Fantastic work finishing today's lesson! Put your mental strategies to the test and solve these decimal equations.

6.3 + 12.27

2.89 - 1.41 =

7.3 + 7.2 =

2.671 + 5.999

4.53 - 4.49

1.82 + 4.08

Applying mental calculation strategies when adding and subtracting decimals

﻿Hi, sorry, I've just been out shopping, and I had a lot of problems. My shopping, I'm not sure if I got the right things. I've just been checking my receipt and all the numbers on it. £11.25, £2.95, 50p. I see lots of decimals on here. Oh, I'm meant to be teaching a maths lesson. Oh, gosh. I completely forgot. Right, we better get started. But luckily, you're here because today, we're doing problem-solving with decimals. Decimal problem-solving comes up all the time in real life, when I'm baking, when I'm cooking, when I'm measuring things, when I'm making crafts, and all the time when I'm shopping. So today, we're going to be looking at some real-life examples with decimals. Let's get started, and I'm so glad you could help with my problems today. Welcome to today's maths lesson. My name is Miss Sew, and we're going to be working together to do problem-solving with decimals using addition and subtraction. You will have done some problem-solving in other maths topics and other maths units, but this might be your first time doing problem-solving with decimals today. I'm going to be using lots of familiar strategies that you will have seen before. Let's get started, and see if you can help me solve some problems. For today's lesson, we're going to do a warm up, doing some adding and subtracting of decimals, we're going to be looking at bar models to represent word problems, and then try and solve some word problems ourselves, drawing our own bar models. At the end of the lesson, you'll have a chance to show what you know with the independent task and quiz. Before we get started, make sure you have everything you need for today's lesson. You will need a pencil and some paper. Pause the video now to go and get what you need. Once you have all your equipment, make sure you're in a calm, quiet place so that you can focus for the next couple of minutes that we're doing our learning. If you have any apps running, make sure you turn off notifications so you're ready to complete the lesson first. For our warm up today, we're going to be adding and subtracting decimals. Take a look at each block in the pyramid. Each block in the pyramid is a sum of two blocks below. So I've done one for you here as an example. 0.6 add 2.1 is equal to 2.7. I added the bottom two blocks to find out the answer for the top block. Solve these two pyramids and have a go at this challenge pyramid to the side here. How many solutions can you find? There is more than one answer. Get ready, pause the video, and have a go by yourself now. Off you go. Okay, time to show you the answers. Okay, let's have a look at the solutions together. So for this bottom pyramid, with 1.85 at the top, we've got a missing one underneath. I know that 0.6 needs to be added together with this missing part to get 1.85. I've currently got six 10ths already, so I know I need another two 10ths, and a whole, and five 100ths. So my missing answer there is 1.25. Now, under the next pyramid, we already had the two parts, 5.3 and 0.61, so I need to add 0.61 onto 5.3, which should get me 5.91, nine 10ths, 100th. And then, for this third one, there were many solutions. Now, you could spend a long time working on this, but I think the best way is to work systematically. So let me show you what I did. I started from 0.01, so 100th, and I added it to 0.55, which I know makes 0.56. And then, I thought, okay, what if I just added 100th at a time? So I went to 0.02 and 0.54, which would also make 0.56. And then, I thought I could continue that pattern and find every single solution. I wonder if you worked systematically to find out your solutions, or if you came up with a different solution that perhaps I hadn't thought of. When we start with problem solving, I find that it really helps to think about bar models. Bar models don't solve the problem for us, but they represent the different quantities in the problem and help us find out what is missing. They are really helpful for showing us what our next step might be. Remember, the bar model doesn't solve the question, but it does represent what is happening in the question. Let's look at this bar model below me. I've got 1.2 as my whole, and then I have three boxes underneath that show 0.4. 0.4 is equal to 0.4 is equal to 0.4. All of the bars underneath with the value of 0.4 are the same value. So from this bar model, and this bar model could represent different problems. Maybe it's the amount of flour that I'm using for cooking, or maybe it's the quantity of string that I need for a craft. I know from this bar model that 0.4 add 0.4 add 0.4 is equal to 1.2. I also know, because it's the same as repeated addition, that 0.4 times by three, three lots of 0.4 is equal 1.2. And I can also infer some division from this bar model. 1.2 divided by three is equal to 0.4, or 1.2 shared into three equal groups is equal to 0.4. So this bar model was really handy and helped represent these three different equations for me. Let's look at this bar model over here. This bar model has two pink bars that are both equal and one purple bar, which could represent the whole. Maybe this bar model represents two pencil cases with equal numbers of pencils, and I need to know how many are in both of them. Have a look at this bar model. This bar model has a small purple bar, and then a longer green bar, and then a whole pink bar underneath. Maybe this bar model could show me, hmm, let's think. Maybe if I was making a salad, I could have 0.1 kilogramme of tomatoes and then 0.6 kilogrammes of salad. And then, if I mix them together, how much would they weigh altogether? And the pink bar shows me the whole. So all of these bar models around me represent different problems. What information could this bar model tell us? Think about the examples I gave on the previous slide. Pause the video and tell me what you know about this bar model. What ideas did you have? I can see from this bar model that the blue bar is the whole, and then these two green bars are of equal size. They aren't the same value as the whole. And I think there's space for something else at the end of this bar model. So maybe something's missing in the problem. Let's find out. Ooh, I've got some new information for you. I now know that one pack of envelopes is equal to £1.75. Hmm, what could this mean? How could this information be applied to this bar model? Could you write a question for me using that information and this bar model. Have a go. Pause the video and write your word problem. Okay, let's have a look at what you could have said is worth 1.75, or £1.75. This is an example of a possible word problem. Sally wants two packs of envelopes. She pays with a £5 note. How much change does she get? In this bar model, the green sections were worth £1.75 each. So if we know that we have two sections worth £1.75, and we pay with a £5 note, which is our whole, how much change is left? That was one possible word problem. Here is another possible word problem. Greg needs a pack of envelopes. In one hand, he has 60p, and in the other, he has an equal amount. How much more money does he need? In this bar model, £1.75 is the blue bar, which is the whole, and our green bars represent equal amounts that are part of my problem. I want you to pause this video now and have a go solving both of these equations. Let's have a look at the first word problem with Sally. Sally wants two packs of envelopes, and she pays with a £5 note. How much change does she get? One back of envelopes costs £1.75, and Sally wants two packs of envelopes. So I know that both of these green bars here are worth £1.75 each. If I add these together, using my column method or another method, I get £3.50. So I know that she spent £3.50. To find out how much change she gets, I have to subtract £3.50 from £5. £5 subtract £3.50 is equal to £1.50. She gets £1.50 change back. Let's have a look at the second word problem. Greg needs a pack of envelopes. In one hand, he has 60p, and in the other hand, he has an equal amount. They both have 60p. How much more money does he need to buy his pack of envelopes? So in this word problem, I know that 60p is equal to 0.6 pounds, and so 0.6 pounds is 60p. 0.6 add 0.6 is equal to 1.2, which is the same as £1.20. If I write 1.2 here, and the next place value column is blank, it means that there's a place value holder. A place value holder is just a digit that represents there's nothing there. So 1.2 and £1.20 is the same value. Let's work this one out using a number line. So I've got £1.20, but how much more money do I need to get £1.75? Let's count on. £1.20 add 50p is going to be £1.70, add 5p more is going to be £1.75. So I have to get 55p more to buy a pack of envelopes. So the missing section in my bar model is 55p. Let's look at this word problem, and this time, we're going to try and draw our own bar model. Kay and Sofia are both 1.63 metres tall. Amina and Ben are both 1.97 metres tall. If they lie down head-to-toe next to the rowing boat, the boat is 5.6 metres longer. How long is the boat? So let's start by drawing out our whole, okay? This is how long the boat is, and we don't know how long the boat is, which is why there's a question mark. I know that Kay and Sofia are both 1.63 metres tall, so I can put both their bars underneath. I know it is much smaller than the rowing boat, so I'm going to make their bars slightly smaller. I know that 1.63 and 1.63 are equal amounts, so I can make their bars the same size. Amina and Ben are both 1.97 metres tall. There are two of them, so I'll make two bars, and it is slightly larger than 1.63, but they are both equal. There are two bars worth 1.97. I have to work out how long the rowing boat is. I know the boat is 5.6 metres longer than both of our boat together. Now that I have drawn my bar model, can you see if you can solve the equation? Pause the video and complete the task. If you're finding this a bit tricky, I'm going to give you a clue. Have a look at all the bars underneath. I want to find out how much this white bar is, what the value of the white bar is. If I add up all of these decimal numbers underneath, I will find out how long the boat is. Right, time to show you the answers. Here, I have my bar model representing my problem. I want to work out how long the entire boat is, so I'm going to add up all these numbers underneath. 1.63 add 1.63 is 3.26. 1.97 add 1.97 is 3.94. And then, both of these values added together is 7.2 metres. If I then add 5.6 metres to this figure, I get 12.8. The boat is 12.8 metres long. Did you find those bar models helpful? Did they help represent what was happening in the question? If you found that a bit tricky, rewind and rewatch it again. Otherwise, if you feel confident, and you were able to solve those equations, we're now getting ready for our independent task. This is your first sheet in your independent task. I've got a range of items that I've bought at the Olympics, and I want to know what I can buy for £20. I also have a bar model, which I'd like you to label and show the value of different objects. Here, I have a bar model, and I want you to write your own word problem to go with it. And lastly, I have a challenge. Here's a word problem that you need draw your own bar model for. If you'd like help with the challenge question, here is a diagram to help you. Pause the video to complete your task. It's time to go through the answers for the independent task. Here's the answers to the first set of questions. Here are the answers for the second question. Here are some of the numbers that you could've used to write your word problem. Here's the answers for the challenge. Thank you for joining in with our lesson today. If you'd like to, please ask your parent or carer to share your work on Instagram, Facebook, or Twitter, tagging @OakNational and #LearnwithOak. Thank you so much for joining in with our maths lesson today, and I hope you enjoyed solving those problems. Now, it's time for you to go and complete your quiz and show what you know. Thank you so much for joining in and have a great day learning with Oak National. Bye!

Exit quiz: Again for this quiz we are revising everything you have learned in the lesson. Which equation will solve each problem?

Sofia is 134.7cm tall. Her sister is 107.4cm tall. How much taller is Sofia than her sister?

How much taller is Sofia than her sister?

It is Grandad’s birthday soon and he wants to hire a sports car for his present. A sports car costs £49.50 initial payment then £29.50 per hour. Grandad is bought 4 hour's hire. How much did Grandad’s present cost?

How much did Grandad's present cost?

To visit his grandmother, Zaid takes a train 6.37 km and a car 5.45 km. How many kilometres is his journey in total?

The temperature in the classroom was 21.8 °C. Claire left the door open and the temperature dropped by 3.7 °C. What was the temperature now?

To solve and represent decimal problems

In this lesson, we will solve addition and subtraction problems with decimals and generate our own word problems to suit equations. We will develop our understanding of decimal problem-solving through bar models and a variety of real life contexts.

Lesson overview:Solving problems with decimals using addition and subtraction

Core Content

Calculating with whole numbers and decimals: