Ganita Prakash, period by period — fitted to your timetable.
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Rakesh's Puzzle: Hunting Pairs by Guess-and-Check
A Quick Recap of Integers · Discovery
Systematic tabulation — not formula — is the method here; watch for students who try to set up an equation rather than guess-and-check, and redirect them to the table. A common error is treating a negative difference as simply 'the smaller minus the larger', losing the sign; the partner game surfaces this quickly. Example 1 at section 10.2 p.35 extends signed arithmetic to scoring contexts and makes a good private read.
0–8Open with Rakesh's puzzle: two numbers have sum 25 and difference 11 — who are they? Students record guesses in a four-column table (first number, second number, sum, difference) and adjust systematically until both conditions are met, arriving at 18 and 7.
8–18Pose the twist: sum 25, difference -11. Students notice that swapping the pair (7 and 18) satisfies the new condition; they articulate why the swap works rather than recalculating from scratch.
18–32Figure it Out, section 10.1 p.25 ("find pairs of numbers from their sums and differences....") — students work in pairs through items (a)–(f), paying particular attention to cases where the sum or difference is negative, recording each pair's guess-and-check table.
32–40Pairs try the partner guessing game from Figure it Out, section 10.1 p.25: one partner secretly picks two integers, announces the sum and difference, and the other hunts the pair. Class shares one surprising case where a negative difference confused them.
Figure it Out, section 10.1 p.25 — Find pairs of numbers from their sums and differences: (a) Sum 27, Diff 9; (b) Sum 4, Diff 12; (c) Sum 0, Diff 10; (d) Sum 0, Diff -10; (e) Sum -7, Diff -1; (f) Sum -7, Diff -13. Then play the sum-and-difference guessing game with a partner.
Two integers have a sum of 0 and a difference of 10. Which of the following is the correct pair?
- A 10 and 0
- B 5 and 5
- C 5 and −5
- D −10 and 0
C. 5 and −5
What each wrong option reveals
- A The student found a pair with difference 10 and sum 10, not sum 0; the sign of the second number was not considered.
- B The student found a pair that sums to 10 (or equals 10) rather than a pair that sums to 0, confusing the two conditions.
- D The student correctly identified a zero-sum pair but reversed the sign assignment, giving difference −10 instead of 10.
Also saved as 7 periods or 10 periods.
- 2Carrom Coin on a Number Line: Direction and Distance
A Quick Recap of Integers - 3Token Model: Adding Zero Pairs to Subtract Integers
A Quick Recap of Integers - 4Token Bags and the Four Sign Cases for Multiplication
Multiplication of Integers - 5Multiplication Patterns Confirm the Sign Rules
Multiplication of Integers - 6Worked Contexts: Exam Marks and the Mining Shaft
Multiplication of Integers - 7Division Sign Rules and Real-World Rate Problems
Multiplication of Integers - 8Commutativity, Associativity, and Distributivity of Integer Multiplication
Multiplication of Integers - 9Sign of Many-Factor Products and Negation by Multiplication
Multiplication of Integers - 10Scoring Contexts, Pibs Currency, and Order of Signed Expressions
Multiplication of Integers - 11Complex Expressions, Pattern Machines, and Maximum-Minimum Tasks
Multiplication of Integers - 12Four Problems, One Chapter: Integers at Work
Synthesis
- 1. Large Numbers Around Us
- 2. Arithmetic Expressions
- 3. A Peek Beyond the Point
- 4. Expressions Using Letter-Numbers
- 5. Parallel and Intersecting Lines
- 6. Number Play
- 7. A Tale of Three Intersecting Lines
- 8. Working with Fractions
- 9. Geometric Twins
- 10. Operations with Integers
- 11. Finding Common Ground
- 12. Another Peek Beyond the Point
- 13. Connecting the Dots
- 14. Constructions and Tilings
- 15. Finding the Unknown
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