Recall the rule for multiplying and dividing by 10, 100 and 1000

What this is

Two rules to be told and then rehearsed as a pair:

• To multiply by 10, 100 or 1000, move every digit to the left, one place for each zero.
• To divide by 10, 100 or 1000, move every digit to the right, one place for each zero.

It is the second step of multiplying or dividing by 10, 100 or 1000 on the place value grid. Students have already put the number in the grid, every digit in its column, zeros included. This rule says what to do next. The point and the column headings never move; the digits do.

The routine

• Explain. Both rules are on screen. Say each one. Students repeat them. Point out that they differ in only two words: multiply and left, divide and right.
• Frame. Choose Multiply or Divide. Say what the rule is for. Students give the rule. Press Reveal to check.
• Reframe. Choose Left or Right. Say the rule on screen. Students say what it is for.
• Rehearse. Nothing on screen. Students give both rules.
• Mix. The page picks Frame or Reframe, multiply or divide, at random. Press Next for another. This is where students have to tell the two rules apart, rather than remember which one comes first.

Run it out loud first (individuals, then the whole class), then again on mini-whiteboards. You choose each time whether students say it or write it; the screen is the same either way. Reveal turns into Hide, so you can put the blank back and ask someone else.

Why the rule says what it is for

The commonest mistake is moving the digits the wrong way (6.4 ÷ 100 = 640). So knowing “move the digits” is not enough: students need to know which way goes with which operation. Frame gives the operation and asks for the direction; Reframe gives the direction and asks for the operation. Mix asks for both, in no fixed order.

Why it can simply be told

Every idea in the rules is already secure or is plain English. “Every digit” comes from Put the number in the grid: every digit is in the grid, zeros included, and every one of them moves. “Left” and “right” are literally true on the grid, and each column is a place. “One place for each zero” means the zeros in the 10, 100 or 1000: one, two or three places. Watch for students who count the zeros in the number instead (4500 ÷ 10).