# Statistics and Probability

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Statistics and Probability TABLE OF CONTENTS 1 Posing Questions and Gathering Data. 2 2 Representing Data. 7 3 Interpreting and Evaluating Data 13 4 Exploring Probability Games of Chance 20 6 Ideas for Data. 23 Student Pages 24 Statistics and Probability, Grades 3-5 1

2 Posing Questions and Gathering Data Mathematical Focus 8 Investigative questions 8 Data investigations that address those questions 8 Collection and organization of data In this activity, students are presented with a pile of 100 pennies. They brainstorm questions they would like to answer about the pennies, for example, How many pennies are in the pile? What is the oldest/newest penny? How many decades are represented? Which decade has the most pennies? For each question posed, students make an initial prediction about the answer. As they begin to gather data on the pennies, they have an opportunity to revise their predictions. Finally, students discuss and explore different strategies for gathering and recording their data. Preparation and Materials pennies You may want to gather the pennies needed for the activity from a variety of sources. This will increase the likelihood of having a range of dates. Save the penny data for future activities. Consider gathering data on two or more different sets of 100 pennies. Students can then make comparisons between the sets. Keep the list of questions students pose at the end of this activity; you will use them again in Activity 2. Statistics and Probability, Grades 3-5 2

5 Are you surprised by anything you discovered? Why or why not? Discussion 1. Think of other types of questions for which you could potentially gather and analyze data. Talk with students about the ways people use data analysis to investigate information about the world. Sometimes the results of these investigations are used to make decisions. Here are some examples to prompt them, if necessary: What is the most popular ice cream flavor (TV program, sport, movie, game, food, playground equipment, etc.) among the students at my school? Who in my class can run the fastest? How many books are checked out from the library in a month? What is the most popular type of book (e.g., biography, mystery, adventure) checked out from the library? 2. Discuss how data could be collected to answer these questions and how this information could be used. Talk about the ways in which students might collect data to answer each question. Suggestions might include surveys, experiments, measurements, or observations. Discuss how information from these investigations might be used; for example, knowing that science fiction books are the most popular type of book checked out from the library could justify ordering additional new science fiction books, or it might indicate the need for a greater selection of books in other categories. Statistics and Probability, Grades 3-5 5

6

7 Representing Data Mathematical Focus 8 Interpretation of graphs 8 Data represented in graphs 8 Comparison of data representations In this activity, students investigate different ways of representing data, using line-plots, bar graphs, and circle graphs. They begin by looking at and analyzing an example of each type of graph. Then, using the penny data they gathered in Activity 1, students create their own line-plots, bar graphs, and circle graphs. Students look for patterns in the data which are highlighted by the different representations. Finally, students extend their investigation by looking for examples of each type of graph in newspapers and magazines. Preparation and Materials 8 Student Page 1: Line-Plot 8 Student Page 2: Grid Paper, several copies, or several sheets of quarter-inch grid paper 8 Student Page 3: Bar Graph 8 Student Page 4: Circle Graph 8 Student Page 5: Blank Circle Graph 8 Penny data from Activity 1 8 Tape Save the graphs created in this activity for use in Activity 3. Statistics and Probability, Grades 3-5 7

8 Line-Plots 1. Tell what you know about graphs. Ask students these questions to help generate what they remember about graphs: What are graphs used for? Who uses them? What are some different types of graphs you ve seen? Where have you seen graphs used? Explain that in this activity students will explore and create three different types of graphs line plots and circle graphs using the penny data they collected in the last activity. line-plots, bar graphs, and circle graphs. 2. Discuss the features of a Line-Plot graph from Student Page 1. Ask questions such as these: What is the title of the graph? What do you think this graph shows? What are the different parts of this graph? What are the numbers below the horizontal line? What do the X s represent? (This line-plot shows the number of pizzas delivered from Tony s Pizza on each day of the month of April. The horizontal line is a segment of a real number line, showing all of the dates in the month of April [not just the ones on which pizzas were sold]. The X s above each date indicate the number of pizzas sold on that date.) Ask students to describe any patterns they notice in the data. (Students might observe that more pizzas seem to be delivered on Fridays and Saturdays than on other days.) 3. Create a line-plot for the penny data you collected in Activity 1. Give students several copies of Student Page 2: Grid paper or several sheets of quarter-inch grid paper that they can tape together to create the graph. Together, walk through the steps of creating the graph. Explain that the first step is to determine the smallest and largest values in the data set. Ask: What are the smallest and largest values in your data set? (This will be the date of the oldest penny and the date of the newest penny.) Have students create a number line with these two numbers at either end and all the years in between filled in, even the ones for which there are no pennies. Explain that the next step is to place an X on the number line to represent each data point, i.e., each penny found for that date. 4. Look for patterns in the penny data, using the line-plot you created. Statistics and Probability, Grades 3-5 8

9 Ask: Bar Graphs What patterns do you notice in the data? What do the patterns tell you about the penny data? Does this graph give you a different picture of the data than the record you made in Activity 1? Why or why not? 1. Compare a Bar Graph from Student Page 3 with the Line-Plot from Student Page 1. Explain that this bar graph also shows the number of pizzas delivered from Tony s Pizza on each day of the month of April. Ask: In what ways are the graphs similar? In what ways are they different? Is it easier to see patterns in one graph than the other? Why or why not? 2. Create a bar graph that shows the total number of pizzas sold on each day of the week for the month of April. Have students describe how they would create a bar graph to show this information. Ask: How would you label the axes? How would you determine the height of each bar? Their graph may look similar to the one below. Pizzas Sunday Monday Tuesday Wednesday Thursday Friday 3. Compare the information that the different graphs show about Tony s Pizza. 4. Construct a bar graph of the penny data. Give students several copies of Student Page 2 or sheets of quarter-inch grid paper that they can tape together to create the graph. Discuss possible categories for the horizontal axis. Students may want to label the horizontal axis with individual years, or they may want to label it with Statistics and Probability, Grades 3-5 9

12

13 Interpreting and Evaluating Data Mathematical Focus 8 Data interpretation using exploratory analysis 8 Development and evaluation of inferences, based on data In this activity, students analyze and interpret the penny data they collected and represented in Activities 1 and 2. They describe the characteristics of their data by identifying important features, such as range, gaps, clusters, and outliers. Students use the median to describe the center point of their data and investigate its significance. After interpreting their penny data, students discuss how data collection methods can influence the data set. They consider the concept of representativeness of a sample within the context of the penny example, asking: Is this set of 100 pennies representative of all pennies? In analyzing and comparing the three graphs, students consider which aspects of the data are highlighted or obscured by each representation. Preparation and Materials 8 Student Page 2: Grid Paper, or quarter-inch grid paper 8 Penny data and graphs from Activities 1 and 2 8 Student Page 6: Interpreting the Data, two copies 8 Photocopy of a short paragraph from a book Statistics and Probability, Grades

14 Interpreting Data 1. Use terms from Student Page 6 to describe your penny data set and graphs. Student Page 6 lists several terms that can be used to describe the shape and important features of a data set. Discuss each of the terms and have students use them to describe their own data set. Range: The range is the interval between the smallest and largest value in the data set. In this case, the range would be the interval between the date of the oldest penny and the newest penny. Have students describe the range of their data set and record it on Student Page 6. Outliers: These are isolated data points. Have students look for outliers in their data set. For example, if they had a really old coin in their collection say, a penny from the 40s or the 50s and most of the others were from the 70s, 80s, 90s, the older coin would be an outlier. Have students list any outliers on Student Page 6. Ask: Why might it be important or useful to look at the outliers in a data set? Clusters: A cluster is a pile-up of data at one point on the number line. Ask what clusters tell you about the data. Gaps: Dates with no X s, or holes in the data, are referred to as gaps. Ask: Are there any gaps in your data? If you added 100 more pennies to the data set, do you think that some of the gaps would be filled in? Have students describe any clusters and gaps in their data on student page Find the median of the penny data by ordering the data from earliest date to latest date and then moving in from each side until you reach the middle. Tell students that the median is the center point of the data; it divides the data into upper and lower halves. Explain that when the data set has an odd number of cases, there will be a single value for the median. If there is an even number of cases, the median is usually considered to be the halfway point between the two middle points. Have students draw a vertical line on the line-plot so that equal numbers of X s (50) are on each side of the line. Statistics and Probability, Grades

16 Encourage students to make inferences about the data, including factors that may affect the representativeness of the sample. Statistics and Probability, Grades

17 Exploring Probability Mathematical Focus 8 Basic ideas of chance and probability 8 A language to discuss informal notions of probability In this activity, students explore probability concepts as they create a probability line, and use informal language to describe the likelihood of various events occurring. The probability line ranges from Impossible to Certain and includes benchmark points in between. Students determine where such events as The probability that the sun will come up tomorrow, and The probability that it will rain tomorrow fall on the line. As numbers are added to the probability line, students begin to use fractions, decimals, and percentages to describe the likelihood of an event occurring. Finally, using the penny data from Activity 1, students explore the probability of drawing a penny of a given date from their collection of 100 pennies. Preparation and Materials 8 Penny data from Activity 1 Statistics and Probability, Grades

19 2. Determine what fraction, percent, or decimal should be written above Maybe, Small Chance, and Good Chance, on a probability line. Create a new probability line using the same informal terms. Write the numbers 0 and 1 at either end of the line. Explain that sometimes people use numbers instead of words to describe the chance of an event occurring. On this new line, 1 means the same thing as 100 percent, and 0 means the same thing as 0 percent. Impossible has a probability of 0, and Certain has a probability of 1. Here is one example: 0% or 0/100 25% or 25/100 50% or 50/100 75% or 75/ % or 100/ Impossible Small Chance Maybe Good Chance Certain 3. Think about the probability of pulling pennies from your group of pennies with various dates on them. Have students look at their penny data. Ask: If you put the 100 pennies in a bucket, reached in and pulled one out, what is the chance of pulling out a penny from 1991? (If there are eight pennies from 1991, students could write that as 8/100,.08, or 8%.) Where would the chance of this event (i.e., drawing a penny from 1991) go on the probability line? What is the chance of pulling out a penny from the 80s? Where would this go on the probability line? What is the chance of pulling out a penny from 1974? What is the chance of pulling out a penny from the 60s? What is the chance of pulling out a penny from the 60s or 70 s? What is the chance of pulling out a penny from the 70s, 80s or 90s? Statistics and Probability, Grades

20 Games of Chance Mathematical Focus 8 Basic notions of chance and probability In this activity, students use games as a way to explore concepts of chance. Through a coin-toss activity, students learn that what happens with one toss cannot possibly influence the outcome of the next toss. The misconception that results will be evened out is clarified; students learn that each toss is independent of the other tosses and has an equally likely chance of coming up heads or tails. Students further explore concepts of chance as they play the Sums Game. On discovering that the original game is unfair, students must use data they have collected to revise the game and make it fair. Preparation and Materials 8 Student Page 7: Coin-Toss Tally 8 Student Page 8: Sums Scorecard 8 A coin 8 Two dice Statistics & Probability, Grades

22 Ask: When I roll two dice, how many sums are possible? Is it possible to roll a sum of 1? 2? 3? The possible sums are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. Sums Game Goal: To have the highest point total at the end of the game. Players: 2 Materials: 2 dice; copies of Student Page 8: Sums Scorecard Instructions: Assign one player to receive a point each time that a sum of 2, 3, 4, 5, or 6 is rolled and the other player to receive a point each time that a sum of 7, 8, 9, 10, or 11 is rolled. No one gets a point if 12 is rolled. Roll the dice 50 times, each time awarding a point to the appropriate player. Keep track of the sums and points on Student Page 8. The player with the highest number of points after 50 rolls wins. After 25 rolls, stop and ask: Do you think this game is fair? Why, or why not? 2. Create a line-plot that shows the frequency with which different sums occur. The categories along the horizontal axis of the line-plot should be the different possible sums. For example: x x x x x x x x x x x Give a possible explanation for why the Sums Game is not fair as written. Ask: Which sums occur most often? Why do you think this is? Have students list all the ways to make each sum. 4. Change the Sums Game rules so that it will be fair. Have students explain how they changed the game and why they think the new version will be more fair. Play the new game a few times to test their theory. Statistics & Probability, Grades

23 Ideas for Data In Activities 1 5, students used a set of 100 pennies to pose statistical questions and gather data, represent the data using different graphs, interpret and evaluate the data, and explore notions of probability. Similar investigations can be carried out, using different data. Suggestions for additional or alternate data explorations are given below, in the categories of: favorites, places, and things. Data explorations may also span the three categories. Favorites 8 What is the most popular flavor of ice cream in my class? 8 Among my friends, family, and/or classmates, what is the most popular field-trip location or excursion in the city? 8 Is the favorite field-trip location the same as the one that has been visited most often? (For example, the zoo might be the favorite spot, but, because of its distance from home or school, it may only have been visited once, whereas the natural science museum, because of its proximity to home or school, has been visited many times.) Places 8 Of the places I have visited, which is the farthest from my home? 8 Of the places I have gone this week, what method of transportation (e.g., bike, car, skateboard, school bus, subway, city bus) did I use most often? Things 8 How many different types of canned goods do we have in our kitchen? Which type do we have the most of? The least? 8 In a bowl of 100 M&M s, how many M&M s are red? Green? Yellow? Blue? Orange? Dark brown? If I were to reach in and pull out one M&M, what is the likelihood that it would be green? Statistics & Probability, Grades

24 Line-Plot Tony s Pizza: Number of Large Pizzas Sold in April X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X T W TH F S S M T W TH F S S M T W TH F S S M T W TH F S S M T W Statistics and Probability, Grades 3 5 Student Page 1 24

25 Grid Paper Statistics and Probability, Grades 3 5 Student Page 2 25

26

27 Bar Graph Tony s Pizza: Number of Large Pizzas Sold in April T W Th F S S M T W Th F S S M T W Th F S S M T W Th F S S Statistics and Probability, Grades 3 5 Student Page 3 27

28 Circle Graph Tony's Pizza Large Pizzas Sold by Day of Week (Month of April) Saturday 25% Monday 8% Tuesday 11% Wednesday 14% Friday 27% Thursday 15% Statistics and Probability, Grades 3 5 Student Page 4 28

29 Blank Circle Graph Statistics and Probability, Grades 3 5 Student Page 5 29

30 Interpreting the Data RANGE: The range is the interval between the smallest and largest value in the data set. In this case, the range would be the interval between the date of the oldest penny and the newest penny. OUTLIERS: These are isolated data points. CLUSTERS: A cluster is a pile-up of data at one point on the number line. GAPS: Dates with no X s or holes in the data, are referred to as gaps. Statistics and Probability, Grades 3 5 Student Page 6 30

31 Coin-Toss Tally Side Tally Total After 25 Tosses Heads Total After 50 Tosses Tails Statistics & Probability, Grades 3-5 Student Page 7 31

32 Sums Scorecard If Sum = 2, 3, 4, 5, or 6, Roll Sum Point for Student(s) If Sum = 7, 8, 9, 10, or 11, Point for Mentor Statistics & Probability, Grades 3-5 Student Page 8 32

33 Statistics & Probability, Grades 3-5 Student Page 8 33

### Statistics Chapter 2

Statistics Chapter 2 Frequency Tables A frequency table organizes quantitative data. partitions data into classes (intervals). shows how many data values are in each class. Test Score Number of Students

### Using Probability Language

-NEM-WBAns-CH 7/0/0 :8 PM Page 7 CHAPTER Using Probability Language Use probability language to describe predictions.. Make a check mark under the probability word that would apply for each sentence. For

### TEACHING ADULTS TO REASON STATISTICALLY

TEACHING ADULTS TO REASON STATISTICALLY USING THE LEARNING PROGRESSIONS T H E N AT U R E O F L E A R N I N G Mā te mōhio ka ora: mā te ora ka mōhio Through learning there is life: through life there is

### It s time to have some fun!

WAKE UP YOUR BRAINS It s time to have some fun! We have put together some great ways to have fun working with math, reviewing math skills, and exploring math in the world all around you! OUR goal is for

### Washington State K 8 Mathematics Standards April 2008

Washington State K 8 Mathematics Standards Data Analysis, Statistics, and Probability Strand In kindergarten through grade 5, students learn a variety of ways to display data, and they interpret data to

### Unit 13 Handling data. Year 4. Five daily lessons. Autumn term. Unit Objectives. Link Objectives

Unit 13 Handling data Five daily lessons Year 4 Autumn term (Key objectives in bold) Unit Objectives Year 4 Solve a problem by collecting quickly, organising, Pages 114-117 representing and interpreting

### Session 8 Probability

Key Terms for This Session Session 8 Probability Previously Introduced frequency New in This Session binomial experiment binomial probability model experimental probability mathematical probability outcome

### Lesson 2: Constructing Line Graphs and Bar Graphs

Lesson 2: Constructing Line Graphs and Bar Graphs Selected Content Standards Benchmarks Assessed: D.1 Designing and conducting statistical experiments that involve the collection, representation, and analysis

### Big Ideas, Goals & Content for 4 th grade Data Collection & Analysis Unit

Big Ideas, Goals & Content for 4 th grade Data Collection & Analysis Unit Big Ideas Graphs are a way of organizing data and they appear in newspapers, magazines, on the Internet and other places in everyday

### This document contains Chapter 2: Statistics, Data Analysis, and Probability strand from the 2008 California High School Exit Examination (CAHSEE):

This document contains Chapter 2:, Data Analysis, and strand from the 28 California High School Exit Examination (CAHSEE): Mathematics Study Guide published by the California Department of Education. The

### Project Maths. Mathematics Resources for Students. Junior Certificate Strand 1. Statistics and Probability

Project Maths Mathematics Resources for Students Junior Certificate Strand 1 Statistics and Probability NCCA 2009 PROJECT MATHS - Mathematics Resources for Students Introduction This material is designed

### Formula for Theoretical Probability

Notes Name: Date: Period: Probability I. Probability A. Vocabulary is the chance/ likelihood of some event occurring. Ex) The probability of rolling a for a six-faced die is 6. It is read as in 6 or out

### MAT 1000. Mathematics in Today's World

MAT 1000 Mathematics in Today's World We talked about Cryptography Last Time We will talk about probability. Today There are four rules that govern probabilities. One good way to analyze simple probabilities

### Unit 19: Probability Models

Unit 19: Probability Models Summary of Video Probability is the language of uncertainty. Using statistics, we can better predict the outcomes of random phenomena over the long term from the very complex,

### Lesson 1: Experimental and Theoretical Probability

Lesson 1: Experimental and Theoretical Probability Probability is the study of randomness. For instance, weather is random. In probability, the goal is to determine the chances of certain events happening.

### Discovering Math: Using and Collecting Data Teacher s Guide

Teacher s Guide Grade Level: 3-5 Curriculum Focus: Mathematics Lesson Duration: Four class periods Program Description Discovering Math: Using and Collecting Data From data points and determining spread

### Mean, Median, Mode and Range

Mean, Median, Mode and Range 8 th grade 5 days of 40 minute class periods Materials used: internet, TI-83, tape measures, magazines and newspapers Kimberly Best 1 Table of Contents Objectives: - - - -

### PROBABILITY AND STATISTICS

PROBABILITY AND STATISTICS Grade Level: Written by: Length of Unit: Middle School, Science and Math Monica Edwins, Twin Peaks Charter Academy, Longmont, Colorado Four Lessons, plus a Culminating Activity

### Gaming the Law of Large Numbers

Gaming the Law of Large Numbers Thomas Hoffman and Bart Snapp July 3, 2012 Many of us view mathematics as a rich and wonderfully elaborate game. In turn, games can be used to illustrate mathematical ideas.

### CAHSEE Algebra Cluster #4: Statistics, Data Analysis, an Probability Name: Cluster #4 Review

CAHSEE Algebra Cluster #4: Statistics, Data Analysis, an Probability Name: Cluster #4 Review 1. The number of classic book Nanette sells in her 2. Which scatterplot shows a positive correlation? bookshop

### We re All Winners Bingo

We re All Winners Bingo Learning objective: Students will recognize the many things they have in common with a child with autism and generate their own ideas about how to support that child. Materials

### Are You Game? Explorations in Probability. Math

Are You Game? Explorations in Probability Supplemental Math Materials for Grades 3 6 Math Academy A Thank You to Our Corporate Sponsors The Actuarial Foundation would like to thank the following sponsors

### WHICH TYPE OF GRAPH SHOULD YOU CHOOSE?

PRESENTING GRAPHS WHICH TYPE OF GRAPH SHOULD YOU CHOOSE? CHOOSING THE RIGHT TYPE OF GRAPH You will usually choose one of four very common graph types: Line graph Bar graph Pie chart Histograms LINE GRAPHS

### Associative Property The property that states that the way addends are grouped or factors are grouped does not change the sum or the product.

addend A number that is added to another in an addition problem. 2 + 3 = 5 The addends are 2 and 3. area The number of square units needed to cover a surface. area = 9 square units array An arrangement

### Discovering Math: Data and Graphs Teacher s Guide

Teacher s Guide Grade Level: K 2 Curriculum Focus: Mathematics Lesson Duration: Two class periods Program Description Discovering Math: Data and Graphs From simple graphs to sampling to determining what

### FIRST GRADE Number and Number Sense

FIRST GRADE Number and Number Sense Hundred Chart Puzzle Reporting Category Number and Number Sense Topic Count and write numerals to 100 Primary SOL 1.1 The student will a) count from 0 to 100 and write

### Grade 6 Math Circles Winter 2013 Mean, Median, Mode

1 University of Waterloo Faculty of Mathematics Grade 6 Math Circles Winter 2013 Mean, Median, Mode Mean, Median and Mode The word average is a broad term. There are in fact three kinds of averages: mean,

### Teaching & Learning Plans. Plan 1: Introduction to Probability. Junior Certificate Syllabus Leaving Certificate Syllabus

Teaching & Learning Plans Plan 1: Introduction to Probability Junior Certificate Syllabus Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson,

### Consolidation of Grade 3 EQAO Questions Data Management & Probability

Consolidation of Grade 3 EQAO Questions Data Management & Probability Compiled by Devika William-Yu (SE2 Math Coach) GRADE THREE EQAO QUESTIONS: Data Management and Probability Overall Expectations DV1

### COMMON CORE STATE STANDARDS FOR

COMMON CORE STATE STANDARDS FOR Mathematics (CCSSM) High School Statistics and Probability Mathematics High School Statistics and Probability Decisions or predictions are often based on data numbers in

### Programming Your Calculator Casio fx-7400g PLUS

Programming Your Calculator Casio fx-7400g PLUS Barry Kissane Programming Your Calculator: Casio fx-7400g PLUS Published by Shriro Australia Pty Limited 72-74 Gibbes Street, Chatswood NSW 2067, Australia

### Bar Graphs and Dot Plots

CONDENSED L E S S O N 1.1 Bar Graphs and Dot Plots In this lesson you will interpret and create a variety of graphs find some summary values for a data set draw conclusions about a data set based on graphs

### Tasks to Move Students On

Maths for Learning Inclusion Tasks to Move Students On Part 1 Maths for Learning Inclusion (M4LI) Tasks to Move Students On Numbers 1 10 Structuring Number Maths for Learning Inclusion (M4LI) Tasks to

### 6th Grade Lesson Plan: Probably Probability

6th Grade Lesson Plan: Probably Probability Overview This series of lessons was designed to meet the needs of gifted children for extension beyond the standard curriculum with the greatest ease of use

### Standard 1: Students can understand and apply a variety of math concepts.

Grade Level: 4th Teacher: Pelzer/Reynolds Math Standard/Benchmark: A. understand and apply number properties and operations. Grade Level Objective: 1.A.4.1: develop an understanding of addition, subtraction,

### Common Tools for Displaying and Communicating Data for Process Improvement

Common Tools for Displaying and Communicating Data for Process Improvement Packet includes: Tool Use Page # Box and Whisker Plot Check Sheet Control Chart Histogram Pareto Diagram Run Chart Scatter Plot

### Probability and Statistics for Elementary and Middle School Teachers

Probability and Statistics for Elementary and Middle School Teachers A Staff Development Training Program To Implement the 2001 Virginia Standards of Learning Revised December 2004 Division of Instruction

### Statistics and Probability (Data Analysis)

Statistics and Probability (Data Analysis) Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 Specific Learning Outcomes Specific Learning Outcomes Specific Learning Outcomes 2.SP.1. Gather and record data about

### 4 th Grade Summer Mathematics Review #1. Name: 1. How many sides does each polygon have? 2. What is the rule for this function machine?

. How many sides does each polygon have? th Grade Summer Mathematics Review #. What is the rule for this function machine? A. Pentagon B. Nonagon C. Octagon D. Quadrilateral. List all of the factors of

### MA 1125 Lecture 14 - Expected Values. Friday, February 28, 2014. Objectives: Introduce expected values.

MA 5 Lecture 4 - Expected Values Friday, February 2, 24. Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the

### PROBABILITY SECOND EDITION

PROBABILITY SECOND EDITION Table of Contents How to Use This Series........................................... v Foreword..................................................... vi Basics 1. Probability All

### Math Games For Skills and Concepts

Math Games p.1 Math Games For Skills and Concepts Original material 2001-2006, John Golden, GVSU permission granted for educational use Other material copyright: Investigations in Number, Data and Space,

Advantages and Disadvantages of Different Graphs Focus on After this lesson, you will be able to... φ compare φ information from different graphs identify the advantages and disadvantages of different

### Grade 8 Classroom Assessments Based on State Standards (CABS)

Grade 8 Classroom Assessments Based on State Standards (CABS) A. Mathematical Processes and E. Statistics and Probability (From the WKCE-CRT Mathematics Assessment Framework, Beginning of Grade 10) A.

The Addition/Subtraction Facts Table Objectives To provide experience exploring patterns in sums of two dice; and to introduce the Addition/Subtraction Facts Table. www.everydaymathonline.com epresentations

### A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes

A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes together with the number of data values from the set that

### DesCartes (Combined) Subject: Mathematics Goal: Data Analysis, Statistics, and Probability

DesCartes (Combined) Subject: Mathematics Goal: Data Analysis, Statistics, and Probability RIT Score Range: Below 171 Below 171 171-180 Data Analysis and Statistics Data Analysis and Statistics Solves

### 3 + 7 1 2. 6 2 + 1. 7 0. 1 200 and 30 100 100 10 10 10. Maths in School. Addition in School. by Kate Robinson

1 2. 6 2 + 1. 7 0 10 3 + 7 1 4. 3 2 1 231 200 and 30 100 100 10 10 10 Maths in School Addition in School by Kate Robinson 2 Addition in School Contents Introduction p.3 Adding in everyday life p.3 Coat

### Grade 7 Mathematics. Unit 7. Data Analysis. Estimated Time: 18 Hours

Grade 7 Mathematics Data Analysis Estimated Time: 18 Hours [C] Communication [CN] Connections [ME] Mental Mathematics and Estimation [PS] Problem Solving [R] Reasoning [T] Technology [V] Visualization

### angle Definition and illustration (if applicable): a figure formed by two rays called sides having a common endpoint called the vertex

angle a figure formed by two rays called sides having a common endpoint called the vertex area the number of square units needed to cover a surface array a set of objects or numbers arranged in rows and

### In the situations that we will encounter, we may generally calculate the probability of an event

What does it mean for something to be random? An event is called random if the process which produces the outcome is sufficiently complicated that we are unable to predict the precise result and are instead

### Standard 12: The student will explain and evaluate the financial impact and consequences of gambling.

STUDENT MODULE 12.1 GAMBLING PAGE 1 Standard 12: The student will explain and evaluate the financial impact and consequences of gambling. Risky Business Simone, Paula, and Randy meet in the library every

### Bar Graphs with Intervals Grade Three

Bar Graphs with Intervals Grade Three Ohio Standards Connection Data Analysis and Probability Benchmark D Read, interpret and construct graphs in which icons represent more than a single unit or intervals

### 1 Teaching the Lesson

Getting Started Mental Math and Reflexes Children solve division number stories. They write answers on slates and explain their strategies to the class. Provide counters. There are children in the class.

### Interpreting Data in Normal Distributions

Interpreting Data in Normal Distributions This curve is kind of a big deal. It shows the distribution of a set of test scores, the results of rolling a die a million times, the heights of people on Earth,

### Math Journal HMH Mega Math. itools Number

Lesson 1.1 Algebra Number Patterns CC.3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Identify and

### Mathematical goals. Starting points. Materials required. Time needed

Level S2 of challenge: B/C S2 Mathematical goals Starting points Materials required Time needed Evaluating probability statements To help learners to: discuss and clarify some common misconceptions about

### Introduction and Overview

Introduction and Overview Probability and Statistics is a topic that is quickly growing, has become a major part of our educational program, and has a substantial role in the NCTM Standards. While covering

### Northumberland Knowledge

Northumberland Knowledge Know Guide How to Analyse Data - November 2012 - This page has been left blank 2 About this guide The Know Guides are a suite of documents that provide useful information about

### Working with Coordinate Planes

Virtual Math Girl: Module 1 (Student) and 2 (Teacher) Working with Coordinate Planes Activities and Supplemental Materials The purpose of Virtual Math Girl Module 1 (Student) and 2 (Teacher) is to familiarize

### Basic Tools for Process Improvement

What is a Histogram? A Histogram is a vertical bar chart that depicts the distribution of a set of data. Unlike Run Charts or Control Charts, which are discussed in other modules, a Histogram does not

### SOL 3.21, 3.22 Date:

SOL 3.21, 3.22 Name: Date: Probability and Statistics: Line Plots, Picture Graphs, and Bar Graphs Pacing: 2 weeks There are several ways to show data (information) that you have gathered to answer a question.

### The Distributive Property

The Distributive Property Objectives To recognize the general patterns used to write the distributive property; and to mentally compute products using distributive strategies. www.everydaymathonline.com

### CC Investigation 5: Histograms and Box Plots

Content Standards 6.SP.4, 6.SP.5.c CC Investigation 5: Histograms and Box Plots At a Glance PACING 3 days Mathematical Goals DOMAIN: Statistics and Probability Display numerical data in histograms and

### Chapter 2: Frequency Distributions and Graphs

Chapter 2: Frequency Distributions and Graphs Learning Objectives Upon completion of Chapter 2, you will be able to: Organize the data into a table or chart (called a frequency distribution) Construct

### Hands-On Data Analysis

THE 2012 ROSENTHAL PRIZE for Innovation in Math Teaching Hands-On Data Analysis Lesson Plan GRADE 6 Table of Contents Overview... 3 Prerequisite Knowledge... 3 Lesson Goals.....3 Assessment.... 3 Common

### Blackline Masters. symbol key indicates items need to be cut apart

ISBN 9781886131873 B1NCTG-B Blackline Masters NC 1 The Days In School chart NC 2 Student Clock NC 3 Number Cards, 1 6 NC 4 Number Cards, 7 12 NC 5 Ladybug NC 6 Tuesday s Temperatures chart NC 7 Mini Calendar

### Probability Using Dice

Using Dice One Page Overview By Robert B. Brown, The Ohio State University Topics: Levels:, Statistics Grades 5 8 Problem: What are the probabilities of rolling various sums with two dice? How can you

### TIME MANAGEMENT ACTIVITY (LED BY GEAR UP MENTORS)

(LED BY GEAR UP MENTORS) Purpose: Students will practice time management skills that are essential to college readiness. Grades: 6-10 WWW.GEARUP4LA.NET @GEARUP4LA TOPIC SCRIPT/ DIRECTIONS MATERIALS 1 copy

### Granny s Balloon Trip

Granny s Balloon Trip This problem gives you the chance to: represent data using tables and graphs On her eightieth birthday, Sarah s granny went for a trip in a hot air balloon. This table shows the schedule

### That s Not Fair! ASSESSMENT #HSMA20. Benchmark Grades: 9-12

That s Not Fair! ASSESSMENT # Benchmark Grades: 9-12 Summary: Students consider the difference between fair and unfair games, using probability to analyze games. The probability will be used to find ways

### Ready, Set, Go! Math Games for Serious Minds

Math Games with Cards and Dice presented at NAGC November, 2013 Ready, Set, Go! Math Games for Serious Minds Rande McCreight Lincoln Public Schools Lincoln, Nebraska Math Games with Cards Close to 20 -

Fourth Grade Fractions http://upload.wikimedia.org/wikibooks/en/9/92/fractions_of_a_square.jpg North Carolina Department of Public Instruction www.ncdpi.wikispaces.net Overview The implementation of the

### Penny: the Forgotten Coin A Teacher s Guide

Penny: the Forgotten Coin A Teacher s Guide Teacher s Guide by Cheryl Grinn based on the book by Denise Brennan-Nelson illustrated by Michael Monroe published by Sleeping Bear Press 310 North Main, Chelsea

### DesCartes (Combined) Subject: Mathematics 2-5 Goal: Data Analysis, Statistics, and Probability

DesCartes (Combined) Subject: Mathematics 2-5 Goal: Data Analysis, Statistics, and Probability RIT Score Range: Below 171 Below 171 Data Analysis and Statistics Solves simple problems based on data from

### Targets for pupils in Reception

Recognising numbers Choose a number for the week, e.g. 2. Encourage your child to look out for this number all the time. Can your child see the number 2 anywhere? at home - in the kitchen - on pages in

### STT 200 LECTURE 1, SECTION 2,4 RECITATION 7 (10/16/2012)

STT 200 LECTURE 1, SECTION 2,4 RECITATION 7 (10/16/2012) TA: Zhen (Alan) Zhang zhangz19@stt.msu.edu Office hour: (C500 WH) 1:45 2:45PM Tuesday (office tel.: 432-3342) Help-room: (A102 WH) 11:20AM-12:30PM,

### C Conversion Tables and Templates

PART C Conversion Tables and Templates Score conversion tables and associated report templates Part C contains the various score conversion tables, student reports and scale descriptor reports associated

### How Long are the Names in my Class?

How Long are the Names in my Class? Overview of Lesson During the first week of school, a third-grade teacher is trying to help her students learn one another s names by playing various games. During one

### Contents. Remember boxes and speech bubbles Important key points and tips. Special Features of Start Up Mathematics 3-5

Contents 1. Numbers Beyond 999 1 2. Roman Numerals 23 3. Addition 26 Assessment Sheet 1 37 4. Subtraction 38 5. Multiplication 50 6. Division 69 Assessment Sheet 2 84 Let s Review 1 85 7. Fractions 87

### Chapter 3: Data Description Numerical Methods

Chapter 3: Data Description Numerical Methods Learning Objectives Upon successful completion of Chapter 3, you will be able to: Summarize data using measures of central tendency, such as the mean, median,

Ohio Standards Connection Data Analysis and Probability Benchmark F Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data. Indicator

### Contemporary Mathematics Online Math 1030 Sample Exam I Chapters 12-14 No Time Limit No Scratch Paper Calculator Allowed: Scientific

Contemporary Mathematics Online Math 1030 Sample Exam I Chapters 12-14 No Time Limit No Scratch Paper Calculator Allowed: Scientific Name: The point value of each problem is in the left-hand margin. You

### Unit 18: Introduction to Probability

Unit 18: Introduction to Probability Summary of Video There are lots of times in everyday life when we want to predict something in the future. Rather than just guessing, probability is the mathematical

### Drawing a histogram using Excel

Drawing a histogram using Excel STEP 1: Examine the data to decide how many class intervals you need and what the class boundaries should be. (In an assignment you may be told what class boundaries to

### Unit 1: Family Letter

Name Date Time HOME LINK Unit 1: Family Letter Introduction to Third Grade Everyday Mathematics Welcome to Third Grade Everyday Mathematics. It is part of an elementary school mathematics curriculum developed

### If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C?

Problem 3 If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C? Suggested Questions to ask students about Problem 3 The key to this question

### Grade 1 Math Expressions Vocabulary Words 2011

Italicized words Indicates OSPI Standards Vocabulary as of 10/1/09 Link to Math Expression Online Glossary for some definitions: http://wwwk6.thinkcentral.com/content/hsp/math/hspmathmx/na/gr1/se_9780547153179

### Differentiated plans for Years 3 & 4 for Chance & Data

Differentiated plans for Years 3 & 4 for Chance & Data Ian Lowe, MAV Professional Officer, 2008 IF YOU USE ANY OF THIS PLEASE PROVIDE FEEDBACK TO IAN AT ilowe@mav.vic.edu.au THIS WILL QUALIFY YOU FOR AN

CCSSM: Grade 7 DOMAIN: The Number System Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Standard: 7.NS.1: Apply

### Lesson 1: Posing Statistical Questions

Student Outcomes Students distinguish between statistical questions and those that are not statistical. Students formulate a statistical question and explain what data could be collected to answer the

### Business Statistics & Presentation of Data BASIC MATHEMATHICS MATH0101

Business Statistics & Presentation of Data BASIC MATHEMATHICS MATH0101 1 STATISTICS??? Numerical facts eg. the number of people living in a certain town, or the number of cars using a traffic route each

Third Grade Math Games Unit 1 Lesson Less than You! 1.3 Addition Top-It 1.4 Name That Number 1.6 Beat the Calculator (Addition) 1.8 Buyer & Vendor Game 1.9 Tic-Tac-Toe Addition 1.11 Unit 2 What s My Rule?

### DesCartes (Combined) Subject: Mathematics Goal: Statistics and Probability

DesCartes (Combined) Subject: Mathematics Goal: Statistics and Probability RIT Score Range: Below 171 Below 171 Data Analysis and Statistics Solves simple problems based on data from tables* Compares

### Assessment For The California Mathematics Standards Grade 3

Introduction: Summary of Goals GRADE THREE By the end of grade three, students deepen their understanding of place value and their understanding of and skill with addition, subtraction, multiplication,

### Fun with Fractions: A Unit on Developing the Set Model: Unit Overview www.illuminations.nctm.org

Fun with Fractions: A Unit on Developing the Set Model: Unit Overview www.illuminations.nctm.org Number of Lessons: 7 Grades: 3-5 Number & Operations In this unit plan, students explore relationships among

### 100 NEWSPAPER CRITICAL THINKING ACTIVITIES

100 NEWSPAPER CRITICAL THINKING ACTIVITIES by: Randee Simon CRITICAL THINKING SKILLS ACTIVITIES 1. Have students find the movie listing's page and study the movies that are presently being shown at theatres

### Graph it! Grade Six. Estimated Duration: Three hours

Ohio Standards Connection Data Analysis and Probability Benchmark A Read, Create and use line graphs, histograms, circle graphs, box-and whisker plots, stem-and-leaf plots, and other representations when