Thanks for a Great Year!

As the end of the school year nears, I just wanted to thank everyone for all of your hard work and effort you've made to learn your math lessons this year. I have enjoyed working with each and every one of you, and you've enriched my life by sharing your smiles, your funny senses of humor and your great stories with me. The theme for the next 12 weeks will be "Enjoying Summer". I look forward to seeing you in the fall.

Tonight's Homework: None!! Have a great summer!

Basketball for Astronauts?

Students used their problem solving skills to create a scale drawing of a basketball court that would be suitable for the toy astronaut they were given. All math used to convert real dimensions of a basketball court must be shown, and the drawing must be neatly drawn and labeled.

Tonight's Homework: Finish working on the scale model of your basketball court for the mini astronaut.

Area of Triangles and Trapezoids

Using pictures of geoboards, students drew a series of different shapes and sizes of triangles and trapezoids. They calculated the area of each figure drawn, and looked for a pattern that could be stated in an equation so one could determine the area of any triangle or trapezoid, if certain dimensions were known.

Tonight's Homework: Finish the green worksheets you started in class today. If you attended the WEB training today, be sure to pick these up on Thursday, and get them done as soon as possible. You are behind! (Thanks to Katie and Danette, who did check in with me after the training.)

Mixed Measurements

Weekly grade slips were distributed today, even though today is Tuesday. The theme for the week is solar energy. Students were asked to carefully measure 20 different objects, using both inches and centimeters. These measurements were recorded in a data table. The information will be used later in the week to help us better understand the notion of slope and where it shows up on the graph and the data table.

Tonight's Homework: Graph your measurement data as precisely and accurately as you can. If you are missing assignments, please plan to get those done and turned in as soon as you can. All late and missing work is due by Wednesday, June 5th. Don't delay, do it today!!!

Solving Problems Through Pattern Finding

After putting a few more pieces of the penny together, we worked on a variety of problems that dealt with discovering patterns today. Students used calculators to solve problems, learned how to use an abacus to represent different types of numbers, and then looked for patterns in groups of numbers. All in all, we worked hard and were successful!

Tonight's Homework: Nothing new. If you have missing assignments, it might be a great time to work on them over the long weekend and bring them in on Tuesday. Enjoy the holiday!

Rectangular Patterns

After putting most of the pieces of our enlarged penny together, we looked at a variety of rectangles to see if there was a pattern between the length and the width of the rectangle. Students sorted the rectangles into piles of similar type, and then recorded length and width data in a table.

Tonight's Homework: Make a line graph of your rectangle data, using different colors for each of your groups of rectangles. Is your penny piece turned in? If not, please finish it.

District Track Meet Wipes Out Our Class

Students who attended class today were given a work day to complete their projects. Some worked on the penny enlargement grid, while others worked on the Transform Your Name or Word puzzles. Most students were able to complete at least one thing, which reduced the amount of homework they had.

Tonight's Homework: Be ready to submit your part of the enlarged penny to me on Thursday.

Enlarging A Penny Takes A Group Effort

Students chose which part of a penny's "tail" they wanted to enlarge, and then picked up supplies (plastic grid, grid paper, magnifying lens, tape) to help them complete the task. Most of the class period was spent working on the enlargement. Students were encouraged to be precise, since their piece would be aligned with several others to create a large version of a penny.

Tonight's Homework: Work on the enlargement of your portion of the penny, and be ready to turn it in on Thursday.

Sub District Track Meet = Work Day in Math

Students who attended class today spent the day working on their "Transform Your Name" project. Some finished solving the puzzle page that was created by another student in the class, while others worked on rotating and dilating pieces for the new assignment.

Tonight's Homework: Continue working on the next parts of the "Transform Your Name" project.

Magic Squares and Algebraic Thinking

Students used their problem solving skills to solve magic square problems and algebraic sentences using fractions. Some students used class time to work on the next step of the "Transform Your Name" project.

Tonight's Homework: Finish the worksheet on fractions and magic squares. If you wish, you can start on the next step of your project by creating a new word that you will break into parts that will either be enlarged, reduced, or rotated.

Dalai Lama Field Trip Cuts Class Size in Half

Because half of our class was gone on a field trip today, we turned our class period into a work session. Students worked on the dilation and rotation worksheets or late assignments. Some students even started on part of next week's homework.

Tonight's Homework: Do something nice for your mother!

Work Day for Transforming Your Name Project

Today's class period was turned into a work day for students to work on one of two assignments: a. Transform Your Name project--students used class time to get clarification, work on, or finish the assignment that was made yesterday. b. Probability and Proportional Thinking worksheet--this was handed out in class today, and will be due on Thursday. Thank you to all for your hard work and respect during class time, as our guests were able to complete a large chunk of their work during our class time today. You rock!

Tonight's Homework: Complete both sides of the worksheet you started in class today. Work on your "Transform Your Name" project. Remember, it will be due by Friday, unless you are planning to be gone on Friday.

Transform Your Name!

To allow students a chance to creatively practice skills related to translating and reflecting objects, we started working on a project called "Transform Your Name". We reviewed the criteria and the scoring rubric for this project. Students had about 30 minutes of class time to working on the project.

Tonight's Homework: Continue working on the project you started in class today. It will be due on Friday, May 10th. If you are planning to miss class because of the field trip to see the Dalai Lama on Friday, plan on having it ready to turn in on Thursday, May 9th.

An Introduction to Transformations

Students were introduced to two of the major transformations today. The first one we looked at was related to reflections. Students found it relatively easy to reflect things across horizontal and vertical lines. Reflecting across a diagonal line proved to be a bit more challenging to some students, but by the end of the period, most students felt proficient in getting objects reflected across lines, regardless of its orientation. The second transformation we looked at was the translation. Once students understood that the top number refers to how the object is moved on the x-axis (side to side), and the bottom number tells how the object is moved along the y-axis (up or down), they were able to perform the slides with relative ease. To review, translations "slide" things and reflections "flip" things over a line.

Tonight's Homework: Complete the two worksheets you received in class today. One is on reflecting objects and the other is on translating objects. Both will create words if done correctly.

Notebook Clean Out and Shortened Classes = Not Much to Do!

Students corrected yesterday's homework and then turned it in. Because classes were shortened, we spent the rest of the period removing work from our notebooks. We kept anything that related to shrinking, enlarging and the shadow work we've been doing. Anything related to surface area and volume was removed from notebooks and either taken home or recycled. Papers that were complete but not graded were turned in.

Tonight's Homework: None. Enjoy the weekend, but don't get sunburned!

More on Ratios and Proportions

We converted our projected height data, recorded in cm, to feet by determining that 30.5 cm is equal to 1 foot. This led us to a conversation about how to set up ratios to help solve problems. We looked at a variety of problems that used rates and created ratios to help solve the problems.

Tonight's Homework: Complete both sides of the white worksheet that we started in class today. Be sure to show your work.

It's May Day!

Today, we took advantage of the gorgeous weather to go outside again and measure the length of shadows of really tall things, like trees, utility poles and flag poles. Using information from yesterday, we talked about ways to determine the actual height of the objects without actually measuring them. We discovered that there is a way to do this, using ratios and proportions. Students began these computations in class, and then were asked to complete them at home. Be sure to graph your data.

Tonight's Homework: Complete the chart you started in class today, and find the projected height of each of the objects using ratios like we did in class today. All of your work related to this activity will be turned in on Thursday.

Projection Enlargements of Objects

Today we finished the Shrink Art activity, and then turned our attention to enlargements. We used the document camera and the projector to determine the enlarged size of things. We discovered that the distance between the projector and the surface your project your objects on does make a difference.

Tonight's Homework: Determine the enlargement ratio of the data you collected in class today. Graph the data and write equations for the three lines.

Test over Surface Area and Volume Taken in Class Today

Because we have finished the unit on surface area and volume, students were given time in class to show their proficiency by taking the unit test.

Tonight's Homework: None. Enjoy the weekend!

Shrink Art, One More Time!

After reviewing answers to last night's homework, we went over specifics about Friday's test. Specifically, students will have access to formulas, and will be able to use calculators. Of course, work will need to be shown! (This is test over finding the surface area and volume, NOT how to multiply and divide, so calculator use is certainly permissible.)

Tonight's Homework: Complete the pink worksheet if you were unsure of how to do the ratio part of it. Be ready to transfer your picture to the plastic if you haven't already done so. Shrinking will take place tomorrow in class.

More on Surface Area and Volume of Spheres, Cones and Pyramids

Students reviewed how to find the surface area and volume of spheres, cones and pyramids by working in groups to answer a series of questions related to real life situations.

Tonight's Homework: Complete the problems on the pink worksheets that you did not finish in class today.

Happy Earth Day!

Students received stickers and bookmarks to commemorate earth day. We also enjoyed treats to celebrate our terrific results on the state math test. We learned how to figure out the surface area and volume of spheres, and tried to make sense of the formulas using pictures.

Tonight's Homework: Home Book, pages 74-75 ( 4 - 15 ).

Round One of OAKS Math Testing is Complete

Students completed the last portion of the state math test today in class. The scores were phenomenal, and a tribute to the hard work, dedication, and determination of all who took the test. I couldn't be prouder of you!

Tonight's Homework: Complete the brown integer computation worksheet if you didn't do so in class today. It's due on Monday, 4/22.

Day Two of OAKS Math Testing is History!

Students completed the next portion of the state math test today in class. While most students took their time to complete the next 15 problems on the test, some were able to finish the test today. The majority of the class will complete the test tomorrow, and I'm hoping most, if not all, students will be pleased with their results. Cross your fingers!

Tonight's Homework: Be sure to get enough rest tonight, and come back refreshed and ready to finish taking the state test!

Day One of OAKS Testing is Complete

Students began the state math test in class today, and most were able to complete the first 15 problems with plenty of time to go back and double check their work.

Tonight's Homework: Be sure to get enough rest tonight, and come back refreshed and ready to continue taking the state test on Thursday!

OAKS Math Testing Begins this Week

Students took a practice test on the computers in class today to ensure that they could properly use all of the tools available to them on the state test when they take it later in the week. I answered a variety of questions as they surfaced.

Tonight's Homework: Be sure to get enough sleep tonight so you are rested and ready to your best on tomorrow's OAKS math test. You are well-prepared and capable of doing very well, especially if you take your time and do your best. Good Luck!! I'm rooting for each and every one of you!

Surface Area of Boxes

Students chose two boxes to create nets and then found the surface area of the boxes. They had ample time to complete the nets, and most had time to find the surface area, as well.

Tonight's Homework: Complete the state test review problems on the worksheets you received in class today. If you did not finish finding the surface area of the two nets you created in class today, please finish this as well.

Spring Break is Officially Here!

Because nearly half of the class was gone today, those present transferred their shrink art pictures onto plastic. They will complete the test we were going to take at home and mail it to me over the break. Most students turned in their Stretching and Shrinking books today.

Tonight's Homework: None, if you have all of your work turned in from the last two weeks. Enjoy your break from school. See you on April 2nd!

Shrinking Art in Math? Yep!

Students took the first part of the unit test over similarity in class today, even though our class time was shortened by 10 minutes because of locker clean out.

Tonight's Homework: Draw your picture for your shrink art project. Fill out the original picture measurements on the accompanying worksheet.

Reviewing for the Stretching and Shrinking Test

As we wind down for the break, students spent the period working with each other to ensure they are ready for the upcoming unit test. The test will be given over two days, as our class on Thursday will be shortened by locker clean out activities.

Tonight's Homework: Complete the 4 worksheets you started in class today. This sounds like a lot, but really, it's not, if you actually used your time in class efficiently.

Similar Figures, Revisited

Today's lesson was designed to help students develop more formal ideas about the meaning of similarity. The idea of scale factor was introduced, and we used the scale factor to predict the lengths, perimeters and areas of figures that are enlarged or reduced. Unfortunately, many students missed today's lesson, either because of absence or lack of attention. That's a shame :(

Tonight's Homework: ACE 2 ( 5 - 13 )

Pi Day, 2013

In honor of pi, students did math activities that emphasized the uniqueness of 3.14 (both the number and the date). First, students measured the radius and diameter of cookies and determined the circumference. Students calculated the area of the cookie before eating it. In the second activity, students used wedge-shaped pieces of a pizza to create a parallelogram. This activity helped students see the relationship between the area of a circle and its formula.

Tonight's Homework: Complete the Pi Day worksheet (both sides). ACE 2 (1 and 2).

Drawing a Wump?

Today, we used the notion of similarity to create a series of drawings on the coordinate plane. The figures we drew were called "wumps", and we looked to see if they were similar to each other. In essence, this activity helped drive home the point that in similar figures, the angle measures are preserved, and the side lengths are some constant factor (bigger or smaller) multiplied by the original length.

Tonight's Homework: Finish problem 2.1 (the one you started in class today).

Rubber Bands Help to Enlarge Pictures

Students used a rubber band chain to help them enlarge a series of figures. At first, students had some difficulty with the procedure, but with a little practice, most were able to create fairly accurate enlargements of the original pictures.

Tonight's Homework: ACE 1 (3, 4, 13, 15 - 18) in the Stretching and Shrinking book.

What Are Similar Figures?

Students received feedback about last Thursday's test and their final grades for winter trimester. Afterwards, they received copies of the "Stretching and Shrinking" book. We talked about what it means to be similar, and then learned about the symbol ~, which means "is similar to". For example, ∆ABC ~ ∆XYZ is read "Triangle ABC is similar to triangle XYZ".

Tonight's Homework: Students who get today's grade slip signed and returned tomorrow will earn double extra credit points. Complete the pink integer worksheet, and do ACE 1 (1, 2, 6 - 12).

Winter Trimester Ends Today

Students removed most math papers from their notebooks today, in preparation for the new trimester, which begins on Monday. After receiving feedback on how they did on yesterday's test, students finished the unit test on Shapes and Designs topics. Those present today turned in their books.

Tonight's Homework: Complete both sides of the worksheet you received in class today.

Part One of Angles Test Taken in Class Today

Students turned in their homework, and then took the first part of the unit test over polygons and angles. This part found students NOT using protractors. Tomorrow, the protractor part of the test will be given.

Tonight's Homework: Be ready to take the rest of the Shapes and Designs test tomorrow. We will be turning in our books, so be sure to bring yours to class.

Class Was How Long?

Class was only 21 minutes today, so we took time to go over homework and make sure everyone understood the problems that were assigned.

Tonight's Homework: Write a thank you note to one of Monroe's fabulous classified employees and bring it to school on Monday so we can celebrate Classified Employees' Appreciation Week in style.

Interior Angle Sums of Polygons Are Predictable

Students got new seats today, as a result of some students choosing to socialize too much during work time. We watched a video about the distributive property, worked on the gray packet, and talked about the sum of interior angles of different types of polygons.

Tonight's Homework: Complete Problem 3.1 in the Shapes and Designs book, and complete the last page of the gray packet. Both are due tomorrow.

Parallel Lines and Transversals

Today's lesson covered Problem 2.5, Parallel Lines and Transversals. Some specific vocabulary is associated with this lesson, so definitions were provided for parallel, transversals, and alternate interior angles. Students worked together as a class to complete problem 2.5, and then got started on their homework.

Tonight's Homework: Complete both sides of the white worksheet you received in class. In addition, complete ACE 2 (21 - 26).

Finishing the Poster Project.

We talked about the relationship between straight angles and the lines that cross them, creating two smaller angles. This is introductory information that will be used next week when we learn about complementary and supplementary angles. Students finished the last part of their poster project.

Tonight's Homework: None (unless you've been sick, and then you should work on missed work).

Happy Valentine's Day!

We continued our study of angles today by talking about circular angles imposed on a coordinate grid. We studied Problem 2.2 today, and by the end of the class period, most everyone was able to use the circular coordinate system with a high degree of accuracy.

Tonight's Homework: ACE 2 (4 - 9).

Playing with Angle Measurements

To begin our study of angles, students used the handheld computers to play a game, trying to estimate the measure of different angles as accurately as possible. We concentrated on interior angles today. This allowed us to talk about the different benchmark angles (0˚, 45˚,90˚, 135˚, and 180˚), as well as acute, obtuse and right angles.

Tonight's Homework: ACE 2 (1 - 3, 29). This assignment is from the red Shapes and Designs book.

Drawers, Stacks and Loose Money

As we continue to practice combining like terms, we used banks as the context for today's lesson. Banks have drawers of money, stacks of banded money, and loose bills. We can combine each of the different types of money amounts, but cannot easily combine the three different types into one grand total unless we know how much money is in each drawer or stack. Students practiced adding and subtracting like terms.

Tonight's Homework: Finish the purple packet problems related to the banks of money. Be prepared to turn the packet in on Wednesday.

Bye, Bye to "Moving Straight Ahead"

Students turned in their "Moving Straight Ahead" books today, and replaced them with red "Shapes and Designs" books. Students practiced combining like terms by using the long and short sides of a paper clip to measure various shapes.

Tonight's Homework: Work on the first half of the purple packet. Finish the problem about the flooring of Tara and Brad's house.

Quiz over Linear Equations

Students completed a series of questions today in class to show me how well they have understood the information they have learned over the last two weeks about linear equations.

Tonight's Homework: Be sure to complete your missing work, especially if you have been absent. For those of you who have been here all week, there is no new homework.

Determining Slope and Y-intercepts

Using equations, we determined that the slope of the line is the determined by the number in front of the "x" term. This number tells us how much you will need to go up and over in order to get to another point on the same line. The y-intercept of the line is the number that is added to or subtracted from the "x" term. It is possible for this number to be zero, and in this case, the line passes through the origin.

Tonight's Homework: ACE 4 (2 - 12). Look over Investigations 2 and 3 to prepare for tomorrow's quiz.

Steps in Real Life Look Like Steps on a Graph!

Using data obtained from last night's measurement of steps, students constructed graphs to show the rise and run of the different types of stairs. We graphed multiple steps using the rise and run information on one grid, and determined that the rise over the run is the slope of the line. This information will be used in future lessons about slope.

Tonight's Homework: ACE 4 (1, 36) and finish the graph you started in class today.

Steps and Risers

To introduce the notion of slope, we looked at steps. We measured the vertical distance (rise) and the horizontal distance (step), and reported this as a ratio. We also started a poster project that will help us review key points related to linear equations, tables, graphs and how they relate to specific situations.

Tonight's Homework: Find at least two different types of stairs (steps) to measure. Measure the riser and and step parts of each. Bring this information to school tomorrow. Start studying for the test you'll be taking on Friday.

Order of Operations and Finding Patterns

We watched a video about order of operations to ensure we remember the steps. Next, we did a couple of activities to help us see the relationship between tables, graphs, pictures and formulas. We agreed that we will finish this unit on Friday, and in doing so, have less homework to complete over the upcoming weekend.

Tonight's Homework: Home Book, page 117 (all). We will have a test over the Moving Straight Ahead material on Friday, February 7th. Start preparing for it now!

Rates of Change and Orders of Operations

Students worked in pairs or by themselves to create a poster to summarize how tables, graphs and equations can be used to find solutions to situations that require variables on both sides of an equal sign. These posters were to be turned in at the end of the period.

Tonight's Homework: Complete pages 34, 35 and 37 of the ivory packet of papers. Be sure to follow the directions printed on each page.

Using Equations to Solve Problems

We looked at equations that can be used to solve real-life problems, such as the formula that allows us to convert temperatures from one scale to another (˚C to ˚F or vice versa). Knowing where to stick the numbers into the equation are key to solving the problems correctly.

Tonight's Homework: ACE 3 (23, 43 - 45)

Finding the Point of Intersection

As we continue our study of linear functions, we spent time today looking at situations where two lines intersect. One common example uses a company's costs vs. income data. Another example looked at speeds of different people walking and when they might be at the same spot. We looked at how using equations could give us the same result as a graph and a table, and might be a quicker way to solve the problem.

Tonight's Homework: Complete the first page of the ivory colored packet called "Does Order Matter?" Then do ACE 3 (25, 27, 38, and 42). For each of these problems, make a graph and a set of equations to help you answer the questions.

Using Algebraic Expressions to Solve Number Tricks

Using algebraic expressions to represent situations can be both educational and useful. Today we looked at another way to use them--for fun! We explored several magic number "tricks" and discovered how they work by using both pictures and symbols to represent the different steps of the "tricks". Students were first amazed, and then satisfied to understand the algebra behind the tricks.

Tonight's Homework: Complete the rest of the pink packet on number tricks. Do ACE 3 (24 and 26).

More on Solving Equations and Looking for Patterns

Today, we focussed on developing strategies for solving linear equations. Once again, order of operations played a big part in ensuring student success in the process. We also worked on recognizing subtle shifts in equations and how these shifts affect the solution to a given problem.

Tonight's Homework: ACE 3 (22, 32) and finish problem 3.4 on page 54 of your book.

Solving One and Two Step Equations

In order to solve equations efficiently, students reviewed the rules for using order of operations. Next, we solved a variety of equations involving either one or two steps to solve. Students realized that to solve equations, you really need to do the opposite of what is asked for in the original equation. Students were introduced to the formal check step today.

Tonight's Homework: ACE 3 (15-19)

Bags and Coins = Two Step Equations!

After going through a number of examples using pictures of bags and coins, students were urged to use expressions to represent the bags and coins. These algebraic expressions were then put into algebraic equations, and we used statements of equality to start solving for the unknown variable.

Tonight's Homework: ACE 3 (6 - 14, 38 - 41)

Looking at Equations

We began our study of solving equations today by looking at pictures and trying to figure out what might be placed in the bags to make each statement true. Then we used symbols to represent the pictures. These introductory steps should help students to transition from the concrete examples to the more abstract nature of algebraic expressions and equations.

Tonight's Homework: ACE 3 ( 2 - 5 )

Checking for Understanding on Rates of Change

During a shortened class period, students turned in homework and then took a quiz over using graphs, tables and equations to represent rates of change for particular situations. Most students had enough time to complete the quiz. Those who didn't finish should plan to come in on Tuesday during lunch or after school to finish.

Tonight's Homework: None. Enjoy the long weekend!

Seriously? The Page Was Ripped From the Teacher's Manual?

We spent the first half of the period reviewing how to use tables, graphs and equations to help with solving problems related to given situations. This review should help students prepare for Friday's quiz. We then looked at ways to solve problems where two different situations end up having one point that works for both of them. On a graph, this is the point where both lines intersect.

Tonight's Homework: Finish all parts of problem 3.1 from the Moving Straight Ahead book.

Odds and Ends

We spent the day completing a variety of tasks. Students started on the Tile problem. Some students made up work they were missing today in class.

Tonight's Homework: Complete the Tile Problem. Do all problems on pages 113 and 114 of the Home Book.

Clear Solo Cups?

Students were served lemonade today, but there was a catch . . . they had to measure the height of the liquid in their glasses as they took drinks, and record the information in a data table. This information will be transformed into a graph and an equation as a part of tonight's homework. Due to changes in my meeting schedule, I have moved the quiz over this material to Friday, January 18th.

Tonight's Homework: Finish the table, graph and equation for the lemonade drinking activity we did in class today. Also, do both problems on page 45 of the Moving Straight Ahead book. Finally, don't forget, there's a quiz over this material on Friday, so start preparing now.

Understanding the Parts of an Equation

An equation can help us understand where points will end up on a grid, and can help us interpret a line. We took some time to identify "up front costs" and the cost per unit, and where these show up in different types of equations. Students will take a quiz over this material on Wednesday.

Tonight's Homework: ACE 2 (15, 16, 29, 33, 34, 38)

Pulling Things Together

Today, we looked at how the equations, graphs and tables can help us triple check our work to ensure we have the right answer. We even did a little algebra to show that it, too, can lead us to the correct answer.

Tonight's Homework: ACE 2 ( 6 - 10 )

Comparing Costs Using Slope and the Y-Intercept

After discovering a page was ripped out of the teacher's manual yesterday, we eventually got back on track and talked about how our equations related to the graphs we could make of them. We identified that the y-intercept would be the value we add or subtract in the equation, and that the slope of the line would be the coefficient of the variable in the equation. We'll continue to explore this relationship in the coming days.

Tonight's Homework: Complete all parts of problem 2.3

Using Tables, Graphs and Equations

Today, a guest teacher taught the lesson, as I was at a district meeting. Students looked at tables, graphs and equations that describe a particular situation to help them answer questions related to the situation. Many of today's problems involved lines that intersected, and what that intersection meant in the context of the situation.

Tonight's Homework: Finish problem 2.2 if you did not do so in class today. Then do ACE 2 (1 - 5)

Happy New Year!!!

Welcome, 2013! Students had a chance to redo a portion of the field trip problem today in class. This allowed everyone to warm up their math brains, while improving their scores on that particular assignment. We revisited walking rates by looking at problem 2.1 and ensuring that everyone understood how using a graph, data table and equation would help to solve the problem.

Tonight's Homework: Get your grade slip signed and bring it back to school tomorrow. Do page 25, problem 2.1, parts A and B. If you didn't turn in the pink worksheet and/or the field trip problem today, be ready to do so tomorrow.