This is a long blog split into three sections.
The first is an attempt to explain chunking as a method of long division. The second and third are much shorter updates on English this week and an overview of where the grammar and composition is heading over the next couple of months. I would appreciate any feedback to gauge whether this type of blog is useful to you or not.
Maths
So this week we have spent most of the time getting to grips with long division using chunking which as expected has caused a few ripples. I’ll try to summarise the process as best I can below, although this is very hard to squeeze into a couple of sentences. There is a summary calculation at the bottom of page 2 if you would like to scroll down to see that first. Here goes.
Step 1:
There are four number sentences that can be derived from a single function calculation.
E.g.
28÷4=7
24÷7=4
4×7=28
7×4=28
We can use this information to rearrange any missing number calculation.
28÷?=7
28÷7=?
7x?=28
?x7=28
From this it is possible to re-arrange a division calculation as a multiplication.
E.g.
‘What is 28 divided by 7?’
becomes
‘How many 7’s make 28?’
Step 2
This can now be applied to larger numbers.
E.g.
255 ÷ 17 = ?
becomes
? x 17 = 255
The simplest method to solving this would be to set out 255 cubes in a line on the floor and then subtract separate groups of 17 until all the cubes were gone or until we had a remainder, and then count how many groups of 17 were collected. Although this is highly inefficient, it does now pave the way to a more succinct method.
Assume that the 255 cubes are set out on the floor as described before. Rather than making single groups of 17, it is possible to use larger ‘chunks’, 10 x 17 for example. If 10 groups of 17 are removed from the line, it would be necessary then to work out how many cubes are left on the floor and try to take away another ‘chunk’ of 17’s.
To this end, 170 (10×17) is subtracted from 255 leaving 85 cubes in the line.
It is not possible to subtract another group of 10 so another chunk is needed. Halving the number fact 10×17= 170 reveals that 5×17=85.
Therefore, a ‘chunk’ of 5 lots of 17 are removed.
In total 15 lots of 17 have been subtracted from 255 leaving no remainders therefore the calculation is completed and expressed as;
255 ÷ 17 = 15
Layout
This calculation is best set out in the following manner with the subtractions being accounted for in the calculation on the left, the number of ‘chunks’ of 17 being used placed next to it, and the collected number facts being kept separated on the right.
255 ÷ 17 = ?
Calculation Chunks of 17 Number facts
____
17 )255 5 x 17 = 85
170 10x
85 10 x 17 = 170
85 5x
0
Total = 15 lots of 17 used
Answer: 255 ÷ 17 = 15
Notes
As a useful rule, 10x is a good starting place for collecting number facts. This can quickly be halved to find 5x and they can both be multiplied easily to find 50x and 100x, 500x and 1000x. 2x would be the next go to when it is needed providing easy access to 20x, 200x and so on. These facts can then be doubled and combined as needed to create other useful number facts as the situation dictates.
In class, collecting the number facts would be the first step. For some longer calculations these facts would be used multiple times, so collecting them in the first instance provides a really useful problem solving scaffold.
Try 8316 ÷ 18 as a good example of using repeated number facts.
English
This week we have been looking closely at developing a more formal voice in writing. We have been looking at some very chatty writing and trying to improve it using formal language and a range of other skills we have developed over the last few weeks. The quest has been to try to describe how the ‘voice’ has changed between the two pieces of writing rather than just to name the changes that have been made.
In grammar we have been looking closely at prepositional phrases, how they are made and how they are used as adjectives to modify nouns and pronouns. The next step is to explore their use as adverbs.
Overview
At this stage we are still working hard to establish grammatical rules at a much deeper level than just a superficial naming of parts. Because of this, I would not expect them to be having any significant impact on the quality of sentence structures at this time. While I am working to embed these concepts I am focusing on broader compositional aspects such as effective planning and the use of Point, Evidence, Explain as methods to expand and control writing, while trying to develop a much more thorough understanding of different writer’s style.
However, next term, once we have nailed prepositions, different objects in sentences, compound subjects and verbs we will be in a much better place to really understand what makes more complicated sentences. It is at this point that the grammar will start to have an impact on the sentence level which will be more meaningful and therefore more lasting.
End
If you have any time to send me feedback regarding this blog that would be most appreciated. I would be very interested to know whether the time taken to put it together is balanced by its usefulness to you. I also hope that you found the extended times on Wednesday useful to look through the books in class.
