Mathematics 2

Ms. MeekGathering Data Review

A Venn diagram uses circles to show the relationship between

sets of information.

Venn Diagrams

Venn diagrams are great organizational tools for certain kinds of math word problems.

They are also useful in organizing lists by

categories or qualities.

Venn Diagrams

Example (organizing a list):In the list below, which of the

following foods are green, which foods are fruit, which are both green and fruit, and which

are neither?

blackberries, peas, limes, carrots, pears, broccoli,

cherries, bananas, cabbage, and lemons

Venn Diagrams

In the list below, which of the following foods are green,

which foods are fruit, which are both green and fruit, and which

are neither?

blackberrieslimes peas cherries

cabbage

pears broccoli bananas lemonscarrots

Venn Diagrams

Fruit green food

blackberrieslimes peas Cherries

cabbage

pears broccoli bananas lemonscarrots

both

Venn Diagrams

Example:At a student breakfast, 30 kids

drank milk with their food, 42 kids drank juice, and 12 kids

had milk and juice. If everyone had at least one drink, how many people had a drink?

Venn Diagrams

Example:At a student breakfast, 30 kids

drank milk with their food, 42 kids drank juice, and 12 kids

had milk and juice. If everyone had at least one drink, how many people had a drink?

Of the 30 kids that drank milk, 12 of them also had juice. This

means, that to find the number who ONLY had milk we must

subtract. The same is true of those who drank juice.

Venn Diagrams

Venn Diagrams

MilkJuice

ONLYONLY

12 30-12 = 42 – 12 =

18 30

both

30

42

Example:At a student breakfast, 30 kids

drank milk with their food, 42 kids drank juice, and 12 kids

had milk and juice. If everyone had at least one drink, how many people had a drink?

18 + 12 + 30 = 60

Venn Diagrams

A bar graph uses bars to represent and display data. The

bottom of the graph (x-axis) lists categories given to the

group surveyed. The side of the graph (y-axis) lists numbers.

Bar Graphs

A grid is simply several horizontal and vertical lines

drawn on a paper.

Grid

Grid lines intersect (cross or meet) at different points on the grid. Today, we will learn how to find points on a grid using coordinates, or ordered pairs.

Grid

Every grid has an x-axis and a y-axis.

The x-axis is used with the first number in an ordered pair, and is on a horizontal line. The y-axis is used with the second

number in an ordered pair, and is on a vertical line.

X- Axis and Y-Axis

A point on a grid can be identified by an ordered pair

such as (3, 2), which names the coordinates of that point.

The first number tells how far to the right or left the point is located on the x-axis. The

second number tells how far up or down the point is

located on the y-axis.

The numbers in an ordered pair are called coordinates.

Ordered Pairs

A point on a grid can be identified by an ordered pair

such as (3, 2), which names the coordinates of that point.

Ordered Pairs

A point on a grid is useful when charting information on a line

graph. Remember, the order of the pair matters. (3, 2) and (2,3) are coordinates for two

different points on a grid.

(2, 3)

Ordered Pairs

Remember, the order of the pair matters. (3, 2) and (2,3) are coordinates for two different points on a grid. Always start at the origin of the grid, move

over, and then move up.

(2, 3)

Origin

Ordered Pairs

Find ordered pair (4, 2)

5

4

3

1

0 1 2 3 4 5 6 7

Practice

2

What is the ordered pair for the point?(5,3)5

4

3

1

0 1 2 3 4 5 6 7

Practice

2

When we look at the relationship between two qualities that may

be described as numbers (temperature, height, weight…)

it is easy to use a line graph.

For example, you might record your height each year to see

how much you have grown, and you could see the changes on a

line graph.

Line Graphs

Since time can be described in numbers, line graphs are useful

for describing changes that happen

over a period of time.

The line graph can show these changes as increases or

decreases.

The direction of the line indicates whether there is an increase

(rise) or decrease (dip).

Line Graphs

Line Graphs

The x-axis and the y-axis are labeled by the qualities being

described.

Labels

Line Graphs

We plot points the same way we plot ordered pairs. Look

first at the value on the x-axis, and then the

value on the y-axis.

(8, 4)

Line Graphs

We can see that as the years increase, so does the height. We know this because the line

is rising. What happens at age 16?

Line Graphs

When we want to record information we have gathered,

we create a graph or chart. One type of graph

is a pictograph.

A pictograph organizes and shows information using

pictures.

Pictograph

Every pictograph has a title, pictures or symbols, labels and

a key.

Pictograph

title

labels pictures

key

Pictograph

The key explains what symbols or

abbreviations mean. A key might show that a picture

stands for one or more than one. Pay careful attention to information in the key and be

prepared to skip-count.

Pictograph

In this pictograph, the key tells us that each crayon represents two children that like that color. This means, that a half crayon

represents one student.How many children like the color

red? 12

Pictograph

Who was surveyed for this information?

The title tells us 3rd grade students.

Practice

According to the key, how many students does each ball

represent?10 students each

Practice

Which sports are represented in the survey?

Baseball, football, soccer, hockey, and basketball

Practice

How many students play football?30 students

Practice

Every bar graph has a title, bars that show data and labels on

each axis.

title\\

labels

Bar Graphs

The numbers on the y-axis do not always increase by 1. In this

graph the numbers increase by 10. The amount by which the

numbers increase is called the scale.

Bar Graphs

In this bar graph, the scale tells us that we are counting by 5 as

we move up the y-axis.

Bar Graphs

What information is being recorded?

The title tells us favorite pizza toppings.

Practice

Which toppings are represented in the survey?

cheese, mushroom, sausage, and pepperoni

Practice

How many orders are for cheese pizza?

25 orders

Practice