Math Core

You already know how to read a line plot: every X stands for one measurement. In 5th grade, you'll measure in eighths too, and you'll use what you know about adding, subtracting and dividing fractions to answer bigger questions, like "How much in all?" and "What if everyone got the same amount?"

Line plots in eighths

Some measurements need finer marks than halves or fourths. A number line marked in eighths has 8 equal spaces between each pair of whole numbers.

Notice that $\tfrac{2}{8} = \tfrac{1}{4}$ , $\tfrac{4}{8} = \tfrac{1}{2}$ and $\tfrac{6}{8} = \tfrac{3}{4}$ , so those marks usually get the simpler labels. When you add or subtract values from a line plot, it helps to write them all as eighths.

Worked example: Rainfall

A class recorded the rainfall, in inches, on 10 rainy days.

Rainfall on rainy days (inches)

What is the difference between the most and the least rain on one day? The greatest value is $\tfrac{3}{4}$ and the least is $\tfrac{1}{8}$ :

\frac{3}{4} - \frac{1}{8} = \frac{6}{8} - \frac{1}{8} = \frac{5}{8} \text{ inch}.

How much rain fell in all? Multiply each value by its number of X's, then add. Use eighths:

\begin{aligned} 2 \times \tfrac{1}{8} &= \tfrac{2}{8} \\ 3 \times \tfrac{1}{4} &= 3 \times \tfrac{2}{8} = \tfrac{6}{8} \\ 1 \times \tfrac{3}{8} &= \tfrac{3}{8} \\ 3 \times \tfrac{1}{2} &= 3 \times \tfrac{4}{8} = \tfrac{12}{8} \\ 1 \times \tfrac{3}{4} &= \tfrac{6}{8} \end{aligned}

Total: $\tfrac{2}{8} + \tfrac{6}{8} + \tfrac{3}{8} + \tfrac{12}{8} + \tfrac{6}{8} = \tfrac{29}{8} = 3\tfrac{5}{8}$ inches.

Sharing equally

Sometimes a problem asks what would happen if the total were shared out evenly. This is called finding the equal share.

Finding the equal share

Find the total of all the measurements on the line plot.
Count the number of X's.
Divide: equal share $=$ total $\div$ number of X's.

Remember that a fraction is a division: $5 \div 8 = \dfrac{5}{8}$ .

Worked example: Pouring it all out evenly

A science class has 8 beakers of water. The line plot shows how much water is in each one.

Water in each beaker (liters)

If the water were poured out and shared equally among all 8 beakers, how much would each beaker hold?

Step 1: total. Use fourths:

2 \times \tfrac{1}{4} + 2 \times \tfrac{2}{4} + 2 \times \tfrac{3}{4} + 2 \times \tfrac{4}{4} = \tfrac{2}{4} + \tfrac{4}{4} + \tfrac{6}{4} + \tfrac{8}{4} = \tfrac{20}{4} = 5 \text{ liters}.

Step 2: count. There are 8 X's, one for each beaker.

Step 3: divide. $5 \div 8 = \tfrac{5}{8}$ .

Each beaker would hold $\tfrac{5}{8}$ liter.

Check: $\tfrac{5}{8}$ is between $\tfrac{1}{2}$ and $\tfrac{3}{4}$ , right in the middle of the data. That makes sense.

Making a line plot in eighths

Worked example: Bolt lengths

Theo measured 9 bolts to the nearest eighth of an inch:

$\tfrac{3}{4}, \ \tfrac{5}{8}, \ \tfrac{7}{8}, \ \tfrac{3}{4}, \ \tfrac{5}{8}, \ \tfrac{3}{4}, \ 1, \ \tfrac{7}{8}, \ \tfrac{3}{4}$

The smallest is $\tfrac{5}{8}$ and the largest is 1, so the number line runs from $\tfrac{5}{8}$ to 1 in eighths. Tally each value: $\tfrac{5}{8}$ appears 2 times, $\tfrac{3}{4}$ appears 4 times, $\tfrac{7}{8}$ appears 2 times and 1 appears 1 time.

Bolt lengths (inches)

Check: $2 + 4 + 2 + 1 = 9$ X's for 9 bolts. ✓

If Theo lines up just the $\tfrac{7}{8}$ -inch bolts end to end, how long is the row? $2 \times \tfrac{7}{8} = \tfrac{14}{8} = 1\tfrac{6}{8} = 1\tfrac{3}{4}$ inches.

Common mistake

When you find a total, don't just add the numbers under the columns. Each value counts once for every X above it. In the rainfall plot, $\tfrac{1}{2}$ has 3 X's, so it adds $3 \times \tfrac{1}{2} = 1\tfrac{1}{2}$ inches to the total, not just $\tfrac{1}{2}$ .

Tip

An equal share should always land between the smallest and largest values on the plot. If your answer is outside that range, check your total and your count.

Practice

This line plot is used in the first three problems.

Ant lengths (inches)

Practice 1

Look at the ant line plot above. How many ants were measured?

Type a number.

Practice 2

Look at the ant line plot above. What is the difference in length between the longest ant and the shortest ant, in inches?

Type a number.

Practice 3

Look at the ant line plot above. If all the ants that are $\tfrac{3}{8}$ inch long lined up end to end, how long would the line be, in inches?

Type a number.

Practice 4

Ella measured 8 pieces of string, in inches:

$\tfrac{1}{2}, \ \tfrac{5}{8}, \ \tfrac{3}{4}, \ \tfrac{5}{8}, \ \tfrac{7}{8}, \ \tfrac{1}{2}, \ \tfrac{5}{8}, \ \tfrac{3}{4}$

She makes a line plot. How many X's are to the right of $\tfrac{5}{8}$ ?

Type a number.

Practice 5

Jin packed bags of trail mix. The line plot shows the weight of each bag.

Trail mix bags (pounds)

What is the total weight of all the bags, in pounds?

Type a number.

Practice 6

Look back at the ant line plot. What fraction of the ants are longer than $\tfrac{1}{2}$ inch? Write it in simplest form.

Type a number.

Practice 7

Four friends poured juice into glasses. The line plot shows how much juice is in each glass.

Juice in each glass (cups)

If they poured the juice together and shared it equally, how many cups would each friend get?

Type a number.

Practice 8

A weather station recorded the snowfall on 6 snowy days.

Snowfall (inches)

If the same total amount of snow had fallen evenly over the 6 days, how many inches would have fallen each day?

Type a number.