The Multiplication Charts

Materials

• Multiplication Chart 1 and Chart 2, printed from this site (open the virtual material and press the "Print control charts" button)
• A set of 81 small answer tiles and a blank 9 × 9 grid for the working chart — or use the on-screen working chart and check against the printed control chart
• Household substitute: hand-rule a 9 × 9 grid with the numbers 1–9 across the top and down the side, and write the 81 products on small squares cut from card stock
• A pencil and paper for writing facts

No materials at home? Use the virtual Multiplication Charts.

Before this lesson

• The Multiplication Bead Board

Aims

Presentation

1. 1 Sit beside your child with Chart 1. Let them explore it for a moment, then read the numbers across the top and down the left side together.This chart holds every fact from the tables you built on the bead board — all of them, from 1 × 1 to 9 × 9.
2. 2 Show the finger gesture. Put your left finger on the 4 at the side and your right finger on the 3 at the top.Four… taken three times.
3. 3 Slide the side finger straight across and the top finger straight down until they meet on one square. Read the product there.My fingers meet at twelve. Four times three is twelve.
4. 4 Hand the chart to your child and call out facts from a table they know well, letting their own fingers find each product. Then bring out Chart 2 and let them notice the missing squares.Half the chart is gone — but no answers are missing. Three times five and five times three are the same fact, so we only keep it once.
5. 5 On another day, show the working chart: a blank grid and a box of answer tiles. Choose a fact your child knows cold, find the tile, and place it on its square.Six times six… thirty-six. The thirty-six tile goes where the two sixes meet.
6. 6 Let your child keep placing tiles from memory, in any order they like — many children work one table at a time. Say nothing about right or wrong while they work.
7. 7 When they want to check, bring the printed control chart alongside and compare square by square — or press "Check my chart" on screen, which marks only the tiles that do not match.The chart will tell you. Compare your square with the same square on Chart 1.
8. 8 Any tile that does not match goes back in the box to be placed again. Fixing and re-checking is the work — the adult never marks the chart.

Points of interest

• The moment the two fingers meet on the product square
• The square numbers (1, 4, 9 … 81) running down the diagonal of Chart 1
• Discovering why Chart 2 can throw half the squares away and lose nothing
• Sorting the tiles first — four different facts all share the 12 tile

Control of error

• The control chart itself: the child compares their work to Chart 1, so the material corrects and the adult never marks
• On screen, the Check button flags only misplaced tiles — it gives no answers and adds no praise
• The tile box holds exactly one tile per fact, so a finished chart with tiles left over shows something is off

Vocabulary

• product
• times
• combination
• chart
• row
• column
• square number

Variations

• Work one table at a time on the working chart — place all nine ×4 facts from memory, then check
• Place the square numbers first and watch the diagonal appear
• Call out a fact and have your child find the product with the finger gesture as fast as they comfortably can

Extensions

• Cover a product square on the printed Chart 1 with a coin, name the fact from memory, then lift the coin to check
• Have your child hand-rule their own blank 9 × 9 chart and fill it in with pencil, checking against the control chart when done
• Hunt for a product: pick a number such as 24 and find every square on Chart 1 that holds it, writing each fact down — then talk about why some numbers appear four times and some only once

Follow-up work (pencil & paper)

• Print a page of times-table facts and let your child answer in pencil, keeping the printed control chart nearby to check any fact they are unsure of after answering.Printable: Math Facts Drill
• Copy one table of Chart 1 onto paper each day — all the ×7 facts, say — writing each as a full equation and reading it aloud.
• Make a personal "tables I know cold" list on paper: each time a whole table comes out instantly three days running, your child writes its heading on the list in pen.

What comes next

When your child can rebuild the working chart with few slips, the tables are truly theirs — and that fluency is exactly what long multiplication needs. Move on to the Checkerboard in the passage-to-abstraction strand, where those memorized facts multiply numbers into the millions.