Tables, Graphs & Patterns in Data — Print · Grade 6 Science

Tables, Graphs & Patterns in Data

Learning goals

I can build a results table with units in the headings and a column for the mean.
I can choose between a bar chart and a line graph from the kind of data I have.
I can tell the difference between reading inside my data and guessing beyond it.

Readings for this unit

A Neat Result Is Not Yet an Explanation

Before this unit

Read the chapter opening and the named observation or diagram. Clarify one word or unit that blocks understanding. Recall the relevant earlier measurement, matter, or energy idea.

Study the unit across three 35–45-minute class sessions. Use the worked examples after an attempt and the supplied records when actual equipment is not available.

Hang masses on a spring and measure how far it stretches. With 100 g the spring extends 18 mm; with 200 g, 36 mm; with 300 g, 54 mm. Each extra 100 g adds another 18 mm, which is a pattern you can almost see in the list but not quite.

Plot those three points with mass along the bottom and extension up the side and the pattern is unmistakable: a straight line through the origin. Keep going and at 600 g the extension is 118 mm instead of the 108 mm the line predicts, and at 700 g it is 150 mm. The line has bent, and the graph shows that long before the table does.

That bend is the interesting part of the investigation, and it is the part a badly drawn graph would hide. This lesson is about recording numbers so the pattern can show itself, and about the ways a graph can mislead you or somebody else.

Build your understanding

Where this fits

The last lesson was about taking an honest measurement. This one is about what to do with a column of them. Every investigation in this course ends in a table and usually a graph, and the chapter investigation will ask you to produce both and to say what the shape of your graph means.

Use three flexible 40-45-minute sessions: building the table; choosing and drawing the graph; reading patterns and spotting misleading ones, then the practice set, revision and the exit check. Workshop, review, quiz and exams have separate time.

Part 1 · The table comes first

A results table has one column for the independent variable, one column for each repeat of the dependent variable, and a column for the mean. Units go in the heading, not beside every number, so the heading reads Mass (g) and the cells below it read 100, 200, 300. Writing the unit once in the heading is not only tidier; it forces you to decide what unit you are using before you start recording, which is where the Mars orbiter went wrong in the last lesson. Leave the table ruled and ready before you take a single reading, because inventing columns while measuring is how repeats get lost.

The repeats earn their place. With three readings of the extension at each mass you can take a mean, and you can also see the spread. If the three readings at 300 g are 53, 54 and 55 mm, your mean of 54 mm is solid and your uncertainty is about 1 mm. If they are 48, 54 and 61 mm, the mean is still 54 mm but it now means something much weaker, and reporting it without the spread would hide that completely. A table that shows only means has thrown away half of what was measured, and no graph drawn from it can get that information back. Add one more column if your investigation has anything you had to hold steady but could not control perfectly -- room temperature, say -- and record it each time rather than assuming it stayed put. A column of readings between 19 and 23 degrees Celsius is useful evidence later if your results look odd.

Picking the wrong form hides the pattern you collected the data to find. Separate categories need gaps between bars; something measured over time needs points joined so the trend is visible.

Pause and explain

Why should a results table keep the individual repeats rather than only the mean?

Check your reasoning after answering

Because the mean alone hides how much the readings varied. Three values of 53, 54 and 55 mm and three of 48, 54 and 61 mm give the same average but very different confidence, and only the first supports comparing results that differ by a couple of millimetres. Once the repeats are discarded that information cannot be recovered.

Part 2 · Which graph, and why

The choice follows from the kind of independent variable you have. If it is a measured quantity that could take any value in between, like mass in grams or temperature in degrees Celsius, use a line graph: points plotted and a line or smooth curve drawn through the trend. If it is a set of separate categories, like four different materials or three brands of battery, use a bar chart with gaps between the bars, because there is nothing in between aluminium and copper for a line to pass through. Drawing a line across categories suggests a trend that cannot exist.

Then draw it properly. The independent variable goes along the bottom and the dependent variable up the side, every axis carries a label and a unit, and the scale rises in even steps that use most of the paper. A scale that jumps 0, 10, 50, 100 makes a straight relationship look like a curve, and one that squeezes the data into the bottom corner wastes the graph's whole purpose. Plot the points first with small neat crosses, then decide what line fits; drawing the line you expected and fitting points to it afterwards is a way of seeing what you wanted to see. One more rule that costs nothing: plot every point you measured, including the ones that sit awkwardly off the trend. An outlier left on the graph is information, and a reader can see you noticed it. An outlier quietly deleted turns a record of what happened into a picture of what you hoped would happen, and nobody looking at the finished graph can tell the difference.

Pause and explain

Why is a bar chart right for comparing four different metals but wrong for a range of masses?

Check your reasoning after answering

Because metals are separate categories with nothing between them, while masses form a continuous scale. There is no value halfway between copper and aluminium for a line to represent, so bars with gaps are honest. Masses of 100 and 200 g do have real values in between, so a line correctly shows that the relationship continues through them.

Part 3 · Reading the shape

A straight line through the origin means the two quantities are proportional: double the mass and you double the extension. A straight line that does not pass through the origin means there is a fixed amount there before you start, like a spring that already hangs 5 mm under the weight of its own hook. A curve that flattens out means the effect is reaching a limit, and a curve that steepens means something is accelerating. Naming the shape is the first sentence of your conclusion, and it should come before any attempt to explain why.

Reading between your points is called interpolation and is usually safe: if the line is straight from 100 g to 300 g, a mass of 250 g almost certainly gives about 45 mm. Reading beyond your points is extrapolation and is where investigations go wrong. The spring at the start of this lesson looked perfectly proportional up to 500 g, and anyone extrapolating that line to 700 g would have predicted 126 mm and got 150 mm, because the spring had started to deform permanently. A graph tells you about the range you measured and makes no promises outside it. This is why a published result almost always states the range it covers. A claim that a relationship is proportional means proportional between the smallest and largest values tested, and the sentence that reports it should say so: proportional from 100 to 500 g is a useful finding, while proportional on its own is a claim nobody measured.

Pause and explain

Why is extrapolation riskier than interpolation?

Check your reasoning after answering

Because it assumes the pattern continues where nothing was measured. Between measured points the behaviour is bounded on both sides by data, but beyond the last point a new effect can take over -- a spring beginning to deform, a solution becoming saturated -- and the graph gives no warning. The spring stretched 150 mm at 700 g where the line predicted 126 mm.

Part 4 · Patterns that are not there

Two quantities can rise together without one causing the other. The classic pair is ice cream sales and drowning deaths, both of which peak in July because of hot weather, and the same trap appears in real investigations whenever something you did not record is driving both columns. A graph showing two lines climbing together is evidence that something connects them, and never by itself evidence of which way the connection runs or whether a third thing is behind both.

The other common distortion is the axis that does not start at zero. If a bar chart of average temperatures runs from 20 to 24 degrees Celsius up the side, a difference of 1 degree fills a quarter of the chart and looks dramatic; the same data on an axis from 0 to 25 looks almost flat. Neither picture is a lie about the numbers, and they give completely different impressions, so a reader has to check the axis before trusting the shape. Starting at zero is the safe default, and if you have a reason to do otherwise, say so on the graph. A third trick to watch for is a graph built on very few points. Two points can always be joined by a straight line, so a two-point graph cannot tell you whether the relationship is straight at all; five or six points are what let a curve reveal itself. When you meet a striking graph anywhere, count the points before you believe the shape.

Pause and explain

What should you check before trusting the shape of a graph you did not draw?

Check your reasoning after answering

Where the axes start and what their steps are. A vertical axis beginning at 20 rather than 0 magnifies small differences until they look dramatic, and uneven steps can bend a straight relationship into a curve. The underlying numbers may be perfectly correct while the picture gives an impression they do not support.

Apply the whole unit · Pick the graph and read it

A class measures how long 5 g of sugar takes to dissolve in 100 mL of water at five temperatures: at 20 degrees Celsius it takes 95 s, at 30 it takes 61 s, at 40 it takes 42 s, at 50 it takes 31 s and at 60 it takes 25 s.

Your task

Choose the right graph, describe the pattern, and state what the data does not support.

What your response should show

Chooses a line graph and justifies it from the type of variable
Labels both axes with quantity and unit, independent along the bottom
Describes the shape, including that the effect diminishes, before explaining it
Distinguishes a safe interpolation from an unsafe extrapolation with reasons

Response guidance — after your attempt

Say which graph type fits this data and why, and state what goes on each axis with its unit.
Describe the shape of the relationship in words, without yet explaining the cause.
Give one value you could read off the graph safely and one you could not, with reasons.

Temperature is a continuous measured quantity, so this is a line graph with temperature in degrees Celsius along the bottom and dissolving time in seconds up the side. The shape is a falling curve that flattens: raising the temperature from 20 to 30 degrees Celsius cuts 34 s off the time, while raising it from 50 to 60 cuts only 6 s. So the time decreases as temperature rises, and each further 10 degrees buys less than the one before. I could safely read off a value at 35 degrees Celsius, since it sits between measured points on a smooth curve and should be around 50 s. I could not read off a value at 90 degrees Celsius: that is well beyond the measured range, the curve is clearly flattening towards some limit, and extrapolating it would also carry me towards 100 degrees Celsius where the water boils and the investigation stops being the same one.

Scientific references for this unit

Parent / teacher teaching notes

Begin with the literal observation, quantity, or diagram relationship. Ask the learner to explain why the evidence supports the claim, check a relevant unit or boundary, then discuss an alternative. The supplied numbers are illustrative, not real observations. A parent can read aloud and allow a spoken rehearsal before writing. Judge science and evidence rather than political, faith, or family agreement. Use the complete data option whenever an actual procedure is unavailable or unsuitable.

The key idea

A table records what you measured; a graph shows what it does. Choosing the wrong graph, or drawing the axes carelessly, can hide a real pattern or invent one that was never in the numbers.

Worked examples

Example 1 · Compare a cooling record

Find each 10-minute temperature change and explain a supported comparison.

Identify the matched start and final time.
Subtract final from initial temperature for each cup.
Describe the difference with a method limit.

Answer: The unwrapped cup decreases by 9 °C and the wrapped cup by 5 °C. The wrapped cup cools less over ten minutes under the stated comparison. This supports slower cooling if volumes, lids, location, and measurement are matched; it does not prove the wrapping prevents all energy transfer.

Example 2 · Transfer to a different case

Two category bars begin at 98 instead of zero and show 100 and 102. What should a reader check?

Identify the distinction and conditions in this new case.
Use the relevant mechanism or quantity; preserve units and the chosen boundary.
Explain why the answer fits and what further evidence would be needed.

Answer: Check the labeled axis and full difference: 2 units. A shortened axis can emphasize that difference, so the graph should make its scale explicit rather than suggest a huge proportional change.

Example 3 · Choose a graph for the relationship · a focused example

What does the downward pattern describe?

State the literal condition or observation in the example.
Apply the distinction explained in this teaching part.
Check whether the claim stays within the given evidence.

Answer: Recorded temperature decreases over those times. It does not identify every energy transfer or predict an exact future value by itself.

Avoid these mistakes

Misleading claim: A missing value is automatically a measured zero.
Misleading claim: A graph’s association automatically establishes a cause.
Omitting units, measurement timing, or a model boundary makes the evidence hard to interpret.
Treating illustrative classroom data as real field measurements or copying a model is not an independent explanation.

Check your understanding

Why must the absent reading stay missing?

Discuss the answer

No measurement establishes its value. Plotting zero would invent an observation and could distort the pattern.

What does the downward pattern describe?

Discuss the answer

Recorded temperature decreases over those times. It does not identify every energy transfer or predict an exact future value by itself.

Does a mean of 7 mean every trial held 7?

Discuss the answer

No. It summarizes three values; the individual loads differ and should remain available.

Can a graph fix a confounded comparison?

Discuss the answer

No. Clear display improves interpretation but cannot remove a problem in how the evidence was collected.

Sustained scientific explanation and revision

These activities are scheduled in the parent plan. Save a first response, a correction, and the reason for the change in the science notebook.

Activity 1 · Tables, Graphs & Patterns in Data · Model and explain

Assigned reading and preparation

Read A Neat Result Is Not Yet an Explanation and the linked unit teaching; use its complete supplied case and diagrams.

Your task

For Tables, Graphs & Patterns in Data, study Parts 3–4 and attempt the worked case: Find each 10-minute temperature change and explain a supported comparison. Explain the steps before opening the model.

Success criteria

An accurate scientific claim answering the actual question.
Relevant evidence or a labeled model with quantities and units when applicable.
Reasoning that connects evidence with the mechanism rather than only repeats it.
A specific method, boundary, scale, or alternative-explanation limit.

Hint

Begin with the actual observation, quantity, or diagram relationship. Explain how it bears on the question before making a broad claim.

Response guidance — discuss after your attempt

The unwrapped cup decreases by 9 °C and the wrapped cup by 5 °C. The wrapped cup cools less over ten minutes under the stated comparison. This supports slower cooling if volumes, lids, location, and measurement are matched; it does not prove the wrapping prevents all energy transfer.

Activity 2 · Tables, Graphs & Patterns in Data · Practice, revise and exit

Assigned reading and preparation

Read A Neat Result Is Not Yet an Explanation and the linked unit teaching; use its complete supplied case and diagrams.

Your task

For Tables, Graphs & Patterns in Data, complete practice questions 1–6 and both choice checks, then answer independently: Two category bars begin at 98 instead of zero and show 100 and 102. What should a reader check? Save a correction explaining one changed claim or method.

Success criteria

An accurate scientific claim answering the actual question.
Relevant evidence or a labeled model with quantities and units when applicable.
Reasoning that connects evidence with the mechanism rather than only repeats it.
A specific method, boundary, scale, or alternative-explanation limit.

Hint

Begin with the actual observation, quantity, or diagram relationship. Explain how it bears on the question before making a broad claim.

Response guidance — discuss after your attempt

Check the labeled axis and full difference: 2 units. A shortened axis can emphasize that difference, so the graph should make its scale explicit rather than suggest a huge proportional change.

Words to know

mean: The sum of comparable values divided by their count.
pattern: A relationship observed in records that may guide a test or explanation.
evidence: A relevant observation, measurement, or record used to evaluate a claim.
system boundary: The chosen limit specifying what is included and which exchanges cross it.
uncertainty: A stated limit in measurement or knowledge, distinct from a careless mistake.

In the real world

Meteorologists live in graphs: they plot temperature and pressure as line graphs to track a storm, and news forecasts show you those same trends so you can decide whether to grab an umbrella tomorrow.

Exit check

Two category bars begin at 98 instead of zero and show 100 and 102. What should a reader check?

Check your explanation after answering

Check the labeled axis and full difference: 2 units. A shortened axis can emphasize that difference, so the graph should make its scale explicit rather than suggest a huge proportional change.

Explain your reasoning without notes. If a key idea is missing, revisit the lesson and try again.

Problem 1

Why must the absent reading stay missing?

Answer and explanation

No measurement establishes its value. Plotting zero would invent an observation and could distort the pattern.