Video: Estimating the Answer to Two-Step Word Problems

In one day, Jacob can decorate 17 cakes and Chloe can decorate 19. Pick the best estimate for the number of cakes they can decorate in 5 days. [A] 30 [B] 80 [C] 100 [D] 200 [E] 300

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Video Transcript

In one day, Jacob can decorate 17 cakes and Chloe can decorate 19. Pick the best estimate for the number of cakes they can decorate in five days. 30, 80, 100, 200, or 300.

This problem has three steps to it. Firstly, we’re told that Jacob can decorate 17 cakes every day. And Chloe can decorate 19. So in step one, we can add 17 and 19 together to find out how many cakes they can decorate altogether in one day. Seven plus nine equals 16. One ten plus one ten equals two tens plus the one we’ve exchanged equals three tens. So altogether, they can decorate 36 cakes in one day.

Now, we need to find out how many cakes they can decorate in five days. So you could think what we need to do is to multiply 36 by five. But we did say there were three steps to this problem, not two. And if we read the question carefully, we can see that we’re asked to pick the best estimate. In other words, we’re not being asked to calculate 36 multiplied by five. To help us estimate this amount, we could round 36 to the nearest multiple of 10. Now, we know 36 is in between 30 and 40. And it’s always useful to mark the midway point. Halfway between 30 and 40 is 35.

So if 35 is in the centre, where will 36 be? It’ll be around here. And so we can see that we can quickly round 36 up to 40. And so to quickly estimate the number of cakes that children can decorate in five days, we need to find five lots of 40. We can use a fact we already know to help here. Five lots of four are 20. And 40 is 10 times greater than four. So five lots of 40 must give an answer 10 times greater than 20, 200.

Another way we could’ve found exactly the same answer is by rounding before we began. We could’ve said, in one day, Jacob can decorate 17 cakes. Well, that’s around about 20. And Chloe can decorate 19. Well, that’s also around about 20. And so they can decorate around about 40 cakes every day. And so the calculation to find the estimate would still be five lots of 40.

The best estimate for the number of cakes the children can decorate in five days is five lots of 40, which is equal to 200.

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