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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
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