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MathBait™ Multiplication

A Riddle (Part 2)

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Help students explore multiples and common multiples to increase fluency with this warm up sure to spark discussion.


Resource Type

Warm Up

Primary Topic








Begin by drawing a 2 by 2 grid with row and column headers for students to see. Place a 6 and 9 in the first row and an 18 in the second blank of the second row. Explain this is just like the multiplication table. The numbers to the left tell us what we are counting by and the numbers on the top tell us how many we have counted.

2 by 2 grid showing empty headers with 6 and 9 in the first row and a blank space followed by 18 in the second

To solve this riddle students may notice that to achieve 9 they must be counting by 1, 3, or 9. They can eliminate 9 from the first row entry as they cannot count by 9's and reach 6. Therefore, the first row entry must be a 1 or a 3. From there, they should be able to fill in the rest of the table.

column head 6 and 9, row head 1 and 2, table contains the product of each row and column
column head 2 and 3, row head 3 and 6, table contains the product of each row and column

An alternative strategy is to consider what 9 and 18 have in common. We can reach both 9 and 18 by counting by 9's or by counting by 3's, so the top of this column must be a 3 or a 9. Similarly, 6 and 9 can be found by counting by 1's or by 3's.

Provide students with time to try to find the missing values and allow them to share their thoughts and strategies.

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