Crow in the Pitcher 8.F.B.4

 

crow picture

This is an 8th grade modeling lesson. In this lesson students will be learning about the linear relationship between two quantities and then analyzing the results on a graph.  How many marbles will it take for the water to rise from 80 liters to 100 liters? In this activity students will be placing marbles into cylinder that is filled with water to see how many marbles it needs for the water can rise.

FunctionsProject (1)

 

 

 

Circle Magic- CCSS.MATH.CONTENT.7.G.B.4

Image result for circles

Purpose– Students will be able to discover the meaning of pi, and how it is related to circles.

Materials-

  • 10 circular objects per table group (Cans work best, or glass jars, plates, Frisbees, cups, etc.)
  • White String
  • Rulers
  • Measurement Activity Worksheet

Directions-

  • Place students in groups of four.
  • Place the ten circular objects in the center of each table group.
  • Give each student a piece of white string (long enough to measure the circumference), and a ruler or meter stick.
  • Hand out a measurement sheet to each student.
  • Review vocabulary of circles, such as circumference, diameter, radius, and proportion.
  • Tell students they will be filling out the first two columns on the table only for now.
  • Demonstrate to students how to use the string to measure the circumference of the circle using the string, and then placing it across the ruler in order to get a measurement. Also demonstrate how they can measure the diameter.
  • Have students share objects, but tell them they each need to measure all ten.
  • Once students have completed their measurements, have the students perform the calculations of dividing the circumference by the diameter.
  • The students should see that the number is always 3.14 or close to it.
  • Work with the students to answer the questions that are below the table.

MeasurementData

 

CCSS.Math.Content.8.G.9 Volume of Cylinders

 

              

Popcorn Geometry

This lesson is great to use at the end of a unit to provide a real world activity that the students can relate the cylinder formulas in an engaging activity. The lesson provides an opportunity for students to test their own knowledge of locating relevant information and measurements, combine it with their formulas and make sense of it. Throughout the lesson the students participate in all of the 8 mathematical practices.

 

 

CCSS.Math.Content.8.G.9

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

 

Mathematical Concepts

Volume of cylinders, area of circle, compare and contrast

 

Math Procedures

Generate geometric formula for cylinders and circles

 

Mathematical practices used in the modeling

  1. Make sense of problems and persevere in solving them.

I implement my strategy and if necessary, try a different approach.

look for and make use of structure

  1. Reason abstractly and quantitatively.

FInd and use the necessary information

Visualize the information in different representations

  1. Construct viable arguments and critique the reasoning of others.

Make reasonable predictions

  1. Model with mathematics.

Solve problems in everyday life.

Apply what I know and show it in a mathematical problem

  1. Use appropriate tools strategically

I need to know the tools that are available to me: Calculator, Ruler, Paper for the model.

  1. Attend to precision.

I need to be precise with my measurements.

I need to be precise with my calculations and round to the same spot if needed.

  1. Look for and make use of structure.

Make predictions, formulas, relationships

  1. Look for and express regularity of repeated reasoning.

 

Aspect of Modeling

1 Make assumptions

  1. Realize relationships between two objects
  2. Analyze relationship mathematically
  3. Interpret the results into context of the problem
  4. Make improvements to the model

 

 

Central Focus-

Justify an argument using geometric equations

 

Related CCSS. Math

CCSS.MATH.CONTENT.8.G

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres

CCSS.MATH.CONTENT.8.G.9

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

 

Learning Targets

Students Will Be Able To:

Use known measurements to find the volume of different cylinders.

Compare volumes of objects.

Problem solve and find information that is not given.

Some possible central foci for this activity

 

Identify Mathematical Concepts

Volume of cylinders, area of circle, compare and contrast

 

Identify Math Procedures

Generate geometric formula for cylinders and circles

 

 

Why it is engaging:

The lesson meets five of the eight multiple intelligences.

Linguistic: Students are having to explain their processes and their answers to others. They do this in small groups and on the worksheet.

Logical-Mathematical: Students have to find what information they need to solve the problem. They are only given limited information, they have to use that to find the missing information.

Intrapersonal: Students take the information they used to solve the problem to figure out how to make a bigger cylinder that holds even more. They then reflect on the lesson and why their change increases the volume.

Interpersonal: Students work as small groups or partners to come up with the answer.

Spatial: Students create the cylinder that they are trying to find the volume of. They make a physical model of the problem at hand.

 

Created by Nichole Kealoha, Stephanie Lynes, Kayla Dubois, and Jared Brown

 

Popcorn Geometry Lesson

Popcorn Geometry Worksheet

Pump Up the Volume! Volume of Cylinders (CCSS.MATH.CONTENT.8.G.C.9)

ContainersCylinders

 

This is a great activity for any middle school class that enjoys going beyond math problems from a book and into the realm of kinesthetic learning. With this activity, students will gain a deeper conceptual understanding of the volume of a cylinder as they determine which cylinder has a larger volume when two different cylinders are formed using an 8.5” by 11” piece of paper. Students will make a prediction, then confirm or reject their prediction using their knowledge of the dimensions of paper and how it relates to finding the volume of a sphere.

Students will also learn how this activity has real world application through the opening exploration activity involving soup and a cylindrical container that ends up being too small. A discussion will revolve around what could have been done to prevent the soup from spilling over the end of the container. Students will then consider the possibility of change the dimensions of the container to increase the volume so that the soup will fit.

Created by: James McInroy, Jehnna Keshishian, Megan Ellis, and Michelle Dollinger

 

Explanation of Engagement

Mathematical Practices

Lesson Plan

Worksheet

How Tall is That? 6.RP.A.3

MATH VisualCan’t measure the height of that tree with your ruler? No problem! Let’s use ratio’s to find it’s height!

This lesson is a great modeling activity where students are able to apply ratios and proportions to real world situations. They will be using the concept illustrated above with objects they find around their school. The students will find their own height and shadow length, and use this ratio to find the heights of several tall objects. Some of these might be basketball hoops, portables, school buildings, soccer goals, railings, and even the height of their own teacher! Continue reading

CCSS.Math.Content.8.SP.A.1 Scattered Data

boys-playing-basketball3

Common Core State Standard for this lesson:

CCSS.Math.Content.8.SP.A.1-Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Instructions for activity:
• Read main question (Central Focus of the activity): How long does it take to pass a ball around in a circle while adding one more person to the circle each time around?
• Make a class prediction for how the data collected will appear.
• Number off students, assign placement of when to join the circle. One student will run stopwatch and record the times in table on worksheet.
• Start the activity with one person and time how long it take to pass the ball, repeat with two students, three student and so on.
• Record number of students and time in seconds
• Organize data in a table with number of students (n) being one variable and time (s) being the other.
• Students do Parts 2 and 3 in their small groups being prepared to discuss answers as a class.
• As a whole class disscuss answers.
Justification for modeling: See Mathematical Practice number 4.

.Tools: Ball, stopwatch, worksheet, paper, and pencil.

Vocabulary: Bivariate, variables, scatter plot, univariate, functions, and first differences.

Mathematical Practices for this lesson:

Practice 1: Make sense of problems and persevere in solving them.
Justification: Students can check that their answers make sense and are able to explain it.
Example: Students discuss Part 3 questions on worksheet in small group.

Practice 2: Reason abstractly and quantitatively.
Justification: Students can find and use the necessary information and are able to break apart a problem.
Example:In worksheet Part 3 questions are answered using the information collected/interpreted from Parts 1 and 2.

Practice 3: Construct viable arguments and critique the reasoning of others.
Justification: Students can use prior learning, make reasonable predictions, and use appropriate definitions and language.
Example: At the beginning of the activity when students are introducted to the activity.

Practice 4: Model with mathematics.
Justification: Students can apply what I know and show it in a mathematical problem, could draw graphs and tables, and reflect and revise on solutions and make changes as needed.
Example: The completing, collection, and using of data from Part 1 and 2 of the worksheet.

Practice 5: Use appropriate tools strategically.
Justification: Students can know the tools that are available and use them appropriately and use tools such as stopwatches and calculators.
Example: Data collection portion of Part 1 and answering of Part 3 question 5-7.

Practice 6: Attend to precision
Justification: Students can provide good explanations that are clear and precise, understand the vocabulary and their definitions, communicate, show their work and check their work.
Example: Completion in small groups of Part 3 of the worksheet and end of class discussion of Part 3 questions and Parts 1 and 2 data.

Practice 7: Look for and make use of structure.
Justification: Students will use patterns or structures to be able to see was to show the same objective or meaning, realize the relationship between the data collected, make predictions, use pictures to show numbers, draw conclusions, use vocabulary and formulas.
Example: Using intro, Part 1, and Part 3 of worksheet.

Practice 8: Look for and express regularity in repeated reasoning.
Justification: Students will explain to a partner how they got their answer.
Example: Part 3 of worksheet and class discussion.

This lesson/activity was a hit with the students, went well with my classroom environment and had minimal misconceptions.

Math 486 Lesson Plan

Scattered Data

Scattered Data Answer Key

Exit Ticket

Posted and Created by: Christine Godfrey, Andrea Hamada, and Megan Kriete.

 

Statistics and Probability 7th Grade CCSS.Math.Content.7.SP.5-8.

UntitledProbability and statistics all around us in the real world; therefore, these two concepts are essential for all math students to learn. This learning progression covers: Define and understand probability, Collecting data, then observing and predicting relative frequency, Probability modeling, Using uniform probability models to find probability, Observing frequencies to find non-uniform probability, Probability of compound events, Sample spaces for compound events, Design & use a simulation to generate frequencies for compound events, and teacher references filled with worksheets and activity aligned handouts for teaching each

of the concepts stated above. The learning progression is really tailored to students who learn better by working with their peers and enjoy hands-on activates. Attached along with this learning progression is a lesson plan that can be used to teach students the definition and basis of the term probability. This lesson includes a great game called Rock, Paper, Scissors, Chance Game where students work in pairs to solve if the game is rock, paper, scissors is truly fair? Haven’t you ever wondered? If you have, this lesson plan will show you how to use this activity to better address to students the definition of an event being equally likely and the essence of something being fair. This learning progression addresses the following common core cluster standards: CCSS.MATH CONTENT.7.SP.5-8.

Math 499E Learning Progression3

Learning Progression Lesson Plan1

8.EE.B / 8.F.A. / HSA-CED.A Time to Sell Some Cars

With this problem, students are able to see an example of a real-world situation and understand how to answer a question about two different scenarios and see how they relate to one another.  It is important that students can see and understand that anything in the world can be related or traced back to math.  This is just one example.

Students in this lesson will have to understand proportional relationships between two linear equations then be able to create those equations from what they already know about what the equation for a line even looks like.  Students will be asked to graph their solutions in a table in order to see the comparisons of the two different car salesman and understand that even though an initial amount may be more than another, over a period of time the rate of change is more important to see who will make more at the end of the year.

Illustrative Mathematics Problem

4.MD – Capture the Area

diceMath Concept: Area

Target Grade Level: 4th Grade

CCSS.Math

4.MD.A.2: Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

  • Students will be applying the area formula for rectangles to determine the total area of each rectangle that they draw. Students will be applying the formula repeatedly with different combinations of dimensions.

CCSS Mathematical Practices

MP2: Reason abstractly and quantitatively.

  • Students can work with the numbers generated by rolling the dice to find an answer, but can also understand that the numbers represent something concrete. Students must realize that the numbers being rolled represent the length and width of their rectangles rather than just numbers. They must also be able to attach the given measurement to the number. For example, a roll of 5 and 6 gives a rectangle with the dimensions of 5m x 6m and an area of 30m2.

MP6: Attend to precision.

  • Students must be able to determine that if each square on the graph paper represents one square meter, then each side is one meter. Students must then be able to apply this when translating the numbers on the dice to the dimensions of the rectangle and when calculating the area of the rectangle. Students can determine if their answer makes sense by looking that the actual rectangle that has been drawn and by paying close attention to the units. For example, a roll of 3 and 4 would have to translate to a 3m x 4m rectangle with an area of 12m2. If students end up with 3m2 x 4m2 then the area would end up being 12m4. Students would need to realize that these units do not make sense when compared with their drawing that shows 12 square meters.

Learning Targets

Students will be able to explain the concept of square units.

Students will be able to apply the area formula for a rectangle.

Academic Language

  • Dimensions (length, width)
  • Area
  • Square unit

Activity Purpose

This activity allows students to see how and why the area formula for a rectangle works. While playing, students can see that multiplying the dimensions will give them the total number of squares that are inside of the rectangle. Students will also be able to see where the idea of square units comes from. Students will be given the opportunity to not only solidify this understanding, but they will be given ample opportunity to practice applying the area formula. On every turn students will be drawing a rectangle and finding the area. Students will also continuously roll different numbers giving them practice with different dimensions, and showing that the area formula works consistently.

Activity: Capture the Area

Objective: To capture as much the “land” as possible

Time: 20-25 minutes

Players: 2-4  players

Materials

  • A pair of dice (1 pair for each group)
  • Centimeter graph paper
  • Colored pencils (crayons and markers will also work)
  • Copy of directions/discussion questions for each group (attached) Capture the Area- Directions

Technology

For this activity there is no need to use technology. A calculator could be used for students who need that adaptation.  However, a primary goal of this activity is to practice mental math and quick recall of multiplication math facts.

Problem

Neighboring farmers trying to acquire unclaimed farmland. The land can only be acquired in rectangular pieces. Instead of fighting for the land, the farmers have decided to take turns claiming pieces of land as determined by rolling dice. Each square plot of land is one square meter. Each farmer wants to get as much land as possible.

Directions/How to Play

  1. Each player starts in a different corner and uses a different color colored pencil.
  2. Players will roll a die to determine who will go first. (Highest roll goes first and game play continues clockwise).
  3. Players roll the dice to find the dimensions of a rectangle that they will draw using their assigned color. Players assign one number to the width and the other number to the length of the rectangle. In addition to drawing the rectangle, players must write inside the rectangle the dimensions and the total area. Players start with the first rectangle in their own corner.
  4. Each rectangle that follows must be drawn so that it is touching one of the sides of that player’s previous rectangles.
  5. Game play ends when all players have met in the center or when no more rectangles can be drawn or at a specified time. To make games quicker use centimeter graph paper. 
  6. Players then find the total amount of area they have acquired.
  7. The player with the greatest total area is the winner.

Example

Capture the Area Student Examples0016 Discussion Questions

These questions are given to students in their groups or pairs to discuss. Students should be encouraged to use academic language (i.e. area, dimensions, square units) when answering the questions. Once students have discussed the questions in their groups, the teacher should initiate a whole class discussion.

  1. As a farmer, why would you want all of your land together?
  2. Why would you want rectangular plots of land?
  3. Who won?
  4. Why did they win?
  5. What kind of dimensions do you want to role? Larger numbers or smaller numbers? Why?
  6. What is the largest area that you can get from rolling the dice? What is the smallest area you can get?
  7. How does the area formula work? Why do we multiple the length and the width?

Assessment

The answers to the discussion questions will serve as a formative assessment. The teacher should also be circulating the room and using observation to formatively assess students’ knowledge of multiplication facts and their ability to apply the area formula.  

Adaptions

There are a number of possible adaptions to make this lesson appropriate for younger or older students.

For younger students:

  •  Add the two numbers rolled to determine the total number of squares that can be claimed.
  • Give students multiple dice so they can practice adding three or more numbers at a time.

For older students (or for students who need an extra challenge):

·         Assign each student a particular crop. Each crop is worth a certain amount of money. In addition to determining the total area, students can also determine the total amount of money they could make.

  • Convert the total area from square meters to square centimeters and/or square kilometers.
  •  Determine the amount of fencing required to enclose all of the acquired land within one fence.
  • Use triangles rather than rectangles. The numbers rolled would indicate the base and the height of a right triangle. Students would then have to determine the area of the triangles.

Additional Teacher Suggestions

We designed the modeling activity “Capture the Area” to allow students the opportunity to apply the area formula in real world problems to meet the CCSS 4.MD.A.2. We also felt that this could be a great activity to connect to students’ prior knowledge about area measurement.  This builds on their initial learning of the third grade standard CCSS 3.MD.C.5.A.

While teaching this activity we realized the importance of relating the activity to student interests.  To do this we discussed with students what they would like to farm on their land such as crops or animals.  This helped to increase their buy in for the activity.

We also noticed that some students struggled with the third grade square unit concept.  This means that this concept may need to be retaught.

Additionally, we learned that using larger graph paper makes it easier for people to see what they are doing and to complete the task. Smaller graph paper made the activity more tedious and made it difficult for students to follow their own work. 

Modeling Activity designed by Julie Murphy and Emily Phillips.

4.MD-Campus Tours!

Campus Tours by Hollie Lamb and Ed Mejia

Target Grade Level:  4th Grade
Map Activity

4.MD.A.1 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

4.MD.A.2 Use the four operations to solve word problems involving distances and intervals of time.

Standards for Mathematical Practices to be Emphasized:

1.A Make sense of problems and persevere in solving them.

  • This practice supports the identified standards by framing clear and explicit mathematical challenges.  The modeling activity prompts are scaffold in such a way that aids students in clarifying the mathematical processes that are required.

1.D Model with mathematics.

  • This activity allows students to transfer skills between general mathematical representations and real-world scenarios.  In this modeling activity, students will be asked to convert distances from a larger unit to a smaller unit whilst using a distance scale key.

1.E Use appropriate tools strategically.

  • In this modeling activity, student swill be referring to the distance scale included in the campus map.  Using index cards to accurately measure scale distances will provide students the opportunity to use tools to attend to precision and accuracy.

1.F Attend to precision.

  • Students will have to be able to use the scale accurately when finding the distances between buildings.  There will be emphasis during the modeling activity to attend to the accuracy of the required operations to answer the prompts.

Materials and Equipment:

  • index cards
  • maps
  • Campus Tours worksheet
  • calculator
  • pencils
  • highlighters (recommended for making paths on map)

Modeling Activity

Purpose:  Students have previously learned grade 3 standards of solving problems involving measurement and estimation of time, volume, and mass.  Students are now ready to extend these skills to develop the abilities to solve problems pertaining to the conversion of larger units to smaller units, and using operations to solve problems dealing with distances and time.

see attachments for worksheet and campus map CWU Campus Map Campus Tours