6th Grade Mathematics, Ms. Chuslo Castonguay
What We're Up To Lately Archive
What We've Been Up To 2018 - 2019
What We've Been Up To (2/25 - 3/8)
It was a long haul to get most students to catch up and to realize that putting in effective, timely work pays off in big dividends. There are still some students who have work and quizzes to make up. Please, families and students, check Powerschool and make sure you are staying on top of your grades. The students who have caught up are enjoying math a whole lot more than they were a month ago.
We are going into the last section of Ratios and Proportions this week. Students will be studying how Percents are related to fractions and decimals. Then they'll do percent problems, solving for various missing terms. This is a unit that has obvious and direct ties to every day life. Students seem to take to it more than the other parts of Ratios and Proportions.
What We've Been Up To (2/11 - 15)
Most students have been in a pickle for the start of the third quarter. They have stopped doing the work for math, and/or they are not doing the work well, and according to expectations. Students were given the week, with two after school days and any Ext. HR they could attend for help, to get in the first 6 assignments, and/or to make corrections on any assignments that were done poorly.
SO MANY students took me up on this. Well done, young mathematicians! They saw their grades rise by large percentages, and they exclaimed that they get it now, and it's not hard. Music, music, music to my ears.
Students who did not put work into the first 6 assignments, you can still get partial credit for doing it well. Anyone who didn't finish the Module 6 quiz, or who earned less than an 80, should retake it. These are good habits that will serve you well in all you do. Make them work for you, 6th graders!
What We've Been Up To (1/30 - 2/8)
Wowie Zowie, the weather just won't let us get up a head of steam. But we've managed to get on to a new quarter anyway, so welcome to the third quarter :) I've been working with students to get them off to a great start, but I have to say they are challenging that idea. I told them we had 3 assignments to start the quarter, and I'd LOVE to have everyone start with at LEAST an 85, so come on, get down to business.
Then I gave them a bunch of time in class, helped them work through issues, gave them more time at home, more time in class...and still many students haven't finished the work, or haven't followed the directions and need to make corrections. We have three more assignments going in this week. Come on, Mathematicians, let's get this going!
What We've Been Up To (1/20 - 29)
It's been difficult to maintain fluidity in lessons because of the confusion caused by weather lately, and students are relying too heavily on extended homerooms to get their work done. When we have a weather delay or a missed day, they find themselves without their work at home. It can be very helpful for families to expect students to bring home their homework every night, even if they have extended homeroom. We know that students tell their families that they finished their homework in school. However, there are no study hall classes, so students should not be doing their work in class. They are permitted to work on homework in extended homeroom, but that is not enough time to finish all their work. Extended homeroom is only on Tuesday and Thursday, and homework is given most days in math, and whenever necessary in other classes.
It is developmentally appropriate for students to try to avoid things they don't want to do, and it is also necessary for us to call them on it for their frontal lobes to develop to help them learn to make better decisions. To help us all keep them honest, the homework is posted on the "Homework Blog" page of this website, and much of it is graded in Powerschool. It will continue to be a big focus of our efforts in the third quarter.
What We've Been Up To (1/14 - 18)
On Monday we summed up the information students worked on at the end of last week. Students were reminded to complete the assignments that were started in class on Thursday and Friday. Then we spent a few days doing the GO Math Benchmark assessment so we can see how students are progressing through the curriculum.
When we returned to the curriculum on Thursday, students created an interactive notebook page for Rates and Unit Rates. They were able to compare how the two are alike, and how they're different, and then to practice creating unit rates from rates.
What We've Been Up To (12/17- 1/11)
We have finished with operations with decimals. Students worked hard to learn new processes, and about half the students had time to work with peers to teach themselves to divide decimals using the information in the book. They did a great job!
We have some students who have started to study for tests, or who have always studied for tests, and they're seeing amazing results. We have other students who believe that people are either good or bad at a subject, and that's just the way it is. I make it clear, as often as I can fit it in and other times when it's just obvious that it needs to be said and demonstrated, that everyone needs to work to be their best at anything. I'm still taking classes and workshops, and I share that with the students. It takes time, investment, and guidance to learn, and everyone is capable of improvement.
We started looking at ratio relationships on Wednesday, Thursday and Friday, the 9-11th. Students practiced writing ratios, using ratio language, simplifying ratios, and expanding on ratio relationships. We'll continue with those concepts as soon as we finish the benchmark testing.
What We've Been Up To (12/10 - 12/14)
Students worked hard on multiplying and dividing fractions. There is still some resistance to cross-simplifying, even though everyone agrees that it makes the problem so much easier. It's hard to add new habits, but it's also very worth the effort. Put in the work, mathematicians, and see the results!
Some students have already finished the quiz and have a grade. If it is lower than an 80, they will be making corrections and retaking on Monday and Tuesday. Focus in, young mathematicians. It's not over until it's over. You have to stay with it until it's done, and you can!
We'll be doing all operations with decimals before the break. We've already had a start on this with changing fractions to decimals, so students will be familiar with it. Some students had trouble with the process when we did it the first time, including comparing fractions and decimals, and comparing decimals. We went over it a number of times, and fatigue set in at the beginning of the quarter, so we took a break. Because we are coming around to decimals again, students who struggled with the Unit 1 test will be taking it again a few days after the return from break. It should be fresh and more comfortable for them then.
What We've Been Up To (11/ 9 - 12/7)
Wow has the time flown by! Students are starting to tie everything we've been doing together. They worked long and hard on making equivalent fractions by multiplying and dividing by one written as a fraction. They simplified fractions by dividing by one written as a fraction. They modeled multiplication fractions using folded paper and using a grid diagram. They multiplied fractions using the standard algorithm (the usual method, numerator times numerator and denominator times denominator). They learned to cross-simplify before using the standard algorithm. They modeled division of fractions using fraction pieces as well. The work in math class is sophisticated and precise. Well done, mathematicians!
What We've Been Up To (10/29 - 11/9)
There has been a lot of effort on my part to get students to complete and hand in work. Students need to be taking on this responsibility on their own. I have asked for assignments to be handed in, and weeks later some students are getting to it. A few students have handed in the assignments unfinished! It has been a struggle. Assignments are marked with "collected" if they are complete and handed in but I have not graded them, "incomplete," "missing," or with a grade, in Powerschool so families and students can keep track of the status of assignments.
There has been a focus on students discussing math concepts with each other. This practice has been proven to help students own vocabulary, concepts, and to structure their thinking. Classes have been doing a great job with it.
What We've Been Up To (10/22 - 26)
Students spent the week working with fractions and division. All fractions are division problems, so students started practicing rewriting fractions as division problems that can be calculated showing the work. They spent a day remembering how to compare decimals by lining them up and making them all have the same number of place value places. Then they worked on changing fractions to decimals. This is a skill we do and redo over and over again all year. They use it a great deal in 7th and 8th grades as well, and somehow they forget how to do it and have to be retaught again! Any practice you can get, students, you should take advantage of it! Students will finish practicing this skill next week, and then use it to compare fractions and decimals. Test on Unit 1 next week.
What We've Been Up To (10/9 -12)
Students completed the sections on GCF and LCM and had a quiz. The corrections on the previous quiz should be completed by now, and the retake will be next week. Students should check Powerschool for any missing assignments.
We will be working with fractions and decimals as well as whole numbers in the coming weeks. (Rational numbers)
What We've Been Up To (10/1 - 5)
We have hit a stride. Students notebooks are getting started, and there was the first quiz. Students will be practicing making corrections on the quiz no matter what they had for a grade to practice finding errors and making corrections. Students had a good start on Greatest Common Factor and Least Common Multiple. They will have a quiz next week.
What We've Been Up To (9/24 - 28)
This week we wrapped up our foundation work on integers. Students are solid on how to write integers, how to place them on a number line, how to compare them, and a long list of words that show movement in either the positive or the negative direction. Students can define, identify, and synthesize the concepts of opposites and absolute value. They took a quiz on Friday.
We also started work on factors. Students learned a way to organize the work when finding factor pairs. They had a quick introduction/reintroduction to the concept of Greatest Common Factors. We have a lot more coming from factors, my mathematicians, so make sure you're very good with your multiplication and division facts!
What We've Been Up To (9/17 - 21)
We have managed to get our notebooks going. The notebooks have, over the course of the year, a combination of interactive notes, guided notes, and handwritten notes. Many students at this age have difficulty reproducing notes they see on the board. They simply don't have the experience with them yet to be able to figure out how to place them. With the combination of note types, students will see how the notes look on the page, and practice using them. Over time, years really, they'll develop their own note-taking style. In the meantime, we'll have some structure to help them along.
What We've Been Up To (9/4-14)
It's been a couple of weeks of setting classroom routines, and setting baselines. Students have been working hard to figure out how to remember what they need for class, to set up for class, and to learn where to find the date and the homework assignment. They have accessed HRW and Fastbridge, and gracefully endured some necessary and informative testing (for which they were handsomely rewarded). They even completed the first homework assignment, and called it "easy." Now that's a good start. Let's go.
What We've Been Up To (8/29-9/1)
Welcome to a new school year! This week students were given lockers and combinations and a tour of the building to get a general idea of where to go. They still ask a lot of questions, and that will continue for a good two more weeks. There was some anxiety around both, and that will probably continue for a good couple of week as well.
They were given a letter to read with their families about how things work in the math class and through the math curriculum. There was a short piece of paper to be signed and returned as a receipt of the letter. That's the students' first homework assignment. It's a great way to practice using the homework folder and the planner, and to bring things home to their families and return them. We have to a bit of that over the course of the year.
We spent a whole class period getting to know each other. This is a big transition. There are pieces of 8 elementary schools converging, and even the most confident of students are going to feel the pressure of finding their place. Please let us know if there are any concerns your students bring to you. We're happy to help.
This week we actually start doing some math. Woohoo! Here we go :)
What We've Been Up To 2017 - 2018
What We've Been Up To (6/4 - 8)
Students were gregarious at the baseball game on Tuesday. There was a lot of waiting in line for food, but I didn't talk to any kids how didn't get what they were looking for :)
We spent 3 days working on the End-of-Year tests. Students worked very hard. We went over a few of the trickier problems afterwords, and we'll go over more of them next week.
It's not over yet, my mathematicians. Stay with it!
What We've Been Up To (5/28 - 6/1)
What FANTASTIC skits! The kids in some classes were able to put together skits to write equations from. Well done!
Students did SO MUCH practice on one-step equations, and inequalities. The last test taken using computers did not go well. We're going to try a different test this coming week. Students, make sure to practice and study!
What We've Been Up To (5/21 - 25)
We had to take some time for end of the year assessments. There will be two more days of this on June 6, and 7. We worked a lot on a computer based test. It didn't go well overall, so I'll give a paper version next week and see the difference, if any.
We had a lovely day on Thursday, so we spent it outside putting fractions, decimals and percents in order and in an appropriate position on a number line. Students worked in teams and literally hung the numbers on a number/clothes line. They said they had fun.
The plan was to start skits for writing equations, but I graded the one-step equation papers and found they were in need of many corrections. Students spent the half-day making corrections on those practice problems. The skits will be next week.
What We've Been Up To (5/13 -17)
Students were given a full class period to work on corrections or missing assignments this week. I did not receive any from students who didn't have them done. Those grades will stay the way they are if students don't fix them. I won't give any more class time.
Students took a test on computer on order of operations, exponents, distributive property, substitution of values for variables, and writing expressions. It did not go well. I will give the students who did well on it the grade as an extra credit grade. Everyone will be retaking the assessment in paper form. We'll take a look at the mistakes that were made and go over them together before the retest.
We'll also be moving on to writing equations and writing inequalities. We'll be doing an activity where students act out a scenario so everyone can write an equation from it. That should be fun :) Some groups had a short opportunity to do an activity involving comparing fractions, decimals and percents and putting them on a number line in teams. It went well, and we're going to do it again, for a more reasonable, longer amount of time, as soon as we have a nice day and dry grass.
What We've Been Up To (5/7 - 11)
We went back to order of operations, exponents, prime factorization, and writing expressions. In addition, we practiced a few percent problems, and wrote a couple of equations. Now that I have a sense of where the students really are, we'll have a test early next week on all but the equations and percents. Then we'll hit the equations much more indepth.
Students have three major assignments that need to be in and may not be: Practice MCAS test, One-step equations, and Distributive Property Activity. Any student who does not have those in needs to see me during extended HR, or after school to get them done.
Students who earn less than an 80 on the practice MCAS will be required to make corrections. Students have one week to get those done and in. I will not be chasing around after them, but I will be sending home a note to be signed by families so you know corrections are needed. There is a sheet to be used to structure the corrections. Students are welcome to come to me for help on those during extended HR or after school. We went over ALL of the problems from the tests in class, and students were required to make corrections or add work as we went. Some students did not do that. The tests may look daunting, but we did it together.
What We've Been Up To (4/30 - 5/4)
Well, the MCAS tests are finally done for 6th grade. YAY! Students worked hard leading up to the test, and on the test itself. Well done, young mathematicians :)
We have moved back for these last two days to concepts we were not able to cover comfortably. Students worked on the Order of Operations, Exponents, Distributive Property.
What We've Been Up To (4/23 - 27)
This week we practiced some one-step equations. Students were given the value of the variable, and they had to use a specific process to prove that value. Students put them on the board, and we checked them over to see if they were missing any parts, were written in any way that would cause problems, etc. Students have grown to a point where they can see mistakes, identify what they were thinking when they made the mistake, and share it with the class. Other students would then say that they made the same mistake, and everyone felt validated, and also learned the correct method. I love it when we get to this point. They own the lesson, and I don't have to talk nearly so much!
We finished the week with an MCAS practice test that we completed together. Students looked at how to correctly read the problems and answer them. (There are some pretty specific ways they have to record their answers). They shared methods to solve problems, and we again noticed and discussed common errors.
The MCAS test is on Tuesday and Wednesday this week.
Over Break
Students may wish to practice some of the concepts we started on just before break. It would be best if they don't come back to school too rusty. Here are some links they may use to prevent that:
Writing Expressions:
Combining Like Terms:
One Step Equations:
What We've Been Up To (4/9-13)
This was the first of 2 weeks that we'll be using to teach and learn some concepts that will be covered on MCAS. Students will not have tests or quizzes during this time, but they will have some class work to do that will have a grade.
This week we practiced substituting values into expressions. We used that process to substitute into formulae to figure out the area of triangles, rectangles, parallelograms, trapezoids, and rhombuses, and the volume of a rectangular prism.
Then we combined like terms, noticing that the rules are a lot like the ones we use to add and subtract fractions.
Finally, students had their first crack at one-step equations using addition and subtraction. The answers were so simple that they tended to miss important parts of the steps needed to do the equations well. Right after break we'll do those again, and also one-step equations with multiplication and division. We'll do a reminder of mean, mode and median, and add just a little more about measures of center in a data set before we look at a very short practice test.
What We've Been Up To (4/2-6)
For the next two weeks (one before break, and one after), students will be learning some foundational pieces of different concepts. We've already reviewed order of operations, but we added exponents. Students translated words into mathematical expressions, and interpreted mathematical expressions using words. This past weekend, they practiced finding the value of an expression when given values for the variables.
This week they'll use that same method to evaluate formulae for area of quadrilaterals and triangles, and for the volume of rectangular prisms. Then we'll pop back to learn one-step equations.
After break, students will spend a couple of days with statistical information, and we'll do some practice for the MCAS test the following week. When that's done, we'll return to these concepts to examine and practice with them more in-depth.
What We've Been Up To (3/19 - 3/30)
We have worked with percents! Yay! Students can change between fractions, decimals, and percents with fluency. Many students have learned to picture benchmark fractions, decimals and percents as well. Students did a LOT of work on deciding if their answer was a reasonable one using those benchmarks. They continued to practice finding errors to correct them instead of just reworking the problem to see if they get a different answer. Students continue to practice using their notes and model problems to help them learn new concepts and to practice them.
Now we move on to expressions and equations. Algebra! Can we get a woohoo!!?
What We've Been Up To (3/5 - 3/16)
All classes have made wonderful progress in writing proportional relationships and using them to solve problems. Students have mastered the art of the Unit Rate, and are now using it to find other rates. I see students thinking in ratios and using logic to figure out answers. What great work! After a very rocky start with rates, and a LOT of weather related interruptions, students are coming around to these processes. Well done, young mathematicians :)
What We've Been Up To (1/2 - 3/2)
The defining factor of the last two months of math is focus on details. We have moved into Proportionality and Ratios, which requires students to use labels and units, and specific processes that are all new. Because so many of the processes result in answers that students feel they can see immediately, they tend to resist using them. They went through some time where the assignments they were handing in did not show their best work. There has been a recent improvement in student follow through, so I'm hopeful that the percents unit will go smoothly.
What We've Been Up To (12/18 - 22)
This week students wrapped up either dividing fractions, or multiplying fractions. We did a number of practices before the tests, and regrettably, we were unable to give them before Friday. However, when students completed the tests we were able to play a little bit in class and just have some fun and make sure students practice each others' names some more.
A reminder that most students have corrections to complete before January 19th. Corrections can be made over and over until the student earns a 100%, and the grade will be changed to that 100%. Students should come see me during extended homeroom, or after school for help with the corrections. I'm happy to guide any and all students who seek help all the way through to the end. If I am not available during extended homeroom, students may check in with Mrs. Bates or Mrs. Manns for the same help.
What We've Been Up To (12/11 - 15)
Students struggled with making corrections on the Unit 1 Test, so we went over it again. They were given more time to correct again, but very few students felt they needed it. Retests were taken and grades will be in next week.
We finished multiplying fractions in some classes. Students enjoyed cross-reducing, which I really LOVE doing, and are still working to find when they can cross-reduce. Again, it's all about knowing those multiplication facts!
Students have started the process of dividing fractions. We used Cuisenaire Rods to model what dividing fractions looks like, and this coming week we'll use the algorithm (math process) we proved to work division of fractions problems.
The corrections on the tests had some problems, so students will have the opportunity to continue to make corrections until January 19, or until they earn a 100%, whichever comes first. The retake grades will not be changing, but the higher grade between the retake and the original will be recorded.
What We've Been Up To (12/4 - 8)
We finalized adding and subtracting fractions with assessments, and students were given their tests to make corrections. Corrections are only made on tests that earned less than 80%. Students who scored less than an 80% will retake the test next week.
Many students began multiplying fractions. We took a look at what's happening when fractions are multiplied using Cuisenaire Rods. Students already knew to multiply across, numerators and denominators, but for many of them cross-reducing was a new concept. We practiced with it quite a few times, but more practice is needed. On Friday students were doing a scavenger hunt with multiplying mixed numbers and there was quite a bit of confusion. We'll practice some more on Monday and/or Tuesday, then take a test to finalize the section.
On Monday, I'll be going over the corrections students made on the Unit 1 test. I've been mulling over how to help them analyze errors on tests and make corrections, and come to the conclusion that we need more practice with it together. On Monday, we'll take a look at that test one more time, then I'll give the "do over" test to those students who scored less than an 80%.
On Tuesday, students who need to will retake the addition and subtraction of fractions test. Then we'll play with multiplication again, and, armed with the fresh knowledge of what they can best focus on for a test, assess multiplying fractions.
What We've Been Up To (11/20 - 12/1)
We've done a review of adding and subtracting fractions using the LCM, and reducing fractions using the GCF. Students did quite a bit of practice with writing equivalent fractions by either multiplying or dividing by one in fraction form. We also took a look at equivalent fractions using fraction pieces, and through Khan Academy videos. Students have quite an extensive interactive notebook built up. We've been concentrating on looking back in the notebook and USING the notes to as a way to remind students of what has been learned and practiced. That last one continues to be a challenge.
And on using the notes, students took a test on Unit 1. Many students did very well, and many students found that they still need to work on concepts from unit 1. Students were allowed to use their notes for the test, but quite a few chose not to. Usually the students who earn less than an 80% are required to correct the test using a systematic method I have for them. For this test, every student was required to make corrections because it's the first time we've done it and they'll understand how to do it with more confidence if we do the first one together. We are still working on them. Many students are STILL not opening their notebooks to find the answers or the help.
What We've Been Up To (11/6 - 17)
We will continue to work with factors and multiples for the rest of the year, but we'll now assume students know what they are and how to find them to solve other problems. There are still students who struggle with multiplication facts, and it's important that they work on those on their own. We have some time during extended homeroom for students to practice, but it isn't enough time. Here's a great place to practice if you are or you know a student who needs it:
https://xtramath.org/#/home/index
http://www.multiplication.com/games/all-games
A quick note: students are starting to resist showing work when it's necessary to complete a problem, or to prove an answer. We go through this every year. The problem seems simple, so they don't see why they have to show their work. I've given them many examples of when they THINK they're using logic to solve a problem, but they're just getting lucky, or when their audience (me usually) needs to see what they were thinking when they were getting their answer. We'll be concentrating on showing work with increased fervor this quarter and for the rest of the year. It's an important part of understanding math.
What We've Been Up To (10/30 - 11/3)
We're still working with factors and multiples of numbers, and for many students it's coming along well. Students also learned to plot fractions and decimals on a number line, and to compare fractions and decimals to each other. They found that opposites and absolute values of rational numbers have the same definition regardless of whether they are integers or fractions or decimals.
A quick note: students are starting to resist showing work when it's necessary to complete a problem, or to prove an answer. We go through this every year. The problem seems simple, so they don't see why they have to show their work. I've given them many examples of when they THINK they're using logic to solve a problem, but they're just getting lucky, or when their audience (me usually) needs to see what they were thinking when they were getting their answer. We'll be concentrating on showing work with increased fervor this quarter and for the rest of the year. It's an important part of the understanding math.
What We've Been Up To (10/23 - 27)
We continue to work with factors and multiples to get to know fractions. Students made a number line showing the relative value of benchmark fractions, and showing some of their equivalent fractions. They took notes on fractions: the numerator and denominator, how to write fractions as division problems and division problems as fractions, and how to reduce fractions. We'll talk just a bit more about how to compare fractions, then we'll look at decimal numbers. Decimal numbers will be introduced (or reintroduced, really) as special fractions that have exponents of 10 as their denominators.
What We've Been Up To (10/10 - 20)
We continue to work with factors and multiples because they are the foundation of everything else we'll work on this year. Students who continue to struggle with multiplication facts need to make sure to come during HR to work on them. Math is so much more fun, and really interesting, when students don't have to work so hard to come up with factors and multiples.
We have also started looking at Rational Numbers. This means that in addition to the whole numbers and their opposites (so the Integers, or both sides of 0 on the number line), we are also going to use fractions and decimals. The students did well with the start of this; they're shaking off the rust from their place value knowledge :)
What We've Been Up To (10/2 - 6)
Students have put in some long, hard work learning to use divisibility rules to help find factors of numbers. When the rules don't help, students have learned to use short division to find out if a number is a factor. When there is a two or more digit divisor, no one needs to try to do the subtraction in his or her head; there are times when we do have to use long division.
We also spent a little time on multiples. Students practiced making lists of multiples to find Least Common Multiples as well.
I'll teach students to use a division ladder to find both Greatest Common Factors (GCF) and Least Common Multiples (LCM) when they can see what both of these look like in a list. It's important for students to see how numbers are related.
There has also been some time spent doing baseline assessing. Pittsfield has some new technology to use to find where students are strong, and where students need support and practice. It's slower this time than it will be in the future because we're getting used to it. The students have done very well with all assessments:)
What We've Been Up To (9/18-22)
We finished working on opposites, absolute value and comparing integers. The test didn't go well because there was a lot of confusion about how to do it digitally. We'll move on to factors, multiples, LCM, and GCF until after we do some baseline testing next week, then we'll take that test again. The students know the material so we just have to go over how to plot points on a number line using the computer software, and do some review.
What We've Been Up To: 9/11-15
The students spent the week learning about integers: the Whole Numbers and their opposites, which means the negative whole numbers. We looked at how they're represented on a number line, and practiced plotting points. The students did an activity where they could see that 0 is the line of symmetry on the number line, separating the positive numbers from the negative numbers. They also noticed that as you go right on the number line, the numbers increase, and as you go left they decrease. Finally, we brainstormed a BUNCH of words that can be used to show movement in the negative or positive direction so that we can use the absolute value of a number and one of the words to describe real world negatives and positives. (ex. spend, drop, decrease; earn, rise, increase).
The students are also continuing to learn the classroom and building routines. Everyone can open their locker independently now, and they're starting to remember what to bring to class :)
What We've Been Up To 2016 - 2017
What we're up to lately...(5/15-26)
We've spent the last two weeks solving one-step equations. All classes have had the opportunity to solve one-step equations that involve addition, subtraction, multiplication and division. As we've progressed through this unit, I've seen big improvements in the organization of the work involved. Students have started to use this process in an efficient and effective manner! Good job!
Many students are still putting in a fabulous effort as we wind down this school year. Other students are not following through anymore. There has been an increase in students not doing homework, or failing to follow through on classwork as we go over it. I've been grading more classwork to hold students accountable, so they don't forget how important it is to their own comprehension of the math for them to make corrections and talk to their table mates about how they did the work. Any encouragement that can be given for them to keep putting in their best effort would be helpful :)
What we're up to lately...(5/8-12)
I'm repeating the first part of last week's update. It still applies :) The new information starts in the third paragraph.
The MCAS tests for the general 6th grade classes are done. Students who missed one part or another of the math MCAS will take make-ups later this week, or early next week.
Students tend to feel that the year is over when the MCAS tests are done. Even without snow days we often have 5 weeks left. This year we still have 7 weeks. It can be helpful for students to maintain routines so they can learn to stay focused on learning even when the seasons change, and we approach the finish of the year. I've returned to most of the routines we had before the MCAS tests. This includes assigning homework about 4 nights a week. Independent practice is an important part of the learning process for math and the other subjects.
Students continue to practice writing and solving equations. All classes have taken notes on and practiced doing one-step equations with addition and subtraction. This is a hard concept for students to comprehend on this first approach. We practice with and talk about equality, but students still get mired in the process and forget why we're doing what we're doing. We're hitting "inverse operation" really hard again. We're driving home that students need to work systematically on their papers so they can see what they've done and what to do next. It seems to be starting to sink in:)
What we're up to lately...(4/24-5/5)
The MCAS tests for the general 6th grade classes are done. Students who missed one part or another of the math MCAS will take make-ups later this week, or early next week.
Students tend to feel that the year is over when the MCAS tests are done. Even without snow days we often have 5 weeks left. This year we still have 7 weeks. It can be helpful for students to maintain routines so they can learn to stay focused on learning even when the seasons change, and we approach the finish of the year. I've returned to most of the routines we had before the MCAS tests. This includes assigning homework about 4 nights a week. Independent practice is an important part of the learning process for math and the other subjects.
We are working on writing and solving equations. The problems start out easy, which means that students know the answer, usually from doing the work in their heads. I'm thrilled they can do that! They need to use what they know, namely what the value of the variable is going to be, to make sure they have created a correct equation. Then they need to use appropriate steps to prove the solution to the equation. If they can find success on these simple problems, they'll have an easier, if not an actually easy time, transfering the knowledge to more abstract expressions. It's a bit of a battle to get them to use methods that show each step in the solving process. They feel like they're wasting their time because they already know the value of the variable. I throw in a few that they can't figure out automatically to help them see the value of the process.
What we're up to lately...(4/3 - 4/13)
During these days we started working on substituting in values for the variables in expressions, then solving them. Students had to use the order of operations after substituting in order to find the correct solution. Most students had a good time with these.
Because being able to use substitution is required for using a formula, we moved on to area of quadrilaterals. We proved that the area of a parallelogram is bh (base x height) by cutting apart a parallelogram and making it into a rectangle. Then we used the formula to find the area. We proved the area of a trapezoid is 1/2(b1+b2)h by putting two trapezoids together, one inverted, to make a parallelogram. Then we used logic to see how the parts match up. Students were engaged and logical. It really went well.
We also spent a couple of days going over a short MCAS practice test. Students practiced organizing their thoughts and work, and using the problem and its questions to help guide them. We talked about ways to stay calm when a problem seems overwhelming, and we practiced how to bubble in the answers correctly. (There are a few more requirements then just bubbling in a letter.) A couple of classes still need to finish up this part. The MCAS test for math is May 2 and 3.
What we're up to lately...(3/27-31)
We are working on writing and understanding how to read and use expressions. This week some classes began writing algebraic expressions to represent real life situations. Students are looking for clue words that tell them whether they need to use addition, subtraction, multiplication or division.
When students translate expressions into words, they are seeing that there are often many ways to show the same expression. For example, x-4 could translate into "x minus 4," "4 less than x," "x less 4," "x decreased by 4," and others. We are making the connection that these are processes that students have been practicing for many years. The biggest difference is that students are creating them from their own problems instead of having the expressions given to them to solve, and there are variables in the problems that are represented by letters. We have already used variables to solve some other problems, so the students are very good at recognizing and using them.
Students were also introduced to substituting values for variables. If they are given, "x=7," then they can put 7 into the expression "x+18" and rewrite it as "7+18." Now that they have actual numerical values, they can find a numerical value for the whole expression, in this case 25. The students are not having any trouble with this. The only slip up so far is that they forget to use exponents correctly. We just learned them, so that's to be expected. We'll keep practicing.
What we're up to lately...(3/20-24)
This was a better week for independent work. More students completed homework and got down to work on Do Now practices on their own. This is an important skill for learning, and life in general, so I'm very glad to see the improvement.
Some students continued working on precent problems this week, and have almost completed the test on ratios and proportions. This was an especially good job as we had some interruptions for other necessities.
Other students practiced with the order of operations. They remembered a great deal from last year. Nice job 5th grade teachers and students! We added exponents to the process. We'll need to do a little bit more practice with these. For now, students sometimes forget to multiply the number by itself when using exponents, and instead multiply by the exponent.
What we're up to lately...(3/13 - 17)
The students who have been doing their homework are solving real world problems with proportions and percents. The students who have not been doing their homework are finding themselves more and more frustrated. This is new stuff. It needs to be practiced even more than the concepts that students have seen before and are just using in new ways. It is always, and especially now, important that students TRY a problem that they feel they do not understand. More often than not, when a student puts down what s/he knows, step by step, suddenly the steps to the solution become clear. Please, students, write the question, write what you know, make an attempt to solve the problem. You can do this!
What we're up to lately...(3/6 - 10)
Yay students! You are setting up proportions to solve problems. Well done :) There was a general starting to follow the models, and students are showing understanding and skill in completing real world problems with proportions. We finished converting measurements and moved on to percents. Percents are going very quickly, I think because students are creating appropriate proportions to solve them. Yay! :)
What we're up to lately...(2/27- 3/3)
I am repeating the post from last week. Students are still digging in their heels about setting up proportions. While they say they don't understand how to do them, when I stand by them, without telling them HOW to write the terms, and have them create the proportion, they do well. Many students are not completing DO NOW practice problems, and way too many students are not doing their homework. These actions are causing the problems we're seeing. I can't help a student if I don't know what they're thinking. They need to write down the work so I can see their thoughts:
Wow, proportions are proving to be very difficult for students. The biggest difficulty is that they are not setting up the proportion in order to work it. The second issue is that many of them are not consistently labeling their terms in the proportion. I have been feeling frustrated that despite practicing them so many times and reminding them so many times to create the proportion, about 35% of the students are still not doing it. We will continue with these after break, and then we'll move on to percents, which will also require the use of ... proportions.
What we're up to lately...(2/13-17)
Wow, proportions are proving to be very difficult for students. The biggest difficulty is that they are not setting up the proportion in order to work it. The second issue is that many of them are not consistently labeling their terms in the proportion. I have been feeling frustrated that despite practicing them so many times and reminding them so many times to create the proportion, about 35% of the students are still not doing it. We will continue with these after break, and then we'll move on to percents, which will also require the use of ... proportions.
What we're up to lately...(2/6-10)
I'm repeating what was reported last week because we're continuing to work on these. This week was very short and choppy. Students lost momentum on working proportions problems, and it showed. They don't feel confident when setting up the relationships, and some of them are not sure how to proceed when they do set them up. With luck, we'll have some days to work on them next week. Once students practice them enough, they will feel natural about them and wonder why they every had trouble.
Finally we're calling equivalent ratios what they are: proportions. Students worked a great deal with equivalent ratios to find rates. Then they graphed them on a coordinate plane. It's important that students use labeling in this section, and for the rest of the year. As long as students label the information they've been given, they will not have any trouble setting up proportions correctly. They can get the units correct in a unit rate. They'll be able to find percents without a problem. They also need to remember to label the axis on a graph, and the points on a number line. It's proving to be a big part of our lessons this year.
What we're up to lately...(1/30-2/3)
Finally we're calling equivalent ratios what they are: proportions. Students worked a great deal with equivalent ratios to find rates. Then they graphed them on a coordinate plane. It's important that students use labeling in this section, and for the rest of the year. As long as students label the information they've been given, they will not have any trouble setting up proportions correctly. They can get the units correct in a unit rate. They'll be able to find percents without a problem. They also need to remember to label the axis on a graph, and the points on a number line. It's proving to be a big part of our lessons this year.
What we're up to lately...(1/23 - 27)
We continued working with equivalent ratios, double number lines, and ratio tables to make sure the concept of equivalency in ratios is well understood. Students took a quiz on Thursday and Friday on these concepts.
Students also organized the notes section of math binders in some classes. There is a table of contents that students will add to as we continue. I've mentioned before that students are not using the many support materials they have to help them with their work, so I'm hoping a bit more organization will help them know where their notes are and use them.
This week I saw the shift in student practice that I've been looking for. In all 5 classes I saw groups of students comparing answers on their work and helping each other out to find and correct mistakes. There were some great discussions about the math behind the work they did, and some equally great explanations of why they chose to do the work they way they did. This is a big step in both independent mathematical thinking, and in collaboration. It's really exciting!
What we're up to lately...(1/17-20)
All classes have finished the "Create a Color" activity and the pictures are on the "Activities Gallery" page. (Hover over the "Home" button to find it). The colors are beautiful, and many of the names are fun. It has been an activity that we can refer to whenever we need a quick mental picture of what ratios and equivalent ratios mean.
We worked a lot with rates and unit rates during these days. Students learned the definition of a rate, and how to use equivalent ratios to find quantities. They are getting really good at it! As long as students remember to put the units in the ratios, the process always goes just fine.
Students looked at two other ways to use equivalency as well. They analyzed tables to compare ratios, and double number lines to compare rates. We'll finish with those this week, and move on to graphing constant rate of change.
What we're up to lately...(1/9-13)
We started right off with creating colors using food coloring and water. Pictures from the activity will be on a new page as soon as I figure out how to do it. Students created a ratio of drops of color to create a new color in one cup of water, then made the exact same color in 2 cups of water by creating an equivalent ratio.
We moved on to Tape Diagrams to figure out how to make ratios help us find quantities of parts. Students drew the tape diagrams to find a pattern in the process, then used the process for more complicated problems. We'll need to do a few more of these to feel competent using them.
Then came rates. Rates are special ratios that compare quantities using different units. We talked about how we can find the best deal when purchasing food by comparing unit rates. We looked at finding miles per hour. We practiced reading and writing rates and unit rates using a slash (/), or the words "per," or "each."
Some classes modeled operations with decimals using 100 grids. Then we used the patterns we noticed to come up with the standard algorithms (the mathy way, as Dr. Who might say) to figure out problems with decimals in them. We began a test on this, and will finish it on Tuesday.
All classes have some students who are struggling to finish corrections and retakes on operations tests. This coming week will be the last time students have a chance to make them up. This is important work. Operations with rational numbers are the building blocks of all the other work we do in middle school...and beyond. Students, make sure to follow through on your corrections!
What we're up to lately...(1/3-6)
Students spent a good deal of time making corrections on tests they took before break. They first found their mistakes, then reworked the problem correctly. They wrote a sentence or two about what they noticed about their mistakes so they can keep their observations in mind next time they go to take a test. These were well thought out comments, I was very happy with students' investment in this activity. Good job, classes!
We also started working on ratios. Ratios so often work the same ways fractions do, but they are also different than fractions. We learned to write rations in 4 different ways, to make equivalent fractions, and we started looking at ways to use fractions to figure out amounts.
This week we'll continue with Tape Diagrams, or a representational way to find quantities using ratios. We'll also begin using rates.
What we're up to lately...(12/5-12/23)
We worked on all operations with fractions and decimals. There are a lot of steps to some of the operations, so we practiced them, wrote them, proved them, so students could become proficient with them. There was a test on them late last week (12/15-16) so they will get them back this week.
Some classes are testing on operations with fractions tomorrow and Wednesday (12/20 and 12/21).
Some classes will begin working with Ratios this week. The main focus will be on how to read and write ratios, and what they mean.
There will not be homework over the break. Any student who would like to earn extra credit can work on IXL according to the instructions below on this page. It's a great way to stay sharp even if a student doesn't really need extra credit. I highly recommend it. There is a link to IXL on the "Math Help" page which can be found as a drop down under "Home" above, or as a link at the bottom of this page.
What we're up to lately...(11/28-12/2)
Students needed a great deal of time to finish the tests from a couple of weeks ago. I'm finding that many students have difficulty organizing their work so that they can find it, or so that I can follow it. We're working on it, and it'll be very important that students hone organization skills for their own access more than for mine.
In one set of classes, we worked long and hard on doing all operations with decimals. First the problems were modeled using 100s grids, and students did a find job with that. Students didn't have any trouble understanding the process, but there are so many parts to it that it was easy to make errors. We'll be looking at how to find errors and correct them this coming week.
In the other set of classes, we're finishing up with operations with fractions. Students did a great job of modeling multiplication and division of fractions using Cuisenaire Rods. We then transferred that to the standard algorithm (the math way to do it). There will be a test later on this coming week.
What we're up to lately...(11/14-22)
We spent a great deal of time working on word problems involving fractions. Some of them were more simple one-step problems, others required a number of steps. Students learned to make important information stand out, to break down the problems, and to make decisions before beginning. We always try to answer the following questions: What is the questions asking me to do? What do I know before I begin? Did I answer the question that was asked? Does my answer make sense?
Students were required to write down the question, or a shortened version of it, and to list the information the problem offered. They then made a decision about how to solve the problem, then showed the work they used in solving it. Finally, they checked their answer to make sure it was reasonable. This is the most difficult part because they have to use estimation, and many of them are not confident in their estimation yet.
It went really well. We'll do plenty more of these as the year goes on. Students also took a test on either dividing fractions, or rational numbers, depending on the period in which they have math. The tests will be returned on Wednesday, November 30. We have to go over how to organize the page they use to show work, and how to check over the paper before handing it in, then I'll grade them.
What we're up to lately...(11/7-10)
Wow, what a short week! Students finished modeling multiplication and division of fractions using Cuisenaire Rods. Then they practiced using the standard algorithms for multiplying and dividing fractions. We also threw in mixed numbers to make it all round out. Many students wondered why we had to model the problems at all. We're going to concentrate on word problems with multiplying and dividing fractions, and it will become very clear. "Word problems" are where the real world can be found in math, so these connections are vital to our math lessons.
What we're up to lately...(10/31-11/4)
This week we practiced how to make corrections in a systematic way. It seemed complicated when we started, but it became easier as we went over it.
Students also made number lines or modeled multiplication and division of fractions using Cuisenaire Rods. We noticed that when we multiply by a number that is less than one, a proper fraction, the product will be less than the number we started with because multiplying by a fraction is the same as taking a piece of something. When we divide by a number that is less than one, the quotient is greater than the dividend because we're fitting something smaller than one into it. We use the sentence, "How many of _____ fit into ____ to help us picture the problem.
Again, it's REALLY important that students know their math facts. Students need to be able to automatically recognize factors and multiples, and to add and subtract to a great extent in their heads. When these skills are automatic, they become tools and students can use math at a more sophisticated level. Students are freed up to notice other number relationships if they're not bogged down in facts. Practice them if you don't know them, young mathematicians! Come and see me for good practice. Use IXL, Kahn Academy, flash cards. You can do this :)
What we're up to lately...(10/24-10/28)
We spent some time talking about how to study for a math test. Students had a study guide to complete, and they wrote their own questions, thinking about what could appear on a test. They shared the questions they wrote at their tables the day of the test for practice.
Students learned the definition of Rational Numbers, and how they relate to Integers and Whole Numbers, which we've already talked about.
Again, it's REALLY important that students know their math facts. Students need to be able to automatically recognize factors and multiples, and to add and subtract to a great extent in their heads. When these skills are automatic, they become tools to use math at a more sophisticated level. Students are freed up to notice other number relationships if they're not bogged down in facts. Practice them if you don't know them, young mathematicians! Come and see me for good practice. Use IXL, Kahn Academy, flash cards. You can do this :)
What we're up to lately...(10/11-10/14)
Students have been stepping it up! We are starting to get to know each other and to work as a team. Students wrote their own word problems, and worked together to write a collaborative word problem. We analyzed how a problem asks a question to get a specific answer, and looked at why anyone would care. This stuff matters!
Again, it's REALLY important that students know their math facts. Students need to be able to automatically recognize factors and multiples, and to add and subtract to a great extent in their heads. When these skills are automatic, they become tools to use math at a more sophisticated level. Students are freed up to notice other number relationships if they're not bogged down in facts. Practice them if you don't know them, young mathematicians! Come and see me for good practice. Use IXL, Kahn Academy, flash cards. You can do this :)
What we're up to lately...(10/3-10/7)
We are still hitting multiples and factors as hard as we can! Please make sure students know their facts, they are the key to our whole year.
Students often confuse factors and multiples. They told me Ms. Abderhalden at Williams told them to remember: factor - fewer, multiple - many. I love that, thanks Ms. Abderhalden!
We're using those factors and multiples to recognize the Greatest Common Factor (GCF) of two or more numbers, and the Least Common Multiple of two or more numbers (LCM). Why do we care about such things? Because they have real life applications. What if we want to set up groups of people doing an activity? The GCF will help us do that. What if we want to know when we'll need more people to staff a store because events occur at the same time? LCM will get us there.
We finished the week by coming up with our own scenarios to use GCF and LCM and we're going to find a way to share them with other students.
What we're up to lately...(9/26 - 9/30)
Students learned how to list factors using factor pairs. It's a method that will all but ensure that they don't leave any out. Students start with 1 and its pair: the actual number. Then they go to 2 and decide if it's a factor. If it is, they write down its pair. They continue with this until they find they have repeated a factor. As soon as a factor is repeated, the factor list is complete.
We also learned how to use some divisibility rules. Many students had seen these last year, but none felt confident using them. We practiced using the divisibility rules for 2, 3, 4, 5, 6, 9, and 10, and found that asking ourselves simple questions for each "test" made the process pretty fast.
In addition, we learned and practiced "short division." This is a form I remember learning in elementary school, but I haven't seen it in a textbook since. It's a really important way of acknowledging that students can do simple multiplication and subtraction mentally, and they don't need to write it down every time. It's quick and simple so it's a tool to be kept in the math toolbox.
Many students are still struggling with organization. If you find that your student has a really messy binder, or never brings anything home, please let one of us know and we'll try to make a time to show them how to get it all under control.
Please remember that there is an extended homeroom every Tuesday and Thursday. If students are getting behind, or if they have questions, please encourage them to go see the teacher during this time. They should also visit each teacher if they have been out so they can find out what they missed.