Lesson video

Hello everyone.

Welcome back to another maths lesson with me, Mrs. Pochciol.

As always, I can't wait to learn lots of new things and hopefully have lots of fun.

So, let's get started.

This lesson is called Use Knowledge of Calculating Within 20 to Solve Problems, and it comes from the unit calculating within 20.

By the end of this lesson, you should be able to use your knowledge of calculating within 20 to solve problems in a range of contexts.

Let's have a look at this lesson's keywords, visualise, represent, calculate, and efficient.

Let's practise them.

My turn, visualise.

Your turn.

My turn, represent.

Your turn.

My turn, calculate.

Your turn.

My turn, efficient.

Your turn.

Fabulous.

Now, that we've said them, let's use them.

Let's have a look at our lesson outline.

In the first part of our learning, we are going to be visualising and representing problems and in the second part of our learning we are going to calculate and check the answer.

Let's get started then with the first part of our learning, visualise and represent problems. For The Big Science Experiment, Laura and Andeep are going to need to share their maths learning with Sam and Lucas.

They've been tasked to design and build a microhabitat for a minibeast in their outdoor classroom.

Let's start by getting them ready.

Wow, they definitely look like they're ready to get started with their activity, so let's join them.

Let's peek at the problems they faced making their microhabitat for their chosen minibeast, woodlice.

We're not going to solve any of the problems just yet.

We are simply going to make sense of them.

To solve any problem, we first need to be able to imagine it in front of us.

We are going to visualise it and then represent it mathematically.

First, Laura and Sam needed to find the right place to set up their microbit habitat.

They find a damp, dark space, which we know that woodlice love and they have some string to section it off.

They've got 11 centimetres of string, but Laura's going to cut it.

Wait, it looks like she's cut off three centimetres.

Sam wants to know how long the string is now.

She wants to check that it's long enough to do the job that they need it for.

Laura suggests that they should find the length of the string without measuring it.

Hmm.

How are they going to do that then? We know that the string was 11 centimetres and that has now cut off three centimetres.

Sam creates a bar model.

Ooh, I like it, Sam.

What does that show us? Sam notices that if we subtract three from 11, this will give us the length of the string now.

She records this as an equation 11 subtract three is equal to something.

Well done Sam and Laura, I love how you represented that problem with a bar model and an equation there.

Remember, this first learning cycle is just visualising and representing, so we visualised using the string and Sam helped us to represent it using a bar model and an equation.

We're not calculating this problem yet.

We're going to calculate in the second learning cycle.

So for now, let's move on and see what Andeep and Lucas are up to.

Andeep and Lucas section off their habitat, they have two pieces of string.

One piece is 10 centimetres long and the other piece is eight centimetres long.

Lucas wants to know what the total length of their pieces of string would be together.

Hmm.

How could we represent this problem? Andeep suggests that if we add together 10 and eight, this will give us the total length of the two pieces of string and he creates his bar model.

Look, I can see that 10 and eight are the two parts and the hole is unknown.

That's because we've not calculated yet, remember? Andeep, can you show this as an equation? 10 plus eight is equal to something.

Well done, Andeep.

Remember, we are not calculating just yet, so we will come back to this problem later.

Let's pop on back over to Laura and Sam to see how they're getting on.

Laura now decides that they're going to gather some stones for their woodlice to hide under.

Oh, I think they'll love that, Laura, what a good idea.

Sam and Laura gather seven stones.

Andeep and Lucas gather five more stones.

How many stones do they have altogether? Hmm.

Let's think about this then.

We know that to calculate the total number of stones we can add together seven and five.

Can you see our two parts there for our bar model, seven and five? If we add together seven and five, that will give us the whole, which at the minute we don't know yet.

That will be the total number of stones.

Laura, what's our equation for this bar model? Seven plus five is equal to something.

Well done.

We'll see this problem again later when we calculate the sum.

Over to you then.

Andeep and Lucas arranged their stones.

They agreed five were too heavy for the woodlice.

So, how many of these stones can they use? Using the pictures, we can now visualise this problem.

Can you create a bar model and an equation to represent this problem, so that we can come back to it later to finally find out many stones they use? Remember, we are not solving this problem just yet.

You are just representing this problem using a bar model and an equation.

Pause this video and come on back once you're ready to see how Lucas and Andeep represented this problem.

Welcome back.

We know that there are 12 stones altogether, so that can be seen as our whole.

We know that five of the stones were too heavy for the woodlice, so we can see this as a part.

If we partition five from 12, we will be able to find out how many stones they actually use.

So our other part is unknown for now.

Well done if your bar model looked like this.

So what would our equation be to find out that missing part? We know that we can subtract the part from the whole to tell us the unknown part.

So, our equation would be 12 subtract five is equal to something.

Well done if you manage to get that.

Let's go back to Laura and Sam to see what they're up to now.

Laura wants to know if the microhabitat is going to be damp enough for their woodlice.

Sam lets her know that on Monday they added five cups of water to the area.

Four cups of water on Wednesday were added.

And finally on Friday, six more cups of water was added.

So, how many is that altogether? Hmm, how are we going to represent this problem? I can see that we have five glasses of water, four glasses of water, and six glasses of water.

I don't know how many there are altogether though, so I know that these three numbers are my parts.

There we go.

So then, what are we going to have to do to try and find out how many glasses of water were put on altogether? Laura thinks that we can add together the three numbers to find out how many cups of water we're put on altogether.

Do you agree? Yes, I agree, Laura.

So, if we add our three parts together, that will give us the whole and the whole will be the amount of cups that we've put on altogether.

What equation is going to represent this then? Let's have a look.

Five plus four plus six is equal to something.

Well done Laura and Sam.

Remember, we'll come back to this problem later to finally find out how many cups altogether.

Over to you then with task A.

Task A is to visualise and represent these problems using a bar model.

Remember, we are not calculating these problems just yet.

We are just visualising and representing them using a bar model and you can record the equation to show the calculations that we are going to make later.

Let's have a look then.

So you have A, the next week the children add more water to their microhabitat.

Andeep adds two cups of water, Laura adds seven cups of water, and Sam adds five cups of water.

How many cups of water have they added altogether? B, Laura, Andeep, Sam, and Lucas use seven stones for their microhabitat.

Another group uses 15 stones.

How many more stones did the other group use than Laura, Andeep, Sam, and Lucas? C, altogether the class had a budget of eight pounds to spend on creating their microhabitats.

They spent seven pound more than their budget.

How much did they spend altogether? And D, altogether the class bought 14 kilogrammes of soil for the base of their microhabitats.

They used nine kilogrammes.

How many kilogrammes of soil were not used? So, have a look at each problem.

Think about your parts and your holes.

What is it that we know? What is it that we need to find out? Once you've created your bar model, think about the equation that you could record that will help us to find the answer.

But remember we are not calculating just yet.

All we are doing is representing.

So, pause this video, have a go at A, B, C, and D and come on back when you're ready to continue the lesson.

Welcome back.

I hope you enjoyed visualising and representing those problems there.

Let's have a look then.

A, the children add more water to their microhabitat.

Andeep adds two cups of water, Laura adds seven cups of water, and Sam adds five cups of water.

How many cups of water do they have altogether? So, I can see straight away the word altogether.

So, I know that I'm finding a sum.

Laura notices that there are three addends in this problem.

So, it's going to be a three addend addition.

If she adds together two, seven and five, it will tell us how many cups we put on altogether.

So, let's have a look.

How did you represent that then Laura? Two is a part, seven is a part and five is a part.

Well done, I can see your parts there Laura, and the whole is unknown.

So, we are going to record that as a question mark.

Two plus seven plus five will help us to calculate how many they've added altogether.

So, well done to you if your bar model looked like this and if your equation looked like Laura's.

Let's have a look at B.

B, we know that our group of children used seven stones for their microhabitat.

Another group used 15 stones.

So, how many more stones did the other group use than Laura, Andeep, Sam, and Lucas? Let's have a look then, Laura.

Laura notices that she's now finding the difference between seven and 15.

So, she records the bars like this.

Laura knows that if she subtracted seven from 15 that will tell her how many more stones the other group used than our group.

So, let's have a look then, Laura.

There's her unknown part and she's recorded the equation 15 subtract seven is equal to something.

Well done to you if your bar model looks like Laura's and you wrote 15 subtract seven as your equation.

C.

Let's have a look then.

They had a budget of eight pounds but they spent seven pounds more than their budget.

How much did they spend altogether? Oh, there's that key word there altogether.

So, already I know that we are finding the whole.

We know that seven and eight are both our parts because they spent eight, they also spent seven more.

So, there's our two parts, and we are trying to find the whole.

So, eight plus seven will give us the whole.

Well to you if your bar model looked like this and you wrote the equation, eight plus seven is equal to something.

And finally, D, altogether the class bought 14 kilogrammes of soil for their base of their microhabitats.

They used nine.

Oh, so I can see here, hmm, how many kilogrammes of soil were not used? So, I think I'm partitioning here.

I know that 14 is our whole and nine is the part that we used.

So, to find how much wasn't used, we can subtract nine from 14.

So, 14 subtract nine is equal to something would represent this bar model.

Well done if your bar model and equation looked like this and well done for completing task A.

Let's move on then to the second part of our learning where we are going to use all of that visualising and representing to now calculate and solve the problems. Over to part two then.

Calculate and check the answer.

Let's recap Laura and Sam's first problem.

They had 11 centimetres of string and Laura cut off three centimetres of string.

So, they recorded that the equation, 11 subtract three is equal to something.

Over to you then, Laura, let's calculate 11 subtract three.

Laura notices that this problem is going to bridge 10.

So the first thing that she does is partitions the three into one and two.

We first subtract that one from 11, which leaves us with 10 and then we subtract the other part which is two.

We know that 10 subtract two is equal to eight.

So, we can say that 11 subtract two is equal to eight.

So that means that 11 centimetres subtract three centimetres will be equal to eight centimetres.

Sam now wants to check that the string does actually measure eight centimetres.

Should we have a look? Let's have a look.

The string goes up to eight, so yes it is eight centimetres long.

Well done Sam and well done Laura.

Let's have a look then.

Andeep and Lucas, remember they're putting their two pieces of string together now to make it longer.

So one piece was 10 centimetres long and one piece was eight centimetres long.

The total length is going to be found with the equation 10 plus eight is equal to something.

Hmm, Andeep, how are you gonna calculate this one? Andeep knows that 10 has no ones.

So, if we add eight ones, the 10 will remain, but there will now be eight ones.

So, that means that the sum of 10 and eight must be 18.

Wow, you didn't have to do any calculating there, Andeep.

You just used the knowledge that you had already.

Well done.

I'm really impressed.

Come on then, Lucas, shall we check that he's correct? Let's check the two pieces of string measure eight centimetres from end to end.

Are we ready? (gasps) There we go.

Let's look.

It goes up to 18.

Well done Andeep.

Your calculating was correct.

Let's look at the stones again then back with Laura and Sam.

We know that Laura and Sam had five stones, and Andeep and Lucas had seven stones.

So, they decided seven add five would give us the total number of stones.

Laura notices that here we can use our make 10 strategy.

So, the first thing we're going to do is to partition that second addend into three and two.

We know that seven and three make 10 and 10 plus the other two, which is the other part is equal to 12.

So we can confidently say that seven plus five is equal to 12.

That's 12 stones altogether.

How many stones did you get, Sam? Oh, Sam tried to count all of those stones but she got a little bit mixed up and made an error when she was counting.

So, it's a good job that Laura reminded her of that make 10 strategy.

Hopefully, Sam, you can use that next time.

Over to you then.

Remember our problem that we visualised and represented earlier in our learning.

Well now it's time to calculate.

We recorded the equation, 12 subtract five, because remember there were 12 stones but five of them were too heavy.

So, Andeep and Lucas decided to remove them.

Now, we want to know how many stones they actually have that they can use.

Pause this video.

Think about the best strategy to solve this problem and come on back once you've found a solution.

Welcome back.

Let's have a look then.

Lucas, Andeep, what did you notice about this problem? Lucas noticed that we added five to seven when we calculated the total of stones.

So if we now subtract the five, that should now be equal to seven.

(gasps) Oh, I like your thinking there, Lucas.

You remembered that seven add five was equal to 12.

So now, your thinking 12 subtract five must be equal to seven.

Andeep, do you think we should check this? Yes, Andeep's going to check and he's going to partition so that can bridge 10 with this problem.

Let's have a look.

Let's partition our five into two and three.

We first subtract the two to get to 10, then we subtract the three, which leaves us with seven.

Yes, Lucas, you are correct.

A beautiful strategy there, Andeep.

Thank you so much for checking Lucas's answer.

I'm really impressed boys.

Well done.

Okay then, let's go back to our cups of water.

Remember they first added five cups of water, then four cups of water, and then six cups of water.

So, we're going to add those three addends together because that's how we're going to find out how many cups were added altogether.

Five plus four plus six.

Hmm, what strategies can we use here then guys? When we add three numbers, we can look for a pair to 10 first.

Well done, Sam.

Well remembered.

So, let's have a look then, five plus four plus six.

Hmm, well done Sam, six and four do make 10.

Fantastic.

So, we can add those together first to make 10 and then we can add five more, which we know is 15.

So, five plus four plus six must be equal to 15.

So, that means that there were 15 cups of water added to the microhabitat altogether.

The woodlice are very lucky that you've created this for them.

Well done for calculating all of those problems that we've previously visualised and represented.

Now it's over to you.

Task B is to now calculate and check the problems that you visualised and represented in task A.

So, you can see that I've recorded the equations and the bar models that Sam and Laura created during task A.

Your job is to think about what strategy you are going to use in order to find out the solution to each problem.

So, we've got A, B, C, and D.

Remember to think about what strategy is going to be most efficient.

Pause this video, have a go at A, B, C, and D and come on back to see how you've got on.

Welcome back.

I hope you enjoyed using all of those strategies there.

Let's have a look at A then.

Laura, what strategy did you use to solve this problem? Laura notices that there were no pairs to 10 this time, but she does know that two add five is equal to seven because remember when we're adding three addends, we can add together a pair of numbers first and then add the third addend.

So, she added two and five, which was equal to seven, and then she's going to add the third addend, which is seven.

So, seven add seven is the same as double seven, which we know is 14.

So, that means that there are 14 cups of water altogether.

Well done to you if you got that one correct.

Let's have a look at B.

B, we know that we had 15 stones and seven stones and we wanted to find out how many more, so we had to find the difference.

Come on then, Laura, what was your strategy here? We know that we can partition the seven here so that we can bridge 10.

So, what did you partition seven into, Laura? We partitioned seven into five and two.

So, first we subtracted the five from 15 to leave us with 10.

Then we subtracted two from 10, which left us with eight.

So, we can say that eight was our missing part.

That now means that the other group must have used eight more stones than Laura's group.

Well done to you if you've got that one correct.

Let's have a look at C.

C, we had a budget of eight pounds, but the group spent seven pound more than their budget.

So, how much did they spend altogether? Eight plus seven is equal to something.

Hmm, what strategy did you use here, Laura? We know that we can partition seven to help bridge 10.

So, let's partition to make ten first.

We know that eight plus two is equal to 10, so we partitioned our seven into two and five.

Then we can add the five, which is the other part that we partitioned seven into.

So, 10 plus five is equal to 15.

Well done if you got 15.

That means that the class spent 15 pounds altogether rather than the eight that they were supposed to spend.

Oh, dear.

And finally, let's have a look at D.

D, they bought 14 kilogrammes of soil for the bases.

They used nine of them and they want to know how much wasn't used.

So, Laura, what strategy did you use here? We can partition nine so that we can bridge 10 because we are bridging 10 again.

Look, 14 subtract nine, The ones that I'm subtracting are larger than the ones in my number 14.

So, that means we are definitely bridging 10.

First we're going to subtract the four to leave us with 10 and then we subtract five which is equal to five.

So, we can now see that 14 subtract nine is equal to five.

So, we can see that there were five kilogrammes of soil not used.

I wonder what the class are going to use that for.

I'm sure they can come up with another habitat to make another minibeast very happy.

Well done to you if you've got that one correct and well done for completing task B and the lesson.

Let's have a look at what we've covered today.

Select the most efficient strategy to solve the problem.

When adding three addends, it is efficient to first add two addends using a known fact, e.

g.

, a pair to 10 or a double.

When adding, we can bridge 10 by partitioning apart so that we can make 10.

When subtracting, we can bridge 10 by partitioning a part to create a part that is equal to the ones digit of the number that we are subtracting from.

Difference can be calculated as subtraction.

Well done for all of your hard work today.

I hope you've enjoyed applying all of that learning into those different contexts and thank you for helping the Oak children to complete their big science experiment.

I can't wait to see you all again soon for some more learning.

See you soon.