During today’s 3-8 ELA sessions, Expeditionary Learning focused on meeting students’ needs by providing participants with transcripts of actual moments observed in classrooms where the modules are being used. The transcripts included exchanges between teachers and their students of various levels of language acquisition. Groups discussed the intervention strategies used by the teachers in the transcripts. They also talked about other interventions the teachers could have used to help more students be successful. Discussions resulted in a great exchange of ideas and the sharing of strategies that have been successful for some and not so successful for others. Teachers reflected on the day’s learning about teachers’ questioning, probing and responding habits in the classroom.

Expeditionary Learning also provided an update on some of the ELA modules currently in revision:

• Grade 4 Module 1A (previously Module 1) is under revision by NYSED and will be posted this summer. This module will still focus on The Iroquois, but it will include Eagle Song as an optional independent read. A new addition will be The Keeping Quilt which will be used as a read aloud and will only require a teacher copy.
• A new option for teachers will be Grade 4 Module 1B, a module with a focus on poetry. Texts will include A River of Words: The Story by Jen Bryant (teacher copy only) and Love That Dog by Sharon Creech (one per student).
• Grade 5 Module 4 is also undergoing some revisions. The text Eight Days will remain, but Dark Water Rising has been removed. Unit 2 will be revised during the 2014-15 school year, with no new texts being required.

# Module Focus: Grade 5 Math Module 5

The Grade 5 presentation focused on the material covered in Module 5: Addition and Multiplication with Volume and Area. Participants practiced lots of hands-on activities in order to experience the progression students experience with developing their concept of volume and area. Students first experience calculating volume by building figures and counting unit cubes. Students construct open boxes and calculate volumes by “filling” in the box. They then experience volume pictorially through the use of dot paper and constructing cubes.

There is much discussion in the module about composing and decomposing right rectangular prisms using layers, which helps with students’ conceptual knowledge of what volume actually means. There is no mention of a volume formula in Topic A. Topic B is where the multiplication formula is introduced with the concept of layers. Students also explore the connection between volume in cm and liquid volume in mL. We were able to see the liquid volume increase by 1 mL after the dropping of a cubic centimeter – very cool!

Application problems were presented at this point, such as:

• A small fish tank is filled to the top with water. If the tank measures 15 cm x 10 cm x 10 cm, what is the volume of the water in the tank? Express answer in Liters. What if after a week, water evaporates so that the water level in the tank is 9 cm high? What effect does that have on the volume of the water? How many Liters?
• This is an interesting problem in that students can just take off the “layer” from the original water level, or they can re-calculate with a new height of 9 cm.
• A shed in the shape of a right rectangular prism measures 6 ft. long by 5 ft. wide by 8 ft. high. The owner realizes that he needs 480 cubic feet of storage. Will he achieve this goal if he doubles each dimension? If he wants to keep the height the same, what could the other dimensions be for him to get the volume that he wants?
• This problem lends itself to discussing what happens to volume when you double one dimension, two dimensions, or all three. The “create a sculpture” activity in lessons 8-9 is an opportunity for students to express their creativity, while at the same time apply the concepts and formula of volume to design a sculpture within a given set of parameters. The activity is graded with a rubric used by the students. Participants discussed the value of having students use a rubric. Peer review always holds students more accountable, but the peer review also ties into the Mathematical Practice of critiquing the reasoning of others.

Topic C shifts the focus from volume to calculating the area of rectangles with fractional side lengths.  Once again, this demonstrated an excellent transition from concrete, pictorial to abstract. Students tile a rectangular region using patty paper, then draw the image on white paper (area model), and then use prior knowledge of area (partial products) and the multiplication of fractions to calculate the area. Participants practiced this transition using mystery rectangles. The topic ends with application problems that ask students to decide which process is more efficient and whether they should deal with improper fractions or convert to mixed numbers.  We want them to say “It depends.”

Topic D uses the cutting apart of trapezoids and parallelograms in order to take a look at the properties that exist for each, leading the student towards success in being able to create a hierarchy of quadrilaterals that go from most general to specific. Excellent visual activities were done here with parallelograms constructed by the group so that participants had a wide range of parallelograms. Activities showed the angle relationships that exist within these shapes (consecutive angles supplementary, all four angles add up to 360). Participants looked at diagonals for parallelograms and great questioning techniques were modeled in regards to answering the question, “will the diagonals always be bisected, or are they ever the same?”  Angle measurement was recommended as a fluency activity. An excellent end to an excellent week here at NTI.

During this morning’s grade 5 math session, participants worked through the Module 3: Addition and Subtraction of Fractions.  The first two lessons (topic A) review grade 4 standards and the concept of equivalent fractions.  Students use paper folding activities to demonstrate equivalent fractions, which helps make the concept very concrete. They use visual modeling via arrays and number lines to help make meaningful connections and the relationships that fractions have to one another.

Topic B is where students encounter fractions with un-like denominators.  They know the language of 1 apple +1 apple, 1 third + 1 third, so when they encounter 1 third +1 half, they know the units are not the same and that they need to make the units the same (common units).  Lots of work with arrays is involved here and there are some struggles, but overall the visual model helps the transition from concrete to abstract.

The group spent a lot of time on a two-step word problem from Lesson 7 that involved subtracting from a whole with uncommon units.  The solution was presented two different ways using visual models (arrays).

For topic C, participants took a look at three student solutions to the problem 3 3/5 – 2 ½.  It was interesting and exciting to see students use unbundling and decomposition that they saw in previous grades with whole numbers, and applying those concepts to their work automatically with fractions.

Topic D focuses on the problem-solving practice and application of the concepts learned. Multi-step problems are tackled with various strategies. The module does a nice job of showing the progression of equivalent fractions, making units pictorially, making units numerically, and then being able to apply knowledge to solve problems that involve addition and subtraction of unlike fractional units.

# Living an Elementary ELA Lesson

During Thursday’s afternoon ELA session, teachers took on the role of the student and started with a reading of the non-fiction article “Characteristics of a Multinational Company” in order to come up with the gist of the article. This activity led into another where the session participants could then read and find the gist of another text around which the lesson is based, “The Red Cross.” The participants then used a graphic organizer (3-column Note Catcher) to complete the tasks associated with the Taking Notes Task card protocol. Through close reading of the article, everyone was able to identify key vocabulary terms and find text-based evidence to justify their definitions, just as their students would do. The graphic organizer is a tool that helps students to define a new term/concept based on the information gleaned from the two texts. In this case, the two articles were used to identify what a multinational aid organization is.

Through a Chalk Talk, the participants discussed their own notes based on the articles they read. Then, through the Think Pair Share protocol, ideas were exchanged about the best way to respond when a community is struck by a natural disaster. Participants shared their ideas with the rest of the group in order to explain key ideas from the texts they read. After “removing their student hats,” the teachers discussed the benefits of the protocols and how they are an effective way to address the Speaking and Listening standards. One major benefit was that the protocols helped to grow their thinking through the sharing of mutual ideas and they can offer help to students who need their thinking redirected.

Session participants read the lesson that was the source of the day’s activities and looked for evidence of collaboration, protocols, and conversations. This lesson is a good example of incorporating the Speaking and Listening standards into a Common Core-aligned curriculum. A question was asked about the appropriateness of the protocols for various lessons. Each protocol in the list provided on EngageNY is prefaced with a purpose so that a teacher can decide which protocol to use depending on the goals of the lesson. The session concluded with teachers reflecting on what kinds of classroom management practices need to be in place in order to foster a collaborative environment.

The remainder of the afternoon was spent looking at how protocols can improve literacy skills and be effective in a collaborative classroom environment. Four Corners and Fishbowl were put into practice in this session. The teachers again played the role of the student for the Four Corners activity. Here, the teacher/students had to choose (from 4 options) the most important thing the Red Cross does when communities are struck by natural disaster. Conversations were text-based and gave the teachers an opportunity to see this protocol in action through the eyes of their students. They then participated in the Fishbowl protocol where volunteers discussed the purposes of the Red Cross based on the notes they had taken throughout the “lesson.” The emphasis here is on relevant notes, relevant information, and relevant evidence. Observers of the Fishbowl conversation had to look for evidence of relevance in the conversations along with other qualities including how the participants in the discussion behaved throughout the exercise. Everyone spent the remainder of the session developing a rubric for Speaking and Listening standards.

The activities and texts in these sessions came from Grade 5, Module 4, Unit 3, Lesson 3.

# Exploring Algorithms in Morning Math Session: Grades PreK-5

The morning Math P-5 session began with participants getting warmed up, spending three minutes doing mental math problems. They discussed how to solve addition, subtraction, multiplication, and division problems not using standard algorithms, and to compensate and deconstruct numbers and use the “hidden” associative and distributive properties. The activity set the focus for the morning which was to examine and practice algorithms for the story of functions. These algorithms will provide a fall-­back strategy for students that will always work.

Participants saw examples of how to use the distributive property for multiplication and how algorithms are cyclic in nature: add ones, add tens. Multiply ones, multiply tens.

Participants looked at an array of examples for multiplication and saw an alternate algorithm for multiplying by multiples of ten. The session also covered decomposition and the role of the magnifying glass in subtraction. One participant said, “I wish my teachers explained what was going on behind the scenes as clearly as these algorithms do!”

Later, the session took a quick trip through division algorithms. Participants went over a place value chart, finding the missing side of the array, dividing by multiples of 10, and the final division algorithm covered in grade 5. Each algorithm builds upon the next step.

The second half of morning session focused on looking at Grade 5 Module 2 – multiplication and division of whole numbers and decimal and fraction operations. Participants read the progressions document for Numbers & Operations in Base 10. A question was raised about how to use the progressions in districts in the current form because they are challenging to read, so districts need to somehow make them more palatable for teachers. Participants reviewed the Module 2 overview and compared lessons 2 and 17. The lessons are very similar in approach, but one deals with multiplication while the other covers division. Both lessons place an emphasis on rounding, place value patterns, and fluency with multiplication facts, and both lessons use examples that clearly show what happens when increasing/decreasing by powers of 10 through multiplication and division.

# Thoughts from the NTI Math Session: Prekindergarten – Grade 5

One of the most popular sessions of the opening day of the July 2013 Network Team Institute focused on PreK-Grade 5 math modules. The morning portion started with Module 2 for fourth grade, and the initial focus was reviewing the geometry progression document and determining the measurement concepts that students are expected to learn. When looking at the module overview, participants liked the foundational standards, particularly the vertical picture and great connection made between Modules 1 and 2.

Taking a look at the end-of-module assessment and how an understanding of it is important for educators, many expressed concerned that the unit is only five days. They wondered if the goals of the assessment could be accomplished. This will be a topic during the afternoon session.