Introduction to the Checkerboard

Materials

• A checkerboard mat: 4 rows × 9 columns of squares colored green, blue, red in the repeating place-value pattern (draw one on poster board with markers, or use the virtual board as your reference)
• Colored bead bars 1–9 (pony beads threaded on pipe cleaners work well: red 1, green 2, pink 3, yellow 4, light blue 5, lavender 6, white 7, brown 8, dark blue 9)
• Two sets of small digit cards 0–9: one set in regular ink, one set written in gray
• Pencil and paper for the child to record what they discover

No materials at home? Use the virtual Checkerboard.

Before this lesson

• The Multiplication Bead Board
• The Large Bead Frame

Aims

Presentation

1. 1 Sit beside your child with the board in front of you. Point to the bottom-right square and trace along the bottom row, right to left, reading each value.This square is worth one. This one is worth ten, this one one hundred, one thousand… all the way to one hundred million.
2. 2 Point out the colors: green for units, blue for tens, red for hundreds, then green, blue, red again. Your child has seen these colors since the golden beads.The colors are old friends — green, blue, red, just like the stamp game and the bead frame.
3. 3 Now move up the right-hand edge and read the row values: 1, 10, 100, 1,000. Show that the square above the 1 square is worth 10, and the square above the 10 square is worth 100.Every time we go up a row, the squares are worth ten times more.
4. 4 Place a single bead bar — say a 3-bar — on the 1 square and ask what it is worth. Move the same bar to the 10 square, then the 100 square, asking each time.The bar did not change. The square changed. Three on the tens square is thirty.
5. 5 Point to any square not on the bottom row, for example the 10 square in the second row. Ask your child to find another square worth 10. Trace the diagonal between them with a finger.Squares that touch at the corners, stepping down toward the bottom-left, are worth the same. We call that a diagonal.
6. 6 Slide a bar diagonally down-left along its diagonal to the bottom row and ask whether its value changed. Let your child test this with several bars on several diagonals.Sliding along the diagonal never changes what the beads are worth.
7. 7 On the virtual board, tap "New problem" just to see the digit cards appear along the bottom and right edges, and name them: the number along the bottom is the multiplicand, the gray number up the side is the multiplier. Then put the board away — the multiplying comes next time.Next time we will use the whole board to multiply big numbers.

Points of interest

• The same bar is worth 3, then 30, then 300 as it moves — the child usually wants to march a bar all the way to 300,000,000
• Finding every square on a diagonal and proving they match by reading the edge labels
• The colors repeating green-blue-red exactly as they do in the stamp game and bead frames
• Reading the enormous values on the top row — a square worth one hundred billion delights most children

Control of error

• The value printed along the bottom and right edges lets the child check any square: multiply the row value by the column value read below
• The repeating color pattern exposes a misread square — a square called "ten" must be blue
• On the virtual board, each square shows its value in the corner, so a wrong reading is self-correcting

Vocabulary

• checkerboard
• square
• diagonal
• place value
• multiplicand
• multiplier
• worth

Variations

• Play "find the square": name a value (say 10,000) and let the child find every square worth that amount
• Reverse roles: the child places a bar and quizzes you on its value — give a wrong answer occasionally and let them correct you
• Cover an edge label with a scrap of paper and ask the child to work out the hidden value from its neighbors

Extensions

• Have the child draw their own miniature checkerboard on grid paper and color the squares in the correct pattern
• Write value riddles on paper: "I am a 4-bar sitting on the 1,000 square. What am I worth?"
• Explore the top row: read and write the giant values (1,000,000,000 and beyond) with commas

Follow-up work (pencil & paper)

• Ask your child to draw a 4 × 9 checkerboard on paper, color the squares green, blue, and red in the correct repeating pattern, and label each square with its value.
• Write ten "bar riddles" on paper for pencil work, such as "a 6-bar on the 100 square = ____" — the child writes each answer as a numeral with commas.
• Have the child list all the squares that share one diagonal and write a sentence explaining why sliding along a diagonal never changes a bar’s value.

What comes next

Once your child can name any square and slide bars along diagonals without changing their value, move on to Checkerboard Multiplication, where the board computes real products like 4,357 × 23.

Next in this strand: Checkerboard Multiplication