1. Planning backward, teaching forward
Backward Planning
Planning backward, teaching forward
We plan backwards (from the end point back to the beginning point)
We must know what we want students to do
We must know what we want them to achieve (this is what we are measuring – why else would you waste their time or yours fluffing around)
We must plan the task for them to do first (what is the verb, what is the skill, what is the knowledge they must have)
We must teach them together with lots of practice together
We must model for them initially so that they know how to do the task (Draw them in, model, do it together
We teach forwards – we are very used to this, uni taught us to teach forward, they also taught us to lead students to the answer through the questioning method – for example when I do observations of people I will often hear them say… What can you tell me about… or Today we are learning about….who know about this…. What do you know.
If you know your class well enough (and have done the learning design exercise plus have conducted some diagnostic assessments so you know where they are at, here’s my two cents and me standing on my soap box, we’re here to teach them, we’re not here to waste their time in the carpet while we fluff around. Turn off the “uni teacher voices” cause its killing the kids, talk to them as if they are the most interesting people in the world and you are happy to download new information to them.

2. Backward Planning Planning backwards Teaching forwards
Be clear on the learning intention – write down what they must achieve
Work out how you are going to measure (assess and record method, checklist, tasksheet, photo)
Design tomorrow’s review questions
Design today’s task
Design some more of today’s tasks to practice with together
Design a today’s task that you are going to demonstrate
Design an engaging story that links them into the concept or find a video clip or something from real life that links to what they are learning
Tell them what they are learning (learning intention)
Tell them how you are going to measure them (assessment)
Draw them in with something that engages (see Learning Design & Mu Model or TL Cycle)
Demonstrate, model, explain the task, knowledge, skills (they shut up and listen – you lend them your thinking)
Do the task together, practice until most everyone has it mastered
Student’s individually demonstrate the task, teacher measures proficiency and provides feedback (tick off on checklist or take photo or collect task sheet?)
Review together at the end of the lesson
Put into tomorrow’s review to continue to consolidate the concept (target those who didn’t get it

3. Pick the learning intention
Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)
Recognise multiplication as repeated addition
Recognise multiplication as groups of
Recognise multiplication in arrays
Represent multiplication as repeated addition
Represent multiplication as groups
Represent multiplication as arrays
Recognise multiplication as repeated addition
Multiplication in arrays
Multiplication in groups
Multiplication written numerically
Represent multiplication as repeated addition
Pick the learning intention
I picked one which was Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)
When I broke the content down I realised that you must teach groups before you teach arrays and then you can teach repeated addition (along a number line works nicely!!)
They must first learn to recognise this (recognise means to identify something as previously seen or known or to perceive as existing or true, then recognise as a verb has synonyms like acknowledge, appreciate, understand, grant, concede)
How do I measure their recognition? I must present them with something where they can say “ooh that’s multiplication in arrays, in groups, as repeated addition)
Represent – to present again or anew – to exemplify or portray. How do I measure this, simply get them to redo something I just taught them.

4. Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)
Recognise multiplication as repeated addition
Recognise multiplication as groups of
Recognise multiplication in arrays
Represent multiplication as repeated addition
Represent multiplication as groups
Represent multiplication as arrays
How am I going to be measuring, assessing or recording their attainment?
Recognise multiplication as groups, arrays, repeated addition
Say and point… this is a group of
Say and point… this is an array… an array is things organised in a row or column
Say and point… this is repeated addition of…. repeated addition can be written as multiplication
Use my checklist to tick off their recognition
Represent multiplication as groups, arrays, repeated addition
Record groups of tasks presented to them
Record arrays of tasks presented to them
Record multiplication as repeated addition when presented to them
Take a picture of their work for a portfolio task
Pick the learning intention
I picked one which was Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)
When I broke the content down I realised that you must teach arrays before you teach groups and then you can teach repeated addition (along a number line works nicely!!)
They must first learn to recognise this (recognise means to identify something as previously seen or known or to perceive as existing or true, then recognise as a verb has synonyms like acknowledge, appreciate, understand, grant, concede)
How do I measure their recognition? I must present them with something where they can say “ooh that’s multiplication in arrays, in groups, as repeated addition)
Represent – to present again or anew – to exemplify or portray. How do I measure this, simply get them to redo something I just taught them.

6. This is multiplication in groups
Multiplication can be shown as groups of things
3 x 4 = 12
Learning Intention:
Multiplication as groups
Specify:
Multiplication as a times table represented with numbers & symbols
Multiplication as repeated addition
Multiplication as arrays
Multiplication as groups of
This is multiplication in groups
Now to planning backwards – I want them to recognise groups – tomorrows review task
This will also be blown up into an a3 coloured poster and laminated (without the descriptor on the side)

7. This is multiplication in an array
Multiplication can be shown in arrays – Arrays are organised into rows and columns
3 x 4 = 12
llll lll
lll
Learning Intention:
Multiplication as arrays
Specify:
Multiplication as a times table represented with numbers & symbols
Multiplication as repeated addition
Multiplication as groups of
This is multiplication in an array
Now to planning backwards – I want them to recognise arrays– tomorrows review task
This will also be blown up into an a3 coloured poster and laminated (without the descriptor on the side)

8. This is multiplication as repeated addition
Multiplication can be shown as repeated addition
3 x 4 = 12
= 12
= 12
Learning Intention:
Multiplication as repeated addition
Specify:
Multiplication as a times table represented with numbers & symbols
Multiplication as arrays
Multiplication as groups of
This is multiplication as repeated addition
Now to planning backwards – I want them to recognise repeated addition– tomorrows review task
This will also be blown up into an a3 coloured poster and laminated (without the descriptor on the side)

9. This is: Groups – Arrays – Repeated addition
llll lll
lll
= = 12
Now to planning backwards – I want them to recognise groups, arrays and repeated addition and tell me each one when I point to it
– I might make up some flashcards of these for the future – this is tomorrows review task

10. Tell me: Groups – Arrays – Repeated addition
= 12
= 12
Today’s task – tell me is this arrays, groups or repeated addition

11. Tell me: Groups – Arrays – Repeated addition
llll lll
lll
Today’s task – tell me is this arrays, groups or repeated addition

12. Tell me: Groups – Arrays – Repeated addition
Today’s task – tell me is this arrays, groups or repeated addition

13. Multiplication as groups
Lesson
Multiplication as groups

14. Groups – this is groups – there are 2 groups of 4
Shut Up I’m teaching you this is groups of

15. Groups – this is groups – there are 5 groups of 4
Shut Up I’m teaching you this is groups of

16. Groups – this is groups – there are 3 groups of 4
Shut Up I’m teaching you this is groups of

17. Groups – can you draw – 2 groups of 3
Lets do this one together, I’ll use the big whiteboard, you use your little whiteboards, draw me circles like mine for our groups, how may groups do I have? Great and how many do I need to put into my groups? Great – draw it then show me with a smile

18. Groups – can you draw – 3 groups of 2
Lets do this one together, I’ll use the big whiteboard, you use your little whiteboards, draw me circles like mine for our groups, how may groups do I have? Great and how many do I need to put into my groups? Great – draw it then show me with a smile

19. Groups – can you draw – 2 groups of 5
Lets do this one together, I’ll use the big whiteboard, you use your little whiteboards, draw me circles like mine for our groups, how may groups do I have? Great and how many do I need to put into my groups? Great – draw it then show me with a smile

20. Worksheet task

21. Multiplication as arrays
Lesson
Multiplication as arrays

22. Arrays– arrays are things organised into rows and columns.
An array of 6 eggs
2 rows of 3 = 6
2 x 3 = 6
An array of 6 eggs
3 columns of 2 = 6
3 x 2 = 6
Shut up I’m teaching you this watch me and learn
Arrays are things organised into rows and columns – I want you to remember this always because I’m going to ask you to tell me this tomorrow, you could tell your mum and dad this tonight, arrays are things organised into rows and columns
See I have an array of 6 eggs here – this is two rows of three eggs, see a row here and a row here, there are three in each row, I’ll count them – it equals 6. I can write this as a multiplication sum, I’ll give you an extra happy smile today if you can remember to write your arrays like this when we do them together later.
See this one is the same, its an array of 6 eggs as well – this is in columns though, its 3 columns of 2 eggs, see a column here, a column here and a column here. There are 6 eggs and I’ve written it as a multiplication sum here!!

23. Arrays – things organised into rows and columns
An array of 12 Grannies
3 rows of 4 grannies = 12 grannies or
4 columns of 3 grannies = 12 grannies
3 x 4 = 12
4 x 3 = 12
Shut up I’m teaching you this watch me and learn
Arrays are things organised into rows and columns
Here I have an array of 12 grannies– this is 3 rows of 4 grannies which is 12 grannies, I can count them but it takes a long time which is why it is quicker to learn our multiplication or times tables and do it this way.
I can also show my array of 12 grannies as 4 columns of 3 grannies, it’s the same 3x4 or 4x3

24. Arrays – things organised into rows and columns
An array of 15 Gummi Bears
5 rows of 3 bears = 15 bears or
3 columns of 5 bears = 15 bears
5 x 3 = 15
3 x 5 = 15
Shut up I’m teaching you this watch me and learn
Arrays are things organised into rows and columns
Yum an array of 15 gummi bears– this is 5 rows of 3 bears which is 15 bears, I can count them but it takes a long time which is why it is quicker to learn our multiplication or times tables and do it this way.
I can also show my array of 15 gummi bears as 3 columns of 5 bears, it’s the same 5x3 or 3x5
They are all 15 yummy bears no matter which way I put them in an array

25. Arrays – can you draw – 2 rows of 3 balls (extra points if you give me the multiplication sum)
Arrays are things organised into rows and columns
Say it with me Arrays are things organised into rows and columns
Tell me what is an array Arrays are things organised into rows and columns
Lets make some arrays, I’ll use the big whiteboard, you use your little whiteboards, draw me 2 rows of 3 balls? Great and how rows do I need to put in my array? Great – can you draw it another way as 2 rows of 3 - show me with a grin
Can you write the multiplication sum? Do you remember how? I can show you, you can copy.

26. Arrays – can you draw – 5 rows of 2 balls (extra points if you give me the multiplication sum)
Arrays are things organised into rows and columns
Sing it with me Arrays are things organised into rows and columns
Tell me what is an array Arrays are things organised into rows and columns
Lets make some arrays, I’ll use the big whiteboard, you use your little whiteboards, draw me 5 rows of 2 balls? Great and how rows do I need to put in my array? Great – can you draw it another way as 2 rows of 5 - show me with a grin
Can you write the multiplication sum? Do you remember how? I can show you, you can copy.

27. Arrays – can you draw – 5 rows of 2 balls (extra points if you give me the multiplication sum)
Arrays are things organised into rows and columns
Whisper it to me Arrays are things organised into rows and columns
Tell me what is an array Arrays are things organised into rows and columns
Lets make some arrays, I’ll use the big whiteboard, you use your little whiteboards, draw me 5 rows of 2 balls? Great and how rows do I need to put in my array? Great – can you draw it another way as 2 rows of 5 - show me with a grin
Can you write the multiplication sum? Do you remember how? I can show you, you can copy me on your little whiteboard

28. Worksheet Task

29. Multiplication as repeated addition
Lesson
Multiplication as repeated addition

30. Multiplication can be shown as repeated addition
3 rows of 3 birds
= __ birds
3 x 3 = __ birds
Multiplication can be shown as repeated addition
This means that instead of counting something that we see in groups or arrays we can write it as repeated addition and add it up
See how I have some birds, I have 3 rows of 3 birds, I can count these or I can add them up quickly
I can also show this as a multiplication sum – like we did with arrays before 3 x 3 = 9

31. Multiplication can be shown as repeated addition
2 groups of 3 cupcakes
3 + 3 = __ cupcakes
2 x 3 = __ cupcakes
Multiplication can be shown as repeated addition
This means that instead of counting something that we see in groups or arrays we can write it as repeated addition and add it up
See how I have some cupcakes, I have 2 groups of 3 cupcakes, I can count these or I can add them up quickly
I can also show this as a multiplication sum – like we did with arrays before 2 x 3 = 6

32. Multiplication can be shown as repeated addition
4 rows of 4 angry birds
= __ birds
4 x 4 = __ angry birds
Multiplication can be shown as repeated addition
This means that instead of counting something that we see in groups or arrays we can write it as repeated addition and add it up
See how I have some birds, I have 4 rows of 4 birds, I can count these or I can add them up quickly
I can also show this as a multiplication sum – like we did with arrays before 4 x 4 = 16

33. Multiplication as repeated addition
3 x 4 = 12
= 12
4 x 3 = 12
= 12
Multiplication can be shown as repeated addition
Say it with me Multiplication can be shown as repeated addition
Tell me what is repeated addition? Multiplication!!! Hooray!!!
Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards,

34. Multiplication can be shown as repeated addition
_ rows of _ angry birds
_ + _ = __ angry birds
_ x _ = __ angry birds
Multiplication can be shown as repeated addition
Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards,

35. Multiplication can be shown as repeated addition
_ row of _ fish
_ + _ = __ fish
_ x _ = __ fish
Multiplication can be shown as repeated addition
Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards,

36. Multiplication can be shown as repeated addition
_ x _ = __ iceblocks
_ + _ = __ iceblocks
Multiplication can be shown as repeated addition
Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards,
_ rows of _ iceblocks

37. Multiplication can be shown as repeated addition
2 x 3 = __ penguins
Multiplication can be shown as repeated addition
Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards,

38. Multiplication as repeated addition
2 x 6 =
+ =
6 x 2 = =
Multiplication can be shown as repeated addition
Say it with me Multiplication can be shown as repeated addition
Tell me what is repeated addition? Multiplication!!! Hooray!!!
Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards,

39. Multiplication as repeated addition
2 x 4 =
+ =
4 x 2 = =
Multiplication can be shown as repeated addition
Say it with me Multiplication can be shown as repeated addition
Tell me what is repeated addition? Multiplication!!! Hooray!!!
Lets do some of these, I’ll use the big whiteboard, you use your little whiteboards,