Question

A multiplication table. In the row labeled 3, the numbers 3, 6, 9, 12, 15, 18, 21, 23, and 27 are highlighted. In the row labeled 7, the numbers 7, 14, 21, 28, 35, 42, 49, 56, and 63 are highlighted.

Here the rows for 3 and 7 are highlighted. How would you find the multiple of 3 that would form a ratio with 35 that is equivalent to 3over7



1. Find 3,7,15,35 in the row for 7.
2. Follow the column up until you reach the row for 3,7,15,35.
3. The number 3,7,15,35.
forms a ratio to 35 that is equivalent to StartFraction 3 Over 7 EndFraction.

Answer 1

The table below shows all the products of pairs of numbers between 1 and 9.

Table1_d31d2c26d0e1b05f05fb2edbbd106bb4

Which numbers appear only once in the table of products? Where are these numbers located in the table? Why?

Which numbers appear the most frequently in the table? Why?

Which numbers between 10 and 20 do not appear in the table? What do these numbers have in common?

IM Commentary

The goal of this task is to encourage students to study the multiplication table, a familiar object, from a novel point of view. The table shows some, but not necessarily all, factorizations of different numbers. For example, 24 appears 4 times in the table:

24=3×8=8×3=6×4=4×6.

Step-by-step explanation: