These exercises and activities are for students to use independently of the teacher to practise number properties.
solve multiplication problems by rounding up to a tidy number and then compensating
solve multiplication problems by rounding down to a tidy number and then compensating
Multiplication and Division, AM (Stage 7)
Practice exercises with answers (PDF or Word)
Prior knowledge
Multiply basic facts with tens, hundreds and thousands eg 3 x 60, 5 x 200
Recall addition and subtraction basic facts
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).
Exercise 2
Exercise 3
Asks students to multiply by a “ten number”. Add on a little, value added could be more than ten.
Exercise 4
Asks students to multiply by a “ten number”. Subtract a little, value subtracted could be more than ten.
Exercise 5
Exercise 6
Asks students to multiply by a “hundred number”. Subtract a little, value subtracted could be more than ten.
Exercise 7
Exercise 8
Asks students to make up their own problems that use the same strategy.