February 8th, 2017
Today in Math we began using the estimation strategies that we learned in our Whole Numbers unit to help us estimate the answers to multiplication questions involving larger numbers. Today we focused on compatible numbers and compensation. Take the example below:
When trying to multiply 48 x 8 we can use a compatible number strategy to help us. We can change 48 to 50. 50 is a more compatible number because it ends in a zero. Why does that make it more compatible? Because we already know how to multiply by multiples of 10, 100, and 100! To solve 50 x 8 we can use the multiplication fact 5 x 8; since we know that 5 x 8 = 40, we know that 50 x 8 = 400 (just add a zero, or go up one place value place). Look at the example below:
Julia delivers 215 flyers each day. There are 7 days in a week. To discover how many flyers Julia delivers each week we can add 215 seven times OR we can use multiplication: 215 x 7. Since the question asks us, "about" how many flyers, we can use estimation. We can use compatible numbers. We can change 215 to 200. This is a multiple of 100 which is easier to use. When solving 200 x 7 we can use the multiplication fact 2 x 7. Since we know that 2 x 7 = 14, we know that 2 x 7 = 1400 (just add 2 zeroes, or move up two place value places). We can also use compensation to help us:
A jug fills 38 glasses. There are 52 jugs. To discover how many glasses can be filled we can add 38 fifty-two times, or we can use multiplication: 38 x 52. Since the question says, "about" how many glasses, we can use estimation. We can round 38 up to the more compatible 40. We can round 52 down to the more compatible 50. This is a compensation strategy. When solving 40 x 50 we can use 4 x 5 = 20, which helps us to know that 40 x 50 = 2 000 (just add 2 zeroes, or move up 2 place value places).