A little bit more/A little bit less

Prior knowledge

Background

This activity uses the multiplication strategy of rounding to a tidy number and then compensating.  Numbers can be rounded up or down to the nearest tidy number. Rounding down to the nearest tidy ten number is effectively using the place value strategy, for example 2 x 73 is (2 x 70) + (2 x 3) = 146.  When rounding up to a tidy number the compensation involves subtraction.  For example 8 x 29 = (8 x 30) - (8 x 1).  Students need to be careful to subtract 8 x 1 and not 29 x 1. Later examples in the activity involve rounding to 15 or 25

Number generalisation:

Ideas that can be developed from this activity:
Eg.
3 x 28 = 3 x 30 – 3 x 2
3 x a = 3 x (a + b) – 3 x b
3 x 31 = 3 x 30 + 3 x 1
3 x a = 3 x (a-b) + 3 x b

Comments on the Exercises

The exercises have been set up in the following way.
Exercises 1 – 7, Student has been given a tidy number statement eg 5 x 20 = 100 and they use this given fact to find the answer to eg 5 x 19 or 5 x 22 (by compensation – add on a little or subtract a little).