Friday, June 02, 2017

Math - It's What's for Breakfast - Day Four

Whoo-wee! It's Friday. It's our last day with this group of students. Next week I will be leading a brand new group with this same information. So next week's posts will just be what I'm noticing instead of a full breakdown, just so you know!

After the math vocabulary stickers and roll call  I jumped in and took over the Estimation Problem for the day. I wanted to get my feet wet and ready for Monday. Today it was about the height of a Ferris Wheel, but they gave us a clue when they included the guy from Monday's estimation. The students had to remember that his height was 6'4". It was funny to watch them all immediately pinch their fingers on the picture and then try to count up how many of those it would take to reach the top of the wheel. Since this was an inaccurate and unsteady way of measuring many only got about half of the correct numbers of people to count.

I also asked the teacher participants to weigh in with their estimations and share their strategies. One of them brought up the idea of just counting up half way and then doubling it. Which leads right into today's Number Talk strand!

If we used 64 x 1 and then showed them 32 x 2 can they 'decompose' (ask them to use the correct terms we discussed yesterday) the 32 into 30 and 2 so that the problem could be (2 x 30) + (2 x 2)? Highlight any strategies shared that came from our lessons this week, such as Area Model or Number Lines.

Today's Activating Strategy was called Eliminate it. There's a table with four two digit numbers in them. They are just random. Tell the students that there is no right or wrong way to answer this question. But look at all four and remove one of them from the rest. Make sure that you stress that the student talks through their math reasoning behind why they selected that number. Have them refer to the place values of the numbers, or the odd-evenness, prime-composite, digit is repeated, etc.

Next was time for only one workstation rotation today.

Yesterday I gave you some homework to do research into Three Act Tasks. Dan Meyers created a google doc that he is sharing about various math problems in LiveBinders. Students watch a little video or look at a picture. Then they talk out what they notice and  IMPORTANTLY try to determine what the video could be asking. They estimate, placing their guesses on a number line with LOW choice at one end, and HIGH choice at the other. Their estimate falls somewhere on this line. Students need to determine what information is needed to solve their selected question. Then they work through the math and offer up suggestions for results, justifying their reasonings.

You get to decide if you reveal the answer, or let them walk away without solving it.

We had a survey for the students to complete, so we stopped today earlier than usual.

Next week is all me with four teachers watching me conduct these lessons for 16 students.


Thursday, June 01, 2017

Math - It's Whats for Breakfast - Day Three

Good morning Mathematicians,

If you're as bad as me at staff developments you see some great ideas and immediately want to try them out. Which translates into DollarStore Run!

My Coordinator had these great little 3x5 corkboard picture frames with the Station Labels attached to them. I had to get them and of course couldn't find exactly what I wanted. I did grab some 3x5 frames with a shadowbox effect. I removed the glass and cut up some scrapbook papers to color coordinate with my table colors (red, blue, green, purple). I have table buckets in these colors to keep materials organized. I have even spray painted the backs of my student white boards to coordinate as well.

Yesterday I noticed that the Coordinator picked out one or two students to highlight for each activity. I found these great small plastic traffic cones printed with "Great Job!" "Awesome!" or "Way to Go!" I grabbed a couple of these to give out at each table to "Make You Famous" and know who to call on when I need a student to explain. I will watch for the student who mostly seems to understand the math behind the concept to give this award to.

I also grabbed some Mardi Gras beads - 8 for a $1 with colors that coordinate with my tables. When the students arrive for my class next week I am going to ask them to select a color and sit at that table as a means of separating my groups on the first day. I will then assign tables according to ability for the next two days. This requires some quick assessment of these new students as they work through the math activities on Day One.

Now, on for today's Math Work:
Focus - Variables - a symbol that takes place of the unknown

We started with Math Vocabulary and worked through their definitions. Another estimation from this great site called Estimation 180. It has enough for EVERY day of the school year...umm, hence the name, right?

We worked through another set of Number Talks. Today the strand was Doubling and Halving where the students will try to break apart or 'decompose' one of the factors - 3 x 2 x 6 - to make it easier to handle. My Fourth Graders haven't been introduced to PEMDAS, so that conversation didn't come up. The students did fine with this and even with the Commutative Property problem. What caused them trouble was when we extended it to a four digit expression - 6 x 6 x 2 x 12. They started zoning out and were not confident in their strategies. We moved on after some extended Wait Time. Remember - Today is not the time to teach new concepts.

Currently, we are working through some Multiplicative Comparison Problems. Asking the students to discuss what they already know and what they need to know gives them a focus. The problems were picked because they included skills that the students should already posses, they required them to explain or prove their thinking, and included an engaging portion that activates what they will be learning in an upcoming lesson.

There is an Activating Question first, kind of a We Do. A Teach Question, like an I do. Then an Active Engagement Question, You Do. Students need to talk out what they already know and what is the question asking us to solve. Can they write an equation? You can refer back to the Anchor Chart to help them understand that words like 'is' and 'times' translate into math symbols. We want to get the students to be thinking about the 'variables.' They can use their number lines to show the sets from the problems.

We moved into Workstations next. There are four and students are given 20 minutes at each. There is an I\ndependent station where students work with pencil paper questions. There's a Group Work station where they are to discuss with each other how to approach and solve the problems provided. The Teacher Led Workstation has three Multiplicative Comparison problems that uses the same numbers each time, however you are guiding the students to see that the product will NOT always be the same. Students are given permission to use number lines, white boards, and snap cubes to help them solve. The computer station uses MathPlayground to check their understanding of multi-step word problems. Students work independently here and if they finish early they can choose a different game from this site to work on.

We started a Three Act Task. If you aren't familiar with teaching method, I'm going to give you some homework to research it before tomorrow's blog post.

See you then!

Math - It's What's for Breakfast Day Two

Teachers, congratulations if you got through yesterday's post. Summer Brain is a real thing, people. Once those school buses drive off the lot, it turns on. So kudos if you managed to get through Day One of Summer Math Institute with me!


Today the teachers arrived a half hour before the students in order to preview the day. The biggest thing our coordinator stressed was that we need to 'Step Back' and let the students take over. This session is not for teaching any new skills, it's strictly to observe how students approach and attack math problems. We want to witness their reasoning skills in action. As teachers we can notice concepts that we need to address during tomorrow's mini-lesson or bringing up in small groups as needed.


12 students came tumbling into our room and we got right to work asking them to pick out a Math Vocabulary Sticker to wear for the day. In their journals they have a spot for them to write out what they think their term means and illustrate it. We shared those out loud with the group. They were a bit shy and needed some coaxing, but this activity got them talking and thinking about math already.


We are focusing on strategies to bring NUMBER LINES into more math lessons this week. So we had some activating strategies to see what the group was already capable of doing. We handed out a plastic one that had a blank side and a ticked side. It was interesting to see how few of them actually understood how to use these as a tool.


Another issue I noticed to address with these students is as they approach math exemplars, or word problems, they seemed obsessed with taking whatever the first two numbers are in the problem and adding or multiplying them. To slow them down at the beginning of the year don't stress out on finding the answers but rather concentrating on deciphering the problem. What do you know? What do the numbers mean? What are they asking you to do?


Number Talks was a huge "Aha Moment" for me when I first saw this strategy at an earlier institute. Sherry Parrish (pdf - Number Talks video - Sherry Parrish ) is the Number Talks guru. It basically asks children to explain their thinking and use those strategies to teach the rest of the class additional ways of solving problems. It was interesting to listen to the students talk through their math. We had to cringe when students were off with their reasoning, but it helped us to see where holes were and how to address them in later math lessons.


The students were also asked to reflect on the class. They had a survey to complete sharing what they are already comfortable with in mathematics and then they wrote in their journals about Something I found challenging today… Tomorrow I am excited about…


Day One was a juggling act as we got used to the kids and they got used to us. Using the materials and showing their math thinking caused a lot of confusion. But by Day Three I think they will be experts.

Wednesday, May 31, 2017

Math-It's What's for Breakfast - Day One

Umm, what was I thinking? It is 8:05 A.M. on my first official day of summer vacation. Here I sit in a school cafeteria, learning about how to teach MATH! It is start of the 2017 Summer Math Institute. I have attended several of these in the past and gotten tons out of them, but only as a participant. Somewhere along the way my name was submitted to TEACH the class this year.

Our first order of business was an ice breaker called Math Mingle. Think of those fresh faces on the first day of school full of interest, yet still doubtful. Ask them to stand up and introduce themselves to other people in the room, a.k.a. mingle. After a brief period call "Freeze" and give them a task to solve such as: "Make a group of people that share the same number of letters in their first name." Students will arrange themselves into groups by calling out numbers or holding up fingers, etc. Once that is settled ask them to start mingling again and repeat the process. Depending on the age of your students you can create appropriate math level tasks. Since I teach Fourth Grade I could ask my class to "Form groups that equal the same number of cups in 2 quarts," or "Form groups that has the same number of equal sides as an isosceles triangle."

Next was a 5-minute game of Math Pictionary. One person is given a card with 18 grade level appropriate terms on it. They will draw each term without speaking, trying to get their team to say the correct word. A point is scored for each correct guess. Extra point is given at the end if the drawer used no numbers or words in their drawing. You can use this as another ice breaker to see how much they already know or retained from last year. You could also use this as a review once you are finished a new unit.

Here is a suggested vocabulary list for the beginning of Fourth Grade:

1. Commutative Property 2. Array 3. Isosceles Triangle 4. Pictograph 5. Fraction 6. Elapsed Time 7. Tens Place 8. Rounding 9. Sum 10.

Time for some professional development. We read an article on the research behind introducing algebra at the elementary level and shared sentences, phrases, and words that stood out to us. It was interesting to think that primary students could still reason out answers to expressions that ask them to solve for unknowns without any direct instruction.

Now we are thinking about Vertical Progression of a standard. Our county has broken down each standard and provided Achievement Level Descriptors in grades 3-5. They are finalizing the K-2 as we speak. We were given a table with Emerging, Developing, Proficient, and Distinguished. The standard was broken into each category onto small cards. Our table was charged with the task to organize them into the correct categories. We were successful at our table, by the way. It's important to think about how students are performing on each standard as you form groups and assign tasks. This is a great way to create your small groups and differentiate according to their strengths. It also helps to think about how to reduce a standard down to its smallest parts in order to scaffold for those students that are starting at the Emerging Level.

After a short break we are smacked back awake. We are struggling through a Mobile Puzzle, or Logical-mathematical puzzle.

To me this is a Distinguished Level Task. To give this to a student who is working off of an Emerging Level, like me, they would check out pretty quickly after being easily frustrated. This task would require a lot of scaffolding for them to see the rules and patterns of how these numbers balance and relate to each other.

We broke for the day. Whew! Summer Brain is already setting in.