Missing Multipliers
Why do this problem?
This problem offers an opportunity for students to consider common factors while gaining fluency in multiplication facts. The interactivity engages students' curiosity and perseverance by challenging them to complete the grid using a minimum number of 'reveals'.
Multiplication tables are often presented with row and column headings filled in, with students challenged to fill in the products. This task inverts that concept, as students can reveal chosen products and work out possibilities for the headings.
Possible approach
If computers or tablets are available, students could work in pairs using the interactivity. Students could try a few examples to get the idea, and then work on the challenge of trying to find the grid headings by revealing as few cells as possible. Once they have developed some strategies, they could try the larger grids that include bigger numbers.
Key questions
Which numbers give lots of possibilities for row and column headings?
Can you find a way to work out the row and column headers using only 6 reveals?
Possible support
Mystery Matrix works in the same way, but some helpful cells have already been revealed.
Possible extension
Gabriel's Problem and Product Sudoku would make nice follow-up activities.
Related Collections
You may also like
Pebbles
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
It Figures
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Bracelets
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?