Understand Decimal Size Using Models and Number Lines

Students use hundredths grids, base-ten blocks, and number lines to reason about the size of decimals to the hundredths place. They identify which decimals are larger or smaller by examining the place value of each digit.

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Grade 4 · Comparing Decimals · question 1 of 3

0 of 20

20 rungs. A star at the top.

On this line from 0, what decimal is at arrow E?

Your answer:

How it is taught

0:00 of 3:59

A decimal's size is its place on the number line.

Tenths sit between wholes; hundredths sit between tenths.

Read it: Farther right is greater

Which is greater, 3.26 or 3.3? 3.26 has more digits, but on the line 3.3 sits farther right, so 3.3 is the greater.

Put both decimals on the same line, from 3.1 to 3.4.
Find each dot: 3.26 sits between 3.2 and 3.3.
Name the dot farther right as the greater: 3.3.

Numbers grow as you move right along a line, so the dot farther right is always the greater number.

Write 3.3 as 3.30 and the two line up: 3.30 is more than 3.26.

Tenths count first: 3.3 has more tenths than 3.26, and the extra hundredths in 3.26 never make up a whole tenth.

On the same line, the decimal farther right is the greater one, however many digits it has.

Calling 3.26 greater than 3.3 because it has more digits.

Look at the line, not the length: 3.3 sits farther right, so 3.3 > 3.26.

Which is smaller, 2.02 or 2.1? — 2.02. On a line 2.02 sits farther left than 2.1, and how many digits a decimal has says nothing about its size.

Compare 0.7 and 0.4

Today we'll compare two decimals: zero point seven and zero point four. Which one is bigger?

Let's draw zero point seven as a bar split into ten equal parts.

Zero point seven means seven out of ten parts are shaded.

Now zero point four — another bar split into ten equal parts.

Zero point four means four parts are shaded.

Look! The first bar has more shaded parts, so zero point seven is bigger.

Grade 4 · Which decimal is bigger — 0.7 or 0.4?

We can also use a number line from zero to one, split into ten equal jumps.

Zero point seven sits seven jumps from zero.

Zero point four sits four jumps from zero — closer to zero.

On a number line, the number farther to the right is always bigger.

We can also check place value. Seven tenths is greater than four tenths.

So zero point seven is greater than zero point four. Both models agree!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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