Comparing Data Sets: a week of ready-to-teach maths

Five days of lessons for Year 6 Statistics. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus variable sort cards and Match the data cards, 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. Cut out the variable sort cards for Day 1 and the Match the data cards for Day 4, one set for each pair.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. For Day 5, have a spreadsheet open on the board; the worksheet also works without one.

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: data comes in kinds (named categories, ordered categories, counts and measurements), and two groups are compared fairly by drawing them side by side on the same scale. Three plain summaries do the comparing: the mode (the most common value), the range (largest take away smallest) and the shape (how the values are spread across the range).

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.

Words to watch

Nominal data are categories with no order (sports); ordinal data are categories with an order (T-shirt sizes); discrete data are counts (pets); continuous data are measurements that can take any value in between (heights, times). A distribution is how a data set’s values are spread out. Skewed means the values bunch at one end with a long tail at the other.

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 sorts the kinds of data and compares categories side by side; Day 2 finds the mode and range of counts; Day 3 compares two groups by mode and range; Day 4 adds the shape of a distribution, with measurements grouped into intervals; and Day 5 lets a spreadsheet do the working while children do the comparing. It builds on the Year 5 work of representing data and describing its mode and shape (AC9M5ST01). It leads to critiquing statistical claims (AC9M6ST02) and running a statistical investigation (AC9M6ST03).

Materials for the week (one trip)

• All week: grid paper, rulers and two colours of pencil.
• For Day 1: the variable sort cards, one set for each pair.
• For Day 3: paper for paper planes and a long tape measure, if you want class data.
• For Day 4: a stopwatch, if you want class data, and the Match the data cards. For Day 5: a spreadsheet on the board.

Words for the word wall

data, variable, categorical, nominal, ordinal, numerical, discrete, continuous, mode, range, distribution, shape, symmetric, skewed, interval, scale

Dear families

This week in maths, Year 6 compares data sets: two groups side by side, using the mode (the most common value), the range (how spread out) and the shape of the data.

Try this at home

• Time how long everyone in the family takes to tie their shoes. What is the range of the times?
• Count the letters in each family member’s first name. What is the mode?
• Look at a graph in a newspaper or online. Are the two things being compared on the same scale?
• Talk about which kind of data each is: favourite food, shoe size, number of cousins, height.

Our family data

Fill one row a day. Write a question, the answers you collected, and the mode or range.

Printed from the free seegongsik Comparing Data Sets teaching pack · seegongsik.com/au/y6/statistics/AC9M6ST01/pack

Categories side by side

Data comes in four kinds: nominal categories (no order), ordinal categories (an order), discrete counts and continuous measurements. To compare two groups’ categories, draw their columns side by side on one scale, with a key; ordinal categories keep their order along the bottom. Children sort variables, draw a side-by-side column graph for two classes, and find each class’s mode.

We are learning to

• sort variables into nominal, ordinal, discrete and continuous,
• draw and read a side-by-side column graph,
• compare two groups’ categories, including their modes.

Success criteria

• I can say why T-shirt size is ordinal but favourite sport is nominal.
• I can find the mode of each class from a side-by-side column graph.

You need

The worksheet, one per child, the variable sort cards (cut-outs), and two colours of pencil.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the sort; start Session B with the graph in Part B.

Watch for these ideas

• Calling any data with numbers in it numerical, such as a 1-to-5 star rating.
• Drawing one class’s columns, then the other’s, instead of pairing them in each category.
• Putting ordinal categories in any order, which hides the pattern.

Answers

• Part A: (1) N, (2) O, (3) D, (4) C, (5) N, (6) O, (7) D, (8) C.
• Part B: modes 6R Car, 6T Bus; biggest difference bike (6T has 4 more); 26 children in each class.
• Part C: the categories are out of order. In order they are not at all 2, a little 6, quite a lot 9, a lot 7: 16 of 24 chose quite a lot or a lot, a pattern the jumbled order hides.

Categories side by side

A. What kind of data?

Write N (nominal), O (ordinal), D (discrete) or C (continuous).

B. How do you get to school?

Draw the two classes’ columns side by side for each way of travelling. Colour them to match the key.

Mode for 6R: ________ Mode for 6T: ________ Biggest difference between the classes: ____________________

C. In order?

Mode and range

The mode is the value that occurs most often; a set can have two modes, or none when nothing repeats. The range is the largest value take away the smallest, and tells how spread out the values are. On a dot plot the mode is the tallest stack and the range runs from the left-most dot to the right-most. Children plot a class’s data, find its mode and range, and decide which summary a question needs.

We are learning to

• show discrete data on a dot plot,
• find the mode and the range of a data set,
• choose whether a question needs the mode or the range.

Success criteria

• I can find the range of a list that is not in order.
• I can say when a data set has two modes, or none.

You need

The worksheet, one per child, and sticky notes if you want to build a class dot plot first.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Giving the number of times the mode occurs instead of the mode itself.
• Taking the first value from the last, without putting the values in order.
• Giving the range as two numbers, such as 2 to 11, instead of one difference.

Answers

• Part A: mode 4; range 11 − 2 = 9.
• Part B (mode, range): (1) 15, 8; (2) 7, 7; (3) 6 and 8, 4; (4) no mode, 9; (5) 4, 4.
• Part C: (1) the mode; (2) the range; (3) Ari: the range uses the largest and smallest values, wherever they are in the list.

Mode and range

A. Books read this term

Class 6R: 4, 6, 3, 5, 8, 4, 5, 6, 4, 2, 7, 4, 4, 9, 5, 6, 3, 4, 11, 6, 5, 4, 7, 5

Plot each child’s number of books as a dot. Stack dots that are the same.

Mode: ______    Range: ______ − ______ = ______

B. Find the mode and the range

C. Mode or range?

1. A shoe shop wants to order more of the most popular size. Mode or range? ________

2. A coach wants to know how steady a player’s scores are from game to game. Mode or range? ________

3. For 3, 9, 4, Ari says the range is 9 − 3 = 6. Jo says it is 4 − 3 = 1, because 4 is last. Who is right? Why? ____________

Compare two groups

Two groups are compared fairly when their dot plots sit one above the other on the same scale. The modes say which value was most usual in each group; the ranges say which group was more spread out, or less consistent. A group can be higher but less steady, so a good comparison uses both. Children compare two paper-plane designs and two classes’ game scores and write comparison sentences.

We are learning to

• draw two groups on dot plots with the same scale,
• compare two groups by their modes and their ranges,
• write a comparison that uses the data.

Success criteria

• I can say which plane design was more consistent, and give the ranges as evidence.
• I can explain why the two dot plots must use the same scale.

You need

The worksheet, one per child, and two colours of pencil. If you have time, fly real paper planes and measure in metres.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Comparing only the highest values, so one long throw decides the whole comparison.
• Thinking a bigger range means a better group.
• Comparing dot plots drawn on different scales by eye.

Answers

• Part A: Dart mode 11, range 10; Glider mode 9, range 4; the Dart usually flew further, the Glider was more consistent.
• Part B: Year 4 mode 5, range 5; Year 6 mode 7, range 5; Year 6 usually scored higher; both groups were equally spread.
• Part C: the scales differ, so Year 6’s scores look spread across the whole line and lower than they are; draw both from 0 to 10.

Compare two groups

A. Paper planes: distance flown (metres)

Dart: 9, 11, 7, 12, 4, 10, 11, 13, 6, 11, 8, 14, 11, 5, 10

Glider: 8, 9, 9, 10, 8, 9, 7, 9, 10, 8, 9, 11, 9, 8, 10

Dart: mode ______ range ______ Glider: mode ______ range ______

Which design usually flew further? Which was more consistent? Use the data. ____________________________

B. A reaction game: score out of 10

Write two sentences comparing the groups, one using the mode and one using the range. ______________________

C. Same scale?

These plots show the Part B data on different scales. What wrong idea could they give? ______________________

The shape of the data

Measurements such as times hardly ever repeat exactly, so a dot plot of them is a row of single dots. Instead, count the values into equal intervals and draw a column for each, the columns touching because the intervals join on. The outline is the shape: symmetric piles up in the middle and tails off evenly; skewed bunches at one end and is named for the side its long tail points to. Children tally two year levels’ puzzle times and compare shapes, modes and ranges.

We are learning to

• count measurements into equal intervals,
• describe a distribution as symmetric, skewed or even,
• compare two groups by shape as well as by mode and range.

Success criteria

• I can put a time that sits on a boundary, such as 40.0 seconds, in the right interval.
• I can explain why a long tail of slow times makes a shape skewed to the right.

You need

The worksheet, one per child, the Match the data cards (cut-outs) for each pair, and a stopwatch if you want class data.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Putting a time on a boundary, such as 40.0, in the lower interval: 40 to under 50 starts at 40.0.
• Reading skewed to the right as most values on the right; the name follows the long tail.
• Leaving out an empty interval, which squeezes the shape and stops two graphs lining up.

Answers

• Part A: Year 3 0, 4, 12, 4, 0; Year 6 3, 12, 3, 1, 1 (intervals in order).
• Part B: Year 3 symmetric, most times 40 to under 50 seconds, range 20.1 s; Year 6 skewed to the right, most times 30 to under 40 seconds, range 34.3 s. Year 6 usually finished sooner, but their times were more spread, with a tail of slow times.
• Part C: (1) two peaks, (2) skewed to the right, (3) symmetric, (4) skewed to the left.

The shape of the data

A. Puzzle times (seconds)

Year 3: 41.2, 38.5, 44.9, 53.8, 47.3, 42.8, 39.6, 51.4, 45.0, 33.7, 43.5, 40.0, 48.8, 37.9, 46.1, 44.0, 52.6, 50.9, 42.1, 49.5

Year 6: 29.8, 33.4, 31.6, 38.2, 27.5, 44.7, 35.9, 32.3, 61.8, 30.0, 36.6, 41.3, 34.8, 28.9, 57.2, 33.1, 39.4, 31.9, 47.6, 35.2

B. Draw the shapes

Draw a column for each interval from your counts. Make the columns touch.

Year 3 shape: ______________ Year 6 shape: ______________

Compare the year levels. Use the interval with the most times, the range and the shape. ______________________________

C. Name the shape

Use a word from this list. One word is not used: symmetric · skewed to the right · skewed to the left · even · two peaks

Let the spreadsheet help

A spreadsheet finds the mode and the range of a long list in a moment and never miscounts, but it cannot decide what the numbers mean. Typed into a cell, =MODE(B2:B17) gives the most common value in cells B2 to B17, and =MAX(B2:B17)-MIN(B2:B17) gives the range. Children read a spreadsheet of two classes’ standing long jumps, check it by hand, and report a comparison using mode, range and shape.

We are learning to

• read the mode and the range a spreadsheet works out,
• write a spreadsheet formula for the range,
• report a comparison that uses the mode, the range and the shape.

Success criteria

• I can write a formula for the range of the values in a column.
• I can explain why two classes with the same mode can still be very different.

You need

The worksheet, one per child, and a spreadsheet on the board if you have one; the worksheet works without it.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Leaving out the equals sign, so the cell shows the words instead of working anything out.
• Using the wrong cells, such as B2:B16, which leaves out the last child.
• Stopping at the mode: the same mode can sit in very different spreads and shapes.

Answers

• Part A: (1) the most common jump in 6R, 150 cm, by 3 children; (2) no: 6R runs from 136 to 174 cm, 6T runs from 112 to 188 cm; (3) =MAX(B2:B17)-MIN(B2:B17); (4) 6R 174 − 136 = 38 cm, 6T 188 − 112 = 76 cm.
• Part B: 6R symmetric, 6T even.
• Part C, for example: both classes’ most common jump was 150 cm, but 6T’s jumps were far more spread out (range 76 cm against 38 cm), with about the same number in every interval, while 6R’s were symmetric and bunched in the middle.

Let the spreadsheet help

A. Standing long jumps (centimetres)

B. The spreadsheet’s graphs

The spreadsheet counted each class’s jumps in 10 cm intervals.

6R shape: ______________ 6T shape: ______________

C. Report

Write a short report comparing the two classes’ jumps. Use the mode, the range and the shape.

________________________________________________________________________________

________________________________________________________________________________

Variable sort cards

Print one set for each pair and cut along the dashed lines. Lay out the four heading cards, then sort the variables under them.

Teacher note: nominal 3, 6, 9, 12; ordinal 1, 7, 11, 15; discrete 4, 8, 13, 16; continuous 2, 5, 10, 14. Card 7, the star rating, uses numbers but is ordinal: two stars is not twice as good as one.

Match the data cards

Print one set for each pair and cut along the dashed lines. Match each dot plot to the card that describes it.

Teacher note: A 3, B 6, C 2, D 5, E 1, F 4. Every card needs all three clues: some share a mode, some share a range, and some share a shape.

What we know: Comparing Data Sets

Work on your own. Show your thinking if you can.

1. Write N (nominal), O (ordinal), D (discrete) or C (continuous).

   (a) the mass of a watermelon ____	(b) the colour of your front door ____
   (c) the number of cousins you have ____	(d) a school report grade: A, B, C, D or E ____

2. Find the mode and the range of 7, 9, 9, 10, 12, 9, 15. Mode: ______ Range: ______
3. Find the mode of 3, 6, 6, 2, 8, 2, 5. ______________
4. Two classes chose their favourite fruit. Which fruit is the mode for each class? Which fruit shows the biggest difference between the classes? ______________________________
5. Goals scored in each game. Which team scores more consistently? Give the evidence. ______________________________
6. Name the shape of this graph of test scores. Which way does its tail point? ______________________________
7. A spreadsheet has the heights of a class in cells C2 to C25. Write a formula that works out the range. ______________________
8. Two classes both have a mode of 7 for a spelling test. Kai says the classes did equally well. Give a reason Kai could be wrong. ______________________________________________

Answers and marking guide

Answers

1. (a) C, (b) N, (c) D, (d) O.
2. Mode 9; range 15 − 7 = 8.
3. 2 and 6: both occur twice, so the set has two modes.
4. 6A banana, 6B mango; the biggest difference is banana (5 children).
5. Team X: both teams’ mode is 3, but Team X’s range is 3 and Team Y’s is 7.
6. Skewed to the left: the long tail points to the low scores.
7. =MAX(C2:C25)-MIN(C2:C25)
8. The same mode can sit in different spreads and shapes: one class could bunch near 7 while the other spreads from low scores to high ones.

A quick three-level guide

Eight questions, four ideas. A child at standard sorts the four kinds of data, finds a mode and a range, and compares two groups using mode, range and shape.

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: kinds of data and side-by-side graphs, mode and range, comparing two groups, shape, and the spreadsheet.