Decimals & Percents · grades 5–8

Decimals & Percents.

One tiny step at a time — place value, comparing, rounding, the four operations with decimals, and percents from "out of 100" to discount, tax, and tip. With a hundred-grid, a place-value chart, a step solver, and an engine-graded pad.

Understand decimals

Place value, compare, round.

1.1
Decimal place value
Tenths, hundredths, thousandths.
1.2
Decimals on the number line
Place a decimal between wholes.
1.3
Compare & order decimals
Line up the place values.
1.4
Round decimals
To the nearest whole, tenth, hundredth.
1.5
Decimals ↔ fractions
0.75 = 3/4.

Add & subtract decimals

Line up the points.

2.1
Add decimals
Line up the points.
2.2
Subtract decimals
Line up the points.
2.3
Decimals & money
Add and subtract dollars.

Multiply decimals

Count the decimal places.

3.1
Decimal × whole
Multiply, then place the point.
3.2
Decimal × decimal
Count the decimal places.
3.3
Multiply by 10, 100…
Shift the point right.
3.4
Estimate to place the point
Use a rough size to check.

Divide decimals

Shift the points.

4.1
Decimal ÷ whole
Keep the point lined up.
4.2
Divide by a decimal
Make the divisor whole.
4.3
Divide by 10, 100…
Shift the point left.
4.4
Divide & round
Round the quotient.

Understand percents

Out of one hundred.

5.1
Percent means “out of 100”
37% = 37 per hundred.
5.2
Percent ↔ decimal
×100 and ÷100.
5.3
Percent ↔ fraction
75% = 3/4.
5.4
Benchmark percents
10, 25, 50, 75%.

Percent of a number

"Of" means multiply.

6.1
Find a percent of a number
“Of” means multiply.
6.2
Mental percents
10%, 5%, 1% building blocks.
6.3
Percent of a number
The general method.
6.4
What percent is A of B?
Part over whole, ×100.
6.5
Find the whole
Work back from the part.

Percent in the real world

Change, discount, tax, tip.

7.1
Percent increase & decrease
By what percent did it change?
7.2
Discount & sale price
Take the percent off.
7.3
Tax & tip
Add the percent on.
7.4
Percent change mastery
Increase or decrease, both ways.

Capstone

Pick the right move.

C1
Pick the right move
Convert, compute, or apply.

Decimals & Percents.

Understand decimals

Decimal place value

Decimals on the number line

Compare & order decimals

Round decimals

Decimals ↔ fractions

Add & subtract decimals

Add decimals

Subtract decimals

Decimals & money

Multiply decimals

Decimal × whole

Decimal × decimal

Multiply by 10, 100…

Estimate to place the point

Divide decimals

Decimal ÷ whole

Divide by a decimal

Divide by 10, 100…

Divide & round

Understand percents

Percent means “out of 100”

Percent ↔ decimal

Percent ↔ fraction

Benchmark percents

Percent of a number

Find a percent of a number

Mental percents

Percent of a number

What percent is A of B?

Find the whole

Percent in the real world

Percent increase & decrease

Discount & sale price

Tax & tip

Percent change mastery

Capstone

Pick the right move