Decimal In Between

Grade 3 Mathematics
Routine - Decimal In Between

Standards: 4.NF.7, 5.NBT.3, 5.NBT.4

In this routine, the teacher gives the students two whole numbers, decimals, or fractions, or a combination of these, using the two numbers as endpoints on a number line. Each student must find a decimal number that falls between the two given numbers. Students are also asked to identify the location where their decimal number would fall on the number line and justify their thinking.

Routine - Decimal Between Links to an external site. on Vimeo Links to an external site..

Below are examples of number pairs you might use as endpoints for the number line.

As your students work through the routine and identify numbers and then describe where that particular decimal would be located on the number line, you might ask them:

• How did you decide where your decimal would fall on this number line?

• Is the decimal that ______ named closer to the lower endpoint or the higher endpoint? How do you know?

• What is a decimal that would fall between the first (or second) endpoint and the number that ______ named?

How do you know it falls in that range on the number line?

• What is a decimal that would not be placed between these endpoints because it is too small? Too large?

Grade 4

The grade 4 decimal standards focus on understanding decimals through hundredths and representing numbers between whole numbers as decimals and decimal fractions (fractions with 10, 100, etc. as the denominator). The sample number pairs below reflect this focus in the fourth grade standards.

whole number endpoints	decimal endpoints	fraction & decimal endpoints
between 7 and 8 between 16 and 17 between 29 and 30 between 56 and 62	between 7.3 and 7.4 between 16.2 and 16.8 between 29.35 and 29.7 between 56.5 and 62.05	between $\frac{3}{10}$ $\frac{3}{10}$ and 1 between $4 \frac{2}{10}$ $4\frac{2}{10}$ and 5 between 13.4 and $13 \frac{75}{100}$ $13\frac{75}{100}$ between $42 \frac{45}{100}$ $42\frac{45}{100}$ and 42.8

whole number endpoints

decimal endpoints

fraction & decimal endpoints

between 7 and 8

between 16 and 17

between 29 and 30

between 56 and 62

between 7.3 and 7.4

between 16.2 and 16.8

between 29.35 and 29.7

between 56.5 and 62.05

between $\frac{3}{10}$ $\frac{3}{10}$ and 1

between $4 \frac{2}{10}$ $4\frac{2}{10}$ and 5

between 13.4 and $13 \frac{75}{100}$ $13\frac{75}{100}$

between $42 \frac{45}{100}$ $42\frac{45}{100}$ and 42.8

Grade 5

The grade 5 decimal standards focus on understanding decimals through thousandths. The sample number pairs below reflect this focus in the fifth grade standards.

whole number endpoints	decimal endpoints	fraction & decimal endpoints
between 7 and 8 between 16 and 17 between 29 and 30 between 56 and 62	between 7.3 and 7.45 between 16.058 and 16.3 between 29.3 and 29.715 between 56.529 and 56.58	between $\frac{23}{100}$ $\frac{23}{100}$ and 0.904 between $4 \frac{235}{1000}$ $4\frac{235}{1000}$ and 5 between 13.018 and $13 \frac{7}{100}$ $13\frac{7}{100}$ between $42 \frac{45}{100}$ $42\frac{45}{100}$ and 42.863

whole number endpoints

decimal endpoints

fraction & decimal endpoints

between 7 and 8

between 16 and 17

between 29 and 30

between 56 and 62

between 7.3 and 7.45

between 16.058 and 16.3

between 29.3 and 29.715

between 56.529 and 56.58

between $\frac{23}{100}$ $\frac{23}{100}$ and 0.904

between $4 \frac{235}{1000}$ $4\frac{235}{1000}$ and 5

between 13.018 and $13 \frac{7}{100}$ $13\frac{7}{100}$

between $42 \frac{45}{100}$ $42\frac{45}{100}$ and 42.863

An excellent online tool for this routine is Zoomable Number Line Links to an external site.. This interactive tool allows the user to move forwards and backwards on a number, showing any integer, and then to zoom in or out, showing the numbers between those numbers or the multiples of 10, 100, 1,000 etc. that those numbers fall between.

Click the arrows to shift the number line to the right or left, and then click on the number line to begin zooming in on one of the numbers in between. Zooming in on 7 and 8 would eventually show the tenths that fall between those numbers...

Zoomable number line 1.png