160 = −142 |
2. Write a story/situation for each expression and find its value.
(b) 5 × 12 − 6 = 54 — There are 5 boxes with 12 pencils each. 6 pencils are broken and removed. How many good pencils are left?
(c) 4 × 9 + 2 × 6 = 48 — There are 4 tables with 9 chairs each and 2 benches with 6 seats each. How many people can sit in all?
3. Write the expression, identify its terms, and find the value.
Expression: 100 × 2 + 100 ÷ 2 Terms: 100 × 2, 100 ÷ 2 Value = 200 + 50 = 250 coins
(b) Adult ticket = ₹40, Child ticket = ₹20
(i) 4 adults + 3 children: 4 × 40 + 3 × 20 = 160 + 60 = ₹220
(ii) Two groups of 3 adults each (6 adults): 6 × 40 = ₹240
(c) Window height — border 3 cm (top & bottom), grill 2 cm, gap 5 cm, repeated as shown:
Expression: 2 × 3 + 5 × 2 + 4 × 5 = 6 + 10 + 20 = 36 cm (based on the pattern of borders, grills and gaps shown in the picture)
✏️ Figure It Out – 2.3 (Page 118)
1. Fill in the blanks with numbers and boxes with operation signs so both sides are equal.
| (a) 24 + (6 − 4) = 24 + 6 − 4 |
| (b) 38 + (9 − 4) = 38 + 9 − 4 |
| (c) 24 − (6 + 4) = 24 − 6 − 4 |
| (d) 24 − 6 − 4 = 24 − 6 − 4 |
| (e) 27 − (8 + 3) = 27 − 8 − 3 |
| (f) 27 − (8 − 3) = 27 − 8 + 3 |
2. Remove the brackets and write the expression having the same value.
| (a) 14 + (12 + 10) = 14 + 12 + 10 |
| (b) 14 − (12 + 10) = 14 − 12 − 10 |
| (c) 14 + (12 − 10) = 14 + 12 − 10 |
| (d) 14 − (12 − 10) = 14 − 12 + 10 |
| (e) −14 + (12 − 10) = −14 + 12 − 10 |
| (f) 14 − (−12 − 10) = 14 + 12 + 10 |
3. Find the values. Are the two expressions equal? When?
(b) 16−(8−3) = 11 and (16−8)−3 = 5 → Not equal (terms differ in sign of the third term)
(c) 27−(18+4) = 5 and 27+(−18−4) = 5 → Equal (same terms: 27, −18, −4)
Two expressions are equal whenever they reduce to exactly the same terms, regardless of order or grouping.
4. Identify expressions with the same value (using understanding of terms, not evaluation).
(b) 87 − (46 + 109) has terms {87, −46, −109} = 87 − 46 − 109; and (87 − 46) + 109 has terms {87, −46, 109} = 87 − 46 + 109.
5. Add brackets so the expressions equal the given value. (Example: 65 − 18 + 12 = 35 → 65 − (18+12) = 35)
| (a) 34 − (9 + 12) = 13 |
| (b) 56 − (14 + 8) = 34 |
| (c) −22 − (12 + 10) + 22 = −22 |
6. Fill blanks using reasoning about terms.
(b) 207 − 68 = 210 − 71 (210 is 3 more than 207, so subtract 3 more: 68 + 3 = 71)
7. Using 2, 3, 5 with '+', '−' and brackets, generate different values.
8. Radhika subtracts 9 by subtracting 10 and adding 1 (e.g. 36 − 9 = 26 + 1).
(b) Similar strategies: to subtract 19, subtract 20 and add 1 (n − 19 = n − 20 + 1). To add 9, add 10 and subtract 1 (n + 9 = n + 10 − 1). To subtract 99, subtract 100 and add 1.
9. For a) 73 − 14 + 1 b) 73 − 14 − 1, identify which options equal each.
73 − 14 − 1 (terms 73, −14, −1) is equal to: (a) 73 − (14 + 1) and (d) 73 + (−14 − 1)
In-text question (Page 120): "If Satish also joins Phani and Prem and orders the same items, what is the expression for the total amount to be paid?"
✏️ Figure It Out – 2.4 (Page 126)
1. Fill in the blanks with numbers, and boxes with signs, so both sides are equal.
| (a) 3 × (6 + 7) = 3 × 6 + 3 × 7 |
| (b) (8 + 3) × 4 = 8 × 4 + 3 × 4 |
| (c) 3 × (5 + 8) = 3 × 5 + 3 × 8 |
| (d) (9 + 2) × 4 = 9 × 4 + 2 × 4 |
| (e) 3 × (5 + 4) = 3 × 5 + 3 × 4 |
| (f) (13 + 6) × 4 = 13 × 4 + 24 (i.e. 6 × 4) |
| (g) 3 × (5 + 2) = 3 × 5 + 3 × 2 |
| (h) (2 + 3) × 4 = 2 × 4 + 3 × 4 |
| (i) 5 × (9 − 2) = 5 × 9 − 5 × 2 |
| (j) (5 − 2) × 7 = 5 × 7 − 2 × 7 |
| (k) 5 × (8 − 3) = 5 × 8 − 5 × 3 |
| (l) (8 − 3) × 7 = 8 × 7 − 3 × 7 |
| (m) 5 × (12 − 4) = 5 × 12 − 5 × 4 |
| (n) (15 − 6) × 7 = 15 × 7 − 6 × 7 |
| (o) 5 × (9 − 4) = 5 × 9 − 5 × 4 |
| (p) (17 − 9) × 7 = 17 × 7 − 9 × 7 |
2. Fill '<', '>' or '=' by reasoning (not evaluating fully).
| (a) (8 − 3) × 29 > (3 − 8) × 29 |
| (b) 15 + 9 × 18 < (15 + 9) × 18 |
| (c) 23 × (17 − 9) < 23 × 17 + 23 × 9 |
| (d) (34 − 28) × 42 = 34 × 42 − 28 × 42 |
3. Other ways to make 14 using a × (b + c):
4. Find the sum of numbers in each picture in two different ways.
| 4 | 8 | 4 |
8 | 4 | 8 |
4 | 8 | 4 |
| 5 | 6 | 6 | 5 |
| 6 | 5 | 5 | 6 |
| 6 | 5 | 5 | 6 |
| 5 | 6 | 6 | 5 |
Grid 2 (Total = 88): Row-wise: 22 + 22 + 22 + 22 = 88. By colour: eight 5's and eight 6's → (8 × 5) + (8 × 6) = 40 + 48 = 88.
In-text question (Page 124): "5 × 4 + 5 × 3 = 5 × (4 + 3). Can you explain why? Is 5 × (4+3) = 5 × (3+4) = (3+4) × 5?"
Example 17 & 18 (Page 124):
Effective way to find 97 × 25 → 97 × 25 = (100 − 3) × 25 = 100×25 − 3×25 = 2500 − 75 = 2425
Using this method: (a) 95 × 8 = (100−5)×8 = 800−40 = 760 (b) 104 × 15 = (100+4)×15 = 1500+60 = 1560 (c) 49 × 50 = (50−1)×50 = 2500−50 = 2450
Yes, this method is much quicker than long multiplication for numbers close to a round number like 100 or 50.
✏️ Figure It Out – 2.5 (Page 128)
1. Write appropriate expressions and find their values.
Expression: 7 × 9 + 7 × 11 = 7 × (9 + 11) = 7 × 20 = 140 kg
(b) Bhanu earns ₹20,000/month; spends ₹5,000 + ₹5,000 + ₹2,000.
Monthly saving: 20000 − 5000 − 5000 − 2000 = ₹8,000
Yearly saving: (20000 − 5000 − 5000 − 2000) × 12 = 8000 × 12 = ₹96,000
(c) Snail climbs 3 cm by day, slips 2 cm by night — net gain 1 cm/day; post is 10 cm high.
Day 1: reaches 3, slips to 1. Day 2: reaches 4, slips to 2. Day 3: reaches 5, slips to 3 ... this continues until Day 8, when the snail climbs from 7 cm to 10 cm and reaches the top — it does not slip back once it gets the treat.
Answer: 8 days
2. Murari reads a 2-page story daily except Tuesday & Saturday. Stories completed in 8 weeks?
Matching expressions: (b) (7 − 2) × 8 and (g) 7 × 8 − 2 × 8 — both equal 40 (by the distributive property).
3. Find different ways of evaluating:
(b) 1−1+1−1+1−1+1−1+1−1 = (1−1)×5 = 0
4. Compare using '<', '>' or '=' by reasoning:
| (a) 49 − 7 + 8 > 49 − (7 + 8) |
| (b) 83 × 42 − 18 > 83 × 40 − 18 |
| (c) 145 − 17 × 8 < 145 − 17 × 6 |
| (d) 23 × 48 − 35 > 23 × (48 − 35) |
| (e) (16 − 11) × 12 = −11 × 12 + 16 × 12 |
| (f) (76 − 53) × 88 > 88 × (53 − 76) |
| (g) 25 × (42 + 16) = 25 × (43 + 15) |
| (h) 36 × (28 − 16) > 35 × (27 − 15) |
5. Identify which expressions equal the given expression, without full computation.
(b) 93 + 37 × 44 + 76 is equal to: (iv) 37 × 44 + 93 + 76 (same three terms, just reordered). Not equal to (i), (ii) or (iii), as they use different terms.
6. Choose a number and create ten expressions with that value.
🧩 It's Puzzle Time — Expression Engineer (Page 134)
Using four 4's, create expressions to get values 1 to 20:
| Value | Expression | Value | Expression |
|---|---|---|---|
| 1 | 44 ÷ 44 | 6 | 4 + (4+4) ÷ 4 |
| 2 | 4÷4 + 4÷4 | 7 | 4+4 − 4÷4 |
| 3 | (4+4+4) ÷ 4 | 8 | 4+4+4−4 |
| 4 | 4×(4−4)+4 | 9 | 4+4+4÷4 |
| 5 | (4×4+4) ÷ 4 | 10 | (44−4) ÷ 4 |
Values 11–20 are trickier with just four 4's and +, −, ×, ÷ — this is meant for open class exploration. Try combining "44" as a two-digit number, and check your expressions with a partner or teacher.
Using 1, 2, 3, 4, 5 exactly once with '+' and '−', get values between −10 and +10:
Using 0 to 9 exactly once, make an expression with value 100:
"What other similar interesting questions can you ask?" — This is open-ended; encourage students to invent and share their own number puzzles with classmates.
