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.
Dine Government (3.PO3) Executive Branch (3.PO3): I will describe the purpose of at least one subdivision. Legislative Branch (3.PO3): I will describe the Navajo Nation election process. Judicial Branch (3.PO4): I will analyze the purpose of a judicial system.
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.
CCSS.ELA-LITERACY.W.7.1 Write arguments to support claims with clear reasons and relevant evidence.
Time
45 minutes
Technology Required
Device with web-browser – Chromebook, laptop or desktop computer, phone or tablet
Summary
Students learn about Diné (Navajo) culture from multiple perspectives, first through a presentation on Navajo tribal government and its three branches (executive, legislative, and judicial) that are modeled after the federal government, as well as its security branch. Also included are four cultural laws governing Navajo leadership. A written assignment exploring roles of effective governance follows as assessment. The lesson concludes with a game, Making Camp Navajo, that discusses Diné traditions in sheep ranching and rug weaving.
Class Discussion on Important Issues in Governance
Teachers can use the questions on Slide 26 of the presentation or edit the slides to add their own questions.
Writing Assignment
Students select one or more of the writing prompts and write an essay addressing the prompt. Teachers can use slides 27-31 for the prompts or create their own.
Play a Game
The lesson concludes with the Making Camp Navajo game. Students should play through the introduction and then the activities under the LIFE choices.
Choices Screen – click LIFE button
Life Choices – Select and Play each of these
Assessment
Three types of assessment are included in this lesson. The brainstorming session provides a gauge of the understanding of the class as a whole of the types of issues that can be addressed by government. The writing assignment serves as an individual assessment of student understanding of government. Teacher reports of data collected automatically in Making Camp Navajo document student completion of the activities.
CSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context.
Technology
Students will need a Chromebook, Windows or Mac computer to play the game. Stories can be read on a computer or tablet or printed out.
Time Required
75 -105 minutes.
Summary
This lesson begins with a game teaching statistics, with a level assessing weights of salmon. Next, students read stories about salmon from the Pacific Northwest tribal communities. The lesson ends with a game outdoors or in the gym where students ‘catch’ salmon and learn the impact of overfishing. Optional activity includes creative writing or artwork to accompany the salmon stories.
Lesson
Play a Game (25 minutes)
Play Disaster Deduction Detectives through Level 4 where players compute mean weights of fish caught with and without an outlier. Earlier levels discuss median and statistical questions.
Fish catching game in Disaster Deduction Detectives
Read Salmon Stories (35 minutes)
This 35-page booklet of salmon stories comes from a collaborative effort of the tribal communities of the Pacific Northwest, Northwest Indian Fisheries Commission and Seattle Aquarium. In addition to four stories about salmon, traditional games featuring salmon are described. You can print the booklet or copy the link and assign it in your Google classroom or other online system.
Depending on your available class time and their reading level, you may wish to just assign one or two stories or the whole booklet.
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.
CCSS.MATH.CONTENT.3.MD.D.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. CCSS.Math.Content.3.OA.B.5 Apply properties of operations as strategies to multiply and divide. CCSS.MATH.CONTENT.3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. CCSS.MATH.CONTENT.4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. CCSS.MATH.CONTENT.4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm
Time
Five hours
Technology Required
If teaching in person, the teacher will need a computer and projector or smart board to show the videos, or students can be given the links to watch on their own devices. Students will need a PC, Mac or Chromebook or tablet. Making Camp Premium, Making Camp Lakota and Making Dakota are all playable on any web browser on those devices. Spirit Lake: The Game, playable on Mac or Windows computers also teaches these same concepts or students can watch the videos from the game on any device with a browser.
UNIT SUMMARY
This cross-curricular unit teaches solving word problems with multiplication and division with a variety of strategies and in contexts ranging from agriculture to traditional dwellings.
In this 45-minute lesson, students will learn how to compute perimeter of different polygons using multiplication and apply those skills in game-based practice problems. They will then learn about different Indigenous traditional dwellings. The lesson ends with students contributing to and solving problems that integrate the reading on dwellings and perimeter in an online assessment.
In this 40-minute integrated lesson, students learn about responsibilities of children in traditional Dakota society and discuss their responsibilities today. They learn a problem-solving strategy that can be applied to a wide range of situations, including mathematics. Students play Spirit Lake: The Game or watch videos solving multiplication problems set in the context of a story based on Dakota culture.
In this 45-minute lesson, the students will develop an understanding of the meanings of the four operations of whole numbers through activities and problems involving real life scenarios from Indigenous history. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve using the four operations problems involving single-digit factors. It includes educational videos, games and video presentations that can be used for reviews and daily practice.
This 75-minute cross-curricular lesson includes activities and instruction in agricultural science and math. Students begin by watching a video and learning about pig farms. After making their own pig barn, they watch two short videos about solving math problems. This information is then applied to solve multiplication and division word problems during a presentation on math around the pig farm. Students end playing one of the Making Camp games to reinforce skills and knowledge.
his 40-minute lesson assumes that students have some familiarity with multiplication of one-digit numbers and division with one-digit divisors. Students are introduced to the various means of problem solving in a brief presentation. They watch a video on visualization, then solve a problem that asks them to visualize. After watching a video on building a model, students build and/or draw their own model of a multiplication problem or property. Lesson concludes with game play to reinforce these problem-solving strategies and learn more. T
This 60-minute lesson starts with a video as an ice breaker. Then, students read or listen to a presentation explaining how each math fact is actually four. Students complete an activity where they create their own math facts slides. A recommended video explains features of Google slides. Students complete the lesson playing Making Camp Dakota, solving word problems using division.
CCSS.MATH.CONTENT.3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. CCSS.MATH.CONTENT.3.OA.A.4 – Determine the unknown whole number in a multiplication or division equation relating three whole numbers. CCSS.Math.Content.3.OA.B.5 Apply properties of operations as strategies to multiply and divide. CCSS.MATH.CONTENT.3.OA.C.7– Fluently multiply and divide within 100
Time
Lessons require from 10-40 minutes for a total of 90 minutes. These lessons are recommended more as a review or preview.
Technology Required
Students need a device with web-browser – Chromebook, laptop or desktop computer, phone or tablet. If using a mobile device, we recommend downloading the Making Camp Premium app. It can also be played on the web on any computer.
Unit Summary
Students who have recently learned multiplication tables still need frequent review. These five lessons present multiplication review in a variety of lengths and formats; games, cross-curricular formats integrating Ojibwe history, flash cards, virtual manipulatives, slide presentations and video.
Ojibwe History Integrated with Math + History = Making Camp
That’s Making Camp in a nutshell, um, equation. Each of these only takes about 10 minutes, teaches Ojibwe (Native American) history , multiplication or division. You can do these at the beginning or end of class as a warm-up, as an assignment for those students who finish early or combine all three for a 30-minute lesson.
Students learn about what foods the Ojibwe people ate and how their diet changed when they were forced on to the reservation. They play a multiplication tic-tac-toe to snare rabbits and spend the points earned in the game to outfit their wigwam.
Not strictly multiplication review but this is where students trade in the points they have earned in the prior two lessons for items for their wigwam.Students will watch two brief videos, one on building a wigwam and one on trading between tribes.Clicking on each item gives information on how that item was used by the Ojibwe
Students watch a video on the importance of the Red River cart in expanding trade. The teacher presents (or students may read) a presentation discussing Red River carts followed by two related word problems. The 20-minute lesson concludes with students playing Making Camp Premium, reinforcing multiplication facts and the Ojibwe history lesson learned.
Students watch a video on multiplication terms then review terms with flash cards. Students quiz each other with flash cards. This 40-minute lesson closes with practicing multiplication and division by playing Making Camp Premium.
CCSS.MATH.CONTENT.3.OA.A.1 – Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. CCSS.MATH.CONTENT.3.OA.A.3– Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. CCSS.MATH.CONTENT.3.OA.A.4– Determine the unknown whole number in a multiplication or division equation relating three whole numbers. CCSS.MATH.CONTENT.3.OA.C.7– Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Time
Each lesson will require 20-30 minutes. With the ten lessons, total time is approximately 5 hours spread over one to two weeks.
Technology Required
Making Camp Premium plays in any browser and can also be downloaded on phones or tablets and played offline by students who have limited Internet access. The teacher will need a computer, for showing to students learning from home, and a projector if showing videos in the classroom. If the classroom does not have access to a projector, the videos can be skipped. Spirit Lake: The Game can be downloaded and played on Windows or Mac computers.
Unit Summary
This 10-lesson unit teaches single-digit multiplication. Google slide presentations are provided within each lesson. Students are presented multiplication in a wide variety of formats, including, tables, number sentences, drawings, word problems and virtual manipulatives.
Students use visual drawings, manipulatives, and a number line to learn multiplication of one-digit numbers, coupled with their verbal explanations. Each lesson includes multiple assessments:
Students complete the multiplication tables – these can be shown with a projector (in class), on a screen, if teaching remotely, and on paper for students learning at home.
Students write their own number sentences using the multiplication learned each lesson.
Students complete the problems written by their classmates.
Optionally, students write word problems.
Optionally, student complete word problems written by their classmates.
At the end of lesson 5, students begin playing Making Camp Premium, which has teacher reports showing the number of multiplication problems attempted and answered correctly.
Students use visual drawings, manipulatives, and a number line to learn multiplication of one-digit numbers, coupled with their verbal explanations. Students play the Making Camp Premium game to reinforce learning. Those with access to a Mac or Windows computer can also play Spirit Lake. Each lesson will require 20-30 minutes.
Students use visual drawings, manipulatives, and a number line to learn multiplication of one-digit numbers, coupled with their verbal explanations.
Students will create number sentences independently and with a partner.
Learning and memorizing multiplication patterns will improve later understanding of division.
Determine the unknown whole number in a multiplication equation relating three whole numbers.
Optional Brain Power activities have students write their own word problems.
Students play games that reinforce memory and apply multiplication in word problems.
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. This cross-curricular statistics unit has 12 lessons that total 14 hours of class time, although some assignments could be completed as homework. With the length of this unit, it could be taught as a complete summer school course, addressing primarily mathematics standards but also incorporating English language arts, Social Studies (predominantly Indigenous and Latino history and culture) and science.
Standards
STATISTICS STANDARDS
CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers CCSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. CCSS.MATH.CONTENT.6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. CCSS.MATH.CONTENT.6.SP.B.5 Statistics & Probability: Summarize numerical data sets in relation to their context. CCSS.MATH.CONTENT.7.RP.A.2.B Ratios & Proportional Relationships: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. CCSS.MATH.CONTENT 7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. CCSS.Math.Content.7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. CCSS.Math.Content.7.SP.C.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.
ADDITIONAL MATHEMATICS STANDARDS
CCSS.MATH.CONTENT.5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
CCSS.MATH.CONTENT.7.RP.A.2 Recognize and represent proportional relationships between quantities.
ENGLISH/ LANGUAGE ARTS STANDARDS
CCSS.ELA-LITERACY.RI.6.7 Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue. CCSS.ELA-LITERACY.RI.6.4 Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings. CCSS.ELA-LITERACY.RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.
SCIENCE STANDARDS
Next Generation Science StandardMS-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.
Find your way back using clues from the plants around you
CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers
Teachers begin the lesson with a Google slides presentation explaining the requirements for a statistical question. Students complete an assignment identifying whether or not a question qualifies as a statistical question. After class discussion, students complete a second assignment using a small data set shown on a map. In Part 3, students write and answer their own statistical questions using a data set provided, giving an explanation for their answers. Optionally, students can complete a more challenging assignment drawing conclusions from a graph and/or play a game and identify statistical questions.
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.
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.
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.
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 StandardMS-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.
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.
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 English – for English only lesson, click here. )
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.
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.
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.
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.
CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers CCSS.MATH.CONTENT.7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.
This lesson includes game-based instruction and data analysis. Data can be collected at home on students’ phones or using a computer. Google sheets is used to compute descriptive statistics to answer a statistical question. Lab instructions, Sheet templates and a sample answer are included. You can modify this in an infinite number of ways to compare any two groups on any numeric variable.
CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers
CCSS.MATH.CONTENT.7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.
Technology Required
Computer with projector, for students learning in class. Students will need access to a phone, tablet or computer.
Time Required
75-90 minutes
Summary
This lesson includes game-based instruction and data analysis. Data can be collected at home on students’ phones or using a computer. Google sheets is used to compute descriptive statistics to answer a statistical question. Lab instructions, Sheet templates and a sample answer are included. You can modify this in an infinite number of ways to compare any two groups on any numeric variable.
If students have not completed the lesson, “What is a statistical question?” , you can complete that first. It takes about two hours.
If you are REALLY short on time, or if you are just reviewing the concept you have previously taught, you can just use the first 12 slides of this presentation on What is a Statistical Question?” to give the basic definition and a few examples.
Class Discussion of Research Question
Pose a research question, for example, “Do different Spanish and English speakers differ in their interests, as determined by what they post on Instagram?” Of course, you can easily change the language if you have speakers of other languages in your class.
Next, you need a hypothesis, for example, “Spanish-speakers are more likely to post pictures of food than English speakers” or “English accounts will have more pictures of themselves than Spanish accounts”.
In selecting a hypothesis, you can discuss distribution and probability. If almost no one takes pictures of giraffes then the probability of finding enough giraffe pictures to compare is low. (Be prepared for your students to suggest the hashtag #giraffesofinstagram).
#GiraffesofInstagram
Statistics Lab Assignment : Social Media Analytics
In this assignment, each group of students will collect and analyze social media data from 10 accounts of Spanish speakers and 10 accounts of English speakers. After individual assignments are submitted, data will be combined into a single class data set and the analyses re-computed for the combined data set.
Assign Groups
After you have agreed on one research question, put your class in groups of 4 or 5 students. Ideally, each group would have at least one Spanish speaker and at least one native English speaker. Ask students to raise their hands if they have an Instagram account. Try to put at least one student with an account in each group. Groups can also include students learning from home.
Share lab documents with students to collect, enter and analyze data
Discuss the idea of variation within the accounts. Discuss the idea of variation across the groups. Did the different groups in your class find the exact same results?
Discuss variation in samples. What could have explained the different results? Did some groups have accounts that were all celebrities, all friends, all male?
Play a game
Scene in the Disaster Deduction Detectives Academy
Play Disaster Deduction Detectives to learn how to compute the median in datasets with odd or even numbers of data.
Statistics Lab Assignment 2: Social Media Analytics with Larger Sample
In the second lab exercise (instructions found here) , students combine the data from all groups, and compute descriptive statistics again. They compare their group’s results with the whole class result and discuss possible explanations.
Assessment
Three types of assessment are included. Group assessments are the two lab assignments submitted by students – since each student in the group has the same data he/ she will have the same result. Optionally, teachers may elect to have students submit their labs individually. Individual assessment is included within the DDD game where students must identify a statistical question, compute mean, median and quartiles. Whole class assessment occurs during the two discussion session.
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.
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.
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Technology Required
Summary
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Unit Summary
