WMS: Dividing fractions

Dear Families,

Welcome back from Thanksgiving break! I was a long and short weekend all at the same time. I really noticed today that some of my students were a little rusty with adding and subtracting fractions; but multiplying fractions didn't seem to cause anyone any trouble

Today we started looking at dividing fractions. We use a lot of food when we talk about fractions. I think it's because we are so used to dividing and sharing food.

We looked at an example involving dividing blocks of cheese to make pizzas. If you have 9 blocks of cheese and it takes 1/3 of a block to make a pizza, then how many pizzas can you make?

Using diagrams of cheese blocks, we figured out you could make 27 pizzas. We did the same thing with some different fractions of a block for each pizza. And then I had some students start offering a pattern they thought they saw: it turns out it's the same pattern involved in the "algorithm" of dividing fractions. But the kids had a different way of describing it. I have made a short video to show you the kind of thing we worked on today:

http://www.educreations.com/lesson/view/bp2-inv-4-lt-4-dividing-fractions-1/2914359/?s=hKxHzq&ref=appemail

Remember that I try really hard to have homework posted on my calendar online and that all of these messages are archived. You can reach the calendar and the email archive at http://www.mrmacnevin.com.

Thank you!

Brian MacNevin

WMS: Math and Science quizzes tomorrow:

Dear Families,

Just catching you up to with the new week!

Math

• Tomorrow we will have a quiz on the Math Learning Target "I can multiply fractions and mixed numbers and use this to solve problems." Tonight's homework is some practice problems. In case they have not made it home, I am have a copy with the answers posted here: [link].
• Next week we will start poking at dividing fractions using models before we settle into a calculation method.

Science

• Tomorrow we will have a quiz on these learning targets in science:

• I can show how organisms in an ecosystem are connected with a food web.
• I can show the flow of energy within a food web.
• I can identify an organisms trophic level using a food web.

• Students may be asked to draw a food web, to label parts of it, or be asked to identify labeled parts of a food web. Level four students will be trying to share with me how energy is introduced into the food web and will be able to tell the difference between primary, secondary, and tertiary consumers.
• We are talking more about Photosynthesis right now in class. We went outside in the cold wet weather today to collect some leaves and brought them into the classroom to examine up close. We tried to peel them apart (the leaves) to see how the top surfaces might be different from the bottom surfaces on the inside of the leaf, but it was very difficult to separate them that way and all we had were hand lenses to examine them.
• We'll be learning more tomorrow about a simplified diagram for carbon dioxide fixation in plants (photosynthesis). Next week we'll talk more about energy and we'll start wrapping up our unit on populations and ecosystems.

Have a warm and dry evening!

Brian MacNevin

WMS: Math/Science Update

Dear Families,

Math

• We have been working on multiplying fractions using area models (sometimes called arrays) to help us discover an efficient number relationship to use when multiplying fractions. The learning target is "I can multiply fractions and mixed numbers and can use this to solve problems." But there is a lot inside of that which we've been unpacking.
  

1. Using simple area models, we discovered that you can multiply fractions by multiplying the numerators together for the new numerator and by multiplying denominators together to get the new denominator.
2. We examined the usefulness of simplifying fractions before you multiply them to make the numbers easier to work with.
3. We have looked at multiplying fractions by whole numbers using area models and by seeing that we can treat a whole number like an improper fraction (6 wholes is the same as 6/1) and multiply using our fraction strategy.
4. We looked at multiplying whole numbers by mixed numbers (how many brownies are there in 5 pans that are each 1 3/4 full?). We found that the area models get more difficult to use because you have to draw so many of them, and we found that changing the mixed number into an improper fraction lets us calculate the same thing using our fraction multiplication strategy.
5. Today we looked at mixed numbers of mixed numbers. For example, if you had 2 1/2 boxes of brownies and each box held 1 1/2 pans of brownies, how many pans of brownies would you have? This was a bear. The diagrams quickly became unhelpful because there are several ways to potentially draw them and the answers may appear different depending on how students decided to draw the first part of it. So isntead, we looked at the problem using improper fractions, students told me they could just use their fraction multiplication strategy to solve it without a drawing. The key is, they had to turn the mixed numbers into improper fractions before multiplying. 

• That means we have now unpacked the types of multiplication problems and we have a working strategy that seems to work in all we've seen so far.
• Tomorrow we will have a leveled practice day, next Monday we will have a practice quiz, and next week on Tuesday we will have a quiz for multiplying fractions. 
  

Science

• The Wednesday Early release and holiday on Monday didn't leave me with a chance to do a practice quiz with my students yet on food webs and energy. 
• Tomorrow (Friday) we will have a practice quiz in class so that students can get some feedback on things they need to study or improve on. I usually dislike having quizzes on Mondays, so we will have the official quiz for food webs on Tuesday of next week. 

Archives

These emails are automatically saved on a blog in case you'd like to go back and find resources I've mentioned in them. You can find that blog as well as links to lots of student support materials at http://www.mrmacnevin.com. 

Thank you for all the help and support you provide your children daily!

Sincerely,

Brian MacNevin

Finland's educational success story: Less testing, more trusting | Local News | The Seattle Times

If you're interested in knowing a little more about Finland's remarkable successes in education and how they compare to US-efforts to improve education, here's an interesting article from the Seattle Times.

Finland's educational success story: Less testing, more trusting | Local News | The Seattle Times

WMS: Math Update - Unit Tests sent home today

Dear Families,

Unit Tests Returned Today

• I just wanted to touch base at the end of the week here. I returned the Bits and Pieces Unit Tests today to my students and they were asked to write a reflection letter to me and you. This letter is not due until next Wednesday. But it's a little bit different from the letters on the quizzes. The Unit Test reassessed the same learning targets that were on the quizzes, so it's kind of an automatic re-test to see if students have retained or improved their skills.

The Reflection Letter

• On this letter, I am asking students to compare how they did on each learning target in a quiz to how they did on the learning target on the unit test. Some students told me they had lost their quizzes and their progress reports (I'd told them they should keep them safe for exactly this reason, but stuff happens). So if they need their quiz scores again, they can come to me on their own time to get another progress report printed.

Standards-Based Grading Question From A Student Today

• I had one student ask me today, "how do I figure out if I have an A or a B on the test? Do I just add them up?" I had to reply that I had no idea. It was a strange response to give, so I explained a little more along these lines:
  
• In order to create "percentage-based" tests, you have to create all kinds of "points." You have to offer enough of them so that anyone who misses 1 or 2 problems doesn't end up with a "D" for it. So you create a longer quiz that includes lots of little things to earn points over. Some of it is meaningful, and some of it isn't.
• But the quizzes and tests we are using aren't set up that way. Instead, they offer students some choice opportunities to demonstrate at-grade level proficiency, above-grade-level proficiency, or even below-grade level proficiency. I don't need lots and lots of problems for a student to show me what they can do. How the student answers these choice questions helps me determine if they are demonstrating proficiency (3), demonstrating above grade level understanding or proficiency (4), or showing me that they still need some practice or instruction (2 and 1).
• Standards-based grading is a really different way of approaching things. But I think my student "get it" when they ask about retaking a quiz and I ask them which part!? You can see the relief on their faces when they realize there's no point in retesting something they're already proficient at! :) What a chance to focus and practice a specific idea.

I hope you have a wonderful weekend! 

Sincerely,

Brian MacNevin

WMS: Math/Science Update

Dear Families,

It's funny, this morning I felt like the week was going slowly, but by this afternoon I can't believe we're already done with Wednesday! I just wanted to let you know where we're at and what we're working on.

Math

• On Monday we looked at square models ("brownie pan" models) of multiplying fractions.
• On Tuesday we examined several of those models in class and I asked students to tell me any number relationships they saw in the fraction multiplication problems. Kids recognized pretty quickly that the answer was the same as multiplying the numerators and the denominators together (1/2 x 1/2 = 1/4). We practiced some with this relationship to see if we could trust it (is it reliable?).
• Today we examined what role simplifying the fractions had. I wondered aloud if it mattered if we simplified fractions after multiplying, or before multiplying. We decided that you could simplify before or after, but that if you multiply before it might make the calculations easier.
• With the RED group (mornings this week) I got a little more ambitious and asked them if we had to simplify only within a fraction or was it possible to simplify between fractions. I think I pushed the conversation a little too far there, so I backed off.
• Tonight's homework is to finish working on some fraction multiplication math practice with a Pizzazz math worksheet. The pizzazz sheets seem corny (the jokes are terrible), but they are great homework because they're self-correcting. I also asked students to get a start on a subtraction practice Pizzazz worksheet. We have been reviewing fraction and mixed number subtraction (a 5th grade topic) in our math reviews this week, and I thought it seemed like students needed some more practice with borrowing (that's what's on the Pizzazz puzzles tonight).
• 30-45 minutes tonight! All students must finish the multiplication page (unless I've given them another assignment); and I wanted students to get started on the subtraction practice one. But all together, their math homework tonight should not last longer than 30-45 minutes.

Science

• I decided to use our food webs to introduce some technology tools to the kids. So, it's taking longer to close these up than I anticipated; but we will be done this week.
• EDMODO is a school-specific social network. Students join a "class" with a code and anything they do in there can be seen by anyone else (there is no private messaging except to a teacher). We are using this resource to house the food web assignment and resources.
• WILDCATAPPS.ORG is our Google Apps for Education (GAfE) domain. Essentially, it lets students use all of the great Google Docs tools without needing a Gmail username (technically those are illegal for kids under 13 to have). So GAfE lets kids use those tools without being monitored by Google and without having Email attached to it. But teachers can monitor things and suspend user-accounts. One of the Google Docs tools is a DRAWING tool and we have been using it to make our electronic versions of the food web.
• The trick: Your child has THREE sign-ins. They have the district computer username, an Edmodo username (the same as district username for most kids), and their WildCatApps.Org username... that's a lot to keep track of, but the kids are doing it! I think they must all have the same problem with computer website services they use at home! :)

Enjoy the unexpected sun!

Sincerely,

Brian MacNevin

Multiplying fractions begins! With a twist!

Dear Families,

As promised, we embarked on the good ship "multiplying fractions" today! And as I promised my students, the people who struggled the most with today's introduction are the people who know "the algorithm" for multiplying. It's not because their algorithm gives wrong answers, but because they are also responsible for understanding a mode (drawing method) for multiplying fractions.

Why Does Having a Model Matter?

• If you ask most people to multiply 2x2, they can give you 4. Or 10x10 they can give 100. In their minds, they know right away that when you multiply, things get bigger.
  
• Only, it doesn't always work that way. When I multiply 1/2 x 1/2, I get 1/4, which is smaller than the two numbers I am multiplying! Why on earth does this happen with fractions and decimals!?
• That is what we want kids to understand. Not only how to to the multiplication, but how to be self-aware of if their answer makes sense. The models help develop that number sense of multiplyign fractions.

So What's All This About Brownies?

• We started investigating fractions today by looking at square brownie pans and dividing those up.
• I have prepared a short video for you to describe what the lesson was showing and how students should be answering multiplications problems with fractions using a model. 
• Here's the link: http://www.educreations.com/lesson/view/bp2-3-1/2485420/?s=5CDOGF&ref=app.

So we're not calculating fraction multiplication yet?

• That's exactly right. So far we are just using drawings to help us examine fractions and multiplication.
• For multiplication we are using the "groups of" language. So 1/2 x 1/2 means, "half of half of a pan of brownies." That is something the kids can draw and describe.
• We will be using the calculated fraction strategy that we all know and love by the end of the week. It is an elegant and powerful strategy that we will use all year long and into the future. But right now we want to start by building a visual representation of what it means.

Thank you for your patience in this long(ish) math-y email! :) I hope you a have a great Monday afternoon!

Sincerely,

Brian MacNevin