There is a division hiding inside every fraction. Can you spot which two numbers we would divide to turn 3/4 into a decimal?
You have written three quarters as 3/4 plenty of times. But how would you write the very same amount as a decimal?
Take three hands-up answers, not open call-outs. You are listening for a pupil who says 'divide 3 by 4' — if nobody does, park it; the next step reveals it. Give five seconds of quiet think-time before hands go up.
A fraction is a division: the top number goes in, the machine divides by the bottom number, and a decimal comes out. Watch the working for each one and notice where the division stops exactly and where it never finishes.
Work each division on the board first, then let the interactive confirm it. The point is that pupils see the working, not just the answer.
3/4: say "top first, always" as you set out 3 divided by 4. 4 won't go into 3, so 0 point, carry 30; 4 into 30 is 7 (28), remainder 2, carry to 20; 4 into 20 is 5 exactly, stops. Answer 0.75. Read it together.
1/8: runs to 0.125, three places. Show the last remainder reaching 0 and name this a terminating decimal.
2/5: gives 0.4, short and tidy. Pause and ask "will they all be this neat?" before revealing 1/3.
1/3: the key one. 3 into 10 is 3, remainder 1; carry to 10 again, same thing repeats, so the same remainder 1 keeps coming back and never reaches 0. Gives 0.333... A digit repeating forever is a recurring decimal. Write the notation by hand: 0.3 with a small dot over the 3, so they see the exact mark.
5/8: a final stopper, 0.625, comes out exactly. Contrast once more with 1/3 to fix terminating against recurring.
Today we work through four fractions together, feeding the top number into the divide machine and reading the decimal that comes out: 7/10, then 1/4, then 3/5, then 1/6. Predict 'stops or runs on?' before each reveal.
This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.
Reset the machine for each fraction: set the rule to divide by the bottom number, then send the top number through. Order chosen to build: 7/10 is a one-place decimal, 1/4 goes to two places, 3/5 is another clean one, then 1/6 = 0.1666… is the pause where a fraction runs on. Ask pupils to predict 'stops or runs on?' before each reveal, then reveal on the machine. Revoice a strong answer: 'so we always divide the top by the bottom'.
In your maths copy, set out each of these fractions as a short division, top ÷ bottom, and write the decimal answer beside it. Underline any decimal that runs on forever.
Walk the room glancing at the division layout and the aligned decimal point — this is whole-class copybook practice, not marking. Check pupils divide top by bottom, not bottom by top, and that 1/3 is the one underlined. If the IWB is unavailable, hand out the printable worksheet from the Before-the-Lesson prep (the same four fractions laid out as top ÷ bottom) so pupils can complete the division on paper.
Today we crack these one at a time: feed each fraction's top number through the divide machine to reach its decimal. We start with 7/10, then 5/8, then 3/5, then 1/4, then 1/6. Predict the decimal before each reveal, then check it on the board.
These are the practice questions — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.
Each challenge sets the divide rule to the bottom number; the input is the top number and the answer is the decimal it produces. Have a pupil state the division first ('seven divided by ten'), predict 'stops or runs on?', then Check confirms with a ✓. The last one, 1/6, is the recurring case — make sure pupils name it as a decimal that runs on. Watch for the common slip of dividing bottom by top and catch it fast.
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