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Mathematics 2 Ms. Meek Gathering Data Review. A Venn diagram uses circles to show the relationship between sets of information. Venn Diagrams

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Mathematics 2

Ms. MeekGathering Data Review

A Venn diagram uses circles to show the relationship between sets of information. Venn DiagramsVenn diagrams are great organizational tools for certain kinds of math word problems. They are also useful in organizing lists by categories or qualities.

Venn DiagramsExample (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 DiagramsIn the list below, which of the following foods are green, which foods are fruit, which are both green and fruit, and which are neither?

blackberrieslimespeas cherriescabbagepearsbroccoli bananas lemonscarrots

Venn Diagrams Fruit green food

blackberrieslimespeas Cherriescabbagepearsbroccoli bananas lemonscarrots both

Venn DiagramsExample: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 DiagramsExample: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 DiagramsVenn DiagramsMilkJuice

ONLYONLY12 30-12= 42 12 = 18 30

both3042Example: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 GraphsA 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-AxisA 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

Practice219

What is the ordered pair for the point?(5,3)5 4 3 1 0 1 2 3 4 5 6 7

Practice220When 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 GraphsSince 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 GraphsLine Graphs

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

LabelsLine 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.

PictographEvery pictograph has a title, pictures or symbols, labels and a key.

Pictograph

titlelabels 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 eachPractice

Which sports are represented in the survey?Baseball, football, soccer, hockey, and basketballPractice

How many students play football?30 studentsPractice

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 pepperoniPractice

How many orders are for cheese pizza?25 ordersPractice