Category Archives: statistics

Fishing and Statistics

Standards

CSS.MATH.CONTENT.6.SP.A.3
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
CCSS.MATH.CONTENT.6.SP.B.5
Summarize numerical data sets in relation to their context.

Technology

Students will need a Chromebook, Windows or Mac computer to play the game. Stories can be read on a computer or tablet or printed out.

Time Required

75 -105 minutes.

Summary

This lesson begins with a game teaching statistics, with a level assessing weights of salmon. Next, students read stories about salmon from the Pacific Northwest tribal communities. The lesson ends with a game outdoors or in the gym where students ‘catch’ salmon and learn the impact of overfishing. Optional activity includes creative writing or artwork to accompany the salmon stories.

Lesson

Play a Game (25 minutes)

Play Disaster Deduction Detectives through Level 4 where players compute mean weights of fish caught with and without an outlier. Earlier levels discuss median and statistical questions.

Fish catching game in Disaster Deduction Detectives

Read Salmon Stories (35 minutes)

This 35-page booklet of salmon stories comes from a collaborative effort of the tribal communities of the Pacific Northwest, Northwest Indian Fisheries Commission and Seattle Aquarium. In addition to four stories about salmon, traditional games featuring salmon are described. You can print the booklet or copy the link and assign it in your Google classroom or other online system.

Depending on your available class time and their reading level, you may wish to just assign one or two stories or the whole booklet.

NOTE: You can find the entire 72-page Teachers Guide, One with the Watershed, including the stories, here. It has a wealth of information, games and activities. We highly recommend reading it.

Physical Education and Math – Play the Salmon Catcher Game (15 minutes)

This game is explained on page 30 of the Teacher’s Guide and on page 24 of the Salmon Stories booklet. A group of 4 or 5 students must catch a classmate (a salmon) by forming a net around it by holding hands. Play with lots of salmon and one ‘net’ and then with lots of ‘nets’ and few salmon. After the game, discuss how having too many fishers for the number of fish makes it difficult for each group to get enough salmon for a feast.

Assessment

Students responses to the questions in the Disaster Deduction Detectives game on statistical questions, creating and interpreting dot plots, median and mean with and without an outlier are all scored automatically and can be found in the teacher reports.

Differentiated Instruction

Optional: Creative Writing OR Art and Social Studies (30 minutes)

The Salmon Stories booklet has minimal illustrations. Allow students 30 minutes to create an illustration for one of the stories. For students who would prefer to write a story instead, allow them to select one of the topics suggested in the booklet, for example, on page 23 of the student booklet (page 29 in the Teacher’s Guide) students are asked to imagine a discussion between a salmon and the forest.

Cross-curricular Middle School Statistics Unit

Note: When we surveyed teachers from the 2021-22 academic year, the most requested addition to the site was to combine the lessons into units. This cross-curricular statistics unit has 12 lessons that total 14 hours of class time, although some assignments could be completed as homework. With the length of this unit, it could be taught as a complete summer school course, addressing primarily mathematics standards but also incorporating English language arts, Social Studies (predominantly Indigenous and Latino history and culture) and science.

📖Standards

STATISTICS STANDARDS

CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates
variability in the data related to the question and accounts
for it in the answers
CCSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.
CCSS.MATH.CONTENT.6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
CCSS.MATH.CONTENT.6.SP.B.5 Statistics & Probability: Summarize numerical data sets in relation to their context.
CCSS.MATH.CONTENT.7.RP.A.2.B Ratios & Proportional Relationships: Identify the constant of proportionality (unit rate) in  tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
CCSS.MATH.CONTENT 7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.
CCSS.Math.Content.7.SP.C.5
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
CCSS.Math.Content.7.SP.C.6
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

ADDITIONAL MATHEMATICS STANDARDS

CCSS.MATH.CONTENT.5.NF.B.4   Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

CCSS.MATH.CONTENT.7.RP.A.2 Recognize and represent proportional relationships between quantities.

ENGLISH/ LANGUAGE ARTS STANDARDS

CCSS.ELA-LITERACY.RI.6.7 Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue.
CCSS.ELA-LITERACY.RI.6.4 Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.
CCSS.ELA-LITERACY.RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

SCIENCE STANDARDS

Next Generation Science Standard MS-LS2-1 Ecosystems: Interactions, Energy, and Dynamics: Analyze and interpret data to provide evidence for the effects of resource availability on organisms and populations of organisms in an ecosystem.

SOCIAL STUDIES STANDARDS

D2.His.13.3-5  Use information about a historical source, including the maker, date, place of origin, intended audience, and purpose to judge the extent to which the source is useful for studying a particular topic.

⏰Time Required

About 14 hours for all twelve lessons

📲Technology Required

Projector or smart board for in–class or access to computer or tablet for web meeting for remote learning. Presentations could be printed for students at home without computer access. Some lessons require use of Google sheets or similar spreadsheet software.

🧾Unit Summary

This seven-lesson unit teaches sixth- and seventh-grade standards on statistics integrated with games, Indigenous and Latino history and culture. The complete multi-media unit requires about 14 hours and includes multiple hands-on activities. 

trees in background, grass in foreground
Find your way back using clues from the plants around you

📃 Lesson 1: What is a Statistical Question? (120 Minutes)

CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates
variability in the data related to the question and accounts
for it in the answers

Teachers begin the lesson with a Google slides presentation explaining the requirements for a statistical question. Students complete an assignment identifying whether or not a question qualifies as a statistical question. After class discussion, students complete a second assignment using a small data set shown on a map. In Part 3, students write and answer their own statistical questions using a data set provided, giving an explanation for their answers. Optionally, students can complete a more challenging assignment drawing conclusions from a graph and/or play a game and identify statistical questions.

📃 Lesson 2: Mean, median and mode (35 Minutes)

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context

Students play a game teaching basic statistics and history. Next, they are given a presentation with problems students solve finding mean, median, mode, range and outliers.

This lesson has resources to teach in both Spanish and English, for an English-only lesson, click here.

📃Lesson 3: Understanding averages using skunks (30 minutes)

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context.
CCSS.ELA-LITERACY.RH.6-8.7 Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts.

In this lesson, students will learn how to find the mean and calculate the average and practice finding the average in a game environment. They will learn about skunks and skunk farming through primary source material. Then analyzing historical data, students will calculate the average.

📃Lesson 4: Reflections on the Ojibwe Migration (60 minutes)

CCSS.MATH.CONTENT.5.NF.B.4   Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
CCSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.
D2.His.13.3-5  Use information about a historical source, including the maker, date, place of origin, intended audience, and purpose to judge the extent to which the source is useful for studying a particular topic.

This multi-media lesson begins with a storyboard on the route and major events of the Ojibwe migration. Students then play the Forgotten Trail game, computing the average number of miles a character walked per day, followed by watching a video on map reading. As a group, students reflect on the challenges of the Ojibwe migration, compute the distance for just one segment and convert the distance from miles to kilometers.

📃 Lesson 5: Science, language arts and math with wildflowers (50 Minutes)

CCSS.ELA-LITERACY.RI.6.7 Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue.
CCSS.ELA-LITERACY.RI.6.4 Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.
Next Generation Science Standard MS-LS2-1 Ecosystems: Interactions, Energy, and Dynamics: Analyze and interpret data to provide evidence for the effects of resource availability on organisms and populations of organisms in an ecosystem.
CCSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.

This is a true STREAM lesson. Combining science, reading, art and mathematics. Students read a description of the pine forest ecosystem and life zones. They define any new words in their personal dictionary. Students then use information on plant life to identify life zones and locate these zones in terms of altitude. Students who complete the activity before the allotted class time play a game that teaches fractions and basic statistics.

📃 Lesson 6: Teaching Frequency Tables with Indigenous Communities’ Data (70 minutes)

CCSS.MATH.CONTENT.6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context

With a Google slides presentation, students are introduced to the concept of answering a question with data. A video is also provided for review. Using a data set of all tribal leaders in 2019, they are walked though an example of using Google Sheets to create frequency table and plots of data. Students then use the data set to create their own tables and plots. Students finish the lesson by playing a game where they learn about computing distributions in Mayan history.

📃 Lesson 7: Distributions and Mayan Trading (25 Minutes)

CCSS.MATH.CONTENT 7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.

The two videos here combine math and social studies, because, clearly, the Maya understood math. The concept of distributions is introduced in the context of trading, explaining why some objects are more valuable. Students play AzTech: The Story Begins, which reviews fractions and measures of central tendency. The lesson concludes with a question and another video on distributions.
(NOTE: Videos are available in Spanish and Englishfor English only lesson, click here. )

📃 Lesson 8: Food Deserts, Indigenous Seeds and Data Stories (90 Minutes)

CCSS.ELA-LITERACY.RI.6.4 Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.
CCSS.ELA-LITERACY.RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.
CCSS.MATH.CONTENT.6.SP.B.4 Display numerical data in plots
CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context
CCSS.MATH.CONTENT.7.RP.A.2 Recognize and represent proportional relationships between quantities

This truly cross-curricular assignment begins by watching a video about seed rematriation, that is returning Indigenous seeds to their original lands. They read a short booklet on cooking and nutrition, then do a cooking activity at school or home. A presentation on food deserts includes definitions, data and actions students can take. Students add new words or phrases to their word journal and complete a math assignment using data from the presentation. Advanced students play a game to learn more math and Navajo culture.

📃Lesson 9: Reading and Comparing Bar Graphs (45 Minutes)

CCSS.MATH.CONTENT.6.SP.B.5 Statistics & Probability: Summarize numerical data sets in relation to their context.

CCSS.MATH.CONTENT.7.RP.A.2.B Ratios & Proportional Relationships: Identify the constant of proportionality (unit rate) in  tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

This lesson introduces students to reading and comparing bar graphs with proportional relationships. Students receive a slide or handout with four bar graphs and complete a set of cards with questions on the graphs. They can also complete the activity in Google slides . The lesson ends with an adventure game that includes discussion of interpreting bar graphs.

📃Lesson 10: Google Slides and Math (180 Minutes)

CCSS.MATH.CONTENT.6.SP.B.5.C Giving quantitative measures of center and variability, as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
CCSS.ELA-LITERACY.RH.6-8.7 Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts.

Students play three games that teach fractions and statistics. Students learn enhanced features of Google slides. They then create a Google slides presentation stating which is their favorite game and why.

📃Lesson 11: Probability and Fruits (45 Minutes)

CCSS.Math.Content.7.SP.C.5
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
CCSS.Math.Content.7.SP.C.6
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

The Google slides presentation begins with definitions of probability, impossibility and certainty. Students are then given an example of a basket with different types of fruits and the probability of each. Students each come to the front of the class and pull a piece of fruit from the basket, writing down the probability of their selecting the type they obtained. The class data is used to create a table and compare the obtained probabilities to actual distribution of fruit in the basket. The lesson closes with students creating their own probability question.

NOTE: This lesson plan requires a basket of fruit. You could use pictures of fruit printed out or drawn on paper instead but using actual fruit from your area might be more fun. If you’d rather, though, we do have a random fruit basket generator to use with this lesson.

📃 Lesson 12: Teaching Statistics in Classrooms with English Learners AND Native Speakers (90 minutes)

CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates
variability in the data related to the question and accounts
for it in the answers
CCSS.MATH.CONTENT.7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.

This lesson includes game-based instruction and data analysis. Data can be collected at home on students’ phones or using a computer. Google sheets is used to compute descriptive statistics to answer a statistical question. Lab instructions, Sheet templates and a sample answer are included. You can modify this in an infinite number of ways to compare any two groups on any numeric variable.

Teaching Statistics in Classrooms with English Learners AND Native Speakers

 Standard

CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates
variability in the data related to the question and accounts
for it in the answers

CCSS.MATH.CONTENT.7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.

📲 Technology Required

Computer with projector, for students learning in class. Students will need access to a phone, tablet or computer.

⏰ Time Required

75-90 minutes

📃 Summary

This lesson includes game-based instruction and data analysis. Data can be collected at home on students’ phones or using a computer. Google sheets is used to compute descriptive statistics to answer a statistical question. Lab instructions, Sheet templates and a sample answer are included. You can modify this in an infinite number of ways to compare any two groups on any numeric variable.

Lesson

NOTE: This lesson assumes students understand:

Discuss the definition of a statistical question.

If students have not completed the lesson, “What is a statistical question?” , you can complete that first. It takes about two hours.

If you are REALLY short on time, or if you are just reviewing the concept you have previously taught, you can just use the first 12 slides of this presentation on What is a Statistical Question?” to give the basic definition and a few examples.

Class Discussion of Research Question

Pose a research question, for example, “Do different Spanish and English speakers differ in their interests, as determined by what they post on Instagram?” Of course, you can easily change the language if you have speakers of other languages in your class.

Next, you need a hypothesis, for example, “Spanish-speakers are more likely to post pictures of food than English speakers” or “English accounts will have more pictures of themselves than Spanish accounts”.

In selecting a hypothesis, you can discuss distribution and probability. If almost no one takes pictures of giraffes then the probability of finding enough giraffe pictures to compare is low. (Be prepared for your students to suggest the hashtag #giraffesofinstagram).

#GiraffesofInstagram

Statistics Lab Assignment : Social Media Analytics

In this assignment, each group of students will collect and analyze social media data from 10 accounts of Spanish speakers and 10 accounts of English speakers. After individual assignments are submitted, data will be combined into a single class data set and the analyses re-computed for the combined data set.

Assign Groups

After you have agreed on one research question, put your class in groups of 4 or 5 students. Ideally, each group would have at least one Spanish speaker and at least one native English speaker. Ask students to raise their hands if they have an Instagram account. Try to put at least one student with an account in each group. Groups can also include students learning from home.

Share lab documents with students to collect, enter and analyze data

Social Media Analysis. The assignment instructions, along with a sample of data collected can be downloaded here as a Google doc and printed or added to your Google classroom or other CMS.

The spreadsheet for entering data can be found here. This is a Google sheet but it can also be downloaded and saved as an Excel file if you prefer.

Optional: Provide students starting links for accounts

To help students find accounts, you can include these links in your Google classroom or other classroom management system, or any list of accounts

You can find 50 inspirational accounts in Spanish here ( https://metricool.com/es/50-cuentas-de-instagram-ordenadas-por-tematica-para-inspirarte/ )

and 20 inspirational accounts in English here – ( https://wealthygorilla.com/top-20-motivational-instagram-accounts/ )


Each group analyzes their own data

An example of a social media analysis, with formula for computing each value in Google sheets can be found here.

Class discussion

Discuss the idea of variation within the accounts. Discuss the idea of variation across the groups. Did the different groups in your class find the exact same results?

Discuss variation in samples. What could have explained the different results? Did some groups have accounts that were all celebrities, all friends, all male?

Play a game

Scene in the Disaster Deduction Detectives Academy

Play Disaster Deduction Detectives to learn how to compute the median in datasets with odd or even numbers of data.

Statistics Lab Assignment 2: Social Media Analytics with Larger Sample

In the second lab exercise (instructions found here) , students combine the data from all groups, and compute descriptive statistics again. They compare their group’s results with the whole class result and discuss possible explanations.

Assessment

Three types of assessment are included. Group assessments are the two lab assignments submitted by students – since each student in the group has the same data he/ she will have the same result. Optionally, teachers may elect to have students submit their labs individually. Individual assessment is included within the DDD game where students must identify a statistical question, compute mean, median and quartiles. Whole class assessment occurs during the two discussion session.

Related lessons

We recommend this lesson follow Teaching Frequency Tables with Indigenous Communities’ Data.

Mean, Median and Mode (Bilingual English & Spanish)

by Dr. Craig Waddell

📖 Standard

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context

⏰ Time

30-40 Minutes 

📲 Technology Required

Device with web-browser – Chromebook, laptop or desktop computer, phone or tablet

📃 Summary

Students play a game teaching basic statistics and history. Next, they are given a presentation with problems students solve finding mean, median, mode, range and outliers.

📚Lesson

Play a game teaching basic statistics and Latin American history

Meet the jaguars in AzTech: Meet the Maya

Play AzTech: The story begins. Students who have finished this game can continue on in the series in AzTech: Meet the Maya. Allow students 15-20 minutes to play.

Students can click on a button in the left of their screen to choose the language and play the games in either Spanish or English.

Assess knowledge of Mean, Median and Mode as a class

Use this Google slides presentation to present sets of numbers to the class to use for finding mean, median, mode and range. This is also available as a PowerPoint presentation.

This presentation can also be assigned for students to complete at home, if learning remotely. Slides with answers can be deleted, or left in for students to check their work.

Review as Necessary

If students need a review, they can watch this video on how to find the mean

Finding the Average video

Or, watch the video in Spanish

Encontrando el promedio

ASSESSMENT

You can view your students’ progress on mastering these standards by viewing your teacher reports. AzTech: The Story Begins and AzTech: Meet the Maya links can be found on this reports page. You should have received a password during the Growing Math training.

A second form of assessment is available through this the questions in the presentation.

Related lesson/ Differentiated Instruction

If your students need instruction on computing the mean, try this lesson, Understanding the mean, with skunks. This review can be done with the entire class or assigned to individual students as needed.

Mean, Median and Mode – The English only version of this lesson plan that includes English resources.

Food Deserts, Indigenous Seeds and Data Stories

Standard

CCSS.ELA-LITERACY.RI.6.4 Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.

CCSS.ELA-LITERACY.RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

CCSS.MATH.CONTENT.6.SP.B.4 Display numerical data in plots

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context

CCSS.MATH.CONTENT.7.RP.A.2 Recognize and represent proportional relationships between quantities

⏰ Time

70 – 90 minutes, including cooking activity

📲 Technology Required

A computer with projector or smart board is required to show the video and presentation to students.

Summary

This truly cross-curricular assignment begins by watching a video about seed rematriation, that is returning Indigenous seeds to their original lands. They read a short booklet on cooking and nutrition, then do a cooking activity at school or home. A presentation on food deserts includes definitions, data and actions students can take. Students add new words or phrases to their word journal and complete a math assignment using data from the presentation. Advanced students play a game to learn more math and Navajo culture.

📚 Lesson

Watch this video seed rematriation, that is, growing Indigenous seeds in the lands from which they came originally.

Read a short booklet on cooking and nutrition

Scrambled eggs and spinach – available here as a free pdf from the U.S. Department of Agriculture, is directed at parents but should be at the reading level of most sixth- or seventh-graders.

Make some eggs

It will be a lot more fun for your class if you can actually go to the school kitchen and cook some eggs. Reading the booklet above will give the recipe, optional ingredients and much more. The only 3 ingredients you absolutely need are eggs, spinach and vegetable oil or butter.

Alternative assignment

If you absolutely cannot go to the kitchen at school because of scheduling, safety regulations or other reasons, here are two other options.

  • Assign this activity for students to do with their parents at home. Here is the link for the recipe. You can make this an extra credit activity because not everyone has parents who have time or money to run out for eggs and spinach. Optional: If students have access to a phone or tablet, have them record themselves/ their parent cooking.
  • You can watch a video of kids making the recipe , but doing it with your class will be more fun.

Listen to/ read presentation on food deserts

What if there was nowhere to buy eggs, spinach or even seeds near where you live? You can use this Google slides presentation to present to students in class or assign them to read on their own.

Complete word journal

Students add words or terms with which they are unfamiliar to their word journal. Some teachers call it a personal dictionary, to others it’s a word journal. Regardless, the goal is the same, for students to record new words, give a dictionary definition and “make the word their own”. This can be done by rewriting the definition in their own words, using the word in a sentence or including an illustration of the word.

Two dictionary sites to recommend for definitions are below. An added bonus to mention to students is that they can hear words pronounced.

Since students often ask for an example, here is an example you can link in your lesson

The personal dictionary assignment, with all links, can be found here. Feel free to copy and paste into your Google classroom or other site, or print out for your class.

Math assignment: Using statistics and ratio to answer questions

Copy the assignment into your Google classroom or other system or print out for students. Students will use the data from the Food Deserts presentation to answer questions about percentages. They will also create pie charts (circle graphs) and bar charts. You can have students do this with a calculator or pencil and paper or using Google sheets.

ANSWER KEY for assignment

If you’d like a spreadsheet where these tables and graphs were created, you can find it here.

Differentiated Instruction: For Advanced Students

Challenge more advanced students to watch this video on Making Mounds for Three Sisters Gardens. The vocabulary is a little more advanced than the typical sixth-grade with terms like “nitrogen”, “fish emulsion”. In the first farm, they planted 80 mounds. Students should watch the video and figure out from the information given how wide the plot must be .

More advanced students can also play the Making Camp Navajo game, available from the Games for Kids portal on this site, to learn more about farming and expand their knowledge of ratio and proportion.

Assessment

Word journals are graded based on correct or incorrect definition. Data analysis assignments assess student achievement of math standards above.

Teaching frequency tables with Indigenous communities’ data

STANDARD

CCSS.MATH.CONTENT.6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context

Technology Required

Students will need either a computer or tablet to play the game. Teachers will need a computer connected to a projector or smart board to show the presentation or video.

Time

60-75 minutes including, presentation, analysis and game

Summary

With a Google slides presentation, students are introduced to the concept of answering a question with data. A video is also provided for review. Using a data set of all tribal leaders in 2019, they are walked though an example of using Google Sheets to create frequency table and plots of data. Students then use the data set to create their own tables and plots. Students finish the lesson by playing a game where they learn about computing distributions in Mayan history.

Lesson

1. Presentation on primary sources and frequency distributions with Google sheets.

Give students a slide presentation that asks the question “How wired are tribes?” . This also gives the definitions of data, primary sources, secondary sources and frequency table. Students will learn how to create a frequency table with Google sheets.

Differentiated Instruction: If needed, students can review the information by watching this video on their own.

You can also assign students who were absent to watch the video on their own.

2. Assign Students to Create Their Own Frequency Distribution

A Google doc with the assignment and link to video.

You’ll need the 2019 Tribal Leaders Data Set to complete this assignment. Copy the link into Google classroom for students to access.

Here is the answer key for the teacher

If your students completed the assignment correctly, it will match the answer key here.

Differentiated Instruction: For more advanced students

You may wish to have them compute an additional frequency distribution to show the frequency distribution of tribal entities by BIA region. That answer is also provided in the file above.

3. Play a game that teaches distributions

When students have completed their assignments that can play AzTech: Meet the Maya, a game which teaches statistics, including frequency distributions.

Assessment

Two types of assessment are available, their answers to the assignment with Google sheets, and their responses to the in-app math challenges in AzTech: Meet the Maya, which are graded automatically with data available from the. teacher reports.

Mean, Median and Mode

by Dr. Craig Waddell

📖 Standard

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context

⏰ Time

30-40 Minutes 

📲 Technology Required

Device with web-browser – Chromebook, laptop or desktop computer, phone or tablet

📃 Summary

Students play a game teaching basic statistics and history. Next, they are given a presentation with problems students solve finding mean, median, mode, range and outliers.

📚Lesson

Play a game teaching basic statistics and Latin American history

Meet the jaguars in AzTech: Meet the Maya

Play AzTech: The story begins. Students who have finished this game can continue on in the series in AzTech: Meet the Maya. Allow students 15-20 minutes to play.

Students can click on a button in the left of their screen to choose the language and play the games in either Spanish or English.

Assess knowledge of Mean, Median and Mode as a class

Use this Google slides presentation to present sets of numbers to the class to use for finding mean, median, mode and range. This is also available as a PowerPoint presentation.

This presentation can also be assigned for students to complete at home, if learning remotely. Slides with answers can be deleted, or left in for students to check their work.

Review as Necessary

If students need a review, they can watch this video on how to find the mean.

Finding the Average video

ASSESSMENT

You can view your students’ progress on mastering these standards by viewing your teacher reports. AzTech: The Story Begins and AzTech: Meet the Maya links can be found on this reports page. You should have received a password during the Growing Math training.

A second form of assessment is available through this the questions in the presentation.

Related lesson/ Differentiated Instruction

If your students need instruction on computing the mean, try this lesson, Understanding the mean, with skunks. This review can be done with the entire class or assigned to individual students as needed.

Mean, Median and Mode (Bilingual English and Spanish) – The bilingual version of this lesson plan that includes English and Spanish resources.

Reflections on Ojibwe Migration

by Janna Jensen and AnnMaria De Mars

📖 Standard

CCSS.MATH.CONTENT.5.NF.B.4   Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

CCSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.

D2.His.13.3-5  Use information about a historical source, including the maker, date, place of origin, intended audience, and purpose to judge the extent to which the source is useful for studying a particular topic.

⏰ Time

60 minutes

📲 Technology Required

Students need access to a computer with web browser.

📃 Summary

This lesson begins with a storyboard on the route and major events of the Ojibwe migration. Students then play the Forgotten Trail game, computing the average number of miles a character walked per day, followed by watching a video on map reading. As a group, students reflect on the challenges of the Ojibwe migration, compute the distance for just one segment and convert the distance from miles to kilometers.

📚Lesson

Storyboard on the Ojibwe Migration

Begin with this story board on the route and major events of the Ojibwe migration. We recommend having students read each section of the story as it advances. Alternatively, the teacher may read it to the class or students can read it to themselves either on devices in the classroom or at home.

Watch a video on how to find the mean

Warning: bad singing ahead. This short video tells how to find the mean – in song. You may skip this video if you have already used it in a previous lesson.

Play the Forgotten Trail Game

Map from Forgotten Trail

Students should play the game at least through the first level. The game begins with a middle school class learning about the Ojibwe migration. Students will solve math problems related to the average number of miles walked per day and fraction of distance covered.

Watch a video on using scales in maps

This video is 7 minutes and covers what is a scale, how to use one and that different maps have different scales. If you feel your students are already familiar with this information, you may skip this video. In the days of Google maps and GPS we have found students often are not as familiar with this information as you might assume.

Presentation on Reflections on the Ojibwe Migration

In this Google slides presentation, students are asked to reflect on the Ojibwe migration. What would it have taken to survive such a journey? They use their map skills to estimate the distance of one leg of the journey, in both kilometers and miles.

Presentation is also available as a PowerPoint.

Synonyms Video

Now that students have seen synonyms as words for the same thing and miles and kilometers as measures for the same distance, finish up with this short (less than 2 minutes) video on synonyms.

Assessment

Slides 14, 18 and 21 can be printed out for students to answer individually, or can be answered as a group in class. Data are available on activities completed and math problems answered in the Forgotten Trail reports. For more information, check out our reports page.

What is a statistical question?

📖 Standard

CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates
variability in the data related to the question and accounts
for it in the answers

📲 Technology Required

Computer with projector, for students learning in class. For students learning at home, materials can be accessed on any device with a browser and application to read PDF files or can be printed out and sent home with students.

⏰ Time Required

2 hours (We recommend doing this over two class periods)

📃 Summary

Teachers begin the lesson with a Google slides presentation explaining the requirements for a statistical question. Students complete an assignment identifying whether or not a question qualifies as a statistical question. After class discussion, students complete a second assignment using a small data set shown on a map. In Part 3, students write and answer their own statistical questions using a data set provided, giving an explanation for their answers. Optionally, students can complete a more challenging assignment drawing conclusions from a graph and/or play a game and identify statistical questions.

📚 Lesson

Before you begin, you should have printed out or added to your Google classroom and shared with students the STUDENT handout from the U.S. Census Bureau, “What is a statistical question?” The student version is 11 pages. If you are short on printer paper, you can skip printing page 1. Also, pages 7 and 8 are an optional activity.

You should also print or download the TEACHER version of the Census Bureau handout, “What is a statistical question?” which includes answers to questions in the first two assignments and explanations why each answer was or was not a statistical question.

Introduce students to definition of a statistical question

Begin with the Google Slides presentation, “What is a statistical question?” which breaks down the two components of a statistical question – it must be answered by data and the data must vary.

Students complete assignment on identifying a statistical question

Have students complete Part 1 of the handout “What is a statistical question?” After all students have answered the questions in Part 1, discuss their answers in small groups or as a class.

Students complete Part 2, assignment on identifying a statistical question using real data

Have students complete Part 2 of the handout “What is a statistical question?” After all students have answered the questions in Part 1, discuss their answers in small groups or as a class.

Then, continue with the Google slides presentation and have students complete Part 2 of the student handout from the U.S. Census Bureau (linked above). Have students discuss their answers with one another.

Either correct the answers as a class or collect these to correct yourself. Remember, the teacher handout, linked above, has the correct answers.

We recommend you end the first day’s lesson here and begin the next lesson after students have had the assignments from Part 1 and Part 2 corrected.

Students complete part 3, creating their own statistical questions from data.

Students complete Part 3 of the handout on “What is a statistical question?”

Discuss students’ answers in class. Provide feedback on whether a question really is a statistical question and whether students’ answers to their questions are correct. Allow students time to explain their conclusions.

Optional: Students Complete Part 4

First, use the Google slides presentation, starting on Slide 24, to explain how to read an area chart.

Next, have students complete Part 4 from the student handout, “Drawing conclusions from a graph.”

AzTech: Empiric Empire

Optional: Play Empiric Empire

After students have completed Parts 1 to 3 of the student handout (and, optionally, Part 4), have them play the game Empiric Empire. As an additional optional assignment, ask students to identify statistical questions asked and answered during the game.

If students do not have phones but have Chromebooks, they can play Disaster Deduction Detectives instead – available June, 2022.

Assessment

For assignments in Parts 1 and 2 the teacher version of the handout has correct answers and explanations. For assignments in Parts 3 and 4 of the student handout, examples of correct responses are given but these will vary as students provide their own statistical questions.

For the Empiric Empire game, the teacher reports show student responses to questions. It should be noted that this game does begin with fractions and decimals, which are a prerequisite to statistics.

Google Slides and Math

📖Standards

CCSS.MATH.CONTENT.6.SP.B.5.C Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

CCSS.ELA-LITERACY.RH.6-8.7 Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts.

⏰ Time

120 – 180 minutes (You may wish to use 2-3 class periods)

📲 Technology Required

The games used here require a Chromebook, Windows or Mac computers or iPads.

📃 Summary

Students play three games that teach fractions and statistics. Students learn enhanced features of Google slides. They then create a Google slides presentation stating which is their favorite game and why.

📚 Lesson

0. Optional: Google Slides Basics

If students are not familiar with Google Slides, begin with the Google Slides Basics lessons. If students know how to create slides document, select a theme, add text, images, transitions and animations, you can skip this step.

1. Introduce the assignment

Explain to students that they will be playing three different educational games and making a recommendation for future classes. If there is only time to play one of these games, which should the teacher choose. A copy of the assignment is here with both Chromebook and iPad games included. Save to your Google classroom or other system and delete whichever device is not available to your students. If your students have access to both devices, no editing is required. Since their presentation will be made with Google Slides and they want it to be as convincing as possible, they should include images and video to support their points.

2. Play AzTech: The Story Begins

This game teaches fractions and basic statistics, integrated with social studies terms and Latin American history.

Allow students 10 -15 minutes to play the game.

3. Learn about Google Slides Advanced Features

This presentation has links to six videos beyond Google slides basics.

Click on the links on the left side of the screen to learn about:

  • Modifying the theme
  • Inserting video
  • Adding effects to text and images

Allow 10-15 minutes to watch videos and start on their presentations.

4. Play Forgotten Trail or Fish Lake Adventure

Students play Fish Lake Adventure (iPad) a game that teaches fractions or Forgotten Trail (Chromebook), a game that teaches fractions and statistics.

Allow 10-15 minutes to watch videos and continue their presentations.

5. More Google Slides Advanced Features

Continue with more Google slides basics. Watch three videos on the right side of the screen on :

  • Customizing with Word Art
  • Publishing to the web
  • Presentation notes

Allow 10-15 minutes to watch videos and continue their presentations.

6. Play AzTech: Meet the Maya

Allow students the option of playing AzTech: Meet the Maya or continuing one of the two previous games. Meet the Maya continues the game series that teaches fractions and basic statistics, integrated with social studies terms and Latin American history.

Allow 10-15 minutes to play and continue their presentations.

7. Finish !

It’s decision time. Students will select one game to finish for their presentation. Students who finish ahead of the class may play the other games.

Allow 30 minutes to finish the game they have chosen and continue their presentations.

8. Optional (extra credit) Present or publish

Depending on your class and your own objectives, you may want to end this lesson with students either publishing their presentations to the web or presenting in class and trying to convince their classmates that the game they have chosen is the one students should be using to learn next year.

Allow 30 minutes to finish the game they have chosen and continue their presentations.