6th grade mathematics - orange board of education · web view‘2nd grade mathematics unit 1...

6th Grade Mathematics

‘2nd Grade Mathematics

Unit 1 Curriculum Map: September 8th – November 9th 2016

Table of Contents

I.

Mathematics Mission Statement

p. 2

II.

Mathematical Teaching Practices

p. 3

III.

Mathematical Goal Setting

p. 4

IV.

Reasoning and Problem Solving

p. 6

V.

Mathematical Representations

p. 7

VI.

Mathematical Discourse

p. 9

VII.

Conceptual Understanding

p. 14

VIII.

Evidence of Student Thinking

p. 15

IX.

Second Grade Unit I NJSLS

p. 16

X.

Eight Mathematical Practices

p. 23

XI.

Ideal Math Block

p. 26

XII.

Math Workstations

p. 27

XIII.

Math In Focus Lesson Structure

p.30

XIX.

Ideal Math Block Planning Template

p. 33

XX.

Planning Calendar

p. 36

XXI.

Instructional and Assessment Framework

p. 38

XXII.

Performance Tasks

p. 41

XXIII.

PLD Rubric

p. 47

XXIV.

Data Driven Instruction

p. 48

XXV.

Math Portfolio Expectations

p. 51

Office of Mathematics Mission Statement

The Office of Mathematics exists to provide the students it serves with a mathematical ‘lens’-- allowing them to better access the world with improved decisiveness, precision, and dexterity; facilities attained as students develop a broad and deep understanding of mathematical content. Achieving this goal defines our work - ensuring that students are exposed to excellence via a rigorous, standards-driven mathematics curriculum, knowledgeable and effective teachers, and policies that enhance and support learning.

Office of Mathematics Objective

By the year 2021, Orange Public School students will demonstrate improved academic achievement as measured by a 25% increase in the number of students scoring at or above the district’s standard for proficient (college ready (9-12); on track for college and career (K-8)) in Mathematics.

Rigorous, Standards-Driven Mathematics Curriculum

The Grades K-8 mathematics curriculum was redesigned to strengthen students’ procedural skills and fluency while developing the foundational skills of mathematical reasoning and problem solving that are crucial to success in high school mathematics. Our curriculum maps are Unit Plans that are in alignment with the New Jersey Student Learning Standards for Mathematics.

Office of Mathematics Department Handbook

Research tells us that teacher knowledge is one of the biggest influences on classroom atmosphere and student achievement (Fennema & Franke, 1992). This is because of the daily tasks of teachers, interpreting someone else’s work, representing and forging links between ideas in multiple forms, developing alternative explanations, and choosing usable definitions. (Ball, 2003; Ball, et al., 2005; Hill & Ball, 2009). As such, the Office of Mathematics Department Handbook and Unit Plans were intentionally developed to facilitate the daily work of our teachers; providing the tools necessary for the alignment between curriculum, instruction, and assessment. These document helps to (1) communicate the shifts (explicit and implicit) in the New Jersey Student Learning Standards for elementary and secondary mathematics (2) set course expectations for each of our courses of study and (3) encourage teaching practices that promote student achievement. These resources are accessible through the Office of Mathematics website.

Curriculum Unit Plans

Designed to be utilized as a reference when making instructional and pedagogical decisions, Curriculum Unit Plans include but are not limited to standards to be addressed each unit, recommended instructional pacing, best practices, as well as an assessment framework.

Mathematical Teaching Practices

Mathematical Goal Setting:

· What are the math expectations for student learning?

· In what ways do these math goals focus the teacher’s interactions with students throughout the lesson?

Learning Goals should:

· Clearly state what students are to learn and understand about mathematics as the result of instruction.

· Be situated within learning progressions.

· Frame the decisions that teachers make during a lesson.

Example:

New Jersey Student Learning Standards:

2.OA.1

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

2.NBT.5

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

2.NBT.9

Explain why addition and subtraction strategies work, using place value and the properties of operations.

Learning Goal(s):

Students will use multiple representations to solve multi-step addition and/or subtraction situations (2.OA.1) and explain the connection between various solution paths (2.NBT.5, 2.NBT.9).

Student Friendly Version:

We are learning to represent and solve word problems and explain how different representations match the story situation and the math operations.

Lesson Implementation:

As students reason through their selected solution paths, educators use of questioning facilitates the accomplishment of the identified math goal. Students’ level of understanding becomes evident in what they produce and are able to communicate. Students can also assess their level of goal attainment and that of their peers through the use of a student friendly rubric (MP3).

Student Name: __________________________________________Task: ______________________________School: ___________Teacher: ______________ Date: ___________

“I CAN…..”

STUDENT FRIENDLY RUBRIC

SCORE

…a start

1

…getting there

2

…that’s it

3

WOW!

4

Understand

I need help.

I need some help.

I do not need help.

I can help a classmate.

Solve

I am unable to use a strategy.

I can start to use a strategy.

I can solve it more than one way.

I can use more than one strategy and talk about how they get to the same answer.

Say

or

Write

I am unable to say or write.

I can write or say some of what I did.

I can write and talk about what I did.

I can write or talk about why I did it.

I can write and say what I did and why I did it.

Draw

or

Show

I am not able to draw or show my thinking.

I can draw, but not show my thinking;

or

I can show but not draw my thinking;

I can draw and show my thinking

I can draw, show and talk about my thinking.

Reasoning and Problem Solving Mathematical Tasks

The benefits of using formative performance tasks in the classroom instead of multiple choice, fill in the blank, or short answer questions have to do with their abilities to capture authentic samples of students' work that make thinking and reasoning visible. Educators’ ability to differentiate between low-level and high-level demand task is essential to ensure that evidence of student thinking is aligned and targeted to learning goals. The Mathematical Task Analysis Guide serves as a tool to assist educators in selecting and implementing tasks that promote reasoning and problem solving.

Use and Connection of Mathematical Representations

The Lesh Translation Model

Each oval in the model corresponds to one way to represent a mathematical idea.

Visual: When children draw pictures, the teacher can learn more about what they understand about a particular mathematical idea and can use the different pictures that children create to provoke a discussion about mathematical ideas. Constructing their own pictures can be a powerful learning experience for children because they must consider several aspects of mathematical ideas that are often assumed when pictures are pre-drawn for students.

Physical: The manipulatives representation refers to the unifix cubes, base-ten blocks, fraction circles, and the like, that a child might use to solve a problem. Because children can physically manipulate these objects, when used appropriately, they provide opportunities to compare relative sizes of objects, to identify patterns, as well as to put together representations of numbers in multiple ways.

Verbal: Traditionally, teachers often used the spoken language of mathematics but rarely gave students opportunities to grapple with it. Yet, when students do have opportunities to express their mathematical reasoning aloud, they may be able to make explicit some knowledge that was previously implicit for them.

Symbolic: Written symbols refer to both the mathematical symbols and the written words that are associated with them. For students, written symbols tend to be more abstract than the other representations. I tend to introduce symbols after students have had opportunities to make connections among the other representations, so that the students have multiple ways to connect the symbols to mathematical ideas, thus increasing the likelihood that the symbols will be comprehensible to students.

Contextual: A relevant situation can be any context that involves appropriate mathematical ideas and holds interest for children; it is often, but not necessarily, connected to a real-life situation.

The Lesh Translation Model: Importance of Connections

As important as the ovals are in this model, another feature of the model is even more important than the representations themselves: The arrows! The arrows are important because they represent the connections students make between the representations. When students make these connections, they may be better able to access information about a mathematical idea, because they have multiple ways to represent it and, thus, many points of access.

Individuals enhance or modify their knowledge by building on what they already know, so the greater the number of representations with which students have opportunities to engage, the more likely the teacher is to tap into a student’s prior knowledge. This “tapping in” can then be used to connect students’ experiences to those representations that are more abstract in nature (such as written symbols). Not all students have the same set of prior experiences and knowledge. Teachers can introduce multiple representations in a meaningful way so that students’ opportunities to grapple with mathematical ideas are greater than if their teachers used only one or two representations.

Concrete Pictorial Abstract (CPA) Instructional Approach

The CPA approach suggests that there are three steps necessary for pupils to develop understanding of a mathematical concept.

Concrete: “Doing Stage”: Physical manipulation of objects to solve math problems.

Pictorial: “Seeing Stage”: Use of imaged to represent objects when solving math problems.

Abstract: “Symbolic Stage”: Use of only numbers and symbols to solve math problems.

CPA is a gradual systematic approach. Each stage builds on to the previous stage. Reinforcement of concepts are achieved by going back and forth between these representations

Mathematical Discourse and Strategic Questioning

Discourse involves asking strategic questions that elicit from students both how a problem was solved and why a particular method was chosen. Students learn to critique their own and others' ideas and seek out efficient mathematical solutions.

While classroom discussions are nothing new, the theory behind classroom discourse stems from constructivist views of learning where knowledge is created internally through interaction with the environment. It also fits in with socio-cultural views on learning where students working together are able to reach new understandings that could not be achieved if they were working alone.

Underlying the use of discourse in the mathematics classroom is the idea that mathematics is primarily about reasoning not memorization. Mathematics is not about remembering and applying a set of procedures but about developing understanding and explaining the processes used to arrive at solutions.

Asking better questions can open new doors for students, promoting mathematical thinking and classroom discourse. Can the questions you're asking in the mathematics classroom be answered with a simple “yes” or “no,” or do they invite students to deepen their understanding?

To help you encourage deeper discussions, here are 100 questions to incorporate into your instruction by Dr. Gladis Kersaint, mathematics expert and advisor for Ready Mathematics.

Conceptual Understanding

Students demonstrate conceptual understanding in mathematics when they provide evidence that they can:

· recognize, label, and generate examples of concepts;

· use and interrelate models, diagrams, manipulatives, and varied representations of concepts;

· identify and apply principles; know and apply facts and definitions;

· compare, contrast, and integrate related concepts and principles; and

· recognize, interpret, and apply the signs, symbols, and terms used to represent concepts.

Conceptual understanding reflects a student's ability to reason in settings involving the careful application of concept definitions, relations, or representations of either.

Procedural Fluency

Procedural fluency is the ability to:

· apply procedures accurately, efficiently, and flexibly;

· to transfer procedures to different problems and contexts;

· to build or modify procedures from other procedures; and

· to recognize when one strategy or procedure is more appropriate to apply than another.

Procedural fluency is more than memorizing facts or procedures, and it is more than understanding and being able to use one procedure for a given situation. Procedural fluency builds on a foundation of conceptual understanding, strategic reasoning, and problem solving (NGA Center & CCSSO, 2010; NCTM, 2000, 2014). Research suggests that once students have memorized and practiced procedures that they do not understand, they have less motivation to understand their meaning or the reasoning behind them (Hiebert, 1999). Therefore, the development of students’ conceptual understanding of procedures should precede and coincide with instruction on procedures.

Math Fact Fluency: Automaticity

Students who possess math fact fluency can recall math facts with automaticity. Automaticity is the ability to do things without occupying the mind with the low-level details required, allowing it to become an automatic response pattern or habit. It is usually the result of learning, repetition, and practice.

K-2 Math Fact Fluency Expectation

K.OA.5 Add and Subtract within 5.

1.OA.6 Add and Subtract within 10.

2.OA.2 Add and Subtract within 20.

Math Fact Fluency: Fluent Use of Mathematical Strategies

First and second grade students are expected to solve addition and subtraction facts using a variety of strategies fluently.

1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.

Use strategies such as:

· counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14);

· decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9);

· using the relationship between addition and subtraction; and

· creating equivalent but easier or known sums.

2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on:

· place value,

· properties of operations, and/or

· the relationship between addition and subtraction;

Evidence of Student Thinking

Effective classroom instruction and more importantly, improving student performance, can be accomplished when educators know how to elicit evidence of students’ understanding on a daily basis. Informal and formal methods of collecting evidence of student understanding enable educators to make positive instructional changes. An educators’ ability to understand the processes that students use helps them to adapt instruction allowing for student exposure to a multitude of instructional approaches, resulting in higher achievement. By highlighting student thinking and misconceptions, and eliciting information from more students, all teachers can collect more representative evidence and can therefore better plan instruction based on the current understanding of the entire class.

Mathematical Proficiency

To be mathematically proficient, a student must have:

• Conceptual understanding: comprehension of mathematical concepts, operations, and relations;

• Procedural fluency: skill in carrying out procedures flexibly, accurately, efficiently, and appropriately;

• Strategic competence: ability to formulate, represent, and solve mathematical problems;

• Adaptive reasoning: capacity for logical thought, reflection, explanation, and justification;

• Productive disposition: habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy.

Evidence should:

· Provide a window in student thinking;

· Help teachers to determine the extent to which students are reaching the math learning goals; and

· Be used to make instructional decisions during the lesson and to prepare for subsequent lessons.

Second Grade Unit I

In this Unit Students will:

2.OA.1: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of:

Adding to,

Taking from,

Putting Together,

Taking Apart, and

Comparing with unknowns in all positions

2.O.A.2: Fluently add and subtract within 20 using mental strategies:

Count On/ Count Back

Making Ten/Decomposing (Ten)

Addition and Subtraction Relationship

Doubles +/-

Know from memory all sums of two one digit numbers.

2.MD.1: Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

2.MD.2: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

2.MD.3: Estimate lengths using units of inches, feet, centimeters, and meters.

2.MD.4: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

2.MD.5: Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

Embedded Standards: 2.OA.1 and 2.OA.2

2.MD.6: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

Mathematical Practices

· Make sense of persevere in solving them.

· Reason abstractly and quantitatively.

· Construct viable arguments and critique the reasoning of others.

· Model with mathematics.

· Use appropriate mathematical tools.

· Attend to precision.

· Look for and make use of structure.

· Look for and express regularity in repeated reasoning.

New Jersey Student Learning Standards: Operations and Algebraic Thinking

2.OA.1

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Second Grade students extend their work with addition and subtraction word problems in two major ways. First, they represent and solve word problems within 100, building upon their previous work to 20. In addition, they represent and solve one and two-step word problems of all three types (Result Unknown, Change Unknown, Start Unknown). Please see Table 1 at end of document for examples of all problem types.

One-step word problems use one operation. Two-step word problems use two operations which may include the same operation or opposite operations.

Two-Step Problems: Because Second Graders are still developing proficiency with the most difficult subtypes (shaded in white in Table 1 at end of the glossary): Add To/Start Unknown; Take From/Start Unknown; Compare/Bigger Unknown; and Compare/Smaller Unknown, two-step problems do not involve these sub-types (Common Core Standards Writing Team, May 2011). Furthermore, most two-step problems should focus on single-digit addends since the primary focus of the standard is the problem-type.

New Jersey Student Learning Standards: Operations and Algebraic Thinking

2.OA.2

Fluently add and subtract within 20 using mental strategies.

By end of Grade 2, know from memory all sums of two one-digit numbers.

See standard 1.OA.6 for a list of mental strategies.

Building upon their work in First Grade, Second Graders use various addition and subtraction strategies in order to fluently add and subtract within 20:

1.OA.6 Mental Strategies

· Counting On/Counting Back

· Making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14)

· Decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9)

· Using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4)

· Creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12, 12 + 1 = 13

Second Graders internalize facts and develop fluency by repeatedly using strategies that make sense to them. When students are able to demonstrate fluency they are accurate, efficient, and flexible. Students must have efficient strategies in order to know sums from memory.

Research indicates that teachers can best support students’ memory of the sums of two one-digit numbers through varied experiences including making 10, breaking numbers apart, and working on mental strategies. These strategies replace the use of repetitive timed tests in which students try to memorize operations as if there were not any relationships among the various facts. When teachers teach facts for automaticity, rather than memorization, they encourage students to think about the relationships among the facts. (Fosnot & Dolk, 2001)

It is no accident that the standard says “know from memory” rather than “memorize”. The first describes an outcome, whereas the second might be seen as describing a method of achieving that outcome. So no, the standards are not dictating timed tests. (McCallum, October 2011)

New Jersey Student Learning Standards: Measurement and Data

2.MD.1

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Second Graders build upon their non-standard measurement experiences in First Grade by measuring in standard units for the first time. Using both customary (inches and feet) and metric (centimeters and meters) units, Second Graders select an attribute to be measured (e.g., length of classroom), choose an appropriate unit of measurement (e.g., yardstick), and determine the number of units (e.g., yards). As teachers provide rich tasks that ask students to perform real measurements, these foundational understandings of measurement are developed:

· Understand that larger units (e.g., yard) can be subdivided into equivalent units (e.g., inches) (partition).

· Understand that the same object or many objects of the same size such as paper clips can be repeatedly used to determine the length of an object (iteration).

· Understand the relationship between the size of a unit and the number of units needed (compensatory principal). Thus, the smaller the unit, the more units it will take to measure the selected attribute.

When Second Grade students are provided with opportunities to create and use a variety of rulers, they can connect their understanding of non-standard units from First Grade to standard units in second grade.

For example:

2.MD.2

Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

Second Grade students measure an object using two units of different lengths.

This experience helps students realize that the unit used is as important as the attribute being measured.

This is a difficult concept for young children and will require numerous experiences for students to predict, measure, and discuss outcomes.

Example: A student measured the length of a desk in both feet and centimeters. She found that the desk was 3 feet long.

She also found out that it was 36 inches long.

Teacher: Why do you think you have two different measurements for the same desk?

Student: It only took 3 feet because the feet are so big. It took 36 inches because an inch is a whole lot smaller than a foot.

2.MD.3

Estimate lengths using units of inches, feet, centimeters, and meters.

Second Grade students estimate the lengths of objects using inches, feet, centimeters, and meters prior to measuring.

Estimation helps the students focus on the attribute being measured and the measuring process.

As students estimate, the student has to consider the size of the unit- helping them to become more familiar with the unit size.

In addition, estimation also creates a problem to be solved rather than a task to be completed.

Once a student has made an estimate, the student then measures the object and reflects on the accuracy of the estimate made and considers this information for the next measurement.

Example:

Teacher: How many inches do you think this string is if you measured it with a ruler?

Student: An inch is pretty small. I’m thinking it will be somewhere between 8 and 9 inches.

Teacher: Measure it and see.

Student: It is 9 inches. I thought that it would be somewhere around there.

2.MD.4

Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Second Grade students determine the difference in length between two objects by using the same tool and unit to measure both objects. Students choose two objects to measure, identify an appropriate tool and unit, measure both objects, and then determine the differences in lengths.

2.MD.5

Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

Second Grade students apply the concept of length to solve addition and subtraction word problems with numbers within 100. Students should use the same unit of measurement in these problems.

Equations may vary depending on students’ interpretation of the task.

Example: In P.E. class Kate jumped 14 inches. Mary jumped 23 inches. How much farther did Mary jump than Kate?

Write an equation and then solve the problem.

2.MD.6

Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

Building upon their experiences with open number lines, Second Grade students create number lines with evenly spaced points corresponding to the numbers to solve addition and subtraction problems to 100. They recognize the similarities between a number line and a ruler.

Example: There were 27 students on the bus. 19 got off the bus. How many students are on the bus?

Student A: I used a number line. I started at 27. I broke up 19 into 10 and 9. That way, I could take a jump of 10. I landed on 17. Then I broke the 9 up into 7 and 2. I took a jump of 7. That got me to 10. Then I took a jump of 2. That’s 8. So, there are 8 students now on the bus.

Student B: I used a number line. I saw that 19 is really close to 20. Since 20 is a lot easier to work with, I took a jump of 20. But, that was one too many. So, I took a jump of 1 to make up for the extra. I landed on 8. So, there are 8 students on the bus.

Eight Mathematical Practices

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.

1

Make sense of problems and persevere in solving them

Mathematically proficient students in Second Grade examine problems and tasks, can make sense of the meaning of the task and find an entry point or a way to start the task. Second Grade students also develop a foundation for problem solving strategies and become independently proficient on using those strategies to solve new tasks. In Second Grade, students’ work continues to use concrete manipulatives and pictorial representations as well as mental mathematics. Second Grade students also are expected to persevere while solving tasks; that is, if students reach a point in which they are stuck, they can reexamine the task in a different way and continue to solve the task. Lastly, mathematically proficient students complete a task by asking themselves the question, “Does my answer make sense?”

2

Reason abstractly and quantitatively

Mathematically proficient students in Second Grade make sense of quantities and relationships while solving tasks. This involves two processes- decontextualizing and contextualizing. In Second Grade, students represent situations by decontextualizing tasks into numbers and symbols. For example, in the task, “There are 25 children in the cafeteria and they are joined by 17 more children. How many students are in the cafeteria? ” Second Grade students translate that situation into an equation, such as: 25 + 17 = __ and then solve the problem. Students also contextualize situations during the problem solving process. For example, while solving the task above, students can refer to the context of the task to determine that they need to subtract 19 since 19 children leave. The processes of reasoning also other areas of mathematics such as determining the length of quantities when measuring with standard units.

3

Construct viable arguments and critique the reasoning of others

Mathematically proficient students in Second Grade accurately use definitions and previously established solutions to construct viable arguments about mathematics. During discussions about problem solving strategies, students constructively critique the strategies and reasoning of their classmates. For example, while solving 74 - 18, students may use a variety of strategies, and after working on the task, can discuss and critique each other’s reasoning and strategies, citing similarities and differences between strategies.

4

Model with mathematics

Mathematically proficient students in Second Grade model real-life mathematical situations with a number sentence or an equation, and check to make sure that their equation accurately matches the problem context. Second Grade students use concrete manipulatives and pictorial representations to provide further explanation of the equation. Likewise, Second Grade students are able to create an appropriate problem situation from an equation. For example, students are expected to create a story problem for the equation 43 + 17 = ___ such as “There were 43 gumballs in the machine. Tom poured in 17 more gumballs. How many gumballs are now in the machine?”

5

Use appropriate tools strategically

Mathematically proficient students in Second Grade have access to and use tools appropriately. These tools may include snap cubes, place value (base ten) blocks, hundreds number boards, number lines, rulers, and concrete geometric shapes (e.g., pattern blocks, 3-d solids).

Students also have experiences with educational technologies, such as calculators and virtual manipulatives, which support conceptual understanding and higher-order thinking skills.

During classroom instruction, students have access to various mathematical tools as well as paper, and determine which tools are the most appropriate to use. For example, while measuring the length of the hallway, students can explain why a yardstick is more appropriate to use than a ruler.

6

Attend to precision

Mathematically proficient students in Second Grade are precise in their communication, calculations, and measurements.

In all mathematical tasks, students in Second Grade communicate clearly, using grade-level appropriate vocabulary accurately as well as giving precise explanations and reasoning regarding their process of finding solutions.

For example, while measuring an object, care is taken to line up the tool correctly in order to get an accurate measurement. During tasks involving number sense, students consider if their answer is reasonable and check their work to ensure the accuracy of solutions.

7

Look for and make use of structure

Mathematically proficient students in Second Grade carefully look for patterns and structures in the number system and other areas of mathematics. For example, students notice number patterns within the tens place as they connect skip count by 10s off the decade to the corresponding numbers on a 100s chart. While working in the Numbers in Base Ten domain, students work with the idea that 10 ones equal a ten, and 10 tens equals 1 hundred.

In addition, Second Grade students also make use of structure when they work with subtraction as missing addend problems, such as 50- 33 = __ can be written as 33+ __ = 50 and can be thought of as,” How much more do I need to add to 33 to get to 50?”

8

Look for and express regularity in repeated reasoning

Mathematically proficient students in Second Grade begin to look for regularity in problem structures when solving mathematical tasks. For example, after solving two digit addition problems by decomposing numbers (33+ 25 = 30 + 20 + 3 +5), students may begin to generalize and frequently apply that strategy independently on future tasks.

Further, students begin to look for strategies to be more efficient in computations, including doubles strategies and making a ten.

Lastly, while solving all tasks, Second Grade students accurately check for the reasonableness of their solutions during and after completing the task.

MATH WORKSTATIONS

Math work stations allow students to engage in authentic and meaningful hands-on learning. They often last for several weeks, giving students time to reinforce or extend their prior instruction. Before students have an opportunity to use the materials in a station, introduce them to the whole class, several times. Once they have an understanding of the concept, the materials are then added to the work stations.

Station Organization and Management Sample

Teacher A has 12 containers labeled 1 to 12. The numbers correspond to the numbers on the rotation chart. She pairs students who can work well together, who have similar skills, and who need more practice on the same concepts or skills. Each day during math work stations, students use the center chart to see which box they will be using and who their partner will be. Everything they need for their station will be in their box. Each station is differentiated. If students need more practice and experience working on numbers 0 to 10, those will be the only numbers in their box. If they are ready to move on into the teens, then she will place higher number activities into the box for them to work with.

INCLUDEPICTURE "http://www.scholastic.com/teachers/sites/default/files/posts/u136/images/math_21_lg.jpg" \* MERGEFORMATINET

In the beginning there is a lot of prepping involved in gathering, creating, and organizing the work stations. However, once all of the initial work is complete, the stations are easy to manage. Many of her stations stay in rotation for three or four weeks to give students ample opportunity to master the skills and concepts.

Read Math Work Stations by Debbie Diller.

In her book, she leads you step-by-step through the process of implementing work stations.

MATH WORKSTATION INFORMATION CARD

MATH WORKSTATION SCHEDULE

Week of: _________________

DAY

Technology

Lab

Problem Solving Lab

Fluency

Lab

Math

Journal

Small Group Instruction

Mon.

Group ____

Group ____

Group ____

Group ____

BASED

ON CURRENT OBSERVATIONAL DATA

Tues.

Group ____

Group ____

Group ____

Group ____

Wed.

Group ____

Group ____

Group ____

Group ____

Thurs.

Group ____

Group ____

Group ____

Group ____

Fri.

Group ____

Group ____

Group ____

Group ____

INSTRUCTIONAL GROUPING

GROUP A

GROUP B

1

1

2

2

3

3

4

4

5

5

6

6

GROUP C

GROUP D

1

1

2

2

3

3

4

4

5

5

6

6

Math In Focus Lesson Structure

LESSON STRUCTURE

RESOURCES

COMMENTS

Chapter Opener

Assessing Prior Knowledge

The Pre Test serves as a diagnostic test of readiness of the upcoming chapter

Teacher Materials

Quick Check

Pre-Test (Assessment Book)

Recall Prior Knowledge

Student Materials

Student Book (Quick Check); Copy of the Pre Test; Recall prior Knowledge

Recall Prior Knowledge (RPK) can take place just before the pre-tests are given and can take 1-2 days to front load prerequisite understanding

Quick Check can be done in concert with the RPK and used to repair student misunderstandings and vocabulary prior to the pre-test ; Students write Quick Check answers on a separate sheet of paper

Quick Check and the Pre Test can be done in the same block (See Anecdotal Checklist; Transition Guide)

Recall Prior Knowledge – Quick Check – Pre Test

Direct Involvement/Engagement

Teach/Learn

Students are directly involved in making sense, themselves, of the concepts – by interacting the tools, manipulatives, each other, and the questions

Teacher Edition

5-minute warm up

Teach; Anchor Task

Technology

Digi

Other

Fluency Practice

The Warm Up activates prior knowledge for each new lesson

Student Books are CLOSED; Big Book is used in Gr. K

Teacher led; Whole group

Students use concrete manipulatives to explore concepts

A few select parts of the task are explicitly shown, but the majority is addressed through the hands-on, constructivist approach and questioning

Teacher facilitates; Students find the solution

Guided Learning and Practice

Guided Learning

Teacher Edition

Learn

Technology

Digi

Student Book

Guided Learning Pages

Hands-on Activity

Students-already in pairs /small, homogenous ability groups; Teacher circulates between groups; Teacher, anecdotally, captures student thinking

Small Group w/Teacher circulating among groups

Revisit Concrete and Model Drawing; Reteach

Teacher spends majority of time with struggling learners; some time with on level, and less time with advanced groups

Games and Activities can be done at this time

Independent Practice

A formal formative

assessment

Teacher EditionLet’s Practice

Student BookLet’s Practice

Differentiation OptionsAll: WorkbookExtra Support: ReteachOn Level: Extra PracticeAdvanced: Enrichment

Let’s Practice determines readiness for Workbook and small group work and is used as formative assessment; Students not ready for the Workbook will use Reteach. The Workbook is continued as Independent Practice.

Manipulatives CAN be used as a communications tool as needed.

Completely Independent

On level/advance learners should finish all workbook pages.

Extending the Lesson

Math JournalProblem of the LessonInteractivitiesGames

Lesson Wrap Up

Problem of the Lesson

Homework (Workbook , Reteach, or Extra Practice)

Workbook or Extra Practice Homework is only assigned when students fully understand the concepts (as additional practice)

Reteach Homework (issued to struggling learners) should be checked the next day

End of Chapter Wrap Up

and Post Test

Teacher EditionChapter Review/TestPut on Your Thinking Cap

Student WorkbookPut on Your Thinking Cap

Assessment Book

Test Prep

Use Chapter Review/Test as “review” for the End of Chapter Test Prep. Put on your Thinking Cap prepares students for novel questions on the Test Prep; Test Prep is graded/scored.

The Chapter Review/Test can be completed

· Individually (e.g. for homework) then reviewed in class

· As a ‘mock test’ done in class and doesn’t count

· As a formal, in class review where teacher walks students through the questions

Test Prep is completely independent; scored/graded

Put on Your Thinking Cap (green border) serve as a capstone problem and are done just before the Test Prep and should be treated as Direct Engagement. By February, students should be doing the Put on Your Thinking Cap problems on their own

TRANSITION LESSON STRUCTURE (No more than 2 days)

· Driven by Pre-test results, Transition Guide

· Looks different from the typical daily lesson

Transition Lesson – Day 1

Objective:

CPA Strategy/Materials

Ability Groupings/Pairs (by Name)

Task(s)/Text Resources

Activity/Description

IDEAL MATH BLOCK LESSON PLANNING TEMPLATE

CCSS & OBJ:(s)

Fluency:

2.OA.2

Strategy:

Tool(s):

Math In Focus/EnGageNY

Launch

Exploration

Independent Practice

Differentiation: Math Workstations

Small Group Instruction

Tech. Lab

Problem Solving Lab

CCSS:

2.OA.1

2.NBT.6

2.NBT.7

Fluency Lab

2.OA.2

2.NBT.5

2.NBT.8

Strategy:

Tool(s):

Math Journal

MP3: Construct viable arguments and critique the reasoning of others

Summary

Exit Ticket

Danielson Framework for Teaching: Domain 1: Planning Preparation

Lesson Planning Support Tool

______________________________________________________________________________________________________

Component 1A: Knowledge of Content and Pedagogy

Content

(Fluency Practice and Anchor Problem clearly outlined in lesson plans provide reinforcement of prerequisite knowledge/skills needed;

(Essentials question(s) and lesson objective(s) support learning of New Jersey Student Learning Standards grade level expectations;

Pedagogy

(Daily fluency practice is clearly outlined in lesson plans;

(Multiple strategies are evident within lesson plans;

(Mathematical tools outlined within lesson plans;

___________________________________________________________________________________________________________________________

Component 1B: Knowledge of Students

Intentional Student Grouping is evident within lesson plans:

Independent Practice: Which students will work on:

(MIF Re-Teach

(MIF Practice

(MIF Extra Practice

(MIF Enrichment

Math Workstations: Which students will work in:

(Fluency Lab

(Technology Lab

(Math Journal

(Problem Solving Lab

Component 1C: Setting Instructional Outcomes

(Lesson plan objectives are aligned to one or more New Jersey Student Standards for Learning;

(Connections made to previous learning;

(Outcomes: student artifacts are differentiated;

Component 1D: Demonstrating Knowledge of Resources

District Approved Programs: (Use Math In Focus/EnGageNY/Go Math resources are evident;

Technology: ( Technology used to help students understand the lesson objective is evident;

( Students use technology to gain an understanding of the lesson objective;

Supplemental Resources: ( Integration of additional materials evident (Math Workstations)

________________________________________________________________________________________________________________________

Component 1E: Designing Coherent Instruction

(Lesson Plans support CONCEPTUAL UNDERSTANDING;

(Lesson Plans show evidences of CONCRETE, PICTORIAL, and ABSTRACT representation;

(Alignment between OBJECTIVES, APPLICATION, and ASSESSMENT evident;

___________________________________________________________________________________________________________________________

Component 1F: Assessing Student Learning

Lesson Plans include: ( Focus Question/Essential Understanding

( Anchor Problem

( Checks for Understanding

( Demonstration of Learning (Exit Ticket)

Planning Calendar

September 2016

Monday

Tuesday

Wednesday

Thursday

Friday

1

2

5

6

7

8

9

12

13

14

15

16

19

20

21

22

EnGageNY

End of Module 1

Asssessment

23

26

27

SGO

Diagnostic (BOY)

Assessment

28

SGO

Diagnostic (BOY)

Assessment

29

SGO

Diagnostic (BOY)

Assessment

30

October 2016

Monday

Tuesday

Wednesday

Thursday

Friday

3

4

MIF Ch. 7 Test Prep

&

Performance Task

5

6

7

10

11

Math Workstations:

SGO

Performance Tasks

12

Math Workstations:

SGO

Performance Tasks

13

Math Workstations:

SGO

Performance Tasks

14

17

18

19

EnGageNY

End of Module 2

Assessment

20

21

24

Math Workstations:

SGO

Fluency Assessments

25

Math Workstations:

SGO

Fluency Assessments

26

Math Workstations:

SGO

Fluency Assessments

27

28

31

MIF Ch. 13 Test Prep

&

Performance Task

Planning Calendar

November 2016

Monday

Tuesday

Wednesday

Thursday

Friday

1

2

3

4

7

8

9

Performance Tasks

Fluency Benchmark I END OF MP

10

11

14

15

16

17

18

21

22

23

24

25

28

29

30

December 2016

Monday

Tuesday

Wednesday

Thursday

Friday

1

2

5

6

7

8

9

12

13

14

15

16

19

20

21

22

23

26

27

28

29

30

Grade 2 Unit 1

Instructional and Assessment Framework

Recommended Pacing

Activities

CCSS

Notes

September 8-9, 2016

Setting Up Classroom Routines/Procedures

Introduction to Math Workstations

Routines/Procedures:

Ask 3 Then Me

Math Talk Moves

Math Notebooks

Math Workstations

September 12, 2016

EnGageNY Module A Lesson 1

Practice Making Ten and adding to ten

September 13, 2016

EnGageNY Module A Lesson 2

Practice making the next ten and adding to a multiple of ten

September 14, 2016

EnGageNY Module B Lesson 3

Add and subtract like units

September 15, 2016


Make a ten to add within 20

2.OA.1

2.OA.2

2.NBT.5

EnGageNY Modules provided by Math Department:


50-60 minutes

Continue to reinforce mental strategies:

Count on/Count back;

Making ten/Decomposing ten;

Addition and subtraction relationships; Doubles +/-

Demonstration of Learning:

Exit tickets: (5 min.)

Students complete independently.

Analyze and utilize the results of exit tickets to drive instructional decision making.

Place exit tickets in Student Portfolios

September 16, 2016


Make a ten to add within 100

September 19, 2016


Subtract single-digit numbers from multiples of 10 within 100

September 20, 2016


Take from ten within 20

September 21, 2016


Take from ten within 100

September 22, 2016

EnGageNY End of Module 1 Assessment

September 23, 2016

Math In Focus Ch. 7

Chapter Opener

Recall Prior Knowledge

Quick Check

Pre-Test

September 26, 2016

Math In Focus Ch. 7 Lesson 1

Measuring in Meters

September 27, 2016


Comparing Lengths in Meters

Math Workstation: SGO Diagnostic (BOY) Assessment

September 28, 2016


Measuring in Centimeters


9/27 -9/30

Administer

SGO Assessments

during the last 20 minutes of the math block.

September 29, 2016


Comparing Lengths in Centimeters


September 30, 2016


Real World Problems: Metric Length

October 3, 2016

Math In Focus Ch. 7

Problem Solving

Chapter Wrap-Up

EnGageNY Modules provided by Math Department:


50-60 minutes

Demonstration of Learning:

Exit tickets: (5 min.)

Students complete independently.

Analyze and utilize the results of exit tickets to drive instructional decision making.

Place exit tickets in Student Portfolios

Thinkcentral.com for MIF materials

October 4, 2016

Math In Focus Ch. 7 Test Prep

MIF Ch. 7 Performance Task

October 5, 2016

EnGageNY Module 2 A Lesson 1

Connect measurement with physical units by using multiple copies of the same physical unit to measure

2.OA.1

2.OA.2

2.MD.1

2.MD.2

2.MD.3

2.MD.4

2.MD.5

2.MD.6

October 6, 2016


Use iteration with one physical unit to measure

October 7, 2016


Apply concepts to create unit rulers and measure lengths using unit rulers

October 10, 2016

EnGageNY Module 2 B Lesson 4

Measure various objects using centimeter rulers and meter sticks

October 11, 2016

EnGageNY Module 2 B Lesson 5

Develop estimation strategies by applying prior knowledge of length and using mental benchmarks

October 12, 2016

EnGageNY Module 2 C Lesson 6

Measure and compare lengths using centimeters and meters

October 13, 2016

EnGageNY Module 2 C Lesson 7

Measure and compare lengths using metric length units and non-standard length units;

October 14, 2016

EnGageNY Module 2 D Lesson 8

Solve addition and subtraction word problems using the ruler as a number line

October 17, 2016

EngageNY Module 2 D Lesson 9

Measure lengths of string using measurement tools; and use tape diagrams to represent and compare the lengths

October 18, 2016

EngageNY Module 2 D Lesson 10

Apply conceptual understanding of measurement by solving two-step word problems

Recommended Pacing

Activities

CCSS

Notes

October 19, 2016

EnGageNY End of Module 2 Assessment

October 20, 2016

Math In Focus Chapter 13

Chapter Opener; Recall Prior Knowledge

Quick Check; Pre-Test

October 21, 2016

Math In Focus Chapter 13 Lesson 1

Measuring in Feet

October 24, 2016


Comparing Lengths in Feet

Math Workstations: SGO Fluency Assessments

10/24 -10/26

Administer

SGO Assessments

during the last 20 minutes of the math block.

October 25, 2016


Measuring in Inches


October 26, 2016


Comparing Lengths in Inches and Feet


October 27, 2016


Real World Problems: Customary Length

October 28, 2016

Math In Focus Ch. 13

Problem Solving & Chapter Wrap-Up

October 31, 2016

Math In Focus Ch. 13 Test Prep

MIF Ch. 13 Performance Task

November 1, 2016

EngageNY Module 3 Lesson 1

Bundle and count ones, tens, and hundreds to 1,000.

November 2, 2016


Count up and down between 100 and 220 using ones and tens

November 3, 2016


Count up and down between 90 and 1,000 using ones, tens, and hundreds.

November 4, 2016


Count up to 1,000 on the place value chart.

November 7, 2016


Write base ten three-digit numbers in unit form; show the value of each digit.

November 8, 2016


Write base ten numbers in expanded form.

November 9, 2016

Performance Tasks:

Blocks

Yards

Jumping Contest

2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Blocks

Performance Task (2.OA.1)

Name: ___________________________________________Teacher: ________________ Date: ________

I have some blocks. Dan has some blocks. Together we have 100 blocks.

How many blocks do we each have?

Use word, pictures, and numbers to explain your thinking.

Solution: _________________________________________________________________________

2.OA.1 Compare-Bigger Unknown: Fewer; One-Step

2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

Yards

Performance Task (2.MD.5)


Dan ran 9 fewer yards than Sam. Sam ran for 21 yards. How many yards did Dan run?

Solution: ___________

2.OA.1 Compare – Difference Unknown: More; One-Step

2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

Jumping Contest

Performance Task (2.MD.6)


The class had a jumping contest. Sam jumped 38 inches. Tom jumped 55 inches. How much farther did Tom jump than Sam?

Use a number line to solve.

Solution: ___________

2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

(SAMPLE)

Express Yourself

Math Journal (2.MD.4)


What can you say about the objects below?

Use words, pictures and numbers to express your thinking.

2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

(SAMPLE)

Measurements

Math Journal (2.MD.4)


What can you say about the objects below?

Use words, pictures and numbers to express your thinking.

New Jersey Student Learning Standards

Second Grade Mathematics

Fluency Benchmark 1: Automaticity

Student Name: ________________________________ School: ___________________Teacher: _____________________

BENCHMARK I: FLUENCY WITHIN 10 (10 minutes)

Score: _____/ 40

1

5+5

21

9+0

2

12-3

22

11-4

3

4+6

23

8+1

4

15-6

24

7-3

5

3+7

25

2+7

6

11-3

26

8-6

7

2+8

27

6+3

8

17-12

28

11-8

9

1+9

29

5+4

10

12-6

30

13-9

11

0+10

31

4+4

12

9-3

32

14-9

13

5+3

33

6+2

14

11-9

34

13-7

15

1+7

35

0+8

16

9-7

36

15-8

17

7+0

37

1+6

18

15-3

38

16-8

19

5+2

39

4+3

20

14-7

40

20-11

Got It

Evidence shows that the student essentially has the target concept or big math idea.

Not There Yet

Student shows evidence of a major misunderstanding, incorrect concepts or procedure, or a failure to engage in the task.

PLD Level 5: 100%

Distinguished command

PLD Level 4: 89%

Strong Command

PLD Level 3: 79%

Moderate Command

PLD Level 2: 69%

Partial Command

PLD Level 1: 59%

Little Command

Student work shows distinguished levels of understanding of the mathematics.

Student constructs and communicates a complete response based on explanations/reasoning using the:

· Tools:

· Manipulatives

· Five Frame

· Ten Frame

· Number Line

· Part-Part-Whole Model

· Strategies:

· Drawings

· Counting All

· Count On/Back

· Skip Counting

· Making Ten

· Decomposing Number

· Precise use of math vocabulary

Response includes an efficient and logical progression of mathematical reasoning and understanding.

Student work shows strong levels of understanding of the mathematics.


· Tools:

· Manipulatives

· Five Frame

· Ten Frame

· Number Line


· Strategies:

· Drawings

· Counting All

· Count On/Back

· Skip Counting

· Making Ten



Response includes a logical progression of mathematical reasoning and understanding.

Student work shows moderate levels of understanding of the mathematics.


· Tools:

· Manipulatives

· Five Frame

· Ten Frame

· Number Line


· Strategies:

· Drawings

· Counting All

· Count On/Back

· Skip Counting

· Making Ten



Response includes a logical but incomplete progression of mathematical reasoning and understanding.

Contains minor errors.

Student work shows partial understanding of the mathematics.

Student constructs and communicates an incomplete response based on student’s attempts of explanations/ reasoning using the:

· Tools:

· Manipulatives

· Five Frame

· Ten Frame

· Number Line


· Strategies:

· Drawings

· Counting All

· Count On/Back

· Skip Counting

· Making Ten



Response includes an incomplete or illogical progression of mathematical reasoning and understanding.

Student work shows little understanding of the mathematics.

Student attempts to constructs and communicates a response using the:

· Tools:

· Manipulatives

· Five Frame

· Ten Frame

· Number Line


· Strategies:

· Drawings

· Counting All

· Count On/Back

· Skip Counting

· Making Ten



Response includes limited evidence of the progression of mathematical reasoning and understanding.

5 points

4 points

3 points

2 points

1 point

Second Grade PLD Rubric

DATA DRIVEN INSTRUCTION

Formative assessments inform instructional decisions. Taking inventories and assessments, observing reading and writing behaviors, studying work samples and listening to student talk are essential components of gathering data. When we take notes, ask questions in a student conference, lean in while a student is working or utilize a more formal assessment we are gathering data. Learning how to take the data and record it in a meaningful way is the beginning of the cycle.

Analysis of the data is an important step in the process. What is this data telling us? We must look for patterns, as well as compare the notes we have taken with work samples and other assessments. We need to decide what are the strengths and needs of individuals, small groups of students and the entire class. Sometimes it helps to work with others at your grade level to analyze the data.

Once we have analyzed our data and created our findings, it is time to make informed instructional decisions. These decisions are guided by the following questions:

· What mathematical practice(s) and strategies will I utilize to teach to these needs?

· What sort of grouping will allow for the best opportunity for the students to learn what it is I see as a need?

· Will I teach these strategies to the whole class, in a small guided group or in an individual conference?

· Which method and grouping will be the most effective and efficient? What specific objective(s) will I be teaching?

Answering these questions will help inform instructional decisions and will influence lesson planning.

Then we create our instructional plan for the unit/month/week/day and specific lessons.

It’s important now to reflect on what you have taught.

Did you observe evidence of student learning through your checks for understanding, and through direct application in student work?

What did you hear and see students doing in their reading and writing?

Now it is time to begin the analysis again.

Data Analysis Form

School: __________________

Teacher: __________________________ Date: _______________

Assessment: ____________________________________________

NJSLS: _____________________________________________________

GROUPS (STUDENT INITIALS)

SUPPORT PLAN

PROGRESS

MASTERED (86% - 100%):

DEVELOPING (67% - 85%):

INSECURE (51%-65%):

BEGINNING (0%-50%):

Student Conference Form SCHOOL: ______________________________________

TEACHER: __________________________

Student Name: __________________________________________________________________________

Date: ____________________________

NJSLS:

ACTIVITY OBSERVED:

OBSERVATION NOTES:

FEEDBACK GIVEN:

GOAL SET:

NEXT STEPS:

MATH PORTFOLIO EXPECTATIONS

The Student Assessment Portfolios for Mathematics are used as a means of documenting and evaluating students’ academic growth and development over time and in relation to the CCSS-M. Student Assessment Portfolios differ from student work folders in that they will contain tasks aligned specifically to the SGO focus. The September task entry(-ies) will reflect the prior year content and can serve as an additional baseline measure.

All tasks contained within the Student Assessment Portfolios are “practice forward” (closely aligned to the Standards for Mathematical Practice).

Four (4) or more additional tasks will be included in the Student Assessment Portfolios for Student Reflection and will be labeled as such.

In March – June, the months extending beyond the SGO window, tasks will shift from the SGO focus to a focus on the In-depth Opportunities for each grade.

K-2 General portfolio requirements

· As a part of last year’s end of year close-out process, we asked that student portfolios be ‘purged’; retaining a few artifacts and self-reflection documents that would transition with them to the next grade. In this current year, have students select 2-3 pieces of prior year’s work to file in the Student Assessment Portfolio.

· Tasks contained within the Student Assessment Portfolios are “practice forward” and denoted as “Individual”, “Partner/Group”, and “Individual w/Opportunity for Student Interviews.

· Each Student Assessment Portfolio should contain a “Task Log” that documents all tasks, standards, and rubric scores aligned to the performance level descriptors (PLDs).

· Student work should be attached to a completed rubric; teacher feedback on student work is expected.

· Students will have multiple opportunities to revisit certain standards. Teachers will capture each additional opportunity “as a new and separate score” in the task log and in Genesis.

· All Student Assessment Portfolio entries should be scored and recorded in Genesis as an Authentic Assessment grade (25%).

· All Student Assessment Portfolios must be clearly labeled, maintained for all students, inclusive of constructive teacher and student feedback and accessible for administrator review

MATHEMATICS PORTFOLIO: END OF YEAR REQUIREMENTS

At the start of the school year, you were provided with guidelines for helping students maintain their Mathematics Portfolios whereby students added artifacts that documented their growth and development over time. Included in the portfolio process was the opportunity for students to reflect on their thinking and evaluate what they feel constitutes “quality work.” As a part of the end of year closeout process, we are asking that you work with your students to help them ‘purge’ their current portfolios and retain the artifacts and self-reflection documents that will transition with them to the next grade.

Grades K-2

Purging and Next-Grade Transitioning

During the third (3rd) week of June, give students the opportunity to review and evaluate their portfolio to date; celebrating their progress and possibly setting goals for future growth. During this process, students will retain ALL of their current artifacts in their Mathematics Portfolios. The Student Profile Sheet from the end of year assessment should also be included in the student math portfolio. In the upcoming school year, after the new teacher has reviewed the portfolios, students will select 1-2 pieces to remain in the portfolio and take the rest home.

MATHEMATICIAN: ____________________________________________________SCHOOL: _______________________________TEACHER: _________________________________DATE: __________

MATH PORTFOLIO REFLECTION FORM

PORTFOLIO ARTIFACT: _________________________________________________________________________________________________

THIS IS AN EXAMPLE OF THE WORK THAT I AM MOST PROUD OF BECAUSE…..

_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

THIS WORK ALSO SHOWS THAT I NEED TO WORK ON…

_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

ADDITION FACTS WITHIN 20

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

0+20

20+0

0+19

19+0

0+18

18+0

0+17

17+0

0+16

16+0

0+15

15+0

0+14

14+0

0+13

13+0

0+12

12+0

0+11

11+0

0+10

10 +0

0+9

9+0

0+8

8+0

0+7

7+0

0+6

6+0

0+5

5+0

0+4

4+0

0+3

3+0

0+2

2+0

0+1

1+0

0+0

1+19

19+1

1+18

18+1

1+17

17+1

1+16

16+1

1+15

15+1

1+1414+1

1+1313+1

1+12

12+1

1+11

11+1

1+10

10+1

1+9

9+1

1+8

8+1

1+7

7+1

1+6

6+1

1+5

5+1

1+4

4+1

1+3

3+1

1+2

2+1

1+1

2+18

18+2

2+17

17+2

2+16

16+2

2+15

15+2

2+14

14+2

2+13

13+2

2+1212+2

2+11

11+2

2+10

10+2

2+9

9+2

2+8

8+2

2+7

7+2

2+6

6+2

2+5

5+2

2+4

4+2

2+3

3+2

2+2

3+17

17+3

3+16

16+3

3+15

15+3

3+14

14+3

3+13

13+3

3+12

12+3

3+11

11+3

3+10

10+3

3+9

9+3

3+8

8+3

3+7

7+3

3+6

6+3

3+5

5+3

3+4

4+3

3+3

4+16

16+4

4+15

15+4

4+14

14+4

4+13

13+4

4+1212+4

4+11

11+4

4+10

10+4

4+9

9+4

4+8

8+4

4+7

7+4

4+6

6+4

4+5

5+4

4+4

5+15

15+5

5+1414+5

5+13

13+5

5+12

12+5

5+11

11+5

5+10

10+5

5+9

9+5

5+8

8+5

5+7

7+5

5+6

6+5

5+5

6+14

14+6

6+13

13+6

6+12

12+6

6+11

11+6

6+10

10+6

6+9

9+6

6+8

8+6

6+7

7+6

6+6

7+13

13+7

7+12

12+7

7+11

11+7

7+10

10+7

7+9

9+7

7+8

8+7

7+7

8+12

12+8

8+11

11+8

8+10

10+8

8+9

9+8

8+8

9+11

11+9

9+10

10+9

9+9

10+10

SUBTRACTION FACTS WITHIN 20

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

20-0

20-1

20-2

20-3

20-4

20-5

20-6

20-7

20-8

20-9

20-10

20-11

20-12

20-13

20-14

20-15

20-16

20-17

20-18

20-19

20-20

19-0

19-1

19-2

19-3

19-4

19-5

19-6

19-7

19-8

19-9

19-10

19-11

19-12

19-13

19-14

19-15

19-16

19-17

19-18

19-19

18-0

18-1

18-2

18-3

18-4

18-5

18-6

18-7

18-8

18-9

18-10

18-11

18-12

18-13

18-14

18-15

18-1 6

18-17

18-18

17-0

17-1

17-2

17-3

17-4

17-5

17-6

17-7

17-8

17-9

17-10

17-11

17-12

17-13

17-4

17-15

17-16

17-17

16-0

16-1

16-2

16-3

16-4

16-5

16-6

16-7

16-8

16-9

16-10

16-11

15-12

15-13

16-14

16-15

16-16

15-0

15-1

15-2

15-3

15-4

15-5

15-6

15-7

15-8

15-9

15-10

15-11

15-12

15-13

15-14

15-15

14-0

14-1

14-2

14-3

14-4

14-5

14-6

14-7

14-8

14-9

14-10

14-11

14-12

14-13

14-14

13-0

13-1

13-2

13-3

13-4

13-5

13-6

13-7

13-8

13-9

13-10

13-11

13-12

13-13

12-0

12-1

12-2

12-3

12-4

12-5

12-6

12-7

12-8

12-9

12-10

12-11

12-12

11-0

11-1

11-2

11-3

11-4

11-5

11-6

11-7

11-8

11-9

11-10

11-11

10-0

10-1

10-2

10-3

10-4

10-5

10-6

10-7

10-8

10-9

10-10

9-0

9-1

9-2

9-3

9-4

9-5

9-6

9-7

9-8

9-9

8-0

8-1

8-2

8-3

8-4

8-5

8-6

8-7

8-8

7-0

7-1

7-2

7-3

7-4

7-5

7-6

7-7

6-0

6-1

6-2

6-3

6-4

6-5

6-6

5-0

5-1

5-2

5-3

5-4

5-5

4-0

4-1

4-2

4-3

4-4

3-0

3-1

3-2

3-3

2-0

2-1

2-2

1-0

1-1

0-0

Resources

Engage NY

http://www.engageny.org/video-library?f[0]=im_field_subject%3A19

Common Core Toolshttp://commoncoretools.me/http://www.ccsstoolbox.com/http://www.achievethecore.org/steal-these-tools

Achieve the Corehttp://achievethecore.org/dashboard/300/search/6/1/0/1/2/3/4/5/6/7/8/9/10/11/12

Manipulatives

http://nlvm.usu.edu/en/nav/vlibrary.htmlhttp://www.explorelearning.com/index.cfm?method=cResource.dspBrowseCorrelations&v=s&id=USA-000http://www.thinkingblocks.com/

Illustrative Math Project :http://illustrativemathematics.org/standards/k8

Inside Mathematics: http://www.insidemathematics.org/index.php/tools-for-teachers

Sample Balance Math Tasks: http://www.nottingham.ac.uk/~ttzedweb/MARS/tasks/

Georgia Department of Education:https://www.georgiastandards.org/Common-Core/Pages/Math-K-5.aspx

Gates Foundations Tasks:http://www.gatesfoundation.org/college-ready-education/Documents/supporting-instruction-cards-math.pdf

Minnesota STEM Teachers’ Center: http://www.scimathmn.org/stemtc/frameworks/721-proportional-relationships

Singapore Math Tests K-12: http://www.misskoh.com

Mobymax.com: http://www.mobymax.com

ORANGE PUBLIC SCHOOLS

OFFICE OF CURRICULUM AND INSTRUCTION

OFFICE OF MATHEMATICS

(Pictures)

(Maniplutives)

(Written)

(Real Life Situations)

(Communication)

1st & 2nd Grade Ideal Math Block

Essential Components

Note:

Place emphasis on the flow of the lesson in order to ensure the development of students’ conceptual understanding.

Outline each essential component within lesson plans.

Math Workstations may be conducted in the beginning of the block in order to utilize additional support staff.

Recommended: 5-10 technology devices for use within TECHNOLOGY and FLUENCY workstations.

5 min.

EXIT TICKET (DOL): Individual

Students complete independently; Used to guide instructional decisions;

Used to set instructional goals for students;

Small Group

Instruction

MATH WORKSTATIONS:

Pairs / Small Group/ Individual

DIFFERENTIATED activities designed to RETEACH, REMEDIATE, ENRICH student’s understanding of concepts.

15-20 min.

LAUNCH: Whole Group

Anchor Task: Math In Focus Learn

INDEPENDENT PRACTICE: Individual

Math In Focus Let’s Practice, Workbook, Reteach, Extra Practice, Enrichment

SUMMARY: Whole Group

Lesson Closure: Student Reflection; Real Life Connections to Concept

Technology Lab

Fluency Lab

Math

Journal

Lab

Problem

Solving

Lab

FLUENCY: Partner/Small Group

CONCRETE, PICTORIAL, and ABSTRACT approaches to support ARITHMETIC FLUENCY and FLUENT USE OF STRATEGIES.

5 min.

EXPLORATION: Partner / Small Group

Math In Focus Hands-On, Guided Practice, Let’s Explore

Math Workstation: _____________________________________________________________________ Time: _________________

NJSLS.:

_____________________________________________________________________________________________________________________________________________________________________

______________________________________________________________________________________________________________________________________________________________________

Objective(s): By the end of this task, I will be able to:

________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________

Task(s):

_______________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________________________________________________________________

______________________________________________________________________________________________________________________________________________

Exit Ticket:

______________________________________________________________________________________________________________________________________________

______________________________________________________________________________________________________________________________________________

______________________________________________________________________________________________________________________________________________

PRE TEST

DIRECT ENGAGEMENT

GUIDED LEARNING

POST TEST

POST TEST

ADDITIONAL PRACTICE

INDEPENDENT PRACTICE

� The Mathematics Department will provide guidance on task selection, thereby standardizing the process across the district and across grades/courses.

� The Mathematics Department has propagated gradebooks with appropriate weights.

0

19