Learning Objective: Model positive and negative integers using floors above and below ground level in Bela's Building of Fun.
Starting floor plus button presses determines the target floor: Starting Floor + Movement = Target Floor.
Start at Floor +1 and press +2 to reach Floor +3 (Book Store).
Floors above ground are positive, floors below ground are negative, and ground level is Floor 0.
Vertical building floors provide a real-world model for addition and subtraction of integers.
Learning Objective: Visualize integer addition and subtraction as walking forward (positive) or backward (negative) along an infinite number line.
Starting Number + Movement = Target Number. Positive moves right, negative moves left.
Start at 3 and move -5 steps to land at -2.
Smaller numbers lie to the left of bigger numbers on the number line.
The number line extends symmetrically on both sides of zero.
Learning Objective: Add and subtract integers using green (positive) and red (negative) tokens that form 'zero pairs'.
One positive token and one negative token combine to make a 'zero pair'.
Set +5 and -3 to see 3 zero pairs cancel out, leaving +2.
Remaining uncancelled tokens determine the final integer sign and value.
Zero pairs provide an intuitive physical model for integer arithmetic.
Counting numbers (1, 2, 3, 4...) and zero are not the only numbers. Numbers can also exist to the left of zero on the number line, called negative numbers. Positive numbers, negative numbers, and zero together are called integers.
The ground floor is Floor 0 (Welcome Hall). Floors above ground are positive (+1, +2...), and floors below ground are negative (-1, -2...). Zero is neither positive nor negative.
Page 243: What do you press to go four floors up? What do you press to go three floors down?
Answer: To go four floors up, press ++++ or +4. To go three floors down, press ---- or -3.
Page 245, Q1. You start from Floor +2 and press -3 in the lift. Where will you reach? Write an expression for this movement.
Answer: (+2) + (-3) = -1 (Toy Store).
Page 245, Q2. Evaluate these expressions: (a) (+1)+(+4) (b) (+4)+(+1) (c) (+4)+(-3) (d) (-1)+(+2) (e) (-1)+(+1) (f) 0+(+2) (g) 0+(-2).
Answer: (a) +5 (b) +5 (c) +1 (d) +1 (e) 0 (f) +2 (g) -2.
Page 245, Q3. Starting from different floors, find movements required to reach Floor -5.
Answer: +1 + (-6) = -5; -2 + (-3) = -5; 0 + (-5) = -5.
Page 246: Evaluate expressions for combining button presses: (a) (+1)+(+4) (b) (+4)+(+1) (c) (+4)+(-3)+(-2) (d) (-1)+(+2)+(-3).
Answer: (a) +5 (b) +5 (c) -1 (d) -2.
Every number has an additive inverse that cancels it back to zero (e.g., inverse of +3 is -3, and (+3) + (-3) = 0). Negative numbers are always less than zero, and positive numbers are always greater than zero.
Subtraction can be interpreted as 'making equal' or finding the missing number to be added (Target Floor - Starting Floor = Movement needed). Subtracting a negative number is the same as adding the corresponding positive number.
Page 247, Q1 & Q2. Compare numbers using Building of Fun (< or >).
Answer: (-2) < (+5); (-5) < (+4); (-5) < (-3); (+6) > (-6); 0 > (-4); 0 < (+4).
Page 247, Q3 & Q4. Floor labeling and marker positioning.
Answer: B = -9, C = -6, F = +2, G = +6, H = +11.
Page 249: Complete subtraction expressions.
Answer: (+1)-(+4) = -3; (0)-(+2) = -2; (+4)-(+1) = +3; (0)-(-2) = +2; (+4)-(-3) = +7; (-4)-(-3) = -1; (-1)-(+2) = -3; (-2)-(-2) = 0; (-1)-(+1) = -2; (+3)-(-3) = +6.
Page 251: Complete expressions for larger numbers in mineshaft.
Answer: (+40) + (+160) = +200; (+40) + (-240) = -200; etc.
Page 253, Q1, Q3 & Q4. Number line markings and comparisons.
Answer: 2 > -3 because 2 is to the right of -3; -2 < 3 because 3 is to the right of -2.
Positive (green) and negative (red) tokens can be used to add and subtract integers. A positive token and a negative token combine to make a zero pair, which has a net value of zero.
Page 257, Q1 & Q2. Complete additions using tokens and cancel zero pairs.
Answer: (+6)+(+4) = +10; (-3)+(-2) = -5; (+5)+(-7) = -2; (-2)+(+6) = +4.
Page 258, Q1 & Q2. Evaluate differences using tokens.
Answer: (+10)-(+7) = +3; (-8)-(-4) = -4; (-9)-(-4) = -5; (+9)-(+12) = -3; (-5)-(-7) = +2; (-2)-(-6) = +4.
Page 259, Q1 & Q2. Subtract with zero pair additions (-3 - (+5)).
Answer: -8 (requires putting in 5 zero pairs).
Integers appear in real-world contexts such as banking (credits as positive, debits as negative), geographical cross-sections (heights above sea level as positive, depths below as negative), and temperature measurements (Celsius degrees above and below freezing point of water, 0°C).
Page 260, Q1 & Q2. Bank account balance calculations with credits and debits.
Answer: Q1 Balance = -30.
Page 261, Q1. Geographical cross-section heights labeling.
Answer: A = +1500m, B = -500m, C = +300m, D = -1200m, E = +1200m, F = -200m, G = +100m.
Page 262, Q2. Match Leh temperature readings with times of day.
Answer: 14°C at 02:00 p.m.; 8°C at 11:00 a.m.; -2°C at 11:00 p.m.; -4°C at 02:00 a.m.
Integer grids can be explored for 'border sums' where rows and columns add up to equal totals. Historically, negative numbers and zero were first formalized in ancient India and China for accounting, and Brahmagupta gave explicit rules for operations on all numbers in 628 CE.
Brahmagupta defined rules for adding and subtracting positives, negatives, and zero, forming the foundation of modern arithmetic.
Page 263, Q1 & Q2. Hollow integer grids border sum calculations and completions.
Answer: Verified border sums equal to 0, +4, -2, and -4.
Page 265-266, Q1 through Q9. Ordering integers, dice sums, sequencing, and expression evaluations.
Answer: Fully verified solutions matching chapter review standards.