Place value: blocks to count here or print

What the blocks stand for

• A small block is 1. The digit on the right of a number, the ones place, says how many small blocks there are.
• A rod is 10: ten small blocks joined in a line. The tens place says how many rods there are.
• A big square is 100: ten rods side by side, which is 100 small blocks. The hundreds place says how many big squares there are.
• So 243 is 2 big squares, 4 rods and 3 small blocks: 200 and 40 and 3.
• A zero holds a place. 305 is 3 big squares, no rods and 5 small blocks. Without the 0 in the middle it would read 35, which is a different number.
• The name. Blocks like these are often called base ten blocks, because each bigger block is ten of the one before it.

The three kinds of sheet

• 1 to 20: the numbers up to 9 are small blocks only, 10 is one rod, and 20 is two rods. There are only 20 such numbers, and a sheet has 12 of them.
• 21 to 99: rods and small blocks.
• 100 to 999: big squares, rods and small blocks. The blocks are drawn at half the size of the other two kinds, to fit up to nine big squares in the picture.
• The sheet number: any whole number from 1 to 999999. The same numbers and sheet number make the same twelve pictures on any device, so a whole class can have the same sheet, and no two pictures on a sheet show the same number. If we change how the page picks numbers, a sheet number will make a different sheet.
• The wrong answers on the screen come from slips like these: the tens and the ones the wrong way round, every block counted as one, or a number that is 1, 10 or 100 off.
• How big they print: on a Letter sheet, each of 6 or 9 pictures sits in a square about 6 cm wide, and each of 12 pictures in a square about 4 cm wide. In the 100 to 999 kind a small block then prints about 1 mm wide, so for that kind 6 or 9 pictures to a sheet leaves more room to count.

Every time the page is built, a program makes 1,200 sheets (400 of each kind) and counts all 14,400 pictures back from their drawings, with code written apart from the page’s own: it counts the big squares, the rods and the small blocks, checks that a big square is ten small blocks wide and ten tall and a rod is ten tall, that no two blocks touch, and that 100 for each square, 10 for each rod and 1 for each small block add up to the number on the answer sheet. It does the same for every number from 1 to 999, checks that the four answers on the screen are four different numbers with the right one among them, and measures the 6 ways the page can lay pictures out on a sheet.

What this page does not do

• It stops at 999: no thousands, no zero on its own, no decimals and no money. For bills and coins there is Count the cash.
• It does not add, take away or trade blocks. A picture has at most nine of each block, so there are no ten small blocks waiting to be swapped for a rod.
• It does not write numbers in words or split them into parts like 200 + 40 + 3 on the sheet. For a number in words there is Amount in words.
• It does not check blocks you draw. On paper, a square for 100, a line for 10 and a dot for 1 will do; the answer sheet shows the page’s own picture. On the screen there are only pictures to name.
• It does not keep score after you close or reload the page, or pick another sheet. The sheet number brings back the pictures, not your answers.
• It is not a lesson plan and follows no school’s program or grade. It makes no promise about what anyone will know after using it. It is pictures to practice on.
• It cannot be read from the picture by a screen reader. “What is in the picture?” says in words how many hundreds, tens and ones there are, and a place with no blocks is said as 0. The page has not been tried with a screen reader.
• It cannot see your printer. The blocks are light grey with dark lines, and how they come out depends on the printer. It has been tried in one browser’s print preview (Chromium, saved as PDF), where each sheet came out on one page; it has not been tried on paper from a real printer.