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This activity could just be a warm-up, to draw a class into some mathematical thinking at the start of the lesson. Or it could be the first example of a more open investigation based on place value.
If I did want to make this a more extended activity I might begin with the "
X marks the Spot" puzzle as an example, let the class together try it and discuss it, then invite children to create a puzzle like this for themselves, but to start with something simpler: Multiply two numbers, hide a few digits, then swap
with a friend. Try each other's puzzle, check and discuss together, then share puzzles with other pairs.
There's lots to discuss, of course, but I would want to include consideration of puzzles that have more than one solution.
If none arise naturally from the class, I'd ask them to find the most digits that can be removed until a solution is no longer unique.
Differentiation by challenge is easy enough to achieve. I can control the size of the numbers that children use, and also vary the balance between the use of reasoning and trial and error.
Notes on the construction of X marks the Spot :
For help with Spinners, look back at
October 02 . Increment buttons are very easy to insert and keep attention on the changing numbers, instead of the keyboard.
I have used
Conditional Formatting to create a colour change ( to bright red ) when the right answer occurs. And have also used Conditional Formatting to conceal the ten-millions digit if it's zero ( font colour matched to background ) , and also to turn the border on or off for that cell.
Cell K6 does the multiplication, before the digit boxes each receive their correct value from the digits in that result. Although column & row headers have been turned off in Tools/Options/View, the location reference for the current cell can still be seen beside the Formula bar, immediately above the worksheet.
The individual digits are isolated using the INT function. INT takes just the integer part of a value and ignores the rest, for example INT of 3.845 is just 3. Using G2 as an example, this cell calculates the hundreds digit with the formula : = INT ( $K$6 / 100 ) - 10 * INT ( $K$6 / 1000 ) K6 was only made an absolute reference, $K$6 , to help me copy a basic formula across all the cells for
digits and then just adjust the number of zeros required in each formula. INT ( K6 / 100 ) calculates the number of whole hundreds in the multiplication product. And from this I need to subtract 10 times the number of whole thousands in the product.
This technique of isolating digits was also used in the
Happy Numbers investigation.