Exploring the 120 Chart Patterns - First Grade Mathematics

A 120 chart is one of the most magnificent maps in all of mathematics. It organizes all the numbers from 1 to 120 into a clean grid of rows and columns. When numbers are arranged this way, they reveal hidden geometric patterns, symmetries, and mathematical relationships that make arithmetic easy to understand. By learning how to navigate this chart, you will be able to add and subtract mentally simply by picturing moves on the grid. In this chapter, you will become an expert chart explorer and uncover the rules of the 120 chart.

The Structure of the 120 Chart

The 120 chart is arranged with exactly 10 numbers in each horizontal row and 12 vertical columns.

Top Portion of the 120 Chart:
Row 1:   1   2   3   4   5   6   7   8   9  10
Row 2:  11  12  13  14  15  16  17  18  19  20
Row 3:  21  22  23  24  25  26  27  28  29  30
Row 4:  31  32  33  34  35  36  37  38  39  40
Row 5:  41  42  43  44  45  46  47  48  49  50

Moving Horizontally: Left and Right

When you take one step to the right across any row, the number increases by 1 (+1). When you take one step to the left across any row, the number decreases by 1 (-1). For example, start at 24: one step right is 25; one step left is 23.

Moving Vertically: Up and Down

When you take one step straight down into the next row, the number increases by 10 (+10). The ones digit stays identical, while the tens digit goes up by 1. When you take one step straight up into the previous row, the number decreases by 10 (-10). For example, start at 35: one step down is 45; one step up is 25.

The Chart Cross: Navigating from Any Number

Pick any number in the middle of the chart, and you can create a navigation cross that reveals four neighboring numbers.

The Navigation Cross for 35:
           [ -10 ]
            | 25 |
[ -1 ] 34 - [ 35 ] - 36 [ +1 ]
            | 45 |
           [ +10 ]

The Four Rules of the Cross:

Above is 10 less (35 - 10 = 25). Below is 10 more (35 + 10 = 45). To the left is 1 less (35 - 1 = 34). To the right is 1 more (35 + 1 = 36). This cross works anywhere on the chart!

Diagonal Patterns on the Chart

Moving diagonally combines both horizontal and vertical steps at the same time.

Diagonal from Top-Left to Bottom-Right:
Start at 1 -> 12 -> 23 -> 34 -> 45 -> 56 -> 67 -> 78 -> 89
Each diagonal step adds 11 (+10 down, +1 right = +11)!

Adding Eleven with a Diagonal Slide

When you take one step down (+10) and one step right (+1), you have moved diagonally down-right. You added 11 in a single glide! If you move diagonally down-left (+10 down, -1 left), you add 9 in a single glide!

Practice Exercises

Exercise 1: Look at the number 54 on a 120 chart. What number is directly to its right? What number is directly to its left?

Exercise 2: Look at the number 68 on a 120 chart. What number is directly above it? What number is directly below it?

Exercise 3: If you start on 42 and move two steps straight down, what number do you land on, and how much did you add in total?

Exercise 4: Draw or write the numbers that belong in the navigation cross surrounding the number 73 (above, below, left, right).

Solutions and Explanations

Solution to Exercise 1: Starting at 54, the number directly to its right is 55 (one more, 54 + 1 = 55). The number directly to its left is 53 (one less, 54 - 1 = 53).

Solution to Exercise 2: Starting at 68, the number directly above it is 58 (ten less, 68 - 10 = 58). The number directly below it is 78 (ten more, 68 + 10 = 78).

Solution to Exercise 3: Each step down adds 10. Moving one step down lands on 52; moving a second step down lands on 62. In total, you added 20 (42 + 20 = 62).

Solution to Exercise 4: For the number 73: directly above is 63 (73 - 10), directly below is 83 (73 + 10), directly to the left is 72 (73 - 1), and directly to the right is 74 (73 + 1).