Maths Flipped Learning – Division and interpreting remainders

In Year 6 we are required to know not just how to divide, but how to deal with and understand the remainders we can end up with. The following two videos explain how you might convert these remainders into fractions or decimal depending on the context of the question.

Have a look at how you might create a decimal remainder using division:

Did anyone notice anything about the remainder 0.125 in the previous video? This could be represented as the fraction 125/1000. Yet looking at this fraction it could also be simplifed to 1/8. So the answer could also be correctly shown as either 812.125 or 812  1/8

This second video explains how you can use the short division method (bus stop) to interpret remainders as fractions.

Once you have watched a few examples, use your homework book to pause and have a go at trying to answer some of the next questions in the fraction video and then watch and listen to the explaination to see if you were right. A key thing to remember with fraction remainders is of course to make sure you always SIMPLIFY YOUR FRACTIONS if you can.

(This is also covered in the video but a reminder rap video can be found here if you need a few more reminders: https://www.youtube.com/watch?v=fp0wJ9d3pKE)

EXT:

Hopefully this has been some helpful revision in how to interpret division remainders as either fractions or decimals. There are two important things to remember:

1: It is important to understand the context of the question to decide whether the remainder needs to be looked at as a decimal or a fraction. There are a few questions for you to have a go at below to help you think about this.

a) The buses have broken down and a school has ended up taking 458 children on a school trip to the seaside in cars! Each car can take 5 children. How many cars would be needed for the journey? (Is it possible to take part of a car?)

b) 2536 people applied to preview T.V. shows for a new channel. 9 people were invited to preview each show. How many shows did they preview with full audiences and how many people were not invited? (Would this be best recorded as a fraction? why / why not?)

c) Sunita divides 8541 by 8. She says “I know there will be a remainder before I start.” Is she correct? Explain how you know. (How could you prove this using written workings? Can you find a fraction / decimal answer?)

(Answers are at the bottom of this page but have a go before you peep)

2: Short division (the bus stop method) works for single digit divisiors. However if you were faced with a question that was asking you 6497 divided by 16 then this would NOT be the most efficient method although you would still need to deal with the remainder as either a fraction or a decimal in the same way. How would you find the answer to such a question? We would recommend a fact box. Think of the question as: How many lots of 16 could you find in 6497?

16 x 1 = 16

16 x 2 = 32

16 x 4 = 64

16 x 6 = 96

16 x 10 = 160

16 x 50 = 800

16 x 100 = 1600

16 x 200 =3200

16 x 400 = 6400

Therefore adding together the two facts that will get me closest to my answer:

16 x      6 = 96

16 x 400 = 6400

16 x 406 = 6496  This is as close to my answer as I can get but I am still 1 away from my original answer therefore I have a remainder of 1 – This can also be interpreted as either a fraction using the method shown in the above video e.g. 406 1/16

 

 

 

 

 

 

Answers:

a) 92 Cars – As 458 divided by 5 = 91.6 or 91 3/5 and all the children need to go so you need to round up to 92 cars in this context as you cannot take a part of a car or leave any children behind.

 

b) 281 shows would be previewed and 7 people would not be invited. As 2536 divided by 9 = 281 r 7 or 281 7/9 . This means that there were 7 people who were NOT invited to a show. If you looked at this division problem with a decimal remainder it would have given you a answer that was tricky to interpret – 281.7777777 recurring. What does this mean in terms of people?

 

c)There will be a remainder because multiples of 8 are always even numbers and 8541 ends in the unit 1. I can further prove this by calculating 8541 divided by 8 = 1067.625 or 1067 r 5 or 1067 5/8

 

 

Comments (2)

Year 6 Homework & Spellings

Due in: Tuesday 22nd November

Please stick to 2 pages of A4 only. Take care with your presentation.

Science: Your task is to research a prehistoric creature called the Gastornis, which is a giant flightless bird. You need to create a factfile (details about its fossil, when/where it lived, what it ate & its behaviour) for this animal. Also include a labelled sketch.
A helpful website:
http://www.bbc.co.uk/nature/life/Gastornis
Maths: To strengthen your arithmetic skills, you have been given an arithmetic task to complete. Include jottings/working out where appropriate. If you have misplaced your sheet, please ask your teacher for a new one.

 

Spellings:

The letter-string ‘ough’.

List A

bought thought brought rough tough enough though although thorough plough

From your Year 5/6 word list: awkward forty

List B

bought thoughtful brought rough toughness enough though although thoroughly plough

From your Year 5/6 word list: awkward forty

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Flipped Learning Homework (Children’s) – Due in Monday 14th November

As we explore fractions it is important to recognise fractions in lots of different contexts.

For homework we would like you to watch this video and have a go at making your own Tangram Toast. This should be fun, but you will probably need several pieces of toast and be prepared to stop the video at any point to give yourself to keep up and check your understanding. Most importantly think about the fractions you are creating with the toast every time you cut.

This week your blue bag will contain a fraction wall that you can cut up to compare the fractions with alongside your toast.

What fraction of the whole is the small square? How can you prove it? 

What about the other shapes? 

If you make a picture with some of the shapes, what fraction of the whole do these shapes add up to? Explain how you know this.

What other fractions can you make? Which fractions can you not make with the shapes you have? Why?

You can build your confidence by starting simple and then challenging yourself as much as you want.

Next week you will be adding and subtracting fractions and this will be a good warm up for you to recognise fractions in real objects and seeing what fractions you can make with different combinations of shapes from you tangram. There will be some different colour questions to have a go at answering (a bit like those above) in your homework learning log.

Most importantly have fun doing Maths.

Parents – For the website link for this video follow the link below. There are some good resources for Times Tables on here; particularly Number Rumbler, which is an excellent card came. Your child might like to see the Toasty Tangram gallery too!

Fun maths at home

 

 

 

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Year 6 Homework – Due 15.11.16

Due in: Tuesday 15th November 2016

Literacy:
Next week, we will be working towards writing a diary entry for a character from a new story. To show your current understanding of the features of a diary entry, your task is to write your own diary for one day (or more if you wish!) between today and Monday. Please present this neatly.

Maths:
Your task is to complete an arithmetic sheet to help practise your calculation strategies. You will need to show your jottings/working out for some questions. Ask your teacher if you need a new sheet.

 

Spellings:

For Monday 14th November

Rule: I before e except after c
List A:
receive, deceive, perceive, ceiling, conceive, achieve, mischief, thief, believe, experience

List B:
receive, deceived, perceived, ceiling, receipt, achievement, mischievous
You also have some exceptions to learn: caffeine, protein, seize

A flipped learning video will be posted soon 🙂

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Year 6 Homework + Spellings 03/11/16

Your homework this week is:

Literacy: You need to find out about synonyms and antonyms.
Find a definition for each. Then, find at least 3 synonyms for:
wealthy, innocent, villain and 
Then find an antonym for each word.
Try to find examples that other people won’t have and that you can use in your Oliver news report next week!

You may find this website helpful.

Maths: You have been given an arithmetic sheet to complete to practise your calculation skills. Show your jottings/working out where appropriate. You will need to ask your teacher for a new sheet if you have lost it before the deadline.

Homework due date: Tuesday 8th November

 

Spellings:
Our spellings are set and tested every Monday.

Rule:
Use of hyphens
Hyphens can be used to join a prefix to a root word, especially if the prefix ends in a vowel letter and the root word also begins with one.

List A:

re-enter
re-examine
re-educate
re-explain
co-own
co-author
co-driver
co-operate
co-ordinate
de-stress

List B

co-ordination
co-operation
co-education
re-examine
re-evaluate
re-energise
re-emphasise
re-election
de-escalate
ultra-argumentative

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