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1. Problem solving - teaching and supporting children to work out which strategies to use
1. Problem solving - teaching and supporting children to work out which strategies to use
Try some of the problem solving activities on Trial and Improvement at KS1.
Go to this link (https://nrich.maths.org/10334) if you want to read more about problem solving.
What do you need to know more about in terms of how to support students?
Share your thinking with your classmates or make notes.
Now read the article about problem solving below. It refers to the new English Maths Curriculum but the ideas expressed apply equally to Australian schools.
ProblemSolvingNewCurriculum.pdf2. We need to teach children the strategies and language they require to tackle problems
2. We need to teach children the strategies and language they require to tackle problems
Visit the problem solving strategies toolboxes. There are a range available - see below. Compare and contrast and then think about which version makes sense to you.
Visit the problem solving strategies toolboxes. There are a range available - see below. Compare and contrast and then think about which version makes sense to you.
These sites are good because they model how to use particular strategies when tackling problems:
https://nrich.maths.org/10334 - Problem solving articles, strategies and problems to work through
Polya's Problem Solving.pdfEric the sheep2.pdfhttps://www.maths300.com/lessons?q_id=91 (eric the sheep)
https://www.maths300.com/lessons?q_id=4 (Multo, better than bingo)
Pizza puzzle handout
Age handout
Clothing handout
ice cream data activity https://nrich.maths.org/2438
Fair feast https://nrich.maths.org/2361
3. Now try these problems with a partner or by yourself...make a note of the strategies you use
3. Now try these problems with a partner or by yourself...make a note of the strategies you use
you might use this framework to help you ... https://drive.google.com/file/d/0B7YM6iJAeDKVbklYM1pKLTF2Njg/view
NimHow do we then turn this problem into a numeracy problem? Example https://nrich.maths.org/2656
https://drive.google.com/open?id=19WiVPT7vA5xXu3fWsrXpy_hK2JlCCMZw (read all the information about the problem above)
A Hole New Board Game Puzzle
A Hole New Board Game Puzzle
How do we turn the problem below into numeracy? Look at the problem below called A Hole New Board Game Puzzle and then think about how you could word that as a problem for students.
How about this?
I have a garden bed which needs to be covered in weed matting from edge to edge. The garden bed measures 2m x 12m. You can make one cut only in the 3m x 8m weed matting so that we do not have too many joins. Where will you cut it?
OR
I have a sand pit which needs to be covered by a board to stop the cats and other animals using it. The sand pit measures 2m x 12m. Bunnings only sell masonit in 3mx8m lots. You can make one cut only in the 3m x 8m masonite to make it fit the sand pit as it will be stronger with only one cut. Where will you cut it?
4. Mental computation as part of problem solving - mental computation underpins numeracy in the real world
4. Mental computation as part of problem solving - mental computation underpins numeracy in the real world
One crucial area that must be developed as mathematics understanding develops is mental computation, which refers to a someone's ability to work out something 'in their head' or mentally, without having to draw, write or use a calculator. Often people think that this refers to learning 'times tables' but this is only one small part of mental computation. To find out more about this see the resources on the final page. Go to Resources to see a range of excellent materials to support Mental Computation Learning.
There are lots of sub-skills which need to be taught explicitly as part of mental computation which assist children when they are undertaking any problems.
They need one and two digit strategies such as:
Back through 10 - For example, 52 – 8 = ? can be solved by calculating 52 – 2 = 50 then 50 – 6 = 44.
Equal differences - for example what is the difference between 8 and 13? Well I can work that out by asking what is the difference between 10 and 15? (you find two numbers that are equally close to your original numbers and work out the difference between them). You could also do 5 and 10 in this example.
Near doubles - 9 + 8 is nearly 9+9
Up through ten - 19+9 = 20+8
Splitting arrays - 9x6 is the same as 3x6 + 3x6 + 3x6 or 6x6 + 3x6 or 9x3+9x3 (distributive law or property)
Using 10s - 5000+4000 = 5+4 000; 5000x4000 = 5x4 000 000
Aggregation (eg: 28+35: 28+5=33,33+30=63),
Wholistic addition (eg: 28+35: 30+35=65, 65-2=63)
Separation right to left (eg: 28+35: 8+5=13, 20+30=50, 13+50=63)
Separation left to right (eg: 28+35: 20+30=50, 8+5=13, 50+13=63)
Rounding to add (58+63+81 = 60+60+80 -2+3+1)
Rounding to multiply (59x61 is about 60 by 60 so my answer will be about 3600) - it is important to know an estimate of a written algorithm too
etc etc
Mental computation:
Mental computation:
Practice some of these strategies with a partner https://drive.google.com/file/d/1tdXwrY_jJ-B8byfxVrwNW6TSbToU7Ooi/view?usp=sharing
From the website above and from the Mental Computation books on the Resources page, consider how you might support students to understand some of the mental computation strategies being developed:
Year 3 / 4 - arrays activity with 24 or 36 https://topdrawer.aamt.edu.au/Mental-computation/Activities/How-many-possible-ways
Year 2 / 3 - partial arrays https://topdrawer.aamt.edu.au/Mental-computation/Activities/Partial-arrays
Kinder - Year 1 - https://drive.google.com/file/d/0B75cP9HMyXqtcjUwYmlLdXJyQlk/view - page 11, 13, 15, 17 activities
Year 4/ 5 - https://drive.google.com/file/d/0B75cP9HMyXqtekx4OHFqV2pka3M/view - page 22, 23
Year 5/ 6 - https://drive.google.com/file/d/0B75cP9HMyXqtekx4OHFqV2pka3M/view - page 21, 22, 23 but change the numbers to 100s and 1000s
Now use this sheet to record what it says in the syllabus for your stage or Year level in relation to mental computation strategies:
Hint - which sub-strands might you need to check for mental computation strategies?
https://drive.google.com/file/d/1rc-8qEEUQO62UHK0rSZqbCrMhGNGPumH/view?usp=sharing
5. Mental computation is important because:
5. Mental computation is important because:
mental computation is the most common form of calculation required by adults
mental computation processes are used in about 85% of maths in the real world (numeracy)
it is crucial for estimation
it is needed to check whether answers / responses are correct (think cash register, estimates of cost and time etc)
it is the easiest and most efficient way of doing many problems
it allows us to see how numbers work and use that knowledge in other problems
it supports creativity and problem solving
Research shows it can improve students' development of number, while an early introduction to formal written methods can harm it.
6. Times Tables are taught as one element of Mental Computation. They are only one small part. They rely on rote learning rather than using strategies based on understanding of number.
6. Times Tables are taught as one element of Mental Computation. They are only one small part. They rely on rote learning rather than using strategies based on understanding of number.
There are a range of ways to teach and support the learning of times tables. You might need to support students by:
undertaking activities where they see the patterns in particular times tables
helping them learn tricks such as whether a number is divisible by 9, 2, 5 or 10
http://www.softschools.com/math/topics/the_divisibility_rules_3_6_9/
http://www.softschools.com/math/topics/divisibility_rules_2_4_8_5_10/
using fingers to learn their tables.
7. Numeracy processes - what activities are relevant and appropriate?
7. Numeracy processes - what activities are relevant and appropriate?
There are some maths understandings which need to be taught and practised by students, and some activities and strategies which support that content.
As you select activities or look at work samples consider:
what are the maths/numeracy processes being taught to the student?
what strategies might we use and why would we use them?
is this achieving the learning that is intended or will it achieve it? If not, why not?
There are many many mathematics and numeracy resources on the web and in books which say that they help to teach. What they do is give students lots of practice but do NOT actually teach anything.
Compare these resources. Which ones do you think will better help students to learn? Why?
http://www.snappymaths.com/counting/fractions/interactive/multisharing/multisharing.htm
http://www.k5learning.com/free-math-worksheets/third-grade-3/fractions-and-decimals
Manga Maths Flower Power https://www.mangahigh.com/en-au/games/flowerpower
https://www.scootle.edu.au/ec/pin with the following code
SCFTQG
OR
https://www.scootle.edu.au/ec/pin with the following code
DWRVQG
DWRVQG
https://www.k5learning.com/worksheets/math/grade-1-place-value-a.pdf
https://www.pinterest.com.au/pin/515943701038865564/
https://www.weareteachers.com/place-value-activities/
Use questions such as these to guide your assessment:
what thinking is required?
are the students learning or practising?
does this give feedback to the student in any way or could they give many wrong answers without being corrected?
does it encourage different ways of thinking and working?
8. How do you find the right resource when there are so many to choose from?
8. How do you find the right resource when there are so many to choose from?
It is important when you are supporting students to:
Identify what they need to learn - what outcome are you working towards?
Know where that sits in the curriculum - what stage is this at, what other understandings sit around it?
Read the curriculum to see what sort of strategies they suggest - what am I being told to do?
Consider whether the resource needs to help teach them or just to practice the concept or skill or strategy - how will this help the student's understanding?
Examples of how to find good resources:
Examples of how to find good resources:
Scootle – tied to Australian Curriculum – accessible by teachers, teachers assistants, students – can be organised to suit - http://www.scootle.edu.au/ec/p/home - register if you want access
Scootle – tied to Australian Curriculum – accessible by teachers, teachers assistants, students – can be organised to suit - http://www.scootle.edu.au/ec/p/home - register if you want access
Activity 1 - DBCXUF - Number - use each then consider how you would get students to apply one of the key understandings in a real life situation; identify the Band it would be appropriate for
Activity 2 - KQYRNL - Measurement and geometry - use then consider how you would get students to apply one of the key understandings in a real life situation; identify the Band it would be appropriate for
Activity 3 - SJJCDY - Statistics and probability - use then consider how you would get students to apply one of the key understandings in a real life situation; identify the Band it would be appropriate for
ABC Resources for Primary school math - filter by year, type of resource etc
ABC Resources for Primary school math - filter by year, type of resource etc
https://education.abc.net.au/home#!/resources/-/mathematics/F-1-2-3-4-5-6
Maths / Numeracy activities from the NSW Department of Education
Maths / Numeracy activities from the NSW Department of Education
Use the Australian Curriculum website to find resources
Use the Australian Curriculum website to find resources
For example:
https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/
choose Year 8
browse the learning and resources
do again with year 5
Activity
Activity
Pick one piece of content from the Maths syllabus (or Maths in the Australian Curriculum) that might be taught in your class on work placement. For example, if you working in a Year 3, you would pick something for Stage 2, Part 1.
Search for an activity that might support that learning on one of these sites. You will need to be quite specific about what you want - such as 'rounding two digit numbers':
Password protected sites
https://www.scootle.edu.au/ec/login.action (you will need your login) or go from the Australian Curriculum site
When you have an activity identified, work out whether it teaches the idea or whether it assumes the children have been taught already and practises the idea.
9. After we select the activity that supports learning we can practise adjustment or differentiation
9. After we select the activity that supports learning we can practise adjustment or differentiation
Examples of differentiating activities:
Examples of differentiating activities:
change your target
use 3 dice and go to 4000
use one die
add (do your total) then allow check with calculator
2 x 6 you can double your score (66 becomes 132)
more than one venomous number,
throw a double you have to subtract the score.
start at target and go backwards
add the dice instead of using then as tens and ones.
Make the number (from Whole Numbers, Stage 2, MA2-4NA)
Make the number (from Whole Numbers, Stage 2, MA2-4NA)
The position of a digit in a number is important; it has a different value depending on where it is in the number. Numbers have names and we read them in particular ways.
1. Warm up game - 3 dice - tell children that they will roll the three dice. Each digit or number must be used to make a 3 digit number. We are making the biggest possible number with those three digits.
2. Give each child a card and ask them to write 1 digit/numeral on one side and one on the other. They must write two different digits/numerals. They then choose which one they will use and hold the card with that digit/numeral facing out so others can read it. Tell the children that they are going to use the four digits that they can see to make the biggest possible four digit number (they have to move around and make the number). Ask them now to move around and make the smallest possible four digit number. Ask them to move and make the largest even number. The smallest even number... etc
3 digit number
5 or 6 digit number
change the scoring system
make one number = 0
Play different versions of Wishball - there are 15 different versions of the game
Play different versions of Wishball - there are 15 different versions of the game
Login to https://www.scootle.edu.au/ec/pin
using the PIN - EYCOLF
Consider how one of the above activities can be adapted and differentiated to meet the different needs of children in one group or class. Share your example with classmates.
Questions and discussion points for Make the Number:
Questions and discussion points for Make the Number:
if we have a zero how can we use it?
if no-one is showing an even numeral (number) can we make a four digit even number?
how many even numerals (numbers) do we need to make an even number?
when a numeral moves to a different place in the number what happens to its value?
if no-one is showing an odd numeral (number) can we make a four digit odd number?
how many odd numerals (numbers) do we need to make an odd number?
What would the next number be?
What is the number before this number?
10. Finding the right strategy for the child - example - which one suits you? Why is it important to approach all problems from different perspectives?
10. Finding the right strategy for the child - example - which one suits you? Why is it important to approach all problems from different perspectives?
Use the link below to work out which methods suits you best.
Long multiplicationReport abuse