1. Materials List: One baggie per student: Each baggie contains: 6 blank file cards, 2 sheets dots, dry erase marker, sheet protector, sock to erase Set of these prepared cards This powerpoint introduces students to collections of 2 dots and collections of 3 dots. This prepares them for the Chunk pieces. The intent of these tasks is to build confidence and trust as well as develop descriptive language. Students will be introduced to the equal sign in these tasks. 2 3
three
two

2. Number Sense develops as students build, describe and compare quantities, matching them to numerals. The initial focus is expressions, not equations. I see I see This is additive composition. Ways to describe the collection in front of you. Do not let subtractions interfere.

3. Dot and ChunkitZ collections develop reasoning skills
Dot and ChunkitZ collections develop reasoning skills. They are visual spatial ways to approach number. Moving the parts both physically and mentally supports the development of number properties. Number properties are critical to understanding number operations and build the bridge to algebra.

4. The research on learning mathematics makes clear students need to learn to reason about the relationships between numbers as they build arithmetic skills. Not after. Early math experiences must prepare students to think, not just remember the counting sequence.

5. The human brain can subitize
The human brain can subitize. Your brain can recognize and name collections of 2, 3, and 5 without stopping to count. These tasks build student confidence with using their ability to subitize to determine “counts”.

6. 2 two Your brain knows 2 without stopping to count. Subitize.
Flash 2 fingers, hide, Ask did you see how many fingers I had? Look again: flash again, hide

7. Show me 2 with your fingers...

8. Look around to see what others did
Look around to see what others did. Show me two a different way with fingers.

10. Show me 2 using fingers from both hands.......

11. Still two

12. Match your 2 fingers to someone else’s 2 fingers....
As you touch say “2 equals 2”
Touching to match adds sensory experience to the remembering.... One to one correspondence does not require counting by ones...

13. Your brain can subitize 2..... LOOK

15. Did you see 2 dots?

16. Your brain knows 2 without counting.

17. Look

19. Was it still 2?
You turned the card but there are still 2 dots.

20. Yes, you can subitize 2.

21. Students pick up one file card and put 2 dots on it.

22. Once everyone has done their first card invite them to compare with others, then take a second file card and arrange 2 dots a different way.

23. Lay the cards out for all to see and lead a discussion on comparing the different twos.
Compare any 2 cards the students make to discuss how 2 is always 2 no matter how you arrange it.
Encourage the use of positional language to explain where the dots sit. Invite students to explain using words how to change one card to look like the other.

24. Kindergarten are sharing and comparing cards with 2 dots on them.

25. As students provide descriptors capture them on file cards and start building your wall of attributes. Words, words, words….
Encourage students to explain, not just grunt. Provide support by offering words and gestures to support their explanations. Expect them to repeat what you say. Paraphrase what they say, inserting missing words. This task is about learning to explain orally. The words we develop will be useful all year.

26. I chose this card first and asked students to describe how the dots are arranged.

27. I coaxed and prompted to develop these words.
side by side
close together
to the left
one on top of the other
vertical
I coaxed and prompted to develop these words.

28. How can we describe the way the dots are arranged on this card?
Then I placed this card beside it and asked students to give me words to compare.
How can we describe the way the dots are arranged on this card?
This is your chance to immerse students in vocabulary… Write the words on cards and refer to them often.

29. side by side close together to the right at the bottom horizontal
in a row in a line
We could re use some of the words we already had and we could write some new ones.

30. …. then I chose a new card and asked for more vocabulary
….then I chose a new card and asked for more vocabulary. Can we use any of the words we had? Do we need new descriptions?
center of card
close together
column
vertical
one on top of the other

31. Build a deck of vocabulary cards:
Including but not limited to
right, left, beside, close together, in a row, in a line, diagonal, horizontal, vertical, above, below, beside, parallel, perpendicular
You determine how many words you want to actually put on cards. The words above are key words I focus on all year.

32. Match the symbol 2 and the word two to the dot cards
Match the symbol 2 and the word two to the dot cards. Show the word two on a card. Everyone say then spell aloud. Close your eyes. Can you still see t-w-o. Open and look. Read with me two. T-w-o.
The model to trace or copy from helps prevent or reduce reversals.

33. Print a 2 on board then practice large air 2s with students
Print a 2 on board then practice large air 2s with students. The 2 starts at the top and moves in one flowing motion. 2
The model to trace or copy from helps prevent or reduce reversals.

34. Give students a numeral 2 card and a word two card
Give students a numeral 2 card and a word two card. They can use the cards as models.
Use a dry erase marker and plastic sleeve. Trace right over the 2 on the card.
Practice writing 2 and two. 2

35. =
equal
Introduce the equal sign.
Introduce the word equal.

36. = 2 2 =
Place the equal sign between different collections of 2 and encourage students to “read” the equations with you.

37. Use the equal sign to demonstrate 2 = 2 a variety of ways…

38. The equal sign means “the same amount”, “the same quantity”, “the same value” on each side.

39. To reinforce and practice thinking with twos, students can circle 2s in dot collections.

40. This is not circling in twos.

41. This is not circling in twos.

42. This is not what I mean. Each set needs to be just two.

43. I found and circled 2’s

44. Give students collections for circling 2’s.
Circle 2s quick as you can.
Compare with a partner.
There are collections included in a file with the ppts

45. 2
Some students might want to label their twos.

46. 2 4 6 8
Some might want to orally “count” by twos as they circle or after they finish. On this set I had one left.
In Kindergarten this is just oral work but Grade 1 and 2 can start attaching the numerals to the count whenever it is appropriate to be printing.

47. Keep the focus on seeing and circling twos
Keep the focus on seeing and circling twos.... Encourage students to plan ahead, see two, then circle two...
Listen and watch for students who are focusing on individual dots, not 2 at a time.

48. Push 2, Push 3 cards.
This card deck has sets of dots. Students are given bingo chips, coins or tiles and encouraged to push 2 at a time to cover the dots.

49. In Kindergarten the focus is just pushing twos
In Kindergarten the focus is just pushing twos. Students orally note if there are leftovers. This student did not realize she had 2 left uncovered until I asked if all the dots were covered. Clear off and try again.

50. The red circles show how she pushed her twos.

51. This student saw the twos in a different order and spontaneously circled to explain.
He saw there were 4 sets of two when he explained to me.

52. Practice covering two at a time by setting sets of blocks out
Practice covering two at a time by setting sets of blocks out. (The blocks are pre snapped into twos.

53. Give out baggies of stuff. Invite students to unpack their bag
Give out baggies of stuff. Invite students to unpack their bag. Put everything in one clump, then pull out in sets of 2. Use your cupped hand like a scoop and slide 2 at a time. (Stress the action is to pull or slide 2 together, not count and move one, two but pull 2) Use flat tiles. Have students use 2 fingers, put one each on a tile and slide. Slide another 2 to match. Then another. (organized twos is a pre cursor to multiplicative thinking)

54. Another number your brain just knows….

56. Your brain can subitize 3.
You show 3.
Give students the symbol and word cards to match to threes.

57. Turn and touch your fingers to someone else’s fingers.... Say 3 equals 3.
Give students the symbol and word cards to match to threes.

58. Show 3 another way

59. Three with 2 hands. Match your three to another student.
Say 3 equals 3.

60. Say 3 equals 3.

61. Look....

63. Did you see 3?
Encouarge students to use positional language to explain the change.

64. Your brain can subitize 3

65. Look

66. Encouarge students to use positional language to explain the change.

67. Still 3 ?
Encouarge students to use positional language to explain the change.

68. Have students build 2 different ”3” cards.

69. Use students’ cards to describe arrangements of 3.
Refer to the words we already created or add new cards.

70. These dots look like an L One on top, 2 below Two in a line
Two horizontal
One beside the other, one on top of the other
They make a triangle
One above, 2 below
Two in a line, one above and between
Two horizontal
One beside the other, one on above them
They make a triangle
Encourage students to use positional language to explain the change.

71. center
Triangle shaped
close together
2 in a row
one below

72. horizontal
side by side
close together
in a row
center

73. I put these together because they both have these attributes:
in a row
center
side by side
close together

74. Then I noticed what made them different
horizontal
All one colour
diagonal
2 colours

75. My 3 are in the centre of the card.
They are arranged like a triangle. Two in a row and one underneath the 2 but in between them.
My 3 are in the left hand corner, sitting in a row going across.
My 3 are on the right side of the card. There is 2 one on top of the other and a third one beside the bottom one to the right. They are touching. It looks like an L
My 3 on the diagonal, in the centre of the card. They make a line but they do not touch.
They are pointed to the right hand corner.

76. These threes all have 2 on one side of the card.
These all have 3 dots in a row, side by side

77. Practice with the equal sign.= = 3 = = 3

78. Keep the cards handy and use them to create sorts.
Choose a word from the pocketchart and put together all the 3’s that share that attribute.

79. close together

80. horizontal row

81. Students match 3 the numeral and the word card to their collections.
three

82. Practice air printing 3s.
three 3

83. Slide a three card in your plastic sleeve and practice printing three and 3.

84. Find 3s in collections and circle them.

86. Tape bingo dabbers into 3’s and dab collections made with 3’s
Tape bingo dabbers into 3’s and dab collections made with 3’s. When they dry laminate them and then circle threes.

87. PUSH 3
Students can use the cards to circle sets of 3 or push bingo chips in 3’s. Always pushing 3 at a time, so 3 finger push onto the dots.
If your hand gets tired you can do 2 on one hand and one on the other but you must push them as a three set.

89. Nice try, clear off and try again. Circle in sets of three.

91. If it is appropriate, encourage students to circle each set of 3 and label it 3

92. I can keep embedding each set in the next to see the multiplicative growth.3 6

93. 3 6 9 3 6 9 12

94. Give out bags full of snap cubes.
Students dump, then snap into 3 at a time to sort into threes. The threes can be arranged into an array as you count by multiples of 3. Can you get to 18? 3 6 9 ?

95. Slide tiles in 3’s