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Solve Problems Using Data in Line Plots with Fractions

Students use addition, subtraction, multiplication, and division of fractions to answer questions about data displayed in line plots. Problems include finding totals, differences, and averages from the displayed data.

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Solve Problems Using Data in Line Plots with Fractions

Grade 5 · Line Plots with Fractions · question 1 of 3

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20 rungs. A star at the top.

111411213422142122343straw piece lengths

All the straw pieces together: how many inches?

Add every length on the plot, in inches.

Your answer:

How it is taught

0:00 of 4:12

Total length is value times how many marks.

Same-size lengths add by counting the marks.

Read it: Line plots of fractions

5 ribbons on a line plot: 1 X at 4, 3 X's at 4 1/2 and 1 X at 4 3/4 inches. Count the X's, take the shortest from the longest (3/4 inch), or add every X's length.

  1. Measure each thing and put 1 X above its length on the scale.
  2. Read the plot: count the X's at a length, and find the shortest and the longest.
  3. To add every length, multiply each stack's length by its X's, then add the stacks.

Each X stands for 1 thing, so X's at the same length stack up.

The longest minus the shortest is how far the lengths run: 4 3/4 − 4 = 3/4.

A stack of 3 X's at 4 1/2 is 4 1/2 + 4 1/2 + 4 1/2: its length counts once for every X, so it is 3 × 4 1/2.

One X for each thing: count the X's, take the shortest from the longest, or add the stacks.

Adding each stack's length once, as if every stack were 1 ribbon.

Every X is a ribbon, so the 3 X's at 4 1/2 add 4 1/2 three times.

Ribbons were measured: 2 measure 2 1/8 inches and 1 is 2 3/8 inches long. What is the total length of all the ribbons, in inches? — 6 5/8. 2 × 2 1/8 + 2 3/8 = 4 1/4 + 2 3/8 = 6 5/8 inches.

Total worm length from a line-plot of fractional measurements

Aria measured five worms to the nearest quarter inch. Let's use her line plot to find the total length of all five worms put together.

Here is our number line, marked in fourths from zero to one inch.

Look at this line plot. Each X stands for one worm. One worm is a fourth long, two worms are two-fourths long, and two worms are three-fourths long.

Grade 5 · Add up data from a fractional line plot

To find the total, we multiply each length by how many X's sit above it, and then add the pieces.

One worm at one-fourth. One times one-fourth is one-fourth.

Two worms at two-fourths. Two times two-fourths is four-fourths.

Two worms at three-fourths. Two times three-fourths is six-fourths.

Now add the three pieces: one-fourth plus four-fourths plus six-fourths.

The bottoms are all fourths, so we just add the tops. One plus four plus six is eleven. The total is eleven-fourths.

Eleven-fourths is more than one whole. Eleven divided by four is two with three left over, so it equals two and three-fourths.

All five worms together are two and three-fourths inches long. Nice work pulling answers right out of the line plot!

Now you try. Count the marks above that quarter-inch tick. How many marks sit there?

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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