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I can solve one and two-step problems in different contexts.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

When a part is missing, subtract the other part from the whole.
When the whole is missing, add the parts together.
Look for the strategy which is most efficient.

Common misconception

Pupils may try to solve problems without thinking about the numbers involved.

Encourage pupils to look at the calculations and think about the numbers involved. Pupils may not get the most efficient method first time so encourage them to think about their responses and learn from what other children have done.

Keywords

Efficient - Working efficiently means finding a way to solve a problem quickly whilst also maintaining accuracy.

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Hello there.

My name is Mr. Goldie and welcome to today's maths lesson.

And here is our lesson outcome.

I can solve one and two-step problems in different contexts.

And here's our keyword for today.

Just one keyword.

I'm gonna say the keyword.

Can you repeat it back? The key word is efficient.

Let's look at what that word means.

Being efficient means finding a way to solve a problem quickly, whilst also maintaining accuracy.

So it's about doing something quickly, but getting it right, getting the correct answer as well.

And here's our lesson outline.

So the first part of the lesson is solving missing number problems, and the second part of the lesson is solving word problems. Let's get started.

In this lesson, you will meet Lucas and Izzy and they're going to be helping you with your maths today.

Izzy and Lucas are solving missing number problems. We are going to work out missing numbers in different problems efficiently.

So remember that means working quickly, but getting the right answer.

Each number matches a letter.

We have to work out the hidden word.

So there's the 26 letters of the alphabet and each of them has been given a number.

Now, every time you work out an answer, that will give you one of the letters, and the letters go together to make a missing word.

The hidden word is a type of animal.

Izzy and Lucas start on the first problem.

So the first problem is 96, subtract something, equals 70.

\"How should we calculate the missing number?\" Says Izzy.

\"When a part is missing, subtract the other part from the whole.\" Says Lucas.

So Lucas rearranges that calculation to be 96 subtract 70 equals our mystery number.

\"I'm going to represent the problem with base 10 blocks and a bar model.\" Says Izzy.

Here's the base 10 blocks and Izzy subtracts 70, and that gets her the answer.

And Izzy also represents it as a bar model.

96 is the whole, and 70 is one of the parts.

The other part is 26.

96 subtract 26 equals 70.

\"26 gives us the letter N.\" Lucas and Izzy have worked out the first letter of the missing word.

It's an N.

Izzy and Lucas look at the next problem.

A number, subtract four, equals 27.

\"How can we calculate the missing number?\" Says Izzy.

\"When a whole is missing, add the parts together.\" Says Lucas.

So the calculation would be 27, add four, add the two parts together, and that gives you the whole.

27 add three equals 30.

27 add three add one equals 31.

So Izzy knows that four is one more than three and 27 add four is equal to 27 add three add one.

So 27 add four equals 31.

31 subtract four equals 27.

31 gives us the letter P.

So the next letter they've got is a P.

So, so far they've got N and a P.

Izzy and Lucas look at the next problem.

So we've got a missing number, add 236 equals 240.

\"When a part is missing, subtract the other part from the whole.\" Says Izzy.

Izzy thinks it's best to do the subtraction 240 subtract 236, and that will give the missing number.

Lucas says, \"236 and 240 are close together.

Adding on from 236 to 240 is an efficient way to get the answer.\" So Izzy's method would give her the right answer, but it's not the quickest way of getting the right answer.

So Lucas says, \"236 add our mystery number equals 240\" is a much quicker way of working it out.

\"So six add four equals 10.\" Says Izzy.

36 add 4 equals 40, so 236 add four equals 240.

So the missing number is four.

240 subtract 236 equals four, and four add 236 equals 240.

\"Four gives us the letter D.\" So the next letter is D.

So, so far they've got the letters, N, P, and D.

Izzy and Lucas look at the next problem.

354 subtract 100, add something, equals 255.

\"This looks like a tricky problem.\" Says Izzy.

\"Let's start by calculating 354 subtract 100.\" Says Lucas.

So 354 subtract 100 equals 254.

\"Then we just have to add one to equal 255.\" Says Izzy.

254 add one equals 255.

So the missing number is one.

\"One gives us the letter A.\" Says Lucas.

So which letters have they got so far? They've got N, a P, a D, and an A.

Here's a problem for you to try on your own.

Find the missing number in an efficient way.

So here's your calculation, mystery number add 366 equals 367.

How will you solve the problem? Pause the video and see if you can work out the missing number.

And welcome back.

Did you get an answer? Is it the right answer? Did you work it out in an efficient way? Let's have a look to see how you did it.

So Lucas says, \"When a part is missing, you can subtract the other part from the whole.\" So you could do the subtraction calculation, 367 subtract 366, and that would give you the right answer.

Izzy says though, \"366 and 367 are very close together.

It's more efficient to start on 366 and add on until you get to 367.\" So what number do you have to add to 366 to get to 367? The answer is one.

So the missing number is one.

367 subtract 366 is also one, but adding on is a much more efficient and quick way of getting the right answer.

\"One gives the letter A.\" Says Lucas.

So very well done if you wrote out that one was the right answer.

Very, very well done indeed if you worked it out in an efficient way, probably by adding on to find the difference.

Izzy and Lucas now have all five letters.

N, P, D, A, A.

\"That's not an animal!\" Says Lucas, who's absolutely right.

That definitely isn't an animal.

\"I think we need to reorder the letters to spell out an animal.\" Says Izzy.

Very sensible, Izzy.

So N, P, D, A, A.

Could you rearrange those letters to make a name of an animal? You could rearrange them into panda.

Oh! The mystery animal is a panda! So you see how it works.

You have to work out the clues, that gives you some letters, and then you have to rearrange the letters into the name of an animal.

So your task is to work out the mystery animal by finding the missing numbers.

So you've got five missing numbers to find there.

Each of those will give you a letter, and then you've got to rearrange the letters into the name of an animal.

There are two animals which are hidden.

Can you work out both animals? So pause the video and have a go at task A.

And welcome back.

Did you manage to find the two mystery animals? Let's have a look to see whether you got them right.

So here are the answers for A.

So you had five mystery numbers.

Each of those five numbers corresponded to a letter.

So I gave you the letters, L, S, I, N, A, and then you had to rearrange that into the name of an animal.

So the animal was snail.

\"My favourite animal.\" Says Izzy.

So the first mystery animal was snail.

Let's have a look at the next one.

So there are the answers for those five calculations, those five missing numbers, and they corresponded to the letters G, E, I, R, T.

That's spelled out the name of an animal, and the mystery animal was tiger.

So very well done if you managed to solve one of those.

Excellent work, if you managed to do both.

Very well done indeed.

And let's move on to part two of the lesson.

So part two of the lesson is solving word problems. Izzy and Lucas are calculating the answers to word problems. \"We have to work out what the calculation is.\" Says Izzy.

Each number matches a letter.

We have to work out the name of an animal.

So this time it's a little bit trickier because you've also got to work out what the calculation is before you can work out what the missing number is.

So here's our first problem.

35 snails are on a log.

Some snails creep away.

There are now 28 snails on the log.

How many snails crept away? \"What calculation should I write?\" Says Izzy.

There are 35 snails on a log.

Some snails creep away and there are now 28 snails left on the log.

The calculation would be 35, subtract our missing number, equals 28.

There were 35 snails and now there are 28.

\"When a part is missing, subtract the other part from the whole.\" Says Lucas.

So we can turn that calculation around to be 35 subtract 28.

\"Adding on from 28 to 35 might be a more efficient way of finding the answer.\" Says Lucas.

So rather than subtracting, you could add on to find the number.

So you could do 28 add something equals 35.

The answer is 7.

28 add two equals 30, add five more, we get 35.

So 35 subtract 28 is also seven.

So altogether, seven snails crept away.

\"Seven gives us the letter F.\" So Izzy and Lucas have worked out the first letter for this mystery animal.

Let's look at the next problem.

18 people are on a bus.

At the next stop, 17 people get on and 16 people get off.

How many people are on the bus? \"What calculation should I write?\" Says Izzy.

So there are 18 people on the bus, 17 people get on, 16 people get off.

So the calculation would be 18 add 17 subtract 16.

But there's an easier way of calculating the answer rather than starting on 18 and adding 17, and then subtracting 16.

We can look at the addend and the subtrahend.

Lucas says, \"We can work efficiently by looking carefully at the calculation.

17 is added and 16 is subtracted.\" If 17 people get on the bus and 16 people get off the bus, that's the same really as one person getting on the bus.

17 subtract 16 equals one.

So a more efficient way of calculating the answer would be 18 add one equals 19.

So the answer to 18 add 17 subtract 16 is 19.

\"19 gives us the letter L.\" Says Lucas.

Let's look at the next problem.

276 people are on a train.

Some people get off at the next stop.

There are 120 people still on the train.

How many people got off? \"What calculation should I write?\" Says Izzy.

There are 276 people on a train, some people get off, there are 120 people left on the train.

So the calculation would be 276 subtract something, subtract our number, equals 120.

So we don't how many people got off the train.

How would you work out the missing number? \"When a part is missing, subtract the other part from the whole.\" Says Lucas.

So we could rearrange that calculation into 276 subtract 120.

So what is 276 subtract 120? Well 276 subtract 100 is 176, and then you've got to take away twenty.

166, 156.

So the answer is 156.

276 subtract 156 equals 120.

\"156 gives us the letter W.\" Says Lucas.

And here's one to try on your own.

Pedro has a bowl of 306 cherries.

It's quite a big bowl of cherries for a panda.

I'm sure Pedro is quite excited to see this.

He eats some.

Glad he didn't eat all of them.

There are 276 cherries left in the bowl.

How many did Pedro eat? What calculation should you write? How will you work out the answer? Pause the video and see if you can work out how many cherries Pedro ate.

And welcome back.

Did you manage to find the answer? Did you manage to work out the answer in an efficient way? Let's have a look.

We are trying to work out the missing number, how many Petro ate.

Lucas says, \"You could subtract the known part from the whole.\" So you could change the calculation around to be 306 subtract 276, but \"adding on to find the difference might be more efficient.\" So you could calculate 306 subtract 276, but it's probably easier to do 276 add something equals 306.

So start from 276 and add on until you get to 306.

Well 270 add 30 equals 300, so 276 add 30 must equal 306.

So the missing number is 30.

306 subtract 276 equals 30.

Our missing number is 30.

30 gives us the letter O.

Very well done if you've got the missing number there.

30.

Izzy and Lucas now have all four letters.

So they can now work out the name of the mystery animal.

\"We need to reorder the letters to spell out an animal.\" F, L, W, O.

\"Is a flow an animal?\" Says Lucas.

So we can reorder it into flow.

I'm not sure about that, Lucas.

\"I think the mystery animal is a wolf!\" Says Izzy.

So we can rearrange the letters again to make wolf.

Well done, Izzy and Lucas.

Our mystery animal is a wolf, so let's get started on task B.

So work out the mystery animal by finding the missing numbers.

So for task B, you've got to read the questions carefully, you've got to work out what the calculation is, and you've gotta think about the most efficient way you can do of solving that problem.

There are four questions altogether and they give you four different numbers, which will correspond to four different letters, which then give you the name of an animal.

So one A says, \"There are 401 people on a train.

At the next stop, some people get off.

There are now 396 people on the train.

How many people got off?\" There are four questions altogether, and your mystery animal has four letters in its name.

So pause the video and see if you can work out the name of the mystery animal.

And welcome back.

Did you manage to solve all the problems? Did you work out what the four letters were? Did you work out the name of the mystery animal? Very well done if you did.

Let's take a look to see if you were right.

So here are the answers for task B.

So our first question says, \"There are 401 people on a train.

At the next stop some people get off and there are now 396 people on the train.

How many people got off?\" So the answer is five.

Five people got off.

You could have calculated that as a subtraction, but it's probably easier to start with 396 and add on to get to 401 because the numbers are close together.

Let's look at question B.

There are some cherries in a bowl.

Pedro eats 99 of them and there are 57 left.

My goodness me.

He must've been hungry.

How many cherries were in the bowl to start with? So that's a question where you've got the two parts, but you're looking for the missing whole.

To find the missing whole, you have to add the parts together.

So 57 add 99, or 99 add 57.

Well 57 add 100 is 157, so 57 add 99 must equal 156.

The answer is 156.

Now that's written as a subtraction calculation, but of course, hopefully you added the numbers together to get the answer.

Pedro has done 380 star jumps in a week.

Probably burning off all those calories from eating those cherries.

He does some more and reaches a total of 406.

How many more did he do? So he's done 380 and we are trying to work out the difference between 380 and 406.

380 add 26 equals 406, so he did 26 more.

And our last problem, problem D, there are 29 people on a train.

At the next stop 96 more people get on the train and 86 people get off the train.

How many people are on the train now? So the calculation is 29 add 96 subtract 86, and the answer is 39, but hopefully you thought carefully about the addend and the subtrahend and thought, \"When 96 is being added, and 86 is being subtracted, that is the same as adding 10.\" And 29 add 10 equals 39.

So very well done if you managed to work out those four answers, and that gave you the letters E, W, N, and T, and you should then be able to rearrange those into the name of an animal.

You can rearrange them into the word went.

Went is not an animal.

The animal was in fact newt.

So the mystery animal is newt.

Very well done if you worked that out, and excellent work today.

I hope you're feeling much more confident at solving a range of problems in an efficient way, thinking very carefully about the strategy that you are going to use to give you the answer efficiently, making sure that you have the correct answer.

Excellent work today.

Very well done.

And let's move on to our lesson summary.

So when a part is missing, subtract the other part from the whole.

If the numbers are close together, add on to find the difference.

When the whole is missing, add the parts together.

Think carefully about which solution is most efficient.

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+ 298 = 301" }, "questionType": "Multiple choice", "correct": [ { "text": "Add on from 298 to 301" } ], "choices": [ { "text": "Add 301 and 298 together" }, { "text": "Subtract 298 from 301" }, { "text": "Add on from 298 to 301" } ], "id": "0144811c-4b6f-1136-c9f0-8ace22dad87a", "lessonId": "d88d8c72-4025-dca7-b0ae-23b29a3b8a55" }, { "type": "Question", "question": { "text": "Find the missing number.

\\square

− 7 = 37" }, "questionType": "Multiple choice", "correct": [ { "text": "44" } ], "choices": [ { "text": "30" }, { "text": "34" }, { "text": "43" }, { "text": "44" } ], "id": "e8209aad-2128-ebf6-10f3-7710ffd1e3de", "lessonId": "d88d8c72-4025-dca7-b0ae-23b29a3b8a55" }, { "type": "Question", "question": { "text": "Find the missing number. 41 − ______ = 11" }, "questionType": "Short answer", "correct": [ { "text": "30" }, { "text": "thirty" } ], "id": "4ac9812e-f227-a0c3-b0c6-a1d6521834b0", "lessonId": "d88d8c72-4025-dca7-b0ae-23b29a3b8a55" }, { "type": "Question", "question": { "text": "Find the missing number. 402 + 50 − ______ = 412" }, "questionType": "Short answer", "correct": [ { "text": "40" } ], "id": "874a907b-f08f-34ca-114a-7d78f7a766c2", "lessonId": "d88d8c72-4025-dca7-b0ae-23b29a3b8a55" }, { "type": "Question", "question": { "text": "41 snails are on a log. Some snails creep away. There are now 27 snails on the log. How many snails crept away? " }, "questionType": "Short answer", "correct": [ { "text": "14" }, { "text": "fourteen" } ], "id": "9398a1dd-90e4-e132-8ccd-23cf90fd05d9", "lessonId": "d88d8c72-4025-dca7-b0ae-23b29a3b8a55" }, { "type": "Question", "question": { "text": "285 people are on a train. At the next stop, 59 people get off and 60 get on. How many people are on the train now? " }, "questionType": "Short answer", "correct": [ { "text": "286" }, { "text": "two hundred and eighty-six" } ], "id": "1a295e0c-b5ec-5ba1-be91-1618cf962323", "lessonId": "d88d8c72-4025-dca7-b0ae-23b29a3b8a55" } ], "lessonId": "d88d8c72-4025-dca7-b0ae-23b29a3b8a55", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 3", "topic": null, "unit": "Understand additive relationships and apply them to rearrange equations", "lessonCount": "10", "age": [ 7, 8 ], "gradeId": "age_7_8", "gradeStage": "Key Stage 2", "lesson": "Solve one and two-step problems in different contexts" } } ] }