The Lumenary · K–2

Data, tallies and picture graphs

Name: ______________________

Date: ______________________

You will learn to

Ask a simple question, collect the answers and sort them into categories, with each answer in exactly one category
Record counts with tally marks grouped in fives, and show them in a picture graph or block graph
Answer "which is most?", "how many more?" and "how many altogether?" questions from a graph
Explain why the pictures in a picture graph must be the same size and evenly spaced

1.
A tally shows one gate (four strokes with a fifth stroke across them) and 3 more strokes. How many answers does it show?
2.
A class made a picture graph of their favourite fruits. Each picture is one child, and all the pictures are the same size.
- Mango: 🥭🥭🥭🥭🥭🥭
- Banana: 🍌🍌🍌🍌
- Orange: 🍊🍊🍊🍊🍊🍊🍊
- Apple: 🍎🍎🍎
Which fruit is the most popular?
- A.Mango
- B.Orange
- C.Apple
3.
Use the fruit graph: orange 7, banana 4. How many more children chose orange than banana?
4.
Use the fruit graph again: mango 6, banana 4, orange 7, apple 3. Every child chose exactly one favourite fruit. How many children were asked?
5.
Baraka wants a survey question where every child gives exactly one answer, so the totals add up to the number of children. Which question should he ask?
- A.What is your favourite animal?
- B.Which animals have you seen at the zoo?
- C.How many animals are there in the world?
6.
24 children each gave one answer. But when the class added up their tallies, the total was 26. What probably went wrong?
- A.Some answers were tallied twice
- B.Nothing — totals never add up
- C.Two children were absent
7.
In a pet picture graph, the dog row has 4 big dog pictures 🐕 and the cat row has 6 small cat pictures 🐈. The dog row is longer. Which pet did more children choose?
- A.Dogs, because the row is longer
- B.Cats, because there are more cat pictures
- C.The same number
8.
In a picture graph of favourite sports, the key says one ⭐ stands for 2 children. The football row has ⭐⭐⭐⭐. How many children chose football?
9.
Gideon's game: true or false? "If every child gives exactly one answer, and every answer goes into exactly one category, then the category totals add up to the number of children."
- A.True, for every survey like this
- B.True only for small classes
- C.False
10.
Margaret's program draws a gate of five as ||||\. It printed this tally:

||||\ ||||\ ||

How many answers does the tally show?

Answer key — Data, tallies and picture graphs

1.
The gate stands for 5. Counting on the 3 loose strokes: six, seven, eight. The tally shows 8 answers.
2.
Counting each row: mango 6, banana 4, orange 7, apple 3. Orange has the most. Because the pictures are the same size and evenly spaced, the longest row is also the one with the most pictures.
3.
Pair the 4 banana pictures with 4 orange pictures. 3 orange pictures are left over, so 3 more children chose orange: $7 - 4 = 3$ .
4.
Each child chose one fruit, so each child is counted in exactly one row. Adding the rows: $6 + 4 + 7 + 3 = 20$ . 20 children were asked.
5.
"What is your favourite animal?" gives one answer per child, so each answer goes into exactly one category and the totals add up to the number of children. "Which animals have you seen?" allows several answers, so totals can come to more than the number of children.
6.
With one answer per child, the tallies should add up to 24. A total of 26 is 2 too many, so probably some answers were marked twice (or put in two rows). Counting again, crossing off each answer as it is marked, would find the mistake.
7.
Cats: 6 children chose cats and 4 chose dogs. The dog row only looks longer because the dog pictures are bigger. A fair picture graph uses pictures of the same size, evenly spaced.
8.
Each star stands for 2 children. Counting in twos for 4 stars: two, four, six, eight. 8 children chose football.
9.
True. Each child's answer is in exactly one category, so when we count every category and add, each child is counted exactly once. This works for every class, which is why Lean can prove it for every list of answers — not just check one class.
10.
Two gates make five, ten. Counting on the 2 loose strokes: eleven, twelve. The tally shows 12 answers.