What do you notice about the answers for Questions 11 and 13? Share in the grade.
Observation: Questions 11 and 13 have the same answer: rows 1, 3, 7, and 9.
Reason: These rows have all digits 0-9 appearing exactly once as ones digits.
Explanation: When all digits appear exactly once, 0 appears only once.
- Question 11 identifies rows with all digits
- Question 13 identifies rows where 0 appears only once
- Both conditions are satisfied by the same rows.
∴ The conditions are equivalent for rows 1-10 in the multiplication chart.
Explanation
The chapter helps students see the connection between Questions 11 and 13. If a row has all digits 0-9 appearing as ones digits (Question 11), then each digit appears exactly once, including 0 (Question 13). So rows 1, 3, 7, and 9 satisfy both conditions. This demonstrates a mathematical relationship: having all digits appear means each digit appears exactly once.
Solution Steps
Step 1: Question 11 asks for rows with all digits 0-9 as ones digits
Step 2: Question 13 asks for rows where 0 appears only once
Step 3: Both questions have the same answer: rows 1, 3, 7, 9
Step 4: This is because if all digits appear, each appears exactly once
Step 5: The conditions are equivalent for rows 1-10 in the multiplication chart