A book I had forgotton..

I suddenly remembered a book I had used a few years ago for ideas for open-ended investigations (It All Adds Up by Penny Skinner).  It includes worked examples from students of investigations and Maths Reports and gives some ideas for pedagogical practices that fit with the course.

Here are some examples you could try:
Addtition
What happens when you add numbers ending in 9 to numbers ending in 3?
Investgate what happens when you add 2-digit palndromes such as 66+ 77 or 77+88+99
Investigate what happens when you add 3 consecutive numbers or  3 consecutive even numbers or 3 consecutive odd numbers:

Investigate what happens when you begin with any 3 digit number, reverse it and add to the orginal. Repeat until you have a palindrome.

Subtraction
Wht happens when:

• you subtract a number ending in 7 from a number ending in2?
• you subtract a number  ending in 25 from a number ending in 26 eg 426-225?
• you subtract a number  ending in 26 from a number ending in 25 eg 525-126?

Using the digits 1,2,3 and 4 once only. make pairs of 2 digit numbers and find their differences eg 43-12. Which pair give the smallent difference and which the largest?

Choose 3 different digits and form a number beginning with largest and finishing with smallest. Write the number in reverse and subtract eg 832-238. Now reverse the answer and add it to the answer, so
832-
238
594 +
495
1089
Try it!

Multiplication
Investigate what happens when you multiply:

• numbers ending in 4 by 6
• a number ending in 13 (113, 213) by 6
• 142857 by any single digit number up to 7
• a number ending in 7 by 13

Investigate multiplying odd numbers by odd numbers, odd by even, even by even
Investigate the series: 11x18, 21x18, 31x18...
Investigate the multiples of 99

Decimals
Use a calculator to convert sevenths to a decimal 1/7=, 2/7=, 3/7= etc.
What do you notice?

Let me know if you want to borrow the book!