Question

name:
place value: write the missing numbers set 2
directions: use your knowledge of the 100 chart to fill in the missing numbers.
(charts with numbers 67, 39, 12, 89, 45, 74, 56, 29, 40 in respective cells)

Answer:

To solve this, we use the 100 - chart rules: in a 100 - chart, moving right/left changes the ones place (±1), moving up/down changes the tens place (±10). Let's take the first 3x3 grid with 67 as an example (we'll do the same for others):

For the grid with 67:

Step 1: Top row (10 less than 67)

To find the number above 67, we subtract 10 from 67. So, \(67 - 10=57\) (middle top), \(57 - 1 = 56\) (left top), \(57+1 = 58\) (right top).

Step 2: Middle row (ones place)

The number to the left of 67 is \(67 - 1 = 66\), the number to the right of 67 is \(67 + 1 = 68\).

Step 3: Bottom row (10 more than 67)

The number below 67 is \(67+10 = 77\) (middle bottom), \(77 - 1 = 76\) (left bottom), \(77 + 1 = 78\) (right bottom).

For the grid with 39:

Step 1: Top row (10 less than 39)

Number above 39: \(39 - 10 = 29\) (middle top), \(29 - 1 = 28\) (left top), \(29+1 = 30\) (right top).

Step 2: Middle row (ones place)

Left of 39: \(39 - 1 = 38\), right of 39: \(39 + 1 = 40\).

Step 3: Bottom row (10 more than 39)

Below 39: \(39+10 = 49\) (middle bottom), \(49 - 1 = 48\) (left bottom), \(49 + 1 = 50\) (right bottom).

For the grid with 12:

Step 1: Top row (10 less than 12)

Number above 12: \(12 - 10 = 2\) (middle top), \(2 - 1=- 8\) (invalid, so we consider the 100 - chart structure. Wait, 12 is in the second row. So top row: \(12 - 10 = 2\) (middle), left of 2: \(2 - 1 = 1\), right of 2: \(2+1 = 3\).

Step 2: Middle row (ones place)

Left of 12: \(12 - 1 = 11\), right of 12: \(12 + 1 = 13\).

Step 3: Bottom row (10 more than 12)

Below 12: \(12+10 = 22\) (middle bottom), left of 22: \(22 - 1 = 21\), right of 22: \(22 + 1 = 23\).

For the grid with 89:

Step 1: Top row (10 less than 89)

Above 89: \(89 - 10 = 79\) (middle top), \(79 - 1 = 78\) (left top), \(79+1 = 80\) (right top).

Step 2: Middle row (ones place)

Left of 89: \(89 - 1 = 88\), right of 89: \(89 + 1 = 90\).

Step 3: Bottom row (10 more than 89)

Below 89: \(89+10 = 99\) (middle bottom), \(99 - 1 = 98\) (left bottom), \(99 + 1 = 100\) (right bottom).

For the grid with 45:

Step 1: Top row (10 less than 45)

Above 45: \(45 - 10 = 35\) (middle top), \(35 - 1 = 34\) (left top), \(35+1 = 36\) (right top).

Step 2: Middle row (ones place)

Left of 45: \(45 - 1 = 44\), right of 45: \(45 + 1 = 46\).

Step 3: Bottom row (10 more than 45)

Below 45: \(45+10 = 55\) (middle bottom), \(55 - 1 = 54\) (left bottom), \(55 + 1 = 56\) (right bottom).

For the grid with 74:

Step 1: Top row (10 less than 74)

Above 74: \(74 - 10 = 64\) (middle top), \(64 - 1 = 63\) (left top), \(64+1 = 65\) (right top).

Step 2: Middle row (ones place)

Left of 74: \(74 - 1 = 73\), right of 74: \(74 + 1 = 75\).

Step 3: Bottom row (10 more than 74)

Below 74: \(74+10 = 84\) (middle bottom), \(84 - 1 = 83\) (left bottom), \(84 + 1 = 85\) (right bottom).

For the grid with 56:

Step 1: Top row (10 less than 56)

Above 56: \(56 - 10 = 46\) (middle top), \(46 - 1 = 45\) (left top), \(46+1 = 47\) (right top).

Step 2: Middle row (ones place)

Left of 56: \(56 - 1 = 55\), right of 56: \(56 + 1 = 57\).

Step 3: Bottom row (10 more than 56)

Below 56: \(56+10 = 66\) (middle bottom), \(66 - 1 = 65\) (left bottom), \(66 + 1 = 67\) (right bottom).

For the grid with 29:

Step 1: Top row (10 less than 29)

Above 29: \(29 - 10 = 19\) (middle top), \(19 - 1 = 18\) (left top), \(19+1 = 20\) (right top).

Step 2: Middle row (ones place)

Left of 29: \(29 - 1 = 28\), right of 29: \(29 + 1 = 30\).

Step 3: Bottom row (10 more than 29)

Below 29: \(29+10 = 39\) (middle bottom), \(39 - 1 = 38\) (left bottom), \(39 + 1 = 40\) (right bottom).

For the grid with 40:

Step 1: Top row (10 less than 40)

Above 40: \(40 - 10 = 30\) (middle top), \(30 - 1 = 29\) (left top), \(30+1 = 31\) (right top).

Step 2: Middle row (ones place)

Left of 40: \(40 - 1 = 39\), right of 40: \(40 + 1 = 41\).

Step 3: Bottom row (10 more than 40)

Below 40: \(40+10 = 50\) (middle bottom), \(50 - 1 = 49\) (left bottom), \(50 + 1 = 51\) (right bottom).

We can fill each 3x3 grid with these numbers following the 100 - chart (tens and ones place) rules. The filled grids will have numbers calculated as above for each position relative to the given number.

(Note: Since the problem is to fill the missing numbers, the final answer is the filled 3x3 grids for each given number. For example, the grid with 67 will have:

Top row: 56, 57, 58

Middle row: 66, 67, 68

Bottom row: 76, 77, 78

And similarly for all other grids with 39, 12, 89, 45, 74, 56, 29, 40)