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.
Time
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
Start with a Game (10-20 minutes)
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.
A visual model of equivalent fractions
Watch a video (2.5 minutes)
Visualize! One way of solving a problem
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.
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. So, here is our first unit. More to follow soon.
📖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.
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.
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.
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.
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.
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.
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.
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.
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.
⏰ Time
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.
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.
Read a passage on the life cycle of a dairy cow
You’ll find this on page 14 of the handout linked above or download both reading assignments here (it’s only two pages) or copy the link to assign in your Google classroom to read on line.
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.
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.
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.
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
I pasted in a link starting after the first minute because that is mostly telling you to like/ subscribe and comment. Ah, YouTube!
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
3. Read about flies
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 experiment 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.
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.
The Word Journal assignment is completed individually and submitted.
Math questions answered within the Empiric Empire game are scored automatically with immediate feedback and student results can be viewed in the teacher reports.
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.
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.
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
Start with a game
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.
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.
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.
VIDEO: Irene’s Churro Lambs
YouTube video: Irene’s Churro Lambs
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.
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.
CCSS.MATH.CONTENT.5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
CCSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.
D2.His.13.3-5 Use information about a historical source, including the maker, date, place of origin, intended audience, and purpose to judge the extent to which the source is useful for studying a particular topic.
⏰ Time
60 minutes
📲 Technology Required
Students need access to a computer with web browser.
📃 Summary
This lesson begins with a storyboard on the route and major events of the Ojibwe migration. Students then play the Forgotten Trail game, computing the average number of miles a character walked per day, followed by watching a video on map reading. As a group, students reflect on the challenges of the Ojibwe migration, compute the distance for just one segment and convert the distance from miles to kilometers.
📚Lesson
Storyboard on the Ojibwe Migration
Begin with this story board on the route and major events of the Ojibwe migration. We recommend having students read each section of the story as it advances. Alternatively, the teacher may read it to the class or students can read it to themselves either on devices in the classroom or at home.
Watch a video on how to find the mean
Warning: bad singing ahead. This short video tells how to find the mean – in song. You may skip this video if you have already used it in a previous lesson.
Play the Forgotten Trail Game
Map from Forgotten Trail
Students should play the game at least through the first level. The game begins with a middle school class learning about the Ojibwe migration. Students will solve math problems related to the average number of miles walked per day and fraction of distance covered.
Watch a video on using scales in maps
This video is 7 minutes and covers what is a scale, how to use one and that different maps have different scales. If you feel your students are already familiar with this information, you may skip this video. In the days of Google maps and GPS we have found students often are not as familiar with this information as you might assume.
Presentation on Reflections on the Ojibwe Migration
In this Google slides presentation, students are asked to reflect on the Ojibwe migration. What would it have taken to survive such a journey? They use their map skills to estimate the distance of one leg of the journey, in both kilometers and miles.
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.
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 Standard6.4.1.4 – 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.
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.
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.
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.
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.
