Percent bar model

What the bar model shows

A percent bar is one whole drawn as a bar with two scales: percents from 0% to 100% along the top and the matching amounts along the bottom. In Find the part mode, choose a whole such as $80 and drag the marker to any percent. The readout gives the part and shows how it comes from 10% and 1% of the whole. In What percent? mode, the tool asks a question such as "What percent of 120 is 30?" and you drag until the bottom scale reaches the part. You can also hide the part to work it out first.

Why a bar model helps

A bar model turns percent problems into one picture instead of three formulas. Students who forget whether to multiply or divide can see that 25% of $80 is a quarter of the bar, and that 10% is always one tenth of the whole. The two matching scales make a double number line, which works the same way for finding a part, finding a percent and, later, finding the whole. It also builds estimation: before working out 35% of $60, a student can see the answer must be a little more than a third of $60.

Common mix-ups

• Treating a percent as an amount. 25% is not 25 dollars; it is 25 out of every 100, so 25% of $80 is $20.
• Dividing by the percent. To find 20% of $60, some students divide 60 by 20 and get 3. The bar shows 20% is two tenths of $60, which is $12.
• Assuming a bigger percent always means a bigger amount. 50% of $36 is $18, which is less than 25% of $80. It depends on the whole.
• Reading the part as the percent. 30 out of 120 is not 30%. The part is a quarter of the whole, so it is 25%.

A 10-minute activity

• Minutes 1 to 3: with a whole of $80, drag to 10%. Ask why 10% is $8, then predict 20%, 30% and 50% before dragging.
• Minutes 4 to 6: hide the part, choose 15% or 35%, and ask the child to build it from 10% and 5%.
• Minutes 7 to 9: switch to What percent? and answer two questions. Ask for an estimate first: is the part less than half of the whole, or more?
• Minute 10: ask how 25% of $80 and 50% of $40 can be the same amount.

Where it fits by grade

• Grade 5: the fraction and decimal skills that percents depend on, such as finding 1/4 or 1/10 of a number.
• Grade 6: a percent of a quantity as a rate per 100, and finding the whole from a part and the percent (Common Core 6.RP.A.3c).
• Grade 7: multistep percent problems such as discounts, tax and tips (7.RP.A.3).
• England: Year 5 pupils learn the percent equivalents of halves, quarters, fifths and tenths, and Year 6 pupils solve problems such as finding 15% of 360 and use percentages to compare amounts.

Learning more

Percentages and ratios are skills on Eurekami's skill map, and lessons use bar models like this one when a percent question needs a picture. When a word problem gets tricky, the AI tutor asks guiding questions instead of giving the answer away.