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

Using Visual Models To Compare Fractions

Standards

CCSS.MATH.CONTENT.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2

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.

Technology Required

Students will need a Mac or Windows computer or an iPad to play the Fish Lake game. Alternatively, students can play Forgotten Trail on the web using Chromebooks or any computer with a web browser.

35-45 minutes

Lesson Summary

Students play 2-3 levels of a game that teaches and assesses adding and comparing fractions with different numerators and denominators, with the context of a story from Ojibwe history. They create their own problems using visual models to compare fractions. Students discuss classmates’ problems. The lesson culminates with a video on visualization as a problem-solving strategy.

Lesson

Students play the Fish Lake game through level 2. This requires installing the game on an iPad or a Mac or Windows computer. If only Chromebooks are available, students can play the Forgotten Trail Game instead. We do recommend Fish Lake if iPads are available. Although mathematics and social studies standards taught in both games overlap, the change from using Chromebooks in most lessons to a more console-level game can improve student engagement.

Students create their own problems (10 minutes)

Use slides 1-4 of this Slides presentation to explain the assignment. Optionally, for students learning at home or for homework, it can be assigned to students in Google classroom or similar system.

Discuss math problems students created (10 minutes)

Because students very often ask, “What do you mean?” or “Give me an example?” slides 5-11 of the presentation give an example.

Assessment

This lesson includes three types of assessment. In the games, students are presented with math word problems that relate to the game narrative. Their answers are scored and data can be accessed for each student from the teacher reports. Students submit math problems they have written for teacher feedback. Also, teacher can use whole class discussion of student problems as a gauge for understanding or have students in pairs or small groups submit written discussion of their peers’ math problems.

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.

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

Decimals, Epidemics & Fly Vomit – It’s science!

📖Standards

CCSS.MATH.CONTENT.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths

CCSS.MATH.CONTENT.5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

CCSS.ELA-LITERACY.L.6.6 Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Technology

Students will need a phone or tablet to play the game.

75 minutes

Lesson Summary

Learn decimals while weighing a flies and the food they eat. The lesson begins with a game on decimals and the Aztec smallpox epidemic, then moves to another disease spreader – flies. Students learn the role flies play in our ecosystem, how they eat and reproduce.

Lesson

1. Play a game

Play AzTech: Empiric Empire to learn basic conversions from fractions to decimals. Empiric Empire is available free for iPad or iPhone and for Android phones. As an added bonus, students will also learn about epidemics. It’s worth mentioning that the smallpox epidemic was spread by viruses but a lot of other diseases are spread by flies.

Note: For summer learning, you may want to just copy the paragraph above into your Google classroom for students to download the games to their phones.

2. Watch a video

Bell Ringer – What if flies went extinct ?  This 7:33  minute video discusses flies as agricultural pests and disease vectors, but also their benefits as scavengers eating up decaying carcasses, pollinators and animal feed.

Here is the link if you’d like to post in your Google classroom or other CMS for students to watch at home. https://youtu.be/80Iqp6bqc-0?t=76

Recommended reading: Eat like a house fly. Houseflies and barf

What really happens when a house fly lands on your food? Print out this page from Science World – Canada , include the link in your Google classroom or other CMS for students to read, or just read the page to students during class. The demonstration requires vinegar, jello and a turkey baster – things many people have around the house or can pick up easily at a local store. It also includes a list of vocabulary words and definitions, which fits perfectly with our philosophy of direct teaching of academic language.

4. Complete word journal

This lesson provides the opportunity for students to learn many words, in the reading, in the videos and possibly in the Empiric Empire game as well. 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.

5. Presentation on Decimals in Science (Fly Experiment)

Give this presentation on using decimals to weigh flies, their containers and the food they eat to answer the question, “Do flies really eat 10 times their weight each day?”

Watch a second video

I recommend watching the first 5 1/2 minutes of the Facts About Flies – Secret Nature video  to give the students some idea about both flies as vectors of disease but also important scavengers consuming decaying material. The full documentary is 49 minutes, which I personally found to be more about flies than I wanted to know.

Assessment

Three types of assessment are included in this lesson.

1. The Word Journal assignment is completed individually and submitted.
2. Math questions answered within the Empiric Empire game are scored automatically with immediate feedback and student results can be viewed in the teacher reports.
3. Math questions posed within the presentation can be answered as a whole class, having students hold up a card with their answer or with individual students responding and asking the rest of the class to agree or disagree.

Differentiated instruction

One-minute step-by-step video from TeacherTube on Adding Decimals may be helpful for students who need a review of decimal addition.

Watch the whole video

For students who are extremely interested in insects, watching the entire 49 minute video of Facts about Flies will satisfy their curiosity

Experiments with fly larva

For teachers who want to do a deep dive into the role flies in consuming food waste, the experiment above uses 100 black soldier fly larvae. I am extremely impressed with this lesson because not only does it include a link to where to buy maggots (on Amazon, of course) but also answers the obvious question of what do you do with 100 fly larvae after your experiment is over. The answer is that you feed these to your class reptile. Would I bring 100 maggots into my classroom? Not in a million years, but that is why I am not an entomologist.

Analogies with sheep and goats

📖Standard

CCSS.ELA-LITERACY.L.7.5.B Use the relationship between particular words (e.g., synonym/antonym, analogy) to better understand each of the words.

Dine’ Culture Standards (3.PO2) I will develop an understanding of Dine’ way of life through Iina’. I will implement and recognize the Dine’ lifestyle. I will present the stories related to Land and Water Beings.

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

⏰LESSON TIME

25 -30 minutes including game play

📲TECHNOLOGY REQUIRED

A device with a web-browser – PC, Mac or Chromebook – or phone or tablet.

📃Summary

Students play a game which teaches about raising lambs, the uses of sheep and the ratio of single to twin lambs. The lesson ends with definitions of sheep and goat vocabulary and examples of analogies with sheep and goats. Optionally, students may complete a word journal assignment.

📚Lesson

Students begin by playing Making Camp Navajo. You can just copy and paste these instructions into your Google classroom or other system, or just copy and show in a projector on the board – old school rules!

You can assign your students usernames and passwords or you can send us a list and we will register your students for you. Email the list to growingmath@7generationgames.com . Your students can create their own usernames and password but we do not recommend this, mostly because they will forget what they entered.

Play Making Camp Navajo

There are three activities students should play. If you have not played before, the game will start you at the introduction. If you are a returning user, log in and click on the Life tab.

Learn about sheep in Navajo daily life

On the LIFE page, you’ll see two photos with sheep in them. Play both of those sections.

Next, go to the numbers page and pick this option to learn a little more about sheep.

Now that you have read the instructions, here is the link to go to Making Camp Navajo.

Learn the vocabulary

Now that students have learned about sheep, let’s learn some sheep and goat vocabulary using this Google slides presentation. The presentation ends with two examples of analogies, then asks the students to give their own examples of analogies.

Assessment

This lesson has two types of assessment. Making Camp Navajo automatically records students answer to problems in the three game activities, assessing the Diné and math standards. The analogies produced by students address the ELA standard.

Differentiated Instruction

For students who struggle with vocabulary, including English learners, you may wish to include a word journal assignment. Some teachers call it a personal dictionary. 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.

Related lesson

The Navajo-Churro: America’s first domestic sheep

The Navajo-Churro: America’s First Domestic Sheep

📖STANDARD

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.

7th-8th Diné History Standards – I will understand historical/factual events, people and symbols that influence my family. Concept 1.PO2.  I will identify an event relating to important people in Diné history.

⏰LESSON TIME

90 minutes including time for research

📃SUMMARY

Vocabulary and historical events key to Navajo sheep farming are provided in a slide presentation. Students learn more about Navajo agriculture and history through a video, their own research, and a game combining math and history. Academic vocabulary is at the 7th grade level.

📚Lesson

Navajo-Churros: America’s First Domestic Sheep

Introduce sheep farming in Navajo and southwest history with this presentation, for an editable Google slides version, go here. The same presentation as a PowerPoint is found here. Students will learn vocabulary words related to general livestock farming and specifically to sheep.

Research and Writing Assignments

This assignment has two parts. In the first part, students research one of these events in history to learn more about it. They locate a primary source and a secondary source with citations, and then write an objective summary. In Part B, students select two research questions of interest, from a list provided, and conduct research to find the answers. A Google doc of the assignment can be found here.

Answer key for Part B can be found here.

Differentiated Instruction: Accommodations for learners with special needs

For the assignment above, for learners with special needs, you may wish to assign only one of the two parts. Generally, we would assign Part B, finding the answers to research questions. This is also a modification for students who are English language learners.

GAME: Making Camp Navajo LIFE Module

Students can play the three Making Camp Navajo modules for 20 minutes. The following instructions can be copied into Google classroom, pasted into a Zoom chat or given in class.

Go to Making Camp Navajo https://www.7generationgames.com/making_camp_navajo

Play through until you reach the LIFE tab and play all of the activities you find there.

These are the three activities you will play

• Lots of Lambs
• The Many Uses of Sheep
• Navajo Weaving

ASSESSMENT

This lesson includes three forms of assessment

1. Objective Summary of Research (written assignment)
2. Research to answer questions on an event with primary/secondary sources
3. Making Camp Navajo Gameplay

Making Camp Navajo – Student Activities completed can be seen in the Making Camp Navajo teacher reports

1. Assessment in lamb care/lambing season. (True or False)
2. Assessment in the Many Uses of Sheep for Navajo history. (Matching game)
3. Students can screenshot a picture of their rug design, like below.

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.

60 minutes

📃 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

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.

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.

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.