Category Archives: mathematics

Multiple choice question asking at what age a boy became a buffalo hunter

Math Assessment and Lakota Culture

Standard

CCSS.MATH.CONTENT.8.EE.A.1
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27.

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

NOTE: Although the examples in this assignment primarily use scientific notation, it could be easily modified to include any area of mathematics above the fourth-grade level.

⏰TIME

120 minutes – including time to play game and create problems and activities.

📲TECHNOLOGY REQUIRED

A projector and computer in class or a computer, phone or tablet at home is required to watch the videos, see the Google slides and play the Making Camp Lakota game. It is not required but strongly recommended that students have access to Google apps or Office 365 to edit and store their notes.

📃LESSON SUMMARY

This is the second in a multi-lesson unit designed to assess student mathematics proficiency by playing games that teach about Indigenous cultures that have embedded math problems. It also requires students to create their own math activities and math problems.

📚LESSON

Introduce today’s lesson with slide presentation

This lesson assumes your class did the previous lesson, Math Assessment and Ojibwe culture, where they were introduced to the purposed of the unit and (recommended) created a Google slides or doc file where they are taking notes.

To introduce today’s lesson with Making Camp Lakota, use this PowerPoint on Math Assessment and Lakota culture, with examples of new, more difficult problems using decimals and scientific notation.

Play a Game

Multiple choice problem from game asking the minimum age for a buffalo hunter
Question after culture video on Dakota boyhood

The Making Camp Lakota game teaches Lakota culture and division with single-digit divisors. Even older students should enjoy the game play aspects and the videos on Lakota history and culture. Middle school students should breeze through the math problems. These are recorded in the database for teachers to review student progress.

Each game in the series in this unit is gradually more difficult math problems.

Students create their own, grade-level math problems

The slides presentation instructs students, for each math activity, to create an example that could be used at their grade level. Most of the examples in this presentation are using scientific notation, but students should be instructed that they can use any math problems beyond simple division. That could be fractions, decimals or even long-division. Teachers can modify the slides at the end of the presentation to require a specific topic, for example, adding fractions without a common denominator.

ASSESSMENT

Making Camp Lakota teacher reports are available for assessing student answers in Data and Reports. Students also write their own problems and answers that the teacher can use for assessing abilities at application and creation levels of Bloom’s taxonomy.

Related Lessons

For students who need an introduction to Google apps and Google doc, the lesson Google Apps Basics for Hamsters is recommended. (You don’t need an actual hamster.)

Individualization

This lesson is appropriate for students whose math is from fourth- through eighth-grade level. The mathematics in the game is at the fourth-grade level but student assignments can be as simple as long division or as complex as multi-step equations with negative exponents.

wigwam scene from Making Camp Premium

Math Assessment and Ojibwe Culture

Standard

CCSS.MATH.CONTENT.8.EE.A.1
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27.

NOTE: Although the examples in this assignment use exponents, it could be easily modified to include any area of mathematics above the fourth-grade level.

⏰TIME

120 minutes – including time to play game and create problems and activities.

📲TECHNOLOGY REQUIRED

A projector and computer in class or a computer, phone or tablet at home is required to watch the videos, see the Google slides and play the Making Camp Premium game. It is not required but strongly recommended that students have access to Google apps or Office 365 to edit and store their notes.

📃LESSON SUMMARY

This is the first in a multi-lesson unit designed to assess student mathematics proficiency by playing games that teach about Indigenous cultures that have embedded math problems. It also requires students to create their own math activities and math problems.

📚LESSON

Introduce lesson with slide presentation

The objectives, link to the first game and sample questions can all be found in this Slides presentation. The examples here use Exponent Rules and creating a math problem that can be solved with an equation using exponents. However, teachers are free to download the video and modify to fit their own class.

Watch a video

Even students who are Native American themselves sometimes need to be reminded when asked to apply mathematics to needs of Indigenous communities. This seven-minute video on Tribal Epidemiology Centers is a great example to get students thinking.

Play a Game

The Making Camp Premium game teaches Ojibwe culture, multiplication and division. Even older students should enjoy the game play aspects and the videos on Ojibwe history and culture. Middle school students should breeze through the math problems. These are recorded in the database for teachers to review student progress.

Students create their own, grade-level math problems

The slides presentation instructs students, for each math activity, to create an example that could be used at their grade level. The two examples in the presentation use exponents but students are told they can use any mathematics above multiplication and division. That could be fractions, decimals or even long-division. Teachers can modify the slides at the end of the presentation to require a specific topic, for example, adding fractions without a common denominator.

ASSESSMENT

Making Camp Premium teacher reports are available for assessing student answers in Data and Reports. Students also write their own problems and answers that the teacher can use for assessing abilities at application and creation levels of Bloom’s taxonomy.

Related Lessons

For students who need an introduction to Google apps and Google doc, the lesson Google Apps Basics for Hamsters is recommended. (You don’t need an actual hamster.)

house fly

Unit: Word Problems for fifth-graders

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.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

CCSS.MATH.CONTENT.5.NBT.A.3.A Read and write decimals to thousandths

CCSS.MATH.CONTENT.5.NBT.A.4 Use place value understanding to round decimals to any place.

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.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

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.

Time

Approximately 2.5 hours

Unit Summary

This cross-curricular unit includes a variety of strategies and examples for solving word problems at a fifth-grade level, including division of three-digit numbers, fractions and decimals.

Buffalo Hunts and Division

This lesson begins with a video on long division (optional) or a presentation on uses of division from the playground to the buffalo hunt. Students then watch a short video working long division problems. Finish with practicing long division in Making Camp Dakota. Short videos on Dakota buffalo hunt traditions and related math lessons are also linked.

Watch out for blood-sucking fishes!

This 40-minute lesson introduces new science vocabulary words, teaches about indigenous and invasive species and includes a couple of math problems showing how quickly invasive species multiply. It concludes with students playing the Making Camp Dakota: Past and Present game. Math word problems require finding half of 500 and 10 x 500.

Using Visual Models To Compare Fractions

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. (35-45 minutes)

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

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. (75 minutes)

Differentiation

For students who are struggling with word problems, assign these videos directly teaching strategies or watch together in class.

Codex

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.

Time

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 Story Begins games in English or Spanish.

Recommended Related Lesson

Counting ropes and rational numbers

Fishing and Statistics

Standards

CSS.MATH.CONTENT.6.SP.A.3
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
CCSS.MATH.CONTENT.6.SP.B.5
Summarize numerical data sets in relation to their context.

Technology

Students will need a Chromebook, Windows or Mac computer to play the game. Stories can be read on a computer or tablet or printed out.

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.

NOTE: You can find the entire 72-page Teachers Guide, One with the Watershed, including the stories, here. It has a wealth of information, games and activities. We highly recommend reading it.

Physical Education and Math – Play the Salmon Catcher Game (15 minutes)

This game is explained on page 30 of the Teacher’s Guide and on page 24 of the Salmon Stories booklet. A group of 4 or 5 students must catch a classmate (a salmon) by forming a net around it by holding hands. Play with lots of salmon and one ‘net’ and then with lots of ‘nets’ and few salmon. After the game, discuss how having too many fishers for the number of fish makes it difficult for each group to get enough salmon for a feast.

Assessment

Students responses to the questions in the Disaster Deduction Detectives game on statistical questions, creating and interpreting dot plots, median and mean with and without an outlier are all scored automatically and can be found in the teacher reports.

Differentiated Instruction

Optional: Creative Writing OR Art and Social Studies (30 minutes)

The Salmon Stories booklet has minimal illustrations. Allow students 30 minutes to create an illustration for one of the stories. For students who would prefer to write a story instead, allow them to select one of the topics suggested in the booklet, for example, on page 23 of the student booklet (page 29 in the Teacher’s Guide) students are asked to imagine a discussion between a salmon and the forest.

UNIT: Word Problems with Multiplication and Division

Standards

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.

Lessons

Lesson Multiplying to find perimeter of polygons

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. 

Multiplication word problems

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.

Travois, multiplication and 2-step problems

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.

Problem-solving with pigs: Start at the end

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.

Lesson. Problem-Solving Two ways

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

Learn 4 Math Facts at Once with Google Slides

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.

Unit: Multiplication Review

Standards

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.

Lesson 1: Making Camp – 10-minute multiplication review and Ojibwe history

Do this lesson first. Students sign in to the Making Camp game, play through the introduction, play a memory game and get a virtual dog.

Lesson 2 – 10 Minute Mini-Lesson: Rabbit Stew & Multiplication

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.

Lesson 3 – Trade for a 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

Lesson 4 – Multiplication Review and Red River Carts

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.

Lesson 5- Multiplication Terms

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.

Single-Digit Multiplication Unit

 Standards

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.

Lessons 1-6: Multiplying one-digit numbers: 0 to 5 

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:

  1. 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.
  2. Students write their own number sentences using the multiplication learned each lesson.
  3. Students complete the problems written by their classmates.
  4. Optionally, students write word problems.
  5. 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.

Lessons 7-10: Multiplying one-digit numbers from 6 to 9 

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.

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.

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.

Cross-curricular Middle School Statistics Unit

Note: When we surveyed teachers from the 2021-22 academic year, the most requested addition to the site was to combine the lessons into units. This cross-curricular statistics unit has 12 lessons that total 14 hours of class time, although some assignments could be completed as homework. With the length of this unit, it could be taught as a complete summer school course, addressing primarily mathematics standards but also incorporating English language arts, Social Studies (predominantly Indigenous and Latino history and culture) and science.

📖Standards

STATISTICS STANDARDS

CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates
variability in the data related to the question and accounts
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 Standard MS-LS2-1 Ecosystems: Interactions, Energy, and Dynamics: Analyze and interpret data to provide evidence for the effects of resource availability on organisms and populations of organisms in an ecosystem.

SOCIAL STUDIES STANDARDS

D2.His.13.3-5  Use information about a historical source, including the maker, date, place of origin, intended audience, and purpose to judge the extent to which the source is useful for studying a particular topic.

⏰Time Required

About 14 hours for all twelve lessons

📲Technology Required

Projector or smart board for in–class or access to computer or tablet for web meeting for remote learning. Presentations could be printed for students at home without computer access. Some lessons require use of Google sheets or similar spreadsheet software.

🧾Unit Summary

This seven-lesson unit teaches sixth- and seventh-grade standards on statistics integrated with games, Indigenous and Latino history and culture. The complete multi-media unit requires about 14 hours and includes multiple hands-on activities. 

trees in background, grass in foreground
Find your way back using clues from the plants around you

📃 Lesson 1: What is a Statistical Question? (120 Minutes)

CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates
variability in the data related to the question and accounts
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.

📃 Lesson 2: Mean, median and mode (35 Minutes)

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context

Students play a game teaching basic statistics and history. Next, they are given a presentation with problems students solve finding mean, median, mode, range and outliers.

This lesson has resources to teach in both Spanish and English, for an English-only lesson, click here.

📃Lesson 3: Understanding averages using skunks (30 minutes)

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context.
CCSS.ELA-LITERACY.RH.6-8.7 Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts.

In this lesson, students will learn how to find the mean and calculate the average and practice finding the average in a game environment. They will learn about skunks and skunk farming through primary source material. Then analyzing historical data, students will calculate the average.

📃Lesson 4: Reflections on the Ojibwe Migration (60 minutes)

CCSS.MATH.CONTENT.5.NF.B.4   Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
CCSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.
D2.His.13.3-5  Use information about a historical source, including the maker, date, place of origin, intended audience, and purpose to judge the extent to which the source is useful for studying a particular topic.

This multi-media lesson begins with a storyboard on the route and major events of the Ojibwe migration. Students then play the Forgotten Trail game, computing the average number of miles a character walked per day, followed by watching a video on map reading. As a group, students reflect on the challenges of the Ojibwe migration, compute the distance for just one segment and convert the distance from miles to kilometers.

📃 Lesson 5: Science, language arts and math with wildflowers (50 Minutes)

CCSS.ELA-LITERACY.RI.6.7 Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue.
CCSS.ELA-LITERACY.RI.6.4 Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.
Next Generation Science Standard MS-LS2-1 Ecosystems: Interactions, Energy, and Dynamics: Analyze and interpret data to provide evidence for the effects of resource availability on organisms and populations of organisms in an ecosystem.
CCSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.

This is a true STREAM lesson. Combining science, reading, art and mathematics. Students read a description of the pine forest ecosystem and life zones. They define any new words in their personal dictionary. Students then use information on plant life to identify life zones and locate these zones in terms of altitude. Students who complete the activity before the allotted class time play a game that teaches fractions and basic statistics.

📃 Lesson 6: Teaching Frequency Tables with Indigenous Communities’ Data (70 minutes)

CCSS.MATH.CONTENT.6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context

With a Google slides presentation, students are introduced to the concept of answering a question with data. A video is also provided for review. Using a data set of all tribal leaders in 2019, they are walked though an example of using Google Sheets to create frequency table and plots of data. Students then use the data set to create their own tables and plots. Students finish the lesson by playing a game where they learn about computing distributions in Mayan history.

📃 Lesson 7: Distributions and Mayan Trading (25 Minutes)

CCSS.MATH.CONTENT 7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.

The two videos here combine math and social studies, because, clearly, the Maya understood math. The concept of distributions is introduced in the context of trading, explaining why some objects are more valuable. Students play AzTech: The Story Begins, which reviews fractions and measures of central tendency. The lesson concludes with a question and another video on distributions.
(NOTE: Videos are available in Spanish and Englishfor English only lesson, click here. )

📃 Lesson 8: Food Deserts, Indigenous Seeds and Data Stories (90 Minutes)

CCSS.ELA-LITERACY.RI.6.4 Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.
CCSS.ELA-LITERACY.RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.
CCSS.MATH.CONTENT.6.SP.B.4 Display numerical data in plots
CCSS.MATH.CONTENT.6.SP.B.5 Summarize numerical data sets in relation to their context
CCSS.MATH.CONTENT.7.RP.A.2 Recognize and represent proportional relationships between quantities

This truly cross-curricular assignment begins by watching a video about seed rematriation, that is returning Indigenous seeds to their original lands. They read a short booklet on cooking and nutrition, then do a cooking activity at school or home. A presentation on food deserts includes definitions, data and actions students can take. Students add new words or phrases to their word journal and complete a math assignment using data from the presentation. Advanced students play a game to learn more math and Navajo culture.

📃Lesson 9: Reading and Comparing Bar Graphs (45 Minutes)

CCSS.MATH.CONTENT.6.SP.B.5 Statistics & Probability: Summarize numerical data sets in relation to their context.

CCSS.MATH.CONTENT.7.RP.A.2.B Ratios & Proportional Relationships: Identify the constant of proportionality (unit rate) in  tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

This lesson introduces students to reading and comparing bar graphs with proportional relationships. Students receive a slide or handout with four bar graphs and complete a set of cards with questions on the graphs. They can also complete the activity in Google slides . The lesson ends with an adventure game that includes discussion of interpreting bar graphs.

📃Lesson 10: Google Slides and Math (180 Minutes)

CCSS.MATH.CONTENT.6.SP.B.5.C Giving quantitative measures of center and variability, as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
CCSS.ELA-LITERACY.RH.6-8.7 Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts.

Students play three games that teach fractions and statistics. Students learn enhanced features of Google slides. They then create a Google slides presentation stating which is their favorite game and why.

📃Lesson 11: Probability and Fruits (45 Minutes)

CCSS.Math.Content.7.SP.C.5
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
CCSS.Math.Content.7.SP.C.6
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

The Google slides presentation begins with definitions of probability, impossibility and certainty. Students are then given an example of a basket with different types of fruits and the probability of each. Students each come to the front of the class and pull a piece of fruit from the basket, writing down the probability of their selecting the type they obtained. The class data is used to create a table and compare the obtained probabilities to actual distribution of fruit in the basket. The lesson closes with students creating their own probability question.

NOTE: This lesson plan requires a basket of fruit. You could use pictures of fruit printed out or drawn on paper instead but using actual fruit from your area might be more fun. If you’d rather, though, we do have a random fruit basket generator to use with this lesson.

📃 Lesson 12: Teaching Statistics in Classrooms with English Learners AND Native Speakers (90 minutes)

CCSS.MATH.CONTENT.6.SP.A.1 Recognize a statistical question as one that anticipates
variability in the data related to the question and accounts
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.