F A L L 2 0 1 5
th
As I’m sure many of you have heard, this will be my first year of teaching at Highland’s Elementary.
As part of my contract, I was given
$1500 to spend on materials
(manipulatives, resources, technology, curriculum, etc.) to get my classroom up and running.
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Welcome to Room 205! I have spent the summer eagerly awaiting the arrival of my Highlands Huskies! I can’t wait to get to know you and your children and begin our time of learning together. I have spent countless hours planning lessons for this year, making sure to align the state learning standards for our grade level with my curriculum and personal expectations for my students. This first newsletter will help explain the choices made in the realm of mathematics. Don’t hesitate to contact me with any questions you may have about this newsletter or otherwise.
I spent this summer studying the 5 grade state standards and making decisions about how to best teach this content. Based on these purchase as it aligns to standards and effective teaching strategies. th decisions, I spent my money as best as I could. In this newsletter you will find the breakdown of my expenses and the rationale for each
I’m so thrilled to have this opportunity to enrich my classroom and teaching. As you read on, I hope my passion for teaching and intentionality of instruction are clear.
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September 11
Students go on a nature hike in our local mountains.
September 22
Come learn more about what the students will learn this year.
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October 5
Students work to serve the community.

THE HUSKY WEEKLY FALL 2015
These are the requirements currently set for curriculum in the state of Washington. For each grade they are outlined by categories and sub-categories for each subject. Below are summaries for the 5 th grade math standards and how I will implement teaching them in my classroom.
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There are three main focuses of fifth grade mathematics instruction: developing fluency of fractions, extending knowledge of division and place value concepts to decimals, and forming an understanding of volume. Fractional study includes all four operations. With addition and subtraction, students master computation (including estimates).
With multiplication and division, students use the meaning of fractions to understand why the procedures for these make sense.
With decimals, students will master the same concepts as fractions.
They will understand the procedure based on the properties of operations and the base ten system. They will use place value concepts to apply all four operations to decimals. Students then relate decimals to fractions. Lastly, students learn about volumes and threedimensional space. They understand the concept behind the algorithm through use of unit cubes. Then they use this understanding to solve real world and mathematical problems of volume.
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THE HUSKY WEEKLY FALL 2015
This year marks an introduction to operations and algebra. This involves:
 Writing and solving expressions
 Writing and interpreting simple expressions of calculations without solving them
 Analyzing patterns and relationships between corresponding terms of two numerical patterns
For many students, this may seem like an abstract concept. Therefore, we will introduce it alongside our daily story problems. By combining these two skills, students will be able to better understand where equations come from and what they represent. Cementing a solid basis for these skills at a young age is very important for mathematical growth. Therefore, we will work to incorporate manipulatives into our practice in order to help students visually understand algebra. Both the 2-Color Counters and Unifix Cubes will be useful with this instruction due to their uniform nature. This way, while equations can be a more difficult concept to represent with manipulatives, I can work with the students to understand the process of moving cubes and counters as they are manipulated by the operations. This takes the process and extends it beyond the numbers on the page. Therefore, this will incorporate the
Common Core Standard for Mathematical
Practice (CCSS.MP.2) “Reason abstractly and quantitatively.” While equations have a quantitative aspect, they’re also an abstract concept to comprehend. Therefore, they need to be taught as such. By beginning instruction with manipulatives, students have something concrete to move around for their thinking.
After this, we would move on to a pictorial level where students can use a drawing or diagram to understand the situation. Lastly, we move to the abstract concept where students can model a situation as an equation of numbers and/or letters. This is called a CPA approach. This scaffolding allows students to gradually bring a more tangible concept like equations into an abstract understanding in a less threatening way. CCSS.MP.4 “Model with mathematics” is also tied in with this content. After all, writing equations involves taking something such as a story problem and modeling that situation in a numerical way. Lastly, CCSS.MP.1 “Make sense of problems and persevere in solving them” is especially pertinent with this concept.
Like fractions, algebra can be a difficult concept for students to grasp. Therefore, while this standard will be important for every concept we learn this year, it will be especially necessary with this unit.
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THE HUSKY WEEKLY FALL 2015
This concept will be at the center of our mathematical thinking all school year. This includes skills such as:
 Understand the place value system’s relationships between terms of multi-digit numbers
 Explain patterns with multiplying and dividing by powers of ten and the number of zeros and location of the decimal place
 Use whole-number exponents to write powers of ten
 Read, write, and compare decimals (to thousandths)
 Use place value knowledge to round decimals
 Effectively multiply multi-digit whole numbers
 Find whole-number quotients for division problems with up to four-digit dividends and two-digit divisors, explain with equations, arrays, and/or area models
 Manipulate decimals to hundredths with four operations-use models and explain reasoning
Place value is a very difficult concept for many students to understand. Often, they learn the algorithms (written methods) for addition or multiplication and think that they understand the content, when really they were just memorizing a process. This is the reason I bought so many base-ten manipulatives. This is a concept students need to have down in order progress in math. Therefore, Place Value Safari, Digit Detective, the Place Value Flip Stand, the Unfix cubes, and the 10 Blocks are all to help cement this idea. As with equations, we will use a CPA approach. We will begin by using the manipulatives, move onto diagraming the problems, and finish with the paper algorithm. In general, many students have trouble with place value because of the lack of confidence with memorized facts. Therefore, by using the flashcards I ordered, students are able to practice these facts without assistance. This place value concept involves CCSS.MP.8 “Look for and express regularity in repeated reasoning.” Because baseten is the foundation for our mathematical system, students will be able to use repeated reasoning in the methods used to solve problems to develop proper knowledge and skills for adequately solving addition, subtraction, multiplication, and division problems.
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THE HUSKY WEEKLY FALL 2015
Fractions is a unit quite its own. Like equations, the math often proves simpler than an understanding of the concept as a whole. Below are examples of things we’ll be working on throughout the year:
 Apply knowledge of division to understand, compute, and apply to real world problems the division of unit fractions by whole numbers and visa versa
A conquering of this long list of skills will put
 Use common denominators to add and subtract fractions
 Solve word problems by adding and subtracting fractions with visual models or equations and use number sense to estimate and determine reasonableness of answers
 Understand fractions as division of numerator by denominator and use this to solve word problems that lend an answer in fraction form
 Apply knowledge of multiplication to multiply fractions or whole numbers by fractions and be able to interpret answers
 Use knowledge of multiplication and area to solve those with fractional side lengths and represent with area model
 Understand multiplication as scaling
(resizing) comparing product to factors without performing operation
 Interpret multiplication by explaining what happens when we multiply by fractions less than one and greater than one
 Solve real world problems by multiplication of fractions with models to represent components our students in an advantageous position for middle school math. However, it will not be an easy road. Fractions is a concept that will require ample small group work. Like equations, it is something that students often have a very difficult time wrapping their heads around.
Therefore, like equations, Mathematical
Practices 1, 2, and 4 will be utilized. Likewise, we will use CCSS.MP.7 “Look for and make use of structure” to develop algorithms and strategies for solving fraction problems. As far as instruction is concerned, we will need a CPA approach to survive. This will involve beginning with manipulatives. For this unit, Pattern Blocks and Cuisenaire Rods will prove the most useful.
Both of these manipulatives are made for fractions because certain pieces combine to form others. We will then move on to a pictorial understanding with drawings and diagrams, and finally, only when students are ready will we solve numerical problems without aid of manipulatives or drawings.
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THE HUSKY WEEKLY FALL 2015
Measurement and Data is far beyond measuring lengths. This year, concepts will become much more abstract in the real world with 3D space:
 Convert units within a given system and use these to solve real world problems
 Make line plots to display a data set of fractional measurements, use operations to analyze/manipulate data
 Understand volume as a component of solid figures that is measured in cubic units
 Recognize volume as the amount of unit cubes that can fit inside of a solid figure without gaps/overlaps
 Measure volumes by counting unit cubes (with a multitude of units)
 Relate volume to multiplication of edge lengths through use of a right rectangular prism and unit cube model, use this to represent whole-number products as volumes i.e. associative property of multiplication
 Apply formulas V=l x w x h and V=b x h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths
 See volume as additive and apply this to volumes of solid figures that are made up of two to solve real world problems
Measurement and data are concepts that will be especially fun to study this year. With volume, we will use Unifix Cubes and our Geometric Shapes to discover the formulas for volume of different shapes. In true Dewey fashion we will learn in a hands-on, exploratory way. We will learn to combine these manipulatives to create a solid shape. This will naturally lead us into the topic of volume and what that really means. We will then use drawings to represent these discoveries. Lastly, we will apply this learning to the algorithm on paper. While these processes will reference CCSS.MP 1, 2, and 4, they will also incorporate the use of Practice 5 “Use appropriate tools strategically” and Practice 6 “Attend to precision” due to model making with rulers, tape, and the proper scaling that is necessary in this process. Lastly, Practice 3 “Construct viable arguments and critique the reasoning of others” will play into our study. The applicableness of this unit to the real world will allow us to work through real world problems and how we should solve them. We will look for ample ways to apply our learning in tangible ways in the classroom as well as with problems that professionals may face. It is my hope that this concept will inspire students to care about mathematics. While other units may be difficult to extend past their abstract nature, this unit will naturally fall into place in their everyday lives.
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THE HUSKY WEEKLY FALL 2015
Geometry will be our smallest unit to cover this year. After all, geometry is a very abstract concept and we’ll barely be skimming the surface. We’ll focus on two aspects in order to get a better feel for what geometry is and how it relates to us:
 Understand the coordinate plane and how to graph points and use it to solve real-world problems
 Classify two-dimensional figures in relation to one another based on properties and understand that attributes of a category also describe the subcategories of that category
Thankfully, both of these skills are very tangible to teach to students. We’ll practice graphing on the coordinate plane to ensure its familiarity.
Then we will talk about what these points and lines really mean. While it’s difficult to have a concrete level for graphing, this is a pictorial level skill that is accessible to students. Then we will be able to extend this to a more abstract nature. Because of its application to the real world like measurement and data, geometry will also utilize the Mathematical Practices. In fact, it seems as though all of them could apply to this subject in some way. While
Practices 1, 2, and 4 apply to any concept with abstract and quantitative measures, the other
Mathematical Practices really have to do with the deep thinking that goes along with geometry. After all, taking something from a graph and using that to solve a real world problem requires a fair amount of reasoning, thinking, modeling, structure, and precision.
Classifying two-dimensional figures is really a lesson in patterns and similarity. By classifying these shapes, students are using higher order thinking to compare similarities and differences and the level of each. On the one hand, students need this knowledge for their mathematical learning. On the other hand, this practice will serve useful in other comparisons of patterns and attributes made with more complex math later on.
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THE HUSKY WEEKLY FALL 2015
There are a few ways that technology will be used in my classroom. First and foremost, Powerpoint presentations will be projected daily with key information to guide instruction of content ideas. The document camera (and possibly ACTIVBoard) will be used to demonstrate techniques and walk students through problems in a more actively visual way. Due to a lack of computers for every student, other technology will not be at the core of my instruction. Because students have such different abilities by the 5 th grade, we will be utilizing a district-subscribed program “Dreambox Math.” The beauty of this program is that it helps students by supporting them with educational games in the Common Core areas that they struggle with.
Therefore, this one resource covers all of Common Core, making it all encompassing for all content areas. While some days we will have time to do this in class, the beauty of Dreambox is the accessibility of it on any computer or tablet, therefore extending practice to home.
I believe that students deserve an education. I believe that everyone has the right to learn. Therefore, as an educator, I work to assist students in order to help them learn to the best of their ability. I believe in open discussion in the classroom and exploratory learning. While some people may argue that this approach takes more time than the traditional one, I argue what efficiency is worth in the classroom.
After all, if we spend more time on an activity, but students walk away with a whole understanding of the concept then we’ve used our time much more efficiently than a shorter activity that needs to be repeated several times in order for students to understand. While many people think of math instruction as worksheets and repetition, I take a more Dewey approach. Dewey was a philosopher that believed that you “learn by doing.” This is how I run my classroom. With the CPA approach I discussed earlier, this can become a reality. With each step, students are doing something that extends their knowledge a bit more than before. As the psychologist Bruner believed, students can only base knowledge on concepts that they have already mastered. Therefore the concrete, pictorial, abstract approach guides students through this process in this way. This is the practice that I use to center my classroom. While I will work hard to teach Common Core curriculum, I will never lose sight of my students, their needs, and how I can best differentiate my instruction to help them learn as much as possible.
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THE HUSKY WEEKLY
FALL 2015
Storage closets house math materials, curriculum, and resources not necessarily all used on a daily basis
Shelves above computers hold manipulatives in clear bins for easy access, computers used for math exploration games
Rug used as another center for group work
(student or teacher led)
Tables promote group work and exploratory learning environment
Table used as center to assist struggling students with skills & methods
(whiteboard work for quick practice)
Projector (and possibly
ACTIVBoard) allow technological integration, doc. camera and front board used to demonstrate skills and concepts
While this may seem like a no-brainer, there is a science to storing materials. Shut them away and they are never used, however, it isn’t practical to always have them out. Therefore, I intend to store my manipulatives in bins on shelving in the back of the classroom. Therefore, whenever the students may need them, they are free to walk back there themselves and take them out without disturbing the class. With clear, labeled bins, they are easy to identify and keep organized. Because manipulatives are such an essential tool in mathematics, I will be sure that the students understand that they’re encouraged to use them. For many students, resources like this will help them access previously unreachable grade level content. Therefore, I will rarely discourage their use. Only if the manipulatives are being misused (for reasons other than math) will I make students ask permission to use such resources.
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THE HUSKY WEEKLY FALL 2015
Material
Wooden Base 10 Block Place Value Set
Place Value Safari
Digit Detective
Place Value Flip Stand
Graph Paper (1 cm squares-500 sheets)
Nasco's Dry-Erase Markers (box of 30)
Nasco's Single-Sided Unlined Dry-Erase Math
Board
2-Color Counters (pkg. of 1000)
Unifix Cubes (box of 1000)
Wooden Pattern Blocks (250 blocks)
Individual Cost ($) Quantity
78.50
21.50
17.50
6
1
1
13.95
17.50
23.95
7
1
3
3.55
22.30
77.95
15.95
30
1
2
5
Connecting Cuisenaire Rods (Introductory
Multi-Pack Set: 6 sets of 74 rods)
Cuisenaire Wooden Rods (Introductory Set: 6 trays-444 rods)
Playing Cards-Giant Face (set of 6 decks)
Three-Corner Flash Cards (addition & subtraction)
Three-Corner Flash Cards (multiplication & division)
Clearview Ruler (pack of 12)
14-Piece View-Thru Geometric Shapes Set
Sharp EL-2435 Solar Basic Handheld
Calculator
Common Core Mathematics Collections
Books (Grade 5)
The Hershey's Milk Chocolate Fraction's
Book
Apple Fractions Book
TOTAL
60.50
65.95
6.50
6.90
6.90
4.65
36.50
3.32
59.95
5.16
4.00
1
1
1
1
30
3
5
1
1
5
3
10
Total ($)
471.00
21.50
17.50
97.65
17.50
71.85
106.50
22.30
155.90
79.75
36.50
99.60
59.95
5.16
4.00
1495.56
60.50
65.95
19.50
34.50
34.50
13.95

THE HUSKY WEEKLY
As a first-year teacher, I cannot stress enough what your support means to me. Therefore, I want to thank you ahead of time for giving me your respect this year as I try and teach your children to the best of my ability. I can’t wait for what the year has in store for our 5 th grade class. Highlands is an amazing community that I am blessed to be apart of and I can’t wait to watch Room
205 grow this school year!
FALL 2015
Garrett, L. (1997). Dewey, Dale, and Bruner: Educational philosophy, experiential learning, and library cataloging instruction. Journal of education for library and information science,
38. Retrieved from: http://www.jstor.org/stable/40324216
Gujarati, J. (2013). Deeping mathematics teaching and learning through the concrete-pictorial-abstract approach. Strategies for
Successful Learning, 6. Retrieved from: http://www.ldworldwide.org/educators/strategies-forsuccessful-learning/1096-deepening-mathematics-teaching-andlearning-through-the-concrete-pictorial-abstract-approach
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State
Standards. Washington, DC: Authors.
Van de Walle, J.A. (2012). Elementary and middle school mathematics
(8th ed.). Boston, MA: Pearson.