Grade by Grade
D. Data · Data and Probability

Collecting Data with Two-Way Tally Tables

D1.2 A1About 35 minutes
Learning goals
  • I can ask a data question that collects two pieces of information.
  • I can collect data by interviewing, observing, or doing an experiment.
  • I can organize my data in a two-way tally table.
  • I can count tallies by 5s and 1s and check my totals.

Words to know

data
Information we collect to answer a question.
interview
Collecting data by asking people a question.
observation
Collecting data by watching and recording what you see.
experiment
Collecting data by doing something again and again and recording what happens.
tally mark
A line that stands for 1. The 5th line goes across the first 4 to make a bundle of 5.
two-way tally table
A tally table with rows AND columns, so it can hold two pieces of information about each answer.

Let's get started!

Noah's class wants to know: "What is the favourite season?" Noah wonders, "Do kids and grown-ups like the same season?"

To find out, he needs to collect two pieces of information from each person: their favourite season, and whether they are a kid or a grown-up.

Remember from Grade 1

  • Data is information that answers a question.
  • You can collect data by interviewing (asking), observing (watching), or doing an experiment (trying something many times).
  • A tally mark stands for 1. The 5th mark goes across the first 4. Count bundles by 5s, then count on by 1s.

Questions with two pieces of information

In Grade 2, our data questions can look at two things at once. Here are some examples:

  • What is your favourite season? and Are you a kid or a grown-up?
  • Which birds come to the feeder? and Do they come in the morning or the afternoon?
  • How does a cup land when you toss it? and Is it a paper cup or a plastic cup?

A good question has clear choices, so the answers are easy to sort and count.

The two-way tally table

A two-way tally table has rows for one piece of information and columns for the other. Each answer gets one tally mark in the box where its row and column meet.

Noah interviewed 18 kids and 15 grown-ups. Here is his table:

Our Favourite SeasonKidsGrown-upsWinterSpringSummerFall
Two-way tally table: favourite season of kids and grown-ups.
SeasonKidsGrown-upsTotal
Winter628
Spring246
Summer7512
Fall347
Total181533
The same data with numbers. Source: Noah's interviews.
Worked example

Reading the two-way table

Use Noah's table. How many kids chose winter? How many people chose summer in all?

  1. Find the Winter row. Move across to the Kids column.
  2. The tallies show one bundle of 5 and 1 more: 5, then 6. So 6 kids chose winter.
  3. Now find the Summer row. Kids: one bundle and 2 more = 7. Grown-ups: one bundle = 5.
  4. Add: 7 + 5 = 12.

6 kids chose winter. 12 people chose summer in all.

A two-way table lets us compare the two groups:

  • Kids chose summer the most (7). Grown-ups chose summer the most too (5).
  • More kids than grown-ups chose winter: 6 kids and only 2 grown-ups. Maybe kids love tobogganing and snow days!
Worked example

Collecting data with an experiment

Zara tossed a paper cup 10 times and a plastic cup 10 times. She wrote what happened.

Paper cup: side, side, up, down, side, side, down, side, side, up

Plastic cup: side, down, side, side, side, up, side, down, side, side

Make a two-way tally table.

  1. Rows are the ways the cup can land: on its side, right side up, upside down. Columns are the two cups: paper and plastic.
  2. Go through the paper cup list one at a time. Make a tally in the Paper cup column and cross out each word as you go.
  3. Paper cup: side 6, up 2, down 2. Check: 6 + 2 + 2 = 10.
  4. Now do the plastic cup list in the Plastic cup column.
  5. Plastic cup: side 7, up 1, down 2. Check: 7 + 1 + 2 = 10.

Both cups landed on their side most often. Paper: 6 times. Plastic: 7 times.

How Did the Cup Land?Paper cupPlastic cupOn its sideRight side upUpside down
Zara's two-way tally table for her cup experiment.

Check your totals

Count how many people you asked or how many times you tried. Then add up all the tallies. The two numbers should match! If they don't, something was missed or counted twice.

Just for fun

What did the four tally marks say when the fifth one went across them?

"Hey, no cutting in line!" 🚧

Collecting by observation

You can also watch and record. Sam watched the bird feeder for 10 minutes in the morning and 10 minutes in the afternoon. He tallied each bird in a two-way table with Morning and Afternoon columns.

When you observe, keep your eyes on one place and make your tally right away so you don't forget!

A chickadee, a northern cardinal and a blue jay at a snowy wooden bird feeder in a backyard.
Chickadees, cardinals and blue jays often visit feeders in Ontario in winter. You could tally which birds come in the morning and which come in the afternoon. AI-generated image
Hands-on activity

Be a data collector

Choose one question. Each one collects two pieces of information.

  • Interview: "Which do you like best: apples, bananas, or grapes?" Ask kids and grown-ups (in person, by phone or by video call). Make columns for Kids and Grown-ups.
  • Observation: Look out a window for 10 minutes. Tally vehicles as car, truck, or other, in columns for going left and going right.
  • Experiment: Toss a paper cup 10 times and a plastic cup 10 times. Tally how each one lands.

Then:

  1. Draw a two-way tally table with labels for the rows and columns, and a title.
  2. Make one tally for each answer. Bundle in 5s.
  3. Write the number for each box, and add the totals.
  4. Check that the total matches the number of people or tries.
  5. Tell someone one thing your table shows.

Your turn

1

Which way of collecting data is it? You ask your cousins what pet they want.

2

Which way of collecting data is it? You roll a toy car down a ramp 10 times and record how far it goes.

3

Use Noah's table. How many grown-ups chose spring?

4

Use Noah's table. How many people chose fall in all?

5

Use Noah's table. Which season did the fewest grown-ups choose?

6

How many does this tally show: two bundles of 5 and 3 more?

7

Write a question that collects two pieces of information.

More practice: warm-up

1

How much is one tally mark worth?

2

How much is one bundle of tally marks worth?

3

How many does this tally show: one bundle of 5 and 4 more?

4

Which way of collecting data is it? You count how many people wear toques at the bus stop.

5

In a two-way tally table, where do you put a tally for a grown-up who likes summer?

More practice: on your own

1

Use Zara's cup table. How many times did the plastic cup land right side up?

2

Use Zara's cup table. How many times did both cups together land upside down?

3

Use Noah's table. How many more kids than grown-ups chose winter?

4

Mila asked 12 people a question. Her tally table has 5 + 4 + 2 tallies. What went wrong?

5

Tara wants to know if kids or grown-ups like snow more. Her question is "Do you like snow?" What second piece of information should she collect?

Challenge

1

Here is some data. Each pair is (snack, grade): (apple, Gr 1), (apple, Gr 2), (crackers, Gr 2), (apple, Gr 2), (cheese, Gr 1), (crackers, Gr 1), (apple, Gr 1), (apple, Gr 2), (cheese, Gr 2). Make a two-way tally table.

2

Why is "What do you like?" not a good data question?

3

Sam's bird table: chickadees: morning 8, afternoon 3. Blue jays: morning 2, afternoon 4. Did Sam see more birds in the morning or the afternoon? How many more?

Check your understanding

Quiz

1.

How many does this tally show: three bundles of 5 and 2 more?

2.

Which is an experiment?

3.

A two-way tally table is good for...

4.

Use Noah's table (Winter: kids 6, grown-ups 2). How many people chose winter?

5.

You asked 15 people. Your tallies add up to 16. What does that tell you?

6.

Which question collects two pieces of information?

For parents and teachers

What your child is learning: to collect data by interview, observation or experiment for a question that has two pieces of information, and to organize it in a two-way tally table (rows and columns), as in Ontario expectation D1.2. Asking good questions and checking totals also builds the mathematical processes in Strand A.

Common difficulties:

  • Putting a tally in the right row but the wrong column. Have your child point to the row with one finger and the column with another finger and slide them together.
  • Making the 5th tally a 5th upright line. Practise drawing bundles: four down, fifth across.
  • Losing count while tallying from a list. Cross off each answer as it is tallied.
  • Not checking totals. Always ask, "How many people did you ask? Does your table add up to that?"

At home: collect real data together, for example tally what family members choose for breakfast on Saturday and Sunday, or how cars are parked on your street on two different days.