Meeting Students’ Needs; Grades 3-8 ELA Module Updates

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.
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Module Focus: Grade 4 Math Modules 6 and 7

The focus of Thursday’s grade 4 presentation for mathematics was on the content of Module 6 and Module 7. Module 6, “Decimal Fractions,” allows students to extend prior knowledge of fractions by seeing decimals as an application of fractions. The progression of the module allows students to see that decimal and whole numbers behave the same way, and that working with decimals just increases their sense of number. Participants were reminded that that even though scaffolding is embedded in the lesson content, teachers may need to provide additional scaffolding measures. It is important that throughout any module, teachers amplify language. Teachers need to use academic language and be clear, effective and consistent. Teachers also need to develop conceptual understanding of the content matter by continually going from the concrete to the pictorial to the abstract. Too many visual representations might be ineffective, so teachers need to be strategic when choosing the best modeling techniques to use for the pictorial. Lastly, teachers need to model strong questioning techniques and demonstrate how to speak and write mathematically. Sentence frames and turn/talk opportunities are some examples of how to accomplish this within a lesson.

Participants started off by looking at the end-of-module assessment and working on question 6. They discussed how they could use the assessment as a planning tool and how it would guide the delivery of the lessons.

Module 6 starts off with students exploring tenths concretely through length, weight and capacity. A scale and pre-filled bags of rice was used to demonstrate how students can decompose 1 unit (kg) into 10 bags or tenths. What does the scale say? 0.1. Other decomposition problems are discussed in this module and the number bond is used. The same methodology is used in earlier grades for bundling tens and working with teen numbers. Teachers saw a strong connection here and were excited, saying “We just need to give this process time.” The overall goal of Topic A is for students to build fluency in writing decimal numbers three ways: as a fraction, as a decimal or in words.

In Topic B, students decompose tenths into 10 equal parts to create hundredths. Students model the meter stick with a tape diagram and quickly learn that tenths make us more efficient when counting hundredths. Sometimes we need to adjust the model depending on our learners; therefore, students not only work with tape diagrams but with area models and number disks to see the equivalence of 1 tenth and 10 hundredths.

Topic C gets students to apply their knowledge gained in the first two topics in order to compare decimals. Students continue using tape diagrams and area models to show their conceptual understanding of the decimal comparisons. Participants did an activity from Lesson 11 that involved cutting out decimal flash cards and ordering the decimal numbers from least to greatest. The decimal numbers were represented in various forms. Participants then needed to plot the decimals on a given number line and determine the best endpoints for the number line.

Topic D introduces the addition of decimals with tenths and hundredths, without using any algorithm. Students become more fluent with their conversions between the two in order to add and use decomposition strategies in the process. Lastly, money amounts as decimal numbers are introduced. Money is used to extend the students’ conceptual understanding of decimals while providing an application of the skills learned. Participants ended the morning session by going back to the end-of-module assessment and discussing what they learned as they were going through the lesson that would need to be reflected in the teaching of the modules.

The afternoon focus for grade 4 was on Module 7 that deals with exploring measurement with multiplication. Since fluency for grade 4 is multi-digit addition and subtraction, core fluency differentiated practice sets are used in this module. Lesson 2 contains the master copies for the 4 practice sets. A great feature of these sets is that each one is broken into 2 parts, with part 2 involving problems that do not involve re-grouping. Both parts, however, have the same answer key, which makes for simple grading.

Module 7 allows students to develop an understanding of the two measurement systems (metric and customary) and allows them to become fluent with converting between larger and smaller units. Great application problems that reinforce the RDW process are found throughout the module and students get to connect their problem solving with mixed units. An interesting approach is taken to time, as conversion is taught with the clock being an unwrapped number line. There is a strong connection here with previous work with number lines.

The module ends with 4 lessons that have year-in-review activities that focus on the area of composite figures, more fluency activities and games designed to solidify vocabulary used throughout the year. The presenters gave ample time throughout the day to work on problems and discuss. This was a very informative presentation that once again demonstrated the progressive nature of the modules and how they are written to build off of the prior knowledge of skills.

The materials for this session are available here:
http://www.engageny.org/resource/may-2014-nti-grades-k-5-math-turnkey-kit-for-network-teams

Module Focus: Grade 4 Math Module 5

The Grade 4 Math session on Thursday focused on the Module 5: Fraction Equivalence, Ordering and Operations. Number bonds, tape diagrams, and area models were used consistently throughout the module to strengthen conceptual understanding and develop confidence when working with fractions. This “fractional” confidence allows students to transition to concepts/problems of higher complexity, which was demonstrated as we went through the lessons.

Students start their fraction work off with experiencing problems that involve decomposing fractions using number bonds, similar to the work they did with number bonds and whole numbers in the earlier grades.  How many ways can you represent 5/6 as an addition problem? When answering this problem, students encounter how to express a non-unit fraction as a whole number times a unit fraction. The work here is extended to fractions that are greater than 1, such as decomposing 7/4 = 4/4 + 3/4 .

Fraction equivalence is explored using tape diagrams (paper folding) and area models.  Participants look at an application problem from lesson 5:

A loaf of bread was cut into six equal slices.  Each of the slices was cut in half to make thinner slices for sandwiches.  Mr. Beach used four slices.  His daughter said, “Wow, you used 2/6 of the loaf.” His son said, “No, you used 4/12.” Work with a partner to explain who was correct using a tape diagram.

This problem pulls in all content discussed so far, and solving the problem does not require a fractional algorithm. Fraction equivalence is extended to fraction comparison. Students combine knowledge of benchmark fractions with fraction equivalence to handle comparisons that involve fractions with common numerators, fractions with denominators of related units. The final goal is comparing fractions with denominators of unrelated units.  Topic D shows once again the link of the work done previously with decomposition and composition to the addition and subtraction of fractions with common denominators.  A new visual is added here, the number line with arrows.

Topics E and F add a layer of complexity to what has been learned by extending fractional equivalence and operations to fractions greater than 1. Based on their knowledge, students devise their own strategy for handling problems like 3 3/5 – 4/5. Some might decompose the 4/5 to be 3/5 and 1/5, and then solve the simpler problem of 3 1/5, which is 2 4/5. Others might decompose the 3 as 2 5/5 and now look at the problem 2 8/5 – 4/5, which is 2 4/5. Students practice converting between improper fractions and mixed numbers based on the context of the problem. Never is the traditional algorithm of how to convert a mixed number into an improper fraction discussed.  The module shows that the algorithm is not necessary.  The module ends with a re-visit to repeated addition of fractions as multiplication and shows the connection to the distributive property when solving problems like 2 x 3 1/5.  Visuals are used again here to help make the connection.

The remainder of the session presented educators with a plan on how to make choices with implementing the lessons within the given time frame that remains between now and the assessment. Pacing is a huge area of concern and many teachers are behind the timeline. So how do we adapt the lessons to support successful pacing while bridging gaps in prior knowledge, but not sacrifice the rigor?

A planning protocol was introduced that encourages teachers to look at the lessons further out, not day to day. Reading the module overview and studying the module assessments is the place to start in order to keep the purpose, sequence and delivery fresh in the mind. Next, teachers should read through the lesson and ask what major concept is necessary to successfully complete the exit ticket. Pay attention to the subsequent lesson and examine the exit ticket there. What is the relationship between the two exit tickets and what will be the impact of what gets cut out of the lesson to those two tickets? Teachers also always need to consider the needs of specific students in their classroom.

A Deeper Look at Grade 4 Math Module 4

Thursday’s grade 4 math afternoon session covered lessons from the Grade 4 Module 4: Angle Measure and Plane Figures. This module introduces students to seven new geometry terms in the first lesson that set the foundation for their progression to high school geometry. They draw points, lines, segments, rays, and angles and learn how to identify them with geometrical notation. By using a right angle template, students are taught to easily identify right, acute and obtuse angles in Lesson 2.

Physiometry fluency tasks are introduced in Lesson 2 and involve using arms to construct types of angles, which is fun and engaging. Continuing with the use of the right angle template, students study the relationships of perpendicular and parallel lines. A fun activity involves using the letters of the alphabet to identify segments that are parallel and perpendicular. Students will come to realize that points are needed in order to name segments. Attending to precision and communicating/critiquing the reasoning of others play a key role here.

Students are introduced to the concept of degree after visualizing the progression of ¼ turns, ½ turns, and ¾ turns using the two-circle manipulative that makes angles pop out and come alive. Students transition from using the two-circle manipulative to using a circular protractor, and then to using the 180-degree protractor when identifying angle types and measuring.

A hard-to-grasp concept is angle measure vs. arc length measure. When is an angle larger? Students will explore this concept using two circles, one smaller than the other. Each circle is folded into quarters, showing a right angle. Students will notice that the arc-length of the larger circle is larger than the arc-length of the smaller circle, even though the right angles forming the arcs are the same. The circles are excellent visual aids in this example.

Paper folding exercises that students will be using to understand angle addition and subtraction were demonstrated. These exercises will lead classrooms into the discussion of complementary, supplementary, and vertical angles and students will be able to solve missing angle problems based on these relationships that they can visually recognize. The vocabulary here is not part of the 4th grade, but provides great exposure and provides students with the skill of being able to visually recognize these relationships leaving 4th grade.

The remainder of the module focuses on classifying two-dimensional figures and lines of symmetry. Classifying quadrilaterals is always challenging (i.e., is a rectangle a square, or is a square a rectangle?). A nice presentation on the hierarchy of the “trapezoid” family was drawn out to help the audience. Students/teachers should start with drawing trapezoids based on the fact that they have at least one set of parallel sides. From there, progress to drawing just parallelograms, then just rectangles, then squares. This is a great activity to help students see the progression. The module is loaded with fun, engaging, and solid activities that will build the strong foundation needed for the geometry to come in later modules and grades.

Module Focus: Grade 4 Math Module 3

The morning session for grades 4 and 5 math focused on Grade 4 Module 3: Multi-Digit Multiplication and Division, where students see multiplication and division in action.  The standard algorithm is introduced in grade 4, but it is not a fluency for this grade level.  Multiplication is a fluency in grade 5 and division is a fluency in grade 6, so the intent of the module is to allow for the deep conceptual understanding of the process through the use of modeling techniques.

Participants took a look at division through the use of number bonds, array/area models, and place value/number disk charts.  This exercise provided a great visualization of the process.  Language plays a key role, with the correct use of the terms, “whole,” “quotient,” and “remainder” (how many are left). Phrases like “distributing evenly” and “decomposing” are important in explaining the process.

Teachers need to pick fluency activities that tie into the lesson well.  Participants looked at an example:

How many groups of ____ are in _____? Prove it by counting by ______.

The fluency activity will lead into the concept of “remainders,” an important link to the lesson.  Teachers need to make sure there is a connection with the fluency to the lesson objective.