Week 9 of 10

Data Detective

Students collect data with tally charts, display it in bar graphs and pictographs, and read graphs to answer questions and compare categories - finding the story hidden in the numbers.

Estimated time: 45-60 minutes
Grade range: Grades 2-5
Skill focus: Tally charts, Bar graphs, Pictographs, Interpreting data, Comparing categories
Theme: The Data Detective: turning tally marks into answers

The story

A mystery is buzzing around the classroom: what is everyone's favorite fruit? Rumors say apples, but the Data Detective doesn't trust rumors - the Data Detective collects evidence. You'll survey the class, make tally marks for every vote, then turn those marks into a graph so clear that anyone can see the answer at a glance.

What you'll learn

Collect data with a tally chart and count tallies in groups of five.
Build a bar graph and a pictograph from a data set, including a key for the pictograph.
Read a graph to answer 'how many,' 'which is most/least,' and 'how many more' questions.

Key ideas

Data is information we collect, and a chart keeps it organized.
Bar graphs use bar height and pictographs use pictures to compare categories.
Reading a graph means comparing categories and finding differences.

Words to know

Data: Information you collect to answer a question.
Tally chart: A chart that records counts with marks grouped in fives.
Bar graph: A graph that compares categories using the height of bars.
Pictograph: A graph that uses pictures to stand for amounts.
Key: A note telling how many items each picture in a pictograph stands for.
Category: One group or choice being counted, like 'apples'.

The lesson

Data is information we gather to answer a question. To keep it organized, we use a tally chart: one mark for each item, and every fifth mark drawn across the previous four so we can count by fives. Tally marks make counting a big survey fast and accurate.

A bar graph shows data with bars - the taller the bar, the more there is in that category. Bars make it easy to compare: the tallest bar is the 'most' and the shortest is the 'least,' and you can see it in one glance without doing any arithmetic.

A pictograph uses a picture to stand for a number of items, explained by a key (for example, one apple picture = 2 votes). If a row has 3 apple pictures and each stands for 2 votes, that category has 6 votes. The key is essential - without it, you can't tell what the pictures mean.

The real detective work is reading the graph. You answer questions like 'How many chose bananas?', 'Which fruit was most popular?', and 'How many more chose apples than grapes?' That last one is a subtraction: find both bars and take the difference.

Worked examples

A tally chart shows apples with four vertical marks and one line crossing them. How many votes is that?

5 votes

Four marks with a fifth crossing them is one group of five, which equals 5 votes.

In a pictograph, each apple = 2 votes. A row has 4 apple pictures. How many votes?

8 votes

Multiply the number of pictures by the key value: 4 pictures x 2 votes each = 8 votes.

A bar graph shows apples = 9 and grapes = 4. How many more chose apples?

5 more

Find both bars and subtract: 9 - 4 = 5. Five more people chose apples than grapes.

Try it: interactive practice

This is the week's practice game. Work through it right here - try each step yourself, then check your thinking.

Activity

From Tallies to Graph

Turning the same data set into tallies, a bar graph, and a pictograph shows that a graph is just an easier-to-read picture of the numbers you collected.

This survey asked, “What is your favorite fruit?” Adjust the votes and watch the bar graph update, then answer the questions from the graph.

Apple

Banana

Grapes

Orange

Same data as tally marks

Apple
Banana
Grapes
Orange

Read the graph

Which fruit has the most votes?

Which fruit has the fewest votes?

Hands-on challenge

Run Your Own Survey

What you need

Grid paper
Pencil
A question to survey
Ruler for straight bars

Steps

1
Pick a question with four choices (favorite color, pet, sport, or snack).
2
Ask at least ten people and record each answer with a tally mark.
3
Turn your tallies into a bar graph on grid paper, then write two questions your graph can answer.

You've got it when: Your bar graph has labeled categories and a clear scale, and you can answer 'which is most' and 'how many more' from it.

Checkpoint

Quick checks before you move on. Try each one first, then reveal the answer.

1
How do tally marks help you count a big survey?
Show answer
They group counts into fives, so you can count quickly by 5s instead of one by one.
2
In a pictograph where each star = 5, a row has 3 stars. How many is that?
Show answer
15 (3 stars x 5 = 15).
3
A bar graph shows dogs = 7 and cats = 10. How many more chose cats?
Show answer
3 more (10 - 7 = 3).

Think about it

Why is a graph easier to understand than a long list of tally marks? What does a graph let you see quickly?

Challenge problem

A pictograph of pets uses one paw = 4 pets. Dogs have 5 paws, cats have 3 paws, and fish have 2 paws. How many pets are there in all, and which is the most popular?

Show hint

Find each category's count by multiplying paws by 4, then add all the categories together.

Show answer

40 pets total, and dogs are the most popular. Dogs = 5 x 4 = 20, cats = 3 x 4 = 12, fish = 2 x 4 = 8; 20 + 12 + 8 = 40.

Extension · go further

Collect data on two different days and make two bar graphs side by side. Write one sentence describing how the results changed between the days.

Finished the lesson, activity, and challenge? Mark this week complete to track your progress through the 10-week course.