# Game Design Unit for Middle School

## INTRO TO GAME DESIGN

In this unit, students will:

• Become proficient in use of Google apps Drive, Docs, Slides and Meet software for editing and sharing documents, presentation and videoconferencing.
• Use audio editing software to edit sound files.
• Use educational software to learn and reinforce skills and concepts in mathematics.
• Conduct original research on culture and natural environment of our community through outdoor education.
• Conduct original research on history, culture and natural environment of our community and other Indigenous peoples through Internet and library research.
• Conduct original research on history, culture and natural environment of our community and other Indigenous peoples through oral histories.

Google slides presentation to introduce unit

## Module 1

Introduction to game design: Terms, game review, game design documents.

## Module 2

Understanding software enhancement: Game revisions, bug reporting

## Module 3

Deeper dive into game design: Breaking down elements

## Module 4

Better games, better world: An inside look inside the game design process

## Module 5

Real-world applications: Critical thinking and professional skills development

• Record oral history interviews
• Edit notes to include ideas from the video and interviews from Module 4.
• Outline presentation or report to be given/submitted in Module 7.
• For those opting to present, craft a brief professional email to request a meeting with the software team to present your feedback and game suggestions.

## Module 6

Getting your point across: Preparing presentations/reports

## Module 7

• Prepare feedback/enhancement presentation using Powerpoint or Google Slides. Five-minute presentation plus five-minutes of discussion. For those who prefer not to present, draft a 1-2 page game design report.
• Present to software design team via Google hangout, Zoom or Microsoft Teams

# Learn statistics and history, in English or Spanish

## Standards

CCSS.MATH.CONTENT 5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem.

CCSS.MATH.CONTENT.6.SP.5.c. Calculating quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation).

CCSS.MATH.CONTENT.7.EE.3 Solve multi-step real-life and mathematical problems posed with rational numbers in any form (positive and negative, fractions, decimals, and integers).

CCSS.ELA-LITERACY.RH.6-8.4 Determine the meaning of words and phrases as they are used in a text, including vocabulary specific to domains related to history/social studies.

30-45 minutes

## Summary

This lesson includes game-based instruction and assessment.

Click here for the AZTECH: THE BEGINNING TEACHERS GUIDE with answers to all math and vocabulary questions, game play ‘cheat sheet’ and everything else you need to know.

## Lesson

#### Play a game (yes, it’s free)

1. Assign students to play AzTech: The Beginning. The link to play the game online can be found here. It can also be downloaded from the App Store here.
2. Students register with a username and password, then play the game, in English or Spanish. You can have students register and select their own, or provide usernames and passwords you wish them to use, for example, an existing school login.
3. Each math problem has an EXPLAIN button that students can click to get an explanation of how to solve the problem. Some also have a hint, which is a short suggestion of how to go about solving it. For example, “Subtract the number of days you did not have homework, from the total number of days. Give the answer as a fraction of the total.”

We recommend encouraging students to read the EXPLAIN and any HINT buttons before asking the teacher for help.

4. If students miss a problem twice in a row, they are routed to a LEARN MORE page and need to select an option, which may be a video, web page with voice over or matching terms, to learn more.

## Assessment

Students get immediate feedback on right or wrong answers. Assuming students are playing online, results of in-game math challenges are recorded to a database which teachers can access. Access to reports can be found here.

## Differentiated Instruction

Students who finish ahead of the class can continue the story in AzTech: Meet the Maya, available for the web and also in the Apple App Store for iPads.

Students who are not yet at the sixth-grade level in mathematics and who could benefit from a bilingual game can play Making Camp Bilingual, which address third- and fourth-grade math standards. It is available here for access from the web and in the Apple App Store and Google Play store .

## Related lessons

Teaching statistics in classrooms with English learners AND Native speakers.

# The Codex in Latin American History and Math

## Standards

CCSS.ELA-LITERACY.RH.6-8.2 Determine the central ideas or information of a primary or secondary source; provide an accurate summary of the source distinct from prior knowledge or opinions.

CCSS.MATH.CONTENT.6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations

CCSS.ELA-LITERACY.W.7.1 Write arguments to support claims with clear reasons and relevant evidence.

## Technology required

Device with a browser for AzTech Game. Printer for printing codex and related worksheet and activity pages.

4-5 hours

## Lesson Summary

This is an augmentation of a lesson from the Library of Congress uses a primary source – the Huexotzinco Codex – as a basis for document analysis, inquiry and applied mathematics. Students analyze pages documenting tribute paid to Spanish administrators, compute the tribute paid, read a one-page overview of the codex and analyze the codex. A presentation is given on connections between Aztec, Mayan and contemporary methods. Students begin or end classes playing a game that includes Mayan history and middle school mathematics.

## Lesson

First, some background for the teacher. The Huexotzinco Codex was part of the evidence in a case brought by the Nahuas, Indigenous people of what is now Mexico, against the Spanish administrators, alleging excessive taxation (tribute). This case was won by the Nahuas. In this lesson, students do not learn the full story until the third or fourth class period.

### Analyze Documents

Begin with this link to the Library of Congress lesson, “The Huexotzinco Codex”, and have students complete Activity 1, Document Analysis. This should take one class period- approximately one hour.

NOTE TO THE TEACHER: Allow at least 30 minutes before using this lesson the first time, to read through the Library of Congress lesson, download and print out documents for students.

### Play a game

Have students sign in and begin the game, AzTech: Meet the Maya. Students should play for about 15 minutes.

### Computation – How much was the tribute?

Continue with the second part of Library of Congress lesson, “The Huexotzinco Codex”, and have students complete Activity 2, Computation. After students have completed one tribute sheet and corrected their answers, use this slide presentation to show the connection between the Aztec and Maya codices and our modern system of numbers and graphs. Optionally, have students complete one or two more tribute sheets from the linked lesson. This should take one to two class periods.

### Play a Game

At the beginning of class, have students continue the AzTech: Meet the Maya game. Students should play for 15-20 minutes by which time some of the students should have reached the codex activity and explanation in the game.

### Write a Narrative Explanation

Continue with the third part of Library of Congress lesson, “The Huexotzinco Codex”, and have students complete Activity 3, Narrative Explanation.

## Assessment

Four types of assessments are included; observation of student understanding of historical document analysis in the class discussion, student self-corrected math computation, student written assignments (analysis sheet, observations and scenario outlines) and the math problems in the AzTech game which are scored automatically with data available in teacher reports.

## Differentiated instruction (optional)

Advanced Students who complete their assignments early can continue with the AzTech: Meet the Maya game. If they complete this game, they can choose to play AzTech: The Story Begins or AzTech: Empiric Empire.

English learners can play the AzTech : Meet the Maya and AzTech: The Beginning games in English or Spanish.

### Recommended Related Lesson

Counting ropes and rational numbers

# 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.

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.

### 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
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.

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.

### 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

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: Meet the Maya, which teaches 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
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

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.

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).

### 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

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/ )

## 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

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.

# Ratio and Proportion 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. Of course, your average teacher could do this but your average teacher is also short of time.

## 📖Standards

CCSS.Math.Content.6.RP.A.1 Understand ratio concepts and use ratio reasoning to solve problems.

CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

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

## ⏰Time Required

About 4 hours for all seven lessons

## 📲Technology Required

Projector or smart board for in–class or access to computer or tablet for web meeting for remote learning. Presentation could be printed for students at home without computer access.

# 🧾Unit Summary

This seven-lesson unit teaches sixth- and seventh-grade standards on ratio and proportion using real-world problems. Complete unit requires about 4 hours and includes multiple hands-on activities.

### Lesson 1: Teach Ratio with Math Snacks (90 Minutes)

CCSS.Math.Content.6.RP.A.1 Understand ratio concepts and use ratio reasoning to solve problems.

Students watch a video from Math Snacks in which Isabella uses the ratio of words she speaks to her date to determine if it was a good or bad day. The video has a companion teacher guide with questions to stimulate students’ thinking about ratios and test their understanding. Students play a game where they brew potions with given ratios to defeat an opponent. Students then complete a learner’s guide assessing and reinforcing their knowledge of ratios.

### Lesson 2: Ratios as Fractions (10 Minutes)

Summary

Standard: CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

Yes, this lesson plan is just a video. We watched LOTS of boring videos on ratios and rates to find this one! This video can be used before or after the lesson on Introduction to Ratio and Proportion, either as an introduction for students who need more preparation or a second look for students who could benefit from having the material presented in a different way.

### Lesson 3: Introduce Ratios and Proportion (30 minutes)

Standard: CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

Summary: Students are presented with definitions of ratio and proportion along with multiple examples and ways to solve these problems. This presentation includes multiple explanations for multiple levels of understanding. There is a solution using algebra, with cross-multiplication and an explanation of why cross-multiplication works. There is also an explanation using equivalent fractions. If you are teaching an algebra class, use the first explanation and delete the second. For a more basic math class, delete the first explanation and just use equivalent fractions. Also includes a baking activity, not required but highly recommended.

### Lesson 4: Ratio, Proportion and Animal Identification (65 Minutes)

Standard: CCSS.MATH.CONTENT.7.RP.A.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.

Students hear or read a presentation on ratio, percentage decrease, rate and proportion. They watch a short video on ratio. Students collect data either outdoors or using images provided. They then compute ratio, rate, increase and proportion using the data.

### Lesson 5: Introducing Ratio and Proportion with Making Camp Navajo (30 Minutes)

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

Students play the Making Camp Navajo game, selecting the activity that explains ratio and proportion. The teacher reviews the activity with the class in a presentation, that includes three more problems to be completed as a group.

### Lesson 6: Rates, Ratios and Proportions with Fractions (40 Minutes)

Standards: CCSS.MATH.CONTENT.7.RP.A.1 Compute unit rates, including those that involve complex fractions, with like or different units.
CCSS.MATH.CONTENT.7.RP.A.2.C. Represent proportional relationships by equations

Students watch a 4-minute video giving examples of finding unit rates by simplifying fractions. They solve a problem together as a class and are given a short lecture on solving rate problems with complex fractions. Problems provided can be worked by students individually or done together in class.

### Lesson 7: Discover Dairy – Ratio in the Cow Life Cycle (65 Minutes)

Standards:CCSS.Math.Content.6.RP.A.1 Understand ratio concepts and use ratio reasoning to solve problems.
CCSS.MATH.CONTENT.7.RP.A.2 Recognize and represent proportional relationships between quantities
CCSS.ELA-LITERACY.RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts.

This cross-curricular lesson is from Discover Dairy. Students read a passage on the life cycle of dairy cows. A guided class discussion answers questions on the life cycle. The lesson concludes with a challenging lab in which students create a healthy cow diet.

# 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.”

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: Meet the Maya, which teaches measures of central tendency. The lesson concludes with a question and another video on distributions.

## 📚Lesson Plan

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

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.

### 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.

## Also available in Spanish! (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.

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.

# Discover Dairy: Cow Life Cycle

## 📖 Standards

CCSS.Math.Content.6.RP.A.1 Understand ratio concepts and use ratio reasoning to solve problems.

CCSS.ELA-LITERACY.RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts.

## 📲 Technology Required

Computer with printer to print lab work sheets, for in-class use. Computer or tablet with Internet access for home use.

Heads up! For the lab in this lesson you will need spinach, carrots, cheese sticks, orange juice, and a weight scale and/or measuring cups. It is not required to do the lab 2 component but recommended.

60-70 minutes

## 📃 Summary

This cross-curricular lesson is from Discover Dairy. Students read a passage on the life cycle of dairy cows. A guided class discussion answers questions on the life cycle. The lesson concludes with a challenging lab in which students create a healthy cow diet.

## Lesson

NOTE: While we create most lessons on the Growing Math site ourselves, we do include links to other lessons that are exemplary in their cross-curricular, standards-based design. This lesson is one of two “lessons we love” from Discover Dairy. The entire 14-page guide with two lessons can be downloaded here, including reading passages, lab assignments and answer keys.

You can also go to the Discover Dairy site, which requires a free registration and login to download individual parts of the lesson and see the other lessons they have available.

### Class Discussion on Life Cycle

Using the discussion questions on page 4 of the complete lesson plan, discuss the dairy cow life cycle with students based on their knowledge from the reading.

### Lab Exercise #2 Feeding a Dairy Cow

Each student or group will need a scale or measuring cup and the following:

• 1 cup spinach
• Baby or whole carrots
• 1 cheese stick
• One 12 oz. cup of orange juice

Distribute the materials needed and the lab assignment (pages 11 and 12 of the complete lesson plan or you can link directly to those here, if you want to assign in Google classroom or other management system. Note that link includes both labs 1 and 2.) Lab explanation from page 5 of the complete lesson plan.

Teachers should explain that a healthy, well-cared-for cow will give more milk. The way farmers care for their cows and how they feed them has helped to increase the amount of milk cows give over the past 50 years.  Just like our diets, a cow’s diet must be balanced based on her stage of life. For instance, a baby calf requires higher energy foods to fuel her rapid growth.  A cow that has just given birth requires higher levels of certain nutrients to replenish her body. Farmers must adjust rations to accommodate those needs.  Farmers work closely with an animal nutritionist and use a variety of feed products to balance cows’ diets to meet their precise nutrient needs using a variety of feed products.  Farmers use a large feeding scale to make sure each cow gets the right amount of each feed. Those feeds are blended together to provide a balanced diet called a Total Mixed Ration (TMR). During the lab, students should use the carrots, celery, cheese and orange juice to balance a diet to meet the required nutrients listed on the lab worksheet. They should use a weight scale to measure the right amount of each feed. If they don’t have a weight scale, they can use measuring cups to determine the amount. Complete the ratios in the worksheet.

– Discovery Dairy

### Review and Summarize Dairy Cow Life Cycle: What We’ve Learned

Review questions and summary can be found on pages 5 and 6 of the complete lesson plan.

## ASSESSMENT

This lesson includes three types of assessment – the initial class discussion gives an estimate of the general class understanding of the dairy cow life cycle. The lab provides individual student data on mastery of both the science and math concepts. The concluding review questions can be poised to the whole class or given to students as a quiz.

## Related lesson

Discover Dairy: Selective Breeding

# Discover Dairy: Selective Breeding

## 📖 Standards

CCSS.ELA-LITERACY.RST.6-8.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).

CCSS.ELA-LITERACY.RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts.

## 📲 Technology Required

Computer with projector, for in-class use. Computer or tablet with Internet access for home use.

60-70 minutes

## 📃 Summary

This cross-curricular lesson is one of two “lessons we love” from Discover Dairy. Students watch a short video, read a passage on selective breeding in dairy cows, have a discussion and complete a lab exercise in selective breeding.

## Lesson

NOTE: While we create most lessons on the Growing Math site ourselves, we do include links to other lessons that are exemplary in their cross-curricular, standards-based design. This is one of two lessons we love from Discover Dairy. The entire 14-page lesson can be downloaded here, including reading passages, lab assignments and answer keys.

You can also go to the Discover Dairy site, which requires a free registration and login to download individual parts of the lesson and see the other lessons they have available.

Watch a four-minute video on dairy farms to kick the lesson off.

### Class Discussion on Selective Breeding

See page 2 of the full lesson linked above for suggested discussion questions. Note that the first question asks about the 7 types of dairy cows- the 7 types of cows are picture on the complete lesson plan on page 7.

### Lab Exercise #1 : Selective Breeding

Pass out the lab activity #1 sheets, in pages 9 and 10 of the complete lesson plan. You can link directly to those here, if you want to assign in Google classroom or other management system. Note that link includes both labs 1 and 2.

Once students have the materials, explain the lab activity. You may want to use the explanation given on pages 2-3 of the lesson plan.