One amount, three ways to write it. A percentage is out of 100, so 3/4 = 75/100 = 75% = 0.75. Divide the top by the bottom for a decimal; put a percentage over 100 and simplify for a fraction.
A 25% discount, a quarter off, 0.25 of the price: the same saving, written three ways. Which is easiest depends on the job.
In Equivalent fractions you wrote one amount as different fractions. Percent means "out of 100", so a percentage is a fraction with 100 parts: 75%=10075. A decimal shows tenths, hundredths and thousandths: 0.75 is 75 hundredths.
In this lesson you move between all three, using a hundred grid to see why they match.
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Three quarters
How many of 100 squares is three quarters?
TryTry it on the board and compare the result with your prediction.
Shade the grid
c is the number of squares shaded, out of 100.
Try it yourselfYour edits are saved in this browser.
The bar is 43. Shade the same amount of the hundred grid. Was your prediction right?
Use the board. This ticks when you get there.
InvestigateWork out why it happens, one step at a time.
Converting
Here is how to move between the three.
Worked exampleBefore each step, say what you think comes next.
43=10075=75%Fraction to percentage: make it out of 100 (× 25 on the top and the bottom).
83=3÷8=0.375Fraction to decimal: divide the top by the bottom.
0.375×100=37.5%Decimal to percentage: multiply by 100.
16%=10016=254Percentage to fraction: put it over 100, then simplify.
45%=0.45Percentage to decimal: divide by 100.
Try one: write 83 as a decimal.
Read Max's working. How many hundredths is 0.5?
Write 83 as a decimal.
Max writes 0.5 as a percentage. Click the line where his working goes wrong.
Write 16% as a fraction in its simplest form.
ModifyChange the problem on purpose and see what happens.
One change at a time
Each task changes one thing.
Need a hint?
One fifth of 100 is 20.
Try it yourselfYour edits are saved in this browser.
The bar is 52. Shade the same amount of the grid.
Use the board. This ticks when you get there.
Write 0.6 as a percentage (a number of percent).
Write 35% as a decimal.
Write 207 as a percentage.
PractiseA few on your own, to check you have it.
All three
Write 0.45 as a fraction in its simplest form.
Write 53 as a percentage.
Review: write 129 in its simplest form.
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
Eighths that are whole percentages
Which eighths cannot be shaded exactly on the grid? Why?
Try it yourselfYour edits are saved in this browser.
Need a hint?
1/8 = 12.5%: not a whole number.
Another hint
Try 2/8: simplify it first.
Choose a number of eighths (a) that is a whole-number percentage, then shade the same amount on the grid.
Use the board. This ticks when you get there.
For teachers
Students use a fraction bar and a hundred grid to see one amount as a fraction, a decimal and a percentage, convert in every direction, and meet a recurring decimal (AC9M7N04, node 2). About 40 minutes.
I can convert between fractions, decimals and percentages.
I can explain why 0.5 = 50%, not 5%.
I can compare amounts written in different forms.
Before class
Do the Run board yourself first. Students need Equivalent fractions (the lesson before) and place value with decimals (Year 6).
The one idea: percent means out of 100, so hundredths connect all three. The common mistake is reading the digits after the point as the percentage (0.5 = 5%); it is planted in Max's working and named in the success criteria.
Decimal answers are marked by form (3/8 is told to write a decimal); a percentage can be typed with or without the % sign.
Running the lesson
Predict: take a show of hands. Students who chose 34% are reading digits.
Run: ask how many squares one quarter is, then three.
Investigate: model each line of the worked example with the grid beside it.
Modify: before the 1/3 task, ask students to shade 1/3 of the grid exactly.
Make: ask why odd numbers of eighths cannot be shaded exactly.
When students get stuck
A student writes 0.5 as 5% (Max's mistake). Ask: How many hundredths is 0.5? Shade it on the grid. Fix: × 100: 0.5 = 50%.
A student writes 3/4 as 3.4 or 0.34. Ask: What does the fraction bar mean: 3 of 4 parts. What is 3 ÷ 4? Fix: Divide the top by the bottom: 0.75.
A student cannot simplify a percentage as a fraction. Ask: What do 16 and 100 have in common? Fix: Over 100, then divide by the highest common factor.
Stretch and support
Stretch: Which fractions with a bottom number up to 12 give decimals that stop, and which recur? What do the stopping ones have in common? (In simplest form, bottoms made only of 2s and 5s.)
Support: Use the hundred grid for every conversion; for eighths, allow half squares.
Where it leads
Next: Fractions and decimals on the line (node 3).
Where it leads: percentage of an amount, percentage change and discounts (Year 8), and probability.
What each step is for
three quarters: Committing to a percentage for 3/4 shows whether they treat the digits as the percentage (34%) or think in hundredths.
shade the grid: Shading the hundred grid to match 3/4 turns the fraction into hundredths, which is what a percentage and a two-place decimal both are.
converting: Each conversion goes through a fraction over 100 or a division: fraction to decimal by dividing, decimal to percentage by × 100, percentage to fraction over 100 then simplified. Max's mistake reads the digits after the point as the percentage.
one change at a time: One change at a time: fifths on the grid, each direction of conversion, then the edge case of a decimal that never ends.
all three: Conversions in every direction, mixed, with digit-reading planted again; ordering mixed forms; the review keeps simplifying fresh.
eighths that are whole percentages: Searching eighths for whole-number percentages shows which fractions fit hundredths exactly, and that the rest (3/8 = 37.5%) need a decimal.
Now you can
Convert between fractions, decimals and percentages.