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# Class 2

## Summer Term

## Week 1

## Week 2- Fraction Wall

*The children worked incredibly hard on this one and found it quite a challenge. It was interesting to see the different methods which the children used. Some chose to use their times table knowledge, some used repeated addition and some drew the Zios and Zepts. A massive well done to Joe and David who found a few different solutions. See some of our solutions below.*
##### Stage: 2 Challenge Level:

Place each of the numbers 1 to 5 in the V shape below so that the two arms of the V have the same total.
*We had a whole host of great solutions from the children this week. *
*Class 2 worked really well on this problem and very quickly identified that 5 up and 5 down would require a total of 25 cubes. The class then decided that if you multiplied the number of steps up by itself then you would find the total number of cubes. We then tested this method. The picture below shows how we found this out.*
*This was a challenging problem for class 2. We explored a wide range of ways to find the solution some of which were very logically and would have eventually reach an answer, however we soon realised there were a lot of possibilities so we had to approach it from a different angle. We soon realised we could use our times table knowledge to do 4x4x4x4 which would take into account each of the 4 elves having four options of hat, jacket, trouser and shoes. It was a tricky calculation but we found the answer in the end.*
*The children worked really hard on this problem. We found it quite tricky trying to read the clocks with missing hands but as a class we achieved it in the end.*
*We quickly worked out that if you add together all of the numbers you will calculate the total distance he went. We then decided to draw the journey to scale to solve the second part of the problem.*

Can you sort out the four clues that help and the four clues that do not help in finding the number I am thinking of?
## How Many Times?

*Class 2 worked well to solve this problem. They worked through each hour at a time to see if the pattern occurred in it. There were however a few mistakes when we forgot there were only 60 minutes in each hour! See our solutions below.*
## Picnic. It was super to be able to use our learning from this week and apply it to our problem.

In week 1, Class two were given a problem called "A Square of Numbers". Our aim was to place numbers 1 to 8 in the circles to make the calculations and operations correct. We first started talking about which numbers could be multiplied together.

We decided that numbers 2 and 1 couldn't go together into the division part, as we could only use each number once.

After some time, the children discovered some possible solutions to this problem. Lydia and Alicia found that number 8 could fit into the division calculation with the number 4- giving an answer of 2. They then decided to work out which number they could multiply by 2 to produce another of their numbers. After some trial and error, they discovered that 2x3 is 6. Once they had half of their square completed, they found that the remaining numbers seemed to easily slot into the gaps. These girls showed resilience as they then tried to think of different solutions and number combinations to this problem.

David and Joe. A began their number square by putting a 6 and 3 in the division calculation to produce an answer of 2. The boys then realised that if they put their 1 in the minus calculation, they would have 6-1 to give them an answer of 5. Lastly they worked out how to get an answer of 8. By putting 1 and 7 in the addition bottom line, meant they got an answer of 8. Successfully using all the numbers once to make each calculation correct. Well done boys!

This week, our challenge involved looking closely at an image called a 'Fraction Wall'. The task was to investigate how many different ways 1/2 can be written (equivalent fractions). Rueben particularly impressed us! He went above and beyond, finding several different ways to write 1/2. Most children we're able to come up with 3 to 4 different ways of writing half using the fraction wall to help. We had children come up with answers including- 2/4, 3/6, 4,8, 5/10, 6/12, to some really clever students who wrote 1000/2000 and also 500,000/100,000,000!

The task also involved looking at different ways of writing 1/3 and 3/4. This proved to be a little trickier for some. However the children were able to come up with some alternative fractions for 3/4 and 1/3 by referring to pictorial representations of fractions and then transforming these into numbers.

Rueben came up with a rule while working out how to write 1/2 in different ways. He discovered that the numerator goes up by 1 each time, and the denominator goes up by 2. For example, 1/2, 2/4, 3/6 and so on. He came up with so many different ways of writing a half. Fantastic effort, Rueben!!

Week 1:

This weeks problem was based on the popular television show Countdown. We used an online Countdown program to generate a target number and then give us six numbers to use. We could add, subtract, multiply or divide but could only use each number once. The idea is to get as close to the target number as possible

The children worked very hard and came up with some very close numbers. A huge well done to Reuben and Joe who were the closest in the class! Have a look at some of our solutions below.

Week 2: Zios and Zepts

**Zios and Zepts**

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs.

The great planetary explorer Nico, who first discovered the planet, saw a crowd of Zios and Zepts. He managed to see that there was more than one of each kind of creature before they saw him. Suddenly they all rolled over onto their backs and put their legs in the air.

He counted 52 legs. How many Zios and how many Zepts were there?

Do you think there are any different answers?

Week 3: Magic Vs

Place each of the numbers 1 to 5 in the V shape below so that the two arms of the V have the same total.

How many different possibilities are there?

What do you notice about all the solutions you find?

Can you explain what you see?

Can you convince someone that you have all the solutions?

What happens if we use the numbers from 2 to 6 ? From 12 to 16 ? From 37 to 41 ? From 103 to 107 ?

What can you discover about a V that has arms of length 4 using the numbers 1−7 ?

What do you notice about all the solutions you find?

Can you explain what you see?

Can you convince someone that you have all the solutions?

What happens if we use the numbers from 2 to 6 ? From 12 to 16 ? From 37 to 41 ? From 103 to 107 ?

What can you discover about a V that has arms of length 4 using the numbers 1−7 ?

__Week 4__

**Up and Down Staircases**

One block is needed to make an up-and-down staircase, with one step up and one step down.

4 blocks make an up-and-down staircase with 2 steps up and 2 steps down.

How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

Explain how you would work out the number of blocks needed to build a staircase with any number of steps.

Week 5- Elves

Mrs Claus made four of the workshop elves new suits for Christmas.

Each suit had matching trousers, shoes, jacket and hat.

One suit was all red, one was all green, one was all yellow and one was all blue. The elves were delighted with their presents, but decided it would be fun to wear a different outfit every day for as many days as possible. So they agreed to swap around parts of their suits until they ran out of new combinations.

How many days did their fun last?

Week 6- Christmas shopping

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?

Spring term

Week 1:

Two Clocks

Sam and Julie are friends. Both of them have rather odd clocks at home.

In Sam's bedroom there is an old alarm clock which his Dad had thrown out because it had lost its minute hand. Although it has only its small hand, Sam can still tell the time using it. He can tell the hour, such as midday. He can tell when it is time to get up, time to go to school and time to turn his light out at night.

Which clock is showing it is midday?

At what time does Sam get up?

At what time does Sam go to school?

At what time is Sam supposed to turn out his light?

In Julie's hall there is a very old clock which lost its hour hand a long time ago.

At what time does Sam get up?

At what time does Sam go to school?

At what time is Sam supposed to turn out his light?

In Julie's hall there is a very old clock which lost its hour hand a long time ago.

School finishes at half past three and it takes Julie at least half an hour to get home. Sometimes she goes to the shop on the way, and sometimes she leaves school a bit later. When she first gets home Julie always looks at the clock in the hall to see what time it is.

One week these were the times she saw:

One week these were the times she saw:

On which day was it raining so she hurried straight home?

On which day did she go to the shop to buy some sweets on the way home?

On which day did she stay at school to practise in the band?

On which day did she play with Sam for about half an hour before setting off for home?

On which day did her teacher keep the class in for five minutes?

Week 2

Chippy the Robot was sent on a journey.

Chippy started from his base station and went 2m (metres) N (North).

Then he turned and went 2m E (East), 3m N, then 3m W (West) and 2m S (South).

After that he went 2m E, 3m N and 3m W again.

Then he went 5m S and 4m E.

Finally, he went 1m S.

There he stopped.

How many metres altogether did Chippy travel on that journey?

How far and in what direction must Chippy travel to get back to his base station?

Then he turned and went 2m E (East), 3m N, then 3m W (West) and 2m S (South).

After that he went 2m E, 3m N and 3m W again.

Then he went 5m S and 4m E.

Finally, he went 1m S.

There he stopped.

How many metres altogether did Chippy travel on that journey?

How far and in what direction must Chippy travel to get back to his base station?

Week 3: Kieron's Cats

*We started this problem by considering how we would approach it. David made the suggestion that we could start by halving the combined weight of cat one and two, however Tyrell correctly identified that this wouldn't work due to the fact that each cat must weigh something different. Eventually Lydia suggested that we should work in a logical way starting at 1kg for the first cat so we decided to lay it out in a table. Sophie was the first to successfully find the correct answer. You can see how we solved this below in Louisa's book.*

Week 4: Ring a Ring of Numbers

Choose four of the numbers from this list: 1,2,3,4,5,6,7,8,9 to put in the squares below so that the difference between joined squares is odd.

Only one number is allowed in each square. You must use four different numbers.

What can you say about the sum of each pair of joined squares?

What must you do to make the difference even?

What do you notice about the sum of the pairs now?

*The children began by randomly putting numbers into the format to see what worked and after exploring a few different solutions we spotted a pattern:*

*Tyrell- 'The pattern is odd, even, odd, even.'*

*Suranne- 'Each has 2 odd and 2 even.'*

*We then furthered the investigation to explore how it would change if we were looking for an even difference.*

*Alicia- 'They are all either odd or all even in each one.'*

*See Hollie's book in the image below to see how she solved the problem.*

Spring 2- Week 1

Can you sort out the four clues that help and the four clues that do not help in finding the number I am thinking of?

Four of the clues below are true but do nothing to help in finding the number.

Four of the clues are necessary for finding it.

Here are eight clues to use:

Four of the clues are necessary for finding it.

Here are eight clues to use:

- The number is greater than 9.
- The number is not a multiple of 10.
- The number is a multiple of 7.
- The number is odd.
- The number is not a multiple of 11.
- The number is less than 200.
- Its ones digit is larger than its tens digit.
- Its tens digit is odd.

*Finding the number wasn't too tricky. The class crossed out each number on their hundred square that it wasn't until they were left with just 1 number. The answer was 35.*

*Finding out which clues were important was more of a challenge. The class set of independently but to no avail so we came back together and worked through it as a group. We compared each clue with others to see if they were important and the class came up with the following decisions:*

*'The first clue about the number being greater than 9 is not important because clue number 8 tells us that it's tens digit is odd. None of the numbers less than 9 have a tens digit.'*

*'The second clue about it not being a multiple of ten is not important because number four tells us it is an odd number and all multiples of ten are even.'*

*'The fifth clue about it not being a multiple of 11 is not important because it says later that the ones digit is larger than the tens digit.'*

*'Number six is not important because the number is less than 200 and all of the numbers on the square are less than 200.'*

Week 2 - Fraction Flags

This week we explored fractions. The children had to explore patterns using fractions of the rectangle. To start they hade to create a few different patterns with 1/2 in one colour and 1/2 in another. Next they had to create patterns with 1/2 in one colour, 1/4 in another and 1/4 in another. Next was 3/4 in one and 1/4 in another and finally 1/4 in one colour, 1/8 in another colour and then they had to work out the final fraction.

Find this problem by following the link below:

*The children worked hard to solve this problem and soon identified that the squares in the shape did not have to be grouped together so created a variety of different patterns meeting the fraction requirement.*

*When solving the final problem to work out which fractions was left we coloured a pattern with 6 squares one colour and 3 another leaving 15 squares. We discussed this as a class and identified that this would be 15/24 and could be simplified to 5/8.*

*See some of our patterns in the images below:*

Week 3- How many times?

On a digital 24 hour clock, at certain times, all the digits are consecutive (in counting order). You can count forwards or backwards.

For example, 1:23 or 5:43.

How many times like this are there between midnight and 7:00?

How many are there between 7:00 and midday?

How many are there between midday and midnight?

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