Line Graphs and Change: a week of ready-to-teach maths

Five days of lessons for Year 5 Statistics. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus sketch graphs to match to stories and conclusion cards to sort, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Print the two card sheets once per pair.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.

No maths background needed

This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: a line graph shows how something changes over time. A value is read by going up from the time to the line and across to the scale; the slope says whether it is rising, falling or steady, and how fast; and a fair conclusion says only what the readings show.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 reads single values; Days 2 and 3 read the changes between them; Day 4 draws a line graph and tells its whole story; and Day 5 judges which conclusions the readings support. It builds on reading column graphs and dot plots (AC9M5ST01) and on reading points on a grid (AC9M5SP02), and it leads to Year 6, where data sets are compared side by side (AC9M6ST01).

Materials for the week (one trip)

• From the classroom: rulers, sharp pencils, a coloured pencil each, scissors, this pack printed.
• Print once per pair: the sketch graph and story cards (Day 4) and the conclusion cards (Day 5).

Words for the word wall

line graph, axis, scale, reading, rising, falling, steady, steep, highest, lowest, change, estimate, conclusion

Dear families

This week in maths, Year 5 reads line graphs that show how something changes over time, such as the temperature through a day. We read values, describe parts of the line as rising, falling or steady, and decide which conclusions a graph really supports.

Try this at home

• Look at a weather forecast that shows the temperature hour by hour. When will it be warmest?
• Measure something that changes, such as a plant or a shadow, at the same time each day this week.
• When you see a graph in the news, ask: what does it show, and what can it not tell us?

Changes I noticed this week

Fill one row a day. Write something that changed and whether it was rising, falling or steady.

Printed from the free seegongsik Line Graphs and Change teaching pack · seegongsik.com/au/y5/statistics/AC9M5ST02/pack

Reading a line graph

A line graph shows how something changes over time: time along the bottom, the measurement up the side, and a point for each reading, joined by a line. To read a value, go up from the time to the point, then across to the scale; to find a time, go across from the value, then down. Between two readings the line gives only an estimate: nothing was measured there.

We are learning to

• read a value from a line graph,
• find the time for a given value,
• tell a measured reading from an estimate between readings.

Success criteria

• I can read values from a line graph by counting along its scale.
• I can explain why a value between two readings is only an estimate.

You need

A ruler each, to slide up and across the graph. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with Part B.

Watch for these ideas

• Reading the nearest numbered line instead of counting the light lines in between.
• Reading straight across from the time, instead of going up to the line first.
• Treating the line between two readings as if it had been measured.

Answers

• Part A: 10:00 21 °C, 14:00 28 °C, 18:00 23 °C; 26 °C at 12:00, 27 °C at 16:00.
• Part B: 18:00, by 2 °C. Part C: about 27 °C, halfway between 26 at 12:00 and 28 at 14:00; no reading was taken at 13:00, so the real temperature could have been a little different.

Reading a line graph

A. Read the graph

B. Warmer or cooler?

Was it warmer at 10:00 or at 18:00? By how many degrees?   ______________________

C. Between the readings

Estimate the temperature at 13:00.   ______ °C   Why can it only be an estimate?

Rising, falling, steady

Each part of a line graph tells part of the story: where the line goes up the amount is rising, where it goes down it is falling, and where it is level it is steady. The steeper the line, the faster the change, because more changes in the same time. The change between two readings is the later value take away the earlier one.

We are learning to

• describe each part of a line graph as rising, falling or steady,
• work out the change between two readings,
• link a steeper line to a faster change.

Success criteria

• I can say whether a part of the line rises, falls or stays steady, and by how much.
• I can find where the change was fastest by looking for the steepest part.

You need

The Day 1 worksheet. A ruler each. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the fastest fall.

Watch for these ideas

• Calling a level part ‘nothing’ or ‘zero’. Steady means the same amount, not none.
• Judging how fast from how long a section is, instead of from how steep it is.
• Taking away the wrong way round and calling a fall a rise.

Answers

• Part A: 8:00 to 11:00 rising (+45); 11:00 to 12:00 steady (0); 12:00 to 14:00 rising (+20); 14:00 to 15:00 steady (0); 15:00 to 18:00 falling (-60).
• Part B: 16:00 to 17:00, 25 fewer people; it is the steepest part going down. Part C: stories vary, for example: the pool filled up all morning, stayed busy into the afternoon, then emptied fastest after 16:00.

Rising, falling, steady

A. Describe each part of the day

B. The fastest fall

In which hour did the number of people fall fastest?   ______ to ______   How can you tell from the line?

C. Tell the story of the day at the pool in three sentences

Highest and lowest

The highest point of a line graph is when the amount was greatest, and the lowest point when it was least; the gap between them shows how far the amount moved. The biggest rise or fall between neighbouring readings is the steepest part of the line. Reading these points, with their times, answers most of the questions a line graph is drawn for.

We are learning to

• find the highest and lowest readings and when they happened,
• work out the gap between the highest and lowest,
• find the biggest rise and the biggest fall between readings.

Success criteria

• I can read the highest and lowest points of a line graph, with their times.
• I can find the steepest rise and fall and say how big they were.

You need

The Day 2 worksheet. A ruler each. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the biggest rise and fall.

Watch for these ideas

• Giving the value of the highest point but not when it happened, or the other way round.
• Finding the biggest rise by looking for the highest point instead of the steepest part.
• Reading a fall as a small number when the scale does not start at 0.

Answers

• Part A: highest 84% in September; lowest 48% in April; 84 − 48 = 36 percent. Part B: biggest rise June to July, up 11; biggest fall November to December, down 8.
• Part C: answers vary; the dam rose from April to September, fastest from June to July, so more water came in than went out then, most likely from rain.

Highest and lowest

A. Highest and lowest

B. The biggest changes

C. What the year shows

When in the year do you think most rain fell near this dam? What part of the line makes you think so?

Draw it, tell it

To draw a line graph from a table: time along the bottom, the measurement up the side on a scale with equal steps that fits the biggest value, a point for each reading, then the points joined in order with a ruler. The shape of the whole line is the relationship: a straight line is a steady change, a line that gets steeper is speeding up, and a line that flattens out is slowing down.

We are learning to

• draw a line graph from a table of readings,
• describe the relationship that the whole line shows,
• match the shape of a graph to a story.

Success criteria

• I can plot readings and join them to make a line graph.
• I can say how something changed over time from the shape of its line.

You need

Rulers and sharp pencils. The sketch graph and story cards (cut-out sheet 1), one set per pair, cut out. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with Part B.

Watch for these ideas

• Plotting the heights as columns, or forgetting to join the points.
• Reading the biggest growth from the tallest point instead of the steepest part.
• Matching a story to the sketch that looks like the object, not the one whose line changes the same way.

Answers

• Part A: points at week 0 0, week 1 5, week 2 12, week 3 22, week 4 35, week 5 50, week 6 62, week 7 70, week 8 74 cm, joined in order. Part B: most from week 4 to 5, 15 cm; least from week 7 to 8, 4 cm; it grew slowly at first, fastest in the middle weeks, then slowly again.
• Part C: A 3, B 1, C 4, D 2.

Draw it, tell it

A. Plot the sunflower’s height and join the points

B. Read your graph

C. Match the sketch graphs to the stories

Fair conclusions

A conclusion is fair when the readings support it. Some statements a graph shows; some it shows are not so; and some it cannot tell us at all, such as what happens after the last reading, exactly what happened between readings, and why anything happened. Saying ‘the graph cannot tell us’ is a careful answer, not a wrong one.

We are learning to

• decide whether a line graph supports a conclusion,
• recognise what a graph cannot tell us,
• back up a judgement with readings from the graph.

Success criteria

• I can sort statements into: the graph shows it, shows it is not so, or cannot tell.
• I can point to the readings that back up each choice.

You need

The conclusion cards (cut-out sheet 2), one set per pair, cut out. Mini whiteboards for the quiz. The worksheet.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with Part B.

Watch for these ideas

• Treating ‘cannot tell’ as a wrong answer. It is a careful one.
• Carrying the line on past the last reading as if it had been measured.
• Giving a reason why something happened that the graph does not show.

Answers

• Part A: the graph shows it: 1, 3, 6; the graph shows it is not so: 2, 7; the graph cannot tell us: 4, 5, 8.
• Part B: 12 degrees in the first 2 minutes and 3 in the last 2; the line curves because each 2 minutes it cooled by less than before. Part C: answers vary.

Fair conclusions

A. Sort the conclusion cards. Write the card numbers.

B. How fast did it cool?

1. How many degrees did it cool in the first 2 minutes?   ______   In the last 2 minutes?   ______

2. Why is the line curved and not straight?

C. Your own

Write one conclusion the graph shows, and one thing it cannot tell us.

Sketch graphs and stories

One set per pair (Day 4). Each sketch graph shows how something changed over time, with no numbers. Cut out the eight cards and match each sketch to its story.

Teacher note: each sketch has exactly one story. The matches are on the Day 4 plan.

Conclusion cards: the hot chocolate

One set per pair (Day 5). Each card says something about the hot chocolate graph on the Day 5 worksheet. Sort the cards into three piles: the graph shows it, the graph shows it is not so, and the graph cannot tell us.

Teacher note: the piles are on the Day 5 plan. A card can start an argument; the graph settles it.

What we know: Line Graphs and Change

1. How many cars were there at 9:00?   ______
2. At what time were there the most cars?   ______
3. Between which two hours did the number of cars rise the most?   ______ and ______
4. Describe the line from 9:00 to 14:00.   ______________________________
5. How many fewer cars were there at 17:00 than at 11:00?   ______
6. Estimate the cars at 15:30.   ______   Why is it only an estimate?
7. Write shows or cannot tell for each.
   a. The number of cars fell the most between 15:00 and 16:00.   ______________

   b. The car park will be empty at 20:00.   ______________
8. Tell the story of the car park’s day in one sentence.

Answers and marking guide

Answers

1. 35
2. 11:00 (38 cars)
3. 7:00 and 8:00 (up 18)
4. about steady: it stays between 33 and 38 cars
5. 38 − 4 = 34
6. about 17 or 18, halfway between 25 and 10; no count was made at 15:30
7. a. the graph shows it; b. the graph cannot tell us
8. for example: the car park filled quickly in the morning, stayed nearly full until the afternoon, then emptied

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, by reading each value against the scale and by saying only what the readings show.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: reading values, rising and falling, highest and lowest, drawing and describing, and fair conclusions.