﻿Hello, welcome to today's lesson with me, Miss Jones. Hope you're feeling well today and you're ready to learn. Before we start, let's start by warming our brains up with a little riddle. Are you ready? Today's riddle is what building has the most stories? What building has the most stories? And the answer is a library. Stories is one of those words that have two meanings. It could mean level of stairs, but in this riddle, it means books. Libraries have the most stories. Hope that's warmed your brain up. Now time to start the lesson. In today's lesson, we're going to be consolidating our knowledge of linear sequences and representing problems with algebra. We're going to be looking at two different problems today. One called sticky problems, that you're going to have a go at and then we'll go through together, and then one called vegetable variables, and again, we'll go through it together afterwards. Wow, some interesting problems lined up for today. I bet you're wondering what they are. Let's have a look, but before we start, make sure you've got your pencil and piece of paper ready. If you haven't, go off and get it now. Okay. Task one, sticky problem. There's a clue here, it might involve some sticks. "Darcey is making a triangle pattern. "She wants to investigate "the number of sticks used in each." We need to figure out what the term-to-term rule is and the previous two terms and the next two terms. So we notice the third one in the pattern. We can count the sticks. One, two, three, four, five, six, seven sticks. Then we can count the sticks for each one and find out a sequence. Hmm, how might I present my sequence? Well, I might present it in a table, so we know that the third term has seven sticks. If I count the fourth one, one, two, three, four, five, six, seven, eight, nine. I can see it's two more with nine sticks. I'm going to make a conjecture that this one might be two more with 11. I'm going to check just in case. One, two, three, four, five, six, seven, eight, nine, 10, 11. Okay, so we know it's a linear equation and we can see that each term is increasing by two. So the term-to-term rule is plus two. Okay, so we've got our first part. I've got another question here. Do you spot any other patterns? Hmm, I can't see any just yet, but let's have a think about what our previous terms are and our next terms are and then we'll have a think about it. So if my rule is add two, I know to find my previous term, I need to subtract two. So it'd be five and three. My next terms will be 13 and 15. Now what's really interesting is that we can use this information to start to predict what the next term will be and the next will be. But if I asked you what was the 10th term or the 20th term, how could we work that out? What's sometimes really useful is actually looking at patterns between our term number and our number of sticks used. And we can see here that our term-to-term rule was add two, so this is a little bit like the two times table, going up in twos. However it's not the same as the two times table, cause the two times table would be two, four, six, but looking at it, each one is one more than the multiple of two. Five is one more than four. Seven is one more than six. So I can see here in my seventh pattern, I need to multiply it by two, which is 14, and then add one. So now I can use that to make a prediction about any pattern. So if I was finding out the 10th pattern, for example, I can multiply it by two. Which will be giving me 20 and add one and I think there would be 21 sticks in the 10th pattern. Okay. See if you can spot any patterns of your own in your task today. You've got a similar task. This time we're making square patterns like this. You need to think about the amount of sticks in each pattern. Think about the term-to-term rule and complete the table. If you finish, see if you can notice any other patterns like I did and then we'll use that to solve a reasoning question later on when we go over the answers. I want you to pause the video now and go and do your task. Okay, hopefully you've had a chance to do your first task. Let's go over it together. Okay, so looking at this, the term-to-term rule here was add three, add three. It's a linear sequence increasing by the same amount each time. Previous terms were four and seven. You had to subtract three from 10 and the next term was 19. Did you notice any other patterns? Let's have a look at a reasoning question together. "Lars says to make 10 squares, "all I have to do is double the amount of sticks "used when making five." So he says if five sticks, or the five squares, the fifth pattern would need 16 sticks. He's saying that a 10th need 32. Do you agree or do you disagree? Hmm, I think I disagree with Lars. I think that he hasn't really looked at the pattern carefully. So this pattern we can see was going up three each time. So it's very similar to our three times table, but our three times table would be three, six, nine. And you can see that it's one more than the three times table. So if we're looking at a specific pattern here to get from six to 19, we don't just times by three, we times by three, which is 18, and then we add one. So five times by three is 15, add one is 16. Four times by three is 12, add one is 13. So I think the 10th pattern will be 10 times three, which is 30, add one, which is 31, which isn't the same as just doubling it. I think Lars needs to look for some patterns in order to help him understand. Let's have a look at our second task vegetable variables. What a nice use of alliteration. "Laura has a vegetable garden. "She plants F carrots." Hmm, let's look at this bit of key information. "Create expressions in terms of 'F' "to correctly fill in the blanks for each sentence." Okay, so whatever I write in this blank needs to be an expression in terms of F, okay. She pants the same number of leeks as carrots. She plants hmm leeks. Okay, so if she plants F carrots and the amount of leeks is exactly the same, she must plant F leeks. They're the same amount. Let's have a look at the second one. She plants 10 more potatoes than carrots. She plants hmm potatoes. Well if the amount of carrots was F, and the amount of potatoes is 10 more, then our answer must be F plus 10. That's our expression. There are F plus 10 potatoes. Let's look at the last one. She planted twice as many courgettes as carrots. How do you think we might write the amount of courgettes in terms of F? Pause the video and see if you can do that one. Okay, if there are twice as many courgettes as carrots and the amount of carrots was F, the amount of courgettes we can write as 2F. Which we just write as 2F. Now it's time for you to have a go. In your activity sheets, you'll see this task. "Laura has a vegetable garden." And "She plants Y potatoes." It's very similar to the task we just did with some extra questions. I'd like you to pause the video and go and have a go at this task. Okay, hopefully you've had a chance to complete this task. Let's go over it together. This time in Laura's vegetable garden, she's planting potatoes. We're going to express the potatoes as Y. "She plants Y potatoes." She plants double the amount of carrots as the number of potatoes. So we can express the amount of carrots as double Y, which we can write as two Y. She plants 10 fewer turnips than potatoes. We can express this as Y-10. She plants half as many leeks than potatoes, with the amount of potatoes is Y, the amount of leeks will be Y divided by two. Up here, she plants 13 more tomatoes than potatoes. So we can express the amount of tomatoes as Y+13. Now this one was a challenge. Did you spot why? She plants twice as many courgettes as turnips. Now here, it doesn't mention the potatoes. Hmm, so we need to use what we know. Now, we don't know anything in this problem about courgettes, but we do know some information about turnips. We've already worked out that we can express turnips as Y-10. So she planted twice as much as Y-10 for the courgettes, so we can express this as 2Y-10. I've put my brackets around here to prioritise the subtraction before it gets multiplied. Hope you enjoyed today's lesson. Please ask your parents or carer and then you can share your work. To finish off, we have a multiple choice quiz for you. Thanks guys. Goodbye.

In this lesson we will explore two different types of problems: one that consolidates learning around linear number sequences and one that explores expressing a maths story using algebraic notation.

Maths

Y6 Maths

Key Stage 2

Year 6

Miss

Consolidating linear sequences and representing problems with algebra

Calculation problems

Number

THEME

UNIT

Understanding which operations have equal priority

Order of operations

Consolidating order of operations

Linear number sequences

Expressing missing numbers algebraically

Expressing missing number problems algebraically

Finding solutions to problems with two variables

Reasoning and problem solving

Reasoning and problem solving (Part 2)

Lesson overview: Consolidating linear sequences and representing problems with algebra

Intro Quiz

Video

Presentation

Worksheet

Exit Quiz

Transcript

10 lessons in Calculation problems: