Question

place value: write the missing numbers set 2
directions: use your knowledge of the 100 chart to fill in the missing numbers.
(the chart contains 9 small 3x3 grids, each with a number in the middle of the second row: 67, 39, 12, 89, 45, 74, 56, 29, 40. the other cells are empty, waiting to be filled.)

Answer:

To solve this, we use the 100 - chart rules: in a 100 - chart, numbers increase by 1 horizontally (left to right) and by 10 vertically (top to bottom). Let's take the first 3x3 grid with 67 as an example:

Step 1: Analyze the grid with 67

• Top row (above 67): To find the number above 67, we subtract 10 from 67. So, \(67 - 10=57\). The numbers in the top row (left to right) will be \(57 - 1 = 56\), \(57\), \(57+1 = 58\).
• Middle row (with 67): The number to the left of 67 is \(67 - 1 = 66\), and the number to the right of 67 is \(67+1 = 68\).
• Bottom row (below 67): To find the number below 67, we add 10 to 67. So, \(67 + 10 = 77\). The numbers in the bottom row (left to right) will be \(77-1 = 76\), \(77\), \(77 + 1=78\).

Step 2: Analyze the grid with 39

• Top row (above 39): Subtract 10 from 39: \(39 - 10 = 29\). The top - row numbers: \(29-1 = 28\), \(29\), \(29 + 1=30\).
• Middle row (with 39): Left of 39: \(39 - 1=38\), right of 39: \(39 + 1 = 40\).
• Bottom row (below 39): Add 10 to 39: \(39+10 = 49\). The bottom - row numbers: \(49-1 = 48\), \(49\), \(49 + 1=50\).

Step 3: Analyze the grid with 12

• Top row (above 12): Subtract 10 from 12: \(12-10 = 2\). The top - row numbers: \(2-1 = 1\), \(2\), \(2 + 1=3\).
• Middle row (with 12): Left of 12: \(12-1 = 11\), right of 12: \(12 + 1=13\).
• Bottom row (below 12): Add 10 to 12: \(12 + 10=22\). The bottom - row numbers: \(22-1 = 21\), \(22\), \(22 + 1=23\).

Step 4: Analyze the grid with 89

• Top row (above 89): Subtract 10 from 89: \(89-10 = 79\). The top - row numbers: \(79-1 = 78\), \(79\), \(79 + 1=80\).
• Middle row (with 89): Left of 89: \(89-1 = 88\), right of 89: \(89 + 1=90\).
• Bottom row (below 89): Add 10 to 89: \(89+10 = 99\). The bottom - row numbers: \(99-1 = 98\), \(99\), \(99 + 1=100\).

Step 5: Analyze the grid with 45

• Top row (above 45): Subtract 10 from 45: \(45-10 = 35\). The top - row numbers: \(35-1 = 34\), \(35\), \(35 + 1=36\).
• Middle row (with 45): Left of 45: \(45-1 = 44\), right of 45: \(45 + 1=46\).
• Bottom row (below 45): Add 10 to 45: \(45+10 = 55\). The bottom - row numbers: \(55-1 = 54\), \(55\), \(55 + 1=56\).

Step 6: Analyze the grid with 74

• Top row (above 74): Subtract 10 from 74: \(74-10 = 64\). The top - row numbers: \(64-1 = 63\), \(64\), \(64 + 1=65\).
• Middle row (with 74): Left of 74: \(74-1 = 73\), right of 74: \(74 + 1=75\).
• Bottom row (below 74): Add 10 to 74: \(74+10 = 84\). The bottom - row numbers: \(84-1 = 83\), \(84\), \(84 + 1=85\).

Step 7: Analyze the grid with 56

• Top row (above 56): Subtract 10 from 56: \(56-10 = 46\). The top - row numbers: \(46-1 = 45\), \(46\), \(46 + 1=47\).
• Middle row (with 56): Left of 56: \(56-1 = 55\), right of 56: \(56 + 1=57\).
• Bottom row (below 56): Add 10 to 56: \(56+10 = 66\). The bottom - row numbers: \(66-1 = 65\), \(66\), \(66 + 1=67\).

Step 8: Analyze the grid with 29

• Top row (above 29): Subtract 10 from 29: \(29-10 = 19\). The top - row numbers: \(19-1 = 18\), \(19\), \(19 + 1=20\).
• Middle row (with 29): Left of 29: \(29-1 = 28\), right of 29: \(29 + 1=30\).
• Bottom row (below 29): Add 10 to 29: \(29+10 = 39\). The bottom - row numbers: \(39-1 = 38\), \(39\), \(39 + 1=40\).

Step 9: Analyze the grid with 40

• Top row (above 40): Subtract 10 from 40: \(40-10 = 30\). The top - row numbers: \(30-1 = 29\), \(30\), \(30 + 1=31\).
• Middle row (with 40): Left of 40: \(40-1 = 39\), right of 40: \(40 + 1=41\).
• Bottom row (below 40): Add 10 to 40: \(40+10 = 50\). The bottom - row numbers: \(50-1 = 49\), \(50\), \(50 + 1=51\).

If we were to fill in all the grids completely:

• Grid with 67:
• Top row: 56, 57, 58
• Middle row: 66, 67, 68
• Bottom row: 76, 77, 78
• Grid with 39:
• Top row: 28, 29, 30
• Middle row: 38, 39, 40
• Bottom row: 48, 49, 50
• Grid with 12:
• Top row: 1, 2, 3
• Middle row: 11, 12, 13
• Bottom row: 21, 22, 23
• Grid with 89:
• Top row: 78, 79, 80
• Middle row: 88, 89, 90
• Bottom row: 98, 99, 100
• Grid with 45:
• Top row: 34, 35, 36
• Middle row: 44, 45, 46
• Bottom row: 54, 55, 56
• Grid with 74:
• Top row: 63, 64, 65
• Middle row: 73, 74, 75
• Bottom row: 83, 84, 85
• Grid with 56:
• Top row: 45, 46, 47
• Middle row: 55, 56, 57
• Bottom row: 65, 66, 67
• Grid with 29:
• Top row: 18, 19, 20
• Middle row: 28, 29, 30
• Bottom row: 38, 39, 40
• Grid with 40:
• Top row: 29, 30, 31
• Middle row: 39, 40, 41
• Bottom row: 49, 50, 51

(Note: Since the problem says "write the missing numbers" and the grids are 3x3 with a central number, the above steps show how to fill each 3x3 grid completely using the 100 - chart place - value rules of horizontal (±1) and vertical (±10) number changes.)