1. Structuring numbers

2. Numbers 1 to 10
Teaching Number in the Classroom, Wright et al, 2006

3. Subitising
Ascribing numerosity to a collection of items immediately and without counting, typically up to 5 or 6 items
Regular patterns can be important for young children’s learning – dot cards, dice and domino patterns
Move on to five frames and ten frames
Gradually lessen time pattern is displayed

4. Finger Patterns Encourage use of finger patterns in the early years
Patterns to five on one hand first
Observe – sequential or simultaneous? Do they need to see fingers?
Move on to patterns 6 to 10 – “five and….”
Doubles for numbers 1 to 5
Different ways to make numbers

5. Spatial patterns Start with dice patterns 1 to 6 Flash in random order
What do you see?
What does the four pattern look like?
Can you show me in the air?
Tap it on the table?
Ideas – finger painting, playdough, counters or objects, taking photographs, link to numerals….

6. Pair-wise Patterns
Flash ten frames with pair-wise patterns in random order
How many dots do you see?
What does three look like?
Can you show me in the air?
Show vertically with dots filled from bottom
Ideas?

7. Five-wise Patterns
Flash ten frames with five-wise patterns in random order
How many dots do you see?
What does eight look like?
Can you show me in the air?
Show vertically with dots filled from bottom
Ideas?

8. Partitions of five and ten
I will say a number and you say the numbers that goes with it to make five……
Show on ten frame or five frame
Discuss – were you right? What ones are tricky? How did you know?
Once they know five, move on to ten

9. Adding and Subtracting to 10
Flash the pair-wise pattern for 6 – what number did you see? What is 6 and 2? How did you work it out?
Show first number only. Repeat with different examples.
Flash five-wise pattern for 7. What did you see? What is 7 and 3? How did you know? Repeat with different examples
Try with subtraction.
Remember just to listen to how the child works it out – don’t expect them to use particular strategies or patterns

10. Bunny Ears
Helps develop awareness of combinations and partitioning numbers to 10
Discuss different ways to make numbers
Try to do this without looking, but may have to look to check at first
Try showing a ten frame pattern and asking for Bunny Ears for that amount
Try with numeral cards

11. Quick dots
Flash regular dice patterns for half a second – how many did you see?
Initially they may memorise pattern, then count
Describe the arrangement of dots
Move on to irregular patterns
Make with counters

12. Make Five Concentration
Arrange a set of twelve five frame cards (2 sets 0 – 5) face down on table
Children try to collect pairs that add to five
Winner has most pairs!
Lots of opportunity for discussion and questioning
Try varying with numeral cards, or a mixture

13. Five and Ten frame flashes
Show five frame on Smartboard – how many squares?
Add three dots. How many dots? How many empty squares?
Move on to flashing five frame patterns – half a second
Vary – single decker and double decker buses, own boards and counters, children as teacher

14. Memory Game
Use two or four sets of either pair-wise or five-wise ten frame patterns – mix up and place face down
Children find pairs
Vary – five frames, numeral cards, mix of pair-wise and five-wise patterns

15. Domino patterns
Display large domino card. How many dots can you see? How many on each side? Show me a finger pattern
Domino Fish – ask for a particular card
Domino Snap – matching numerals

16. Make Ten Fish Use numeral cards 1 to 9 (at least four sets)
Deal five cards to each player – remaining cards in pile in middle of table
Players take turn to ask another player for a particular card – aim is to make a pair that equals ten
If player doesn’t have the card they say “Go Fish!” and the seeker takes the top card from the pile in the middle
The game continues till one player has no more cards – winner is the one with most pairs

17. Numbers 1 to 20

18. Rekenrek Also known as Arithmetic Rack Make me……
Work with numbers in groups 1-5, 6-10, 11-15, 16-20
Goal is to be able to make numbers in one or two quick moves without needing to count
Two ways – five/ten structure and doubles structure
Lots of opportunities for discussion, questions, sharing and making connections

19. Rekenrek
Reading numbers on rack…. Teacher screens then flashes – how many?
Different ways to make….
Adding two numbers – use two rows and encourage lots of different ways to work out
Child is ACTIVE not told what to do, or following expectations

20. Rekenrek Doubles and near doubles Five and….to ten Facts to 5
Ten and….
Five and….to fourteen
Facts within ten – one addend 6 – 9, other 1 – 4
Facts within twenty – two addends in range 6 – 9
Make link between commutations too (turnarounds)

21. Rekenreks
Make a pair-wise pattern for 7 screened, then flash. What did you see? Repeat with other numbers to 10. What does 5 look like on the rack when I am building pairs? Repeat with other numbers
Repeat for five-wise patterns
Show in two different ways – two rows, or top row only
Link to ten frames
Move on to patterns for 11 to 20 pair-wise, then five-wise 11 to 14 and ten-wise for

22. Rekenreks
Adding doubles, fives, tens, e.g. make a five-wise 9 using top row and flash. What did you see? Show card Use the rack to work this out – how did you do it?
Look for children using patterns, but try not to communicate expectations
Move on to Subtraction

23. Double Decker Bus Flashes
Show empty bus – available from disc
Flash doubles combinations
Flash “ten and” combinations
Children make given numbers of people on the bus
How many ways could 12 people be arranged on the bus? Lots of discussion. Driver likes all the lower row filled first – ten plus!
Getting on and off the bus

24. Bus Games
Bus snap – numeral cards
Fish – combinations to 20

25. Ten and….
Show 9 on the lower row and 6 on the upper row. What if one person comes down to sit on the lower row? How many now?
Record and discuss
Children can change different upper/lower combinations to “ten and” combinations
Move on to screening, then without bus

26. Five and Ten Games
Two dice – 1-6 and one with just numbers 5 and 10. Roll both dice and record combinations on game sheet
Double ten frame cards – flash and record facts for each. How many in top row? Bottom row? How many altogether? How many more to make twenty? Write on back of card so children can test each other.
Bead strings – make different combinations to explore number relationships

27. Developing further….
Developing Number Knowledge, Wright et al, 2012

28. Moving on….
Tally Marks help children learn to count using five, and helps develop knowledge of “five and” facts
Use these in any classroom scoring game for any context
Model counting in fives and discuss why we find this useful as adults
Talk about why we group things like this

29. Ten frames
Flash five-wise patterns – how many on the top? Bottom? How many altogether? How many more to make ten?
Vary the length of time displayed – move to 0.5 second!
Continue with other patterns
If needing to count, use empty ten frames and counters to scaffold – children recreate flashed pattern
Discuss other patterns that might make the same number

30. Go Fish Use mini ten frames – six full sets
Play game, aiming to match pairs that add to ten
Move on to numeral cards, or playing cards
Extend to pairs to twenty
Vary – Kim’s Game

31. I Wish I Had
Use rekenreks, and ask children to build the number you say on their racks. I wish I had….8.
Choose children to explain how they made 8. Share different patterns and discuss
Repeat with different numbers up to 20
Discuss – how many pushes?
Increase pace as confidence grows. I wish I had 11. I have 11. I wish I had 14. Pause and discuss number of pushes.
Repeat 5, 10, 15 and 20 several time to draw attention to these numbers
Observe numbers that are easier/trickier or requiring more moves and target numbers as needed.
Target related patterns, e.g. I wish I had 12: I have 12. I wish I had 7 – look for children removing just one push of 5.

32. Double-decker Bus Rekenrek for each child
Tell story of double decker bus driving around with passengers getting on and off. Ask children to represent with rack, e.g. there are 9 people on the bus and 7 more get on. How many now? Discuss how we used the rack – I had 9 on the top row and 7 on the bottom – I moved 1 passenger to the top deck which made 10 and 6, so 16.
Share different ways. Discuss – which was quicker?
Vary story contexts as relevant to your children!

33. 9 Plus Game
Materials – 9 plus Game Board, 4 – 9 Spinner, paper clips and pencil, counters.
Player spins and adds the number spun to nine. They give number sentence and puts counter on the answer number on the board. Aim is to get three in a row.
Look for quick strategies, e.g. rounding and compensating
Vary with 8 Plus, or 19 Plus

34. 20 Minus Game
Use 20 Minus Game Board, 0-9 Spinners, paper clip and pencil, counters
As previous game, but subtract spun number from 20
Vary numbers to extend – decuple numbers

35. Make Six Numeral cards 1 – 6 – at least six sets for a group
Show examples of cards totalling 6, e.g. 4 and 2 or 3, 2 and 1
Ask each group to find all the different ways to make up a total of six – not just two numbers, but ALL
Vary resources – Numicon, cubes, or just verbally.
Discuss – how will we know we have found ALL the combinations? Great opportunity for mathematical reasoning and organisation!
Record combinations and share. Extend with other numbers!

36. Crackers the Parrot
Hold up a puppet (parrot or otherwise!) He can only say “five”. We want to make him look clever – can you ask him problems with the answer five? He only answers five to the correct questions!
Follow up with rekenrek to model for younger children
Problems can be as hard as they like – record all the problems they come up with answering five
Vary numbers to challenge and extend
For older children, just use Target Number, and generate as many ways to reach that number as possible!

37. Addition Card Families
Set of cards for each group. A set would be all the additions with totals in the range 1 to 10 for example.
As a child reads out their addition card, children match their cards with the same answer to make “families” of each number.
Share additions for each “family”
Look for relationships, turnarounds, doubles and near-doubles.
Discuss tricky facts.
How else could we sort into families? E.g. doubles, Five plus facts, near doubles? What if they belong in more than one family? What is the BEST way to organise? Why? How quickly can you sort them? How many combinations for each family?

38. Bulls-eye Dice
4 standard dice per pair, or 4 giant dice for whole class version
Player rolls 4 dice. Then they choose some of the numbers to add together, to make a total as close as possible to the bulls-eye of 10. Give a score according to how close to bulls-eye, e.g. 8 or 12 get 2, 9 and 11 get 1, 10 gets 0. Record scores for each player, and the number sentence and total on a table.
Players play six rounds and winner is player with lowest score
Vary – use ALL FOUR dice, add OR subtract, Bonus Die, Whole class play – 20 seconds to write down best combination.
Dice
Number sentence
Total
Score
6 + 4 10 11 1

39. Resources

40. Numicon

41. Glow

42. Highland Numeracy Blog

43. Maths Recovery

44. Rekenreks

45. Significance of structuring numbers
Developing thinking about how numbers are structured helps children develop non-count-by-one strategies
Giving numbers STRUCTURE by thinking of them as constructed from smaller parts helps them organise numbers to make them easier to work with
They can them partition or combine numbers to work out problems mentally
This combination of knowledge of number structure and developing strategies leads to….MENTAL AGILITY!

46. Resources Think about how you can use the resources you have….
How could you vary the activities, or link resources?
Could you arrange to share resources between stages at set times to allow for group or class sets?
Share other great ways to use your resources so others can learn from you!