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Hi, everybody.

It's Miss Hill here.

Today, we are going to be applying all of our place value knowledge to open-ended questions.

So, let's get started.

Put on your hats.

Tighten your ties.

And tell the computer now I'm a mathematician! Super job, everybody.

I'm happy that we're all together, and we go looking at our lesson agenda today.

So we have a quick do now before we start our lesson before looking into open-ended problems. We'll do it together, and it'll be your turn.

So, as always, before we begin, please make sure you have a pencil, a piece of paper, and a ruler in front of you as you will need them today.

If you need to, you can pause this video and go get your resources.

Perfect, let's get started.

So here is a quick do now for you.

Each circle stands for five pieces of fruit.

A fruit shop sold some fruit.

How many plums did they sell? Which two fruits sold the same amount? Which fruit was the most popular? How many pineapples and oranges were sold together? And what is the difference between the number of apples sold and the number of plums sold? So pause this video and answer the questions.

Great job, everybody.

So if we know that each circle stands for five pieces of fruit, we know that in the plums, they sold 10, because two times five is equal to 10.

Which two fruits sold the same amount? Well, we can see the apples and oranges both sold 20 pieces of fruit.

Which fruit was the most popular? Bananas is the most popular by far.

How many pineapples and oranges are sold together? 35 were.

As you can see, there are seven circles, and seven times five is equal to 35.

And what's the difference between the number of apples sold and the number of plums sold? Well, apples, we can see 20 pieces of fruit were sold, and plums, only 10 pieces of fruit were sold, and 20 take away 10 is equal to 10.

Great job.

Here we go.

This is our first problem solving question.

I wrote down a number with one zero in it, but I can't remember what the number was.

All I remember is that it was between 600 and 700.

What number could it be? Well, it could be anywhere from between 601, as we know that has one zero and it's between 600 and 700, but it could also be 790 because that's between 600 and 700 and it's got one zero in it.

The joy of problem solving is that that is a problem and we need to solve it, and 'cause it's open-ended questions there could be lots of different answers.

These are some of the questions, sorry, these are some of the answers that I came up when I was thinking about this.

As you can see, there's quite a lot of answers, so we could pick any of these and write them down as our answer.

Now it's your turn.

What numbers can you make that are less than 500 and have a six in the tens column? Before you make them, can you predict how many there are? I need to give you an idea.

So if we have our hundreds, tens, and ones column, like this, there must be a six in this column, but these two numbers, it's up to you, because the number just has to be less than 500.

So I might choose to do 461, or I might could do 369.

It's up to you.

How many do you think there will be? Have a think.

Pause this video, and can you write those numbers that are less than 500 and have a six in the tens column? Good luck.

Now, I did this question too, and these are all of the ones that I came up with, and as you can see, there's a lot.

Now, I wonder, is the numbers you came up with the same? Pause the video and do some ticking and fixing.

Super duper.

So this is your independent task today.

You have two open-ended questions.

A number has been rounded to 600.

What could the original number have been? Can you find all of the possibilities? Does it matter if you round it to the nearest multiple of 10 or 100? Question two, what numbers can you make using the digits one, seven, and eight? Can you find all of the possibilities? So what you need to do now is pause this video and do some investigating.

Welcome back.

Now, I've been having a think about this question too.

A number's been rounded to 600.

What could the original number have been? Now, when we use our rounding, we have a song.

One to four, we hit the floor, and five to nine, we reach up high.

So, any number that could have been raised, rounded to 600 we know could be from 550 all the way up to 599, but that's not it, is it? There's more.

All the numbers from 649 and down to 601 could have been rounded to 600, and that is a lot of numbers.

Does it matter if you rounded to the nearest multiple of 10 or 100? It doesn't matter, because for 550 we've rounded to the nearest hundred, but for example, 599, we would have rounded to the nearest multiple of 10.

So if you have any of these answers in between here, great job, well done! Question two, what numbers can you make using the digits one, seven, and eight? Can you find all the possibilities? Now, I'd be interested to see what you could find, 'cause I found 178, 718, 187, 781, 817, and 871.

Are there any more than that? I couldn't think of any more, but I'd be interested to see what you could do, 'cause when we're using three digit numbers, those are the only possibilities that we can find.

I hope you enjoyed today's lesson.

It's really good to have a little tickle of that brain sometimes, isn't it? That was a lot of fun.

If you'd like to, please share, please ask your parents or carer to share your work on Instagram, Facebook, or Twitter tagging @OakNational and #LearnwithOak.

Hope to see you again soon.