Tag Archives: statistics

Distributions and Mayan Trading (Bilingual English & Spanish)

📖Standard

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. Understand that random sampling tends to produce representative samples and support valid inferences.

Minnesota State Standard – History Sub-strand 4, Standard 15 “North America was populated by indigenous nations that had developed a wide range of social structures, political systems, and economic activities, and whose expansive trade networks extended across the continent.”

Time

20- 30 Minutes 

📲Technology Required

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

📃Summary

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.

📚Lesson Plan

1. Watch video – Mayan Trading (1:57)

Also available in Spanish! – El Comercio Maya (1:58)

El Comercio Maya

The Mayan trading video is based on an idea from one of my favorite history teachers, who says that history is more than just names and dates but also how people lived, what they used, what they did. It also has a bar chart of the relative value of objects. It explains that the Maya traded less common items for more common ones and that items that were more difficult to obtain were more valuable.

2. Play AzTech: Meet the Maya

Next, have students start the AzTech games series. They can play AzTech: Meet the Maya online or using an iPad. We recommend downloading the game onto your iPhone or iPad for better performance.

3. Question to test understanding

José tried to trade a banana for a quetzal feather and a villager threw a spear at him. Why would the villager do that? Explain using math. Extra points if you can discuss distributions in your explanation.

José ofreció intercambiar un plátano por una pluma de quetzal y un aldeano le lanzó una lanza. ¿Por qué haría eso? Explica usando la matemática. Puntos extra si puedes hablar de distribuciones en tu explicación.

4. Video giving the answer to the word problem on distributions (5:15)

Also available in Spanish! (5:15)

Explicando distribuciones y variabilidad

This five-minute video introduces distributions and variability and gives an example of computing a weighted mean from a frequency distribution.

OPTIONAL You can also copy this Google slides presentation to your own classroom if you’d rather modify the explanation for your own lecture. The slides can also be printed out and sent home with students who do not have Internet access.

Spanish Google Slides presentation – Introduciendo Distribuciones

ASSESSMENT

You can view your students’ progress on mastering these standards by viewing your teacher reports. The link to the teacher dashboard for AzTech: Meet the Maya student reports can be found on this page. You should have received a password during the Growing Math training.

State Standards

Minnesota State Standard 6.4.1.1 – Determine the sample space (set of possible outcomes) for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations.

Related Lesson

Distributions and Mayan Trading – This lesson is the English Only version of the lesson above.

Understanding averages using skunks

📖STANDARDS  

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context, such as by:

  • CCSS.MATH.CONTENT.6.SP.B.5.A Reporting the number of observations.
  • CCSS.MATH.CONTENT.6.SP.B.5.B Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

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.

LESSON TIME

30 minutes 

📃SUMMARY

In this lesson plan, 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.

📲TECHNOLOGY REQUIRED

Device with web-browser (Chromebook, laptop or desktop computer)

📚LESSON

Introduce the Assignment

Students can read the assignment, Going on a Skunk Hunt , on their own or teachers can read it to the class and ask any questions (5 minutes)

Through the next three activities – video, reading and assessment –  students will gather clues to unlock the “secret password” for the Skunk Hunt and get to play a short online game. Individual links to the video, reading and assessment components are included below for your reference, but are all included in the Skunk Hunt activity as well for ease of student access. 

The answer to the Skunk Hunt/secret password is: 3harvestnewyork1911

VIDEO

Watch this animated video explaining how to find the average. The video includes an example problem walking through the process, introduces the formula to find the average and also includes vocabulary to explain that mean and average the same thing. (2:00)

READING

Read this short post, Skunks for Fur and Farming , about the intersection of skunks and agriculture, incorporating information from primary sources and historical data. (5-10 minutes)

ASSESSMENT

In this assessment activity, Playing the Skunk Market ,students will use a table with historical data to solve two to four problems asking students to find the average. Two problems require solving for the average and two problems require solving for the average or estimating the average. (10-15 minutes)

ANSWER KEY AVAILABLE HERE. 

RELATED: This lesson plan corresponds with the math standards covered in and refers to content included in Forgotten Trail. Forgotten Trail is recommended as a supplemental resource for this activity. The image at the top of this post is from that game. You can view your students’ progress on mastering these standards by viewing your teacher reports. You can access the Forgotten Trail reports here.

Probability and fruit

📖Standards

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.

Time

30-45 minutes, depending on whether the final individual activity is performed in class or outside of class.

📲Technology Required

A projector or smart board is required to show the Google slides presentation in class. It can also be shown using any web meeting software for remote learning. The random fruit basket generator can be used by students in anything with a browser, including computers, tablets or phones. This activity is optional.

📃Summary

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 Plan

1. Presentation on 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 are then given an example of a basket with different types of fruits and the probability of each.

2. Individual students compute probability

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. If students are learning at home, we have a random fruit basket generator to use with this lesson. After setting THE SAME NUMBER OF EACH FRUIT for everyone to enter, have each student click on the basket to select a random fruit and see the probability.

3. Group Activity

Complete table included in presentation as a class. Compare obtained probabilities with expected. Discuss that the expected probabilities are for a large number of trials and that it is usual to have the observe probabilities not match up exactly – or even closely – with the actual proportions when the sample size is small.

4. Probing questions

These questions are included in the presentation. Ask the class what the probability is of selecting a kiwi fruit, remembering that there are not any kiwi in the basket. If Annie’s family owns an apple orchard and her basket contains only apples, what is the probability of selecting an apple? If students need a reminder, return to the definitions of probability, impossibility and certainty at the beginning of the lesson.

5. Individual Activity

Students will create their own probability activity using household items. This activity can be performed at home, having family members draw items, or can be performed in the classroom using items in the classroom, such as different colors of pencils, or even pieces of paper with different words or pictures.

Assessment

Individual formative assessment is conducted throughout this activity by having students write the probability of the specific fruit they selected and by their performance on the individual activity creating their own probability sample and recording the results. Students can also write their answers to the in-class questions on probabilities of 0 and 1, then comparing these to the correct answer.

State Standard

Missouri Learning Standards (MLS)●7.DSP.C.5a 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.

Minnesota Math Standard 6.4.1.2 – Determine the probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1 inclusive. Understand that probabilities measure likelihood.

Minnesota Math Standard 6.4.1.4 – Calculate experimental probabilities from experiments; represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown.

Reading & comparing bar graphs

📖Standards

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.

⏰Lesson Time

40- 50 minutes

📲Technology Required

Device with web-browser – Chromebook, laptop or desktop computer, iPhone or iPad

📃Summary

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 or complete the activity in Google slides . The lesson ends with an adventure game that includes discussion of interpreting bar graphs.

📚Lesson Plan

Related lesson plan

If you have not watched the videos on Mayan Trading and Distributions, you may want to check out this lesson plan first.

Preparing for the lesson – Options

Print out the cards if students do not have home Internet access or if you want to use the cards to do the activity in class. (Note: Business card stock may not be the best $10 I have spent as a teacher, but it’s high on the list. I  don’t know what it is about cards that makes something seem like a game but I have had the greatest success with activities like this one.). Here is a PDF for the cards. If you would like to download the cards to edit and add your own questions, here is a Microsoft Word doc.

If students are learning from home, you can copy the Google slides presentation to your Google classroom and assign to students.

1. Individual Activity

Use this Google slides presentation to introduce and explain the assignment.

Print out the “Graphs” page or display it using a Smartboard, projector or in your Google classroom. Each student / group is required to complete the cards using the graphs provided.

Example of card with graph question
One of a pair of cards comparing graphs

2. Class Activity

After the students have completed the assignment, which should take around 10-15 minutes, have students share their findings to these questions with the class. Discuss and review the different questions and answers that can come from the same set of data.

3. Play Games!

Students can play the AzTech: The Story Begins to practice statistics in a history adventure game. Link available from the games page, select the device on which you want students to play. Available free for Chromebook, Android or iOS.

AzTech: The story Begins
Play AzTech: The story begin

Assessment

AzTech Games Teacher Reports – Teachers can access standards-aligned student reports including answers to problems, number of correct answers, quiz results and pre-test/post-test results.

Students’ responses in the activities above, both individually and as a group, provide formative assessment of their ability at interpreting and extrapolating from graphical data.

State Standards

Minnesota Math Standard 7.2.2.1 – Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations.

Distributions and Mayan Trading

📖Standard

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. Understand that random sampling tends to produce representative samples and support valid inferences.

Minnesota State Standard – History Sub-strand 4, Standard 15 “North America was populated by indigenous nations that had developed a wide range of social structures, political systems, and economic activities, and whose expansive trade networks extended across the continent.”

Time

20- 30 Minutes 

📲Technology Required

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

📃Summary

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.

📚Lesson Plan

1. Watch video – Mayan Trading (1:57)

The Mayan trading video is based on an idea from one of my favorite history teachers, who says that history is more than just names and dates but also how people lived, what they used, what they did. It also has a bar chart of the relative value of objects. It explains that the Maya traded less common items for more common ones and that items that were more difficult to obtain were more valuable.

2. Play AzTech: Meet the Maya

Next, have students start the AzTech games series. They can play AzTech: Meet the Maya online or using an iPad. We recommend downloading the game onto your iPhone or iPad for better performance.

3. Question to test understanding

José tried to trade a banana for a quetzal feather and a villager threw a spear at him. Why would the villager do that? Explain using math. Extra points if you can discuss distributions in your explanation.

4. Video giving the answer to the word problem on distributions (5:15)

This five-minute video introduces distributions and variability and gives an example of computing a weighted mean from a frequency distribution.

OPTIONAL You can also copy this Google slides presentation to your own classroom if you’d rather modify the explanation for your own lecture. The slides can also be printed out and sent home with students who do not have Internet access.

ASSESSMENT

You can view your students’ progress on mastering these standards by viewing your teacher reports. The link to the teacher dashboard for AzTech: Meet the Maya student reports can be found on this page. You should have received a password during the Growing Math training.

State Standards

Minnesota State Standard 6.4.1.1 – Determine the sample space (set of possible outcomes) for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations.

Related Lesson

Distributions and Mayan Trading (Bilingual English & Spanish) – This lesson is a bilingual version of the lesson above and features resources in English and Spanish.

Science, language arts and math with wildflowers

📖 STANDARDS

English/ Language Arts

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.

Mathematics Standard

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.

📲 Technology required

Optionally, the teacher will have access to a printer to print pages 2-3 of the book and selected pages to color. Since choke cherry and Simpson’s Ball Cactus are mentioned in the problems, it is recommended that, at a minimum, these pages should be printed. Alternatively, the link can be shared to students who are learning from home to read material on their computer.

📃 Summary

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.

Time Required

50 minutes

📚 Lesson Plan

Read pages two and three of Wildflowers of Ponderosa Pine Forests Coloring Book – These pages explain the pine forest ecosystem, including an illustration of Life Zones.

Complete 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.

Use Life Zones to Solve Problems

Angie and Sam are on their way to Michigan but they have gotten so, so lost! They are somewhere in Colorado. Sam has sent Angie this text:

Hey, Angie! I can’t see you anywhere. All I can see are trees, a whole lot of trees, and if I look up the mountain, I see even more trees, closer together. I recognize this plant with red berries. Grandma called it choke cherry. Where are you? How can I meet you? Should I go up or down?

Angie texts him back,

There aren’t that many trees around me, but there are some of these round cactus plants. We are definitely not in Michigan!

Use the information on life zones to answer these questions. (Hint: You may have to look on the plant pages as well.)

  1. In which of the five life zones is Sam right now? How do you know?
  2. In which of the five life zones is Angie right now? How do you know?
  3. Should Sam go up the mountain or down the mountain to meet up with Angie? Why?

Click here for the life zone assignment as a Google doc.

BONUS 1: Game Play

You might recognize Sam and Angie from the game, Forgotten Trail, where they try to retrace their ancestors’ journey across the U.S. and Canada. If you finish this assignment and your personal dictionary before class time is over, play Forgotten Trail here.

BONUS 2: Art

As an alternate bonus activity, students may color the pictures in the book according to the legend included. This would require that the teacher print pages for students. Since choke cherry and Simpson’s Ball Cactus are mentioned in the problems, it is recommended that, at a minimum, these pages should be printed.

Assessment

Recommended rubric for the Personal Dictionary is as follows:

This assignment is worth 100 points. A minimum of ten words is required. You can include up to two extra  words for an additional 20 points.

Each word is worth 10 points.

  • Dictionary definition – 3 points
  • Definition in your own words – 5 points
  • Use in a sentence or draw a picture – 2 points

Recommended rubric for Life Zone Questions

Each question is worth 25 points.

Sam is in the Montane zone (5 points). We know this because he sees a lot of trees and the Montane zone is a forested area. He said that there are even more trees up ahead so we know he is not in the subalpine area because above that are no trees (10 points). He also saw choke cherry plants and these are at elevation from 7,000 – 9,000 feet. The Montane zone starts at 8,000 feet. (10 points)

Angie is in the Foothills (5 points). We know this because she says there are not many trees (10 points) and she sees the Simpson’s Ball Cactus which is common in the Foothills (10 points).

Sam should go down the mountain to meet Angie (5 points) because Sam is in the Montane zone, which is at 8,000 to 10,000 feet (10 points) and she is in the Foothills which is at (6,000 to 8,000 feet) so he needs to go down in altitude to meet her (10 points).

Assessment for Forgotten Trail math problems

Problems are scored automatically within the game. Teachers who are part of the Growing Math project or with 7 Generation Games site license can access student data from the Reports page.