Learn how a sequence of points becomes a change story. Build one-line and two-line graphs, compare trends, measure increases and decreases, and explain what the evidence really shows.
Plot the points. Connect in order. Measure the change.
The horizontal axis has a meaningful order—often time, test number, age, or distance. Each point gives one measured value. Connecting the points helps us follow change.
time or order → point → point → trend
Bar chart
Separate bars compare named categories such as vegetables, clubs, or sports events. The categories do not have to form a journey through time.
category A | category B | category C
Do not connect unrelated categories just because you can. A line between “vegetables” and “eggs” would suggest a change path that does not exist.
A seedling was measured at the end of five days. Its heights were 4, 6, 7, 7, and 9 centimetres.
Explore: choose a day below to highlight its point.
Read one point as a sentence
Day 1horizontal value
4 cmvertical value
(1, 4)the plotted point
The horizontal segment from Day 3 to Day 4 means both daily measurements were 7 cm. The line joins those readings; it does not provide extra measurements between them.
3
Mission 3
Turn Class A’s table into one line
Not completed
Five tests, each marked out of 100 points, form an ordered sequence. Each listed score is the class mean on that test. Copy each Class A mean score to the matching test column. The preview plots your entries immediately.
Test
1
2
3
4
5
Class A original data
70.0
75.0
84.6
85.3
87.5
Your plotted y-values
Construction rule: each test gets one point at its score, and the points are connected from Test 1 to Test 5.
4
Mission 4
Add Class B—and give each line a name
Not completed
A double line graph places two related series on the same axes. Both lines must use the same tests and the same score scale. A legend tells us which line is which.
Class AClass B
Test
1
2
3
4
5
Class A
70.0
75.0
84.6
85.3
87.5
Class B original data
62.4
69.5
80.1
85.0
93.6
Your Class B y-values
Same axes, two series: compare the two points above the same test before comparing change across tests.
5
Mission 5
Read the two values above the same test
Not completed
Inspection strategy: choose a test, move vertically to both points, then read their y-values from the common scale.
70.0Class A score
62.4Class B score
7.6gap in points (larger mean − smaller mean)
Measured points and crossing: Class A is still slightly higher on Test 4, while Class B is higher on Test 5. The connecting lines suggest that B overtook A somewhere between those two tests, but the graph does not give an exact score at an unmeasured moment.
6
Mission 6
A high point is a level; a steep segment is a change
Not completed
change = later value − earlier value
Choose an interval to highlight it. The panel shows how much each class changed during that one interval.
Compare changes fairly: subtract over the same test interval for both classes. Equal spacing here represents one test interval, not necessarily the same number of days.
Tests 1→2highlighted interval
+5.0Class A change
+7.1Class B change
Tests 1→2A +5.0 B +7.1
Tests 2→3A +9.6 B +10.6
Tests 3→4A +0.7 B +4.9
Tests 4→5A +2.2 B +8.6
7
Mission 7
Name each trend—and inspect the graph’s rules
Not completed
Practice series: 10, 13, 13, 9, 12.
Trend vocabulary
Increase: later value is greater.
No change: later value is equal.
Decrease: later value is smaller.
A line can change direction several times. Describe one segment or one clearly named period at a time.
Steepness warning: visual steepness represents rate only when horizontal spacing correctly represents the amount of time. When intervals have different lengths, calculate change per year.
8
Mission 8
Compare two changing quantities over unequal year gaps
Not completed
A village of 100 households recorded the numbers of mobile phones and computers owned in five years. These are counts of devices, not counts of households that own one. The years are not equally far apart, so the graph spaces them according to the actual gaps. Compare increases in device counts, not percentage increases.
Mobile phonesComputers
Read the missing labels: the computer points at 2011, 2013, and 2014 are marked with blank parentheses. Read their values from the vertical scale, or use the accessible data table below.
Accessible data table
Year
2006
2009
2011
2013
2014
Phones
10
20
60
90
95
Computers
2
5
10
40
70
average yearly change = total change ÷ number of years
From 2011 to 2013, the computer increase is 40 − 10 = 30 over 2 years, so the average is 30 ÷ 2.
9
Mission 9
Find a peak, a long trend, and the greatest monthly change
Not completed
A city recorded the number of rainy days in each month of one year:
Monthly sequence: every point is labeled. Choose a month to inspect its value and the change from the previous month.
Juneselected month
19 daysrainy days
+7change from previous month
original challenge · Put your skills together
A discount changes the graph’s steepness
A seed shop charges 2 yuan per kilogram for the first 5 kg. Only the amount beyond 5 kg costs 80% of the usual rate. Paying 80% means paying 0.8 times the price: 2 × 0.8 = 1.6 yuan per extra kilogram.
The horizontal axis is kilograms bought; the vertical axis is total cost in yuan. This graph describes cost, not a journey.
Graph AGraph BGraph CGraph D
See a worked explanation
First 5 kg: 5 × 2 = 10 yuan. For 7 kg, the extra amount is 7 − 5 = 2 kg, so the cost is 10 + 2 × 1.6 = 13.2 yuan.
Graph B starts at (0,0), reaches (5,10), and then keeps rising more gently. Only the extra kilograms get the lower rate: do not multiply the whole bill by 0.8. Compare this with a journey graph: the slope here is price per kilogram, not speed.
11
Mission 11
Exit ticket
Not completed
Try these five questions on your own first. You can use a hint or check an attempt before opening worked review. The optional reflection is not graded.
↻
Keep tracking
Review exact values, changes, and average yearly change, then try again.
📈
Certificate of Mastery
Line-Graph Trend Tracker
This certifies that
can construct line graphs, compare two changing quantities, and measure trends with evidence.
Lesson 2.6 · Follow Change with Line Graphs
Teaching notes
The seedling and five-point trend examples are original instructional scaffolds added so children can learn the graph structure before tackling the original datasets.
The seed-price challenge uses this lesson Exercise 1 ().