Office of Mathematics Mission Statement

‘2nd Grade Mathematics

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

1 ORANGE PUBLIC SCHOOLS

2 Table of Contents

p. 2 I. Mathematics Mission Statement

p. 3 II. Mathematical Teaching Practices

III. Mathematical Goal Setting p. 4

3 p. 6 IV. Reasoning and Problem Solving

p. 7 V. Mathematical Representations

p. 9 VI. Mathematical Discourse

p. 14 VII. Conceptual Understanding

VIII. Evidence of Student Thinking p. 15

4 p. 16 IX. Second Grade Unit I NJSLS

p. 23 X. Eight Mathematical Practices

XI. Ideal Math Block p. 26

XII. Math Workstations p. 27

XIII. Math In Focus Lesson Structure p.30

5 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

6 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.

7 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

8 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

9 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

10 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

11 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.

12 Mathematical Teaching Practices

13 14 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.

15  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

16 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:

17 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).

18 Student Name: ______Task: ______School: ______Teacher: ______Date: ______

“I CAN…..” SCORE STUDENT FRIENDLY RUBRIC

19 …a start …getting there …that’s it WOW!

1 2 3 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 I can start to use a I can solve it more I can use more than

strategy. strategy. than one way. one strategy and talk

about how they get to

20 the same answer.

Say I am unable to say or I can write or say I can write and talk I can write and say

or write. some of what I did. about what I did. what I did and why I

Write did it.

I can write or talk

21 about why I did it.

I am not able to draw I can draw, but not I can draw and show I can draw, show and Draw

or show my thinking. show my thinking; my thinking talk about my or

or thinking. Show

I can show but not

22 draw my thinking;

23 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.

24 Use and Connection of Mathematical Representations

(Pictures)

(Maniplutives) (Written)

25 (Real Life (Communication)

The Lesh Translation Model

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

26 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.

27 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.

28 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

29 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

30 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.

31 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.

32 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.

33 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

34 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.

35 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.

36 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?

37 38 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.

39 40 41 42 43 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.

44 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.

45 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

46 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

47 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:

48 o place value,

o properties of operations, and/or

o the relationship between addition and subtraction;

49 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.

50 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;

51 • 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.

53 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

54 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.

55 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

56 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.

57  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.

58 New Jersey Student Learning Standards: Operations and Algebraic Thinking

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding

2.OA.1 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

59 types.

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

opposite operations.

60 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.

61 New Jersey Student Learning Standards: Operations and Algebraic Thinking

2.OA.2

Fluently add and subtract within 20 using mental strategies.

62 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

63  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

64 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)

65 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

66 New Jersey Student Learning Standards: Measurement and Data

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

2.MD.1

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

67 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

68 non-standard units from First Grade to standard units in second grade.

For example:

69 Measure the length of an object twice, using length units of different lengths for the two measurements; describe

2.MD.2

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.

70 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.

71 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.

72 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.

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

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

2.MD.4

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.

74 Students choose two objects to measure, identify an appropriate tool and unit, measure both objects, and then determine the differences in

lengths.

Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same

2.MD.5 units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown

number to represent the problem.

75 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.

76 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding

2.MD.6 to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line

diagram.

77 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?

78 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.

79 80 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

81 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

82 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

83 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.

84 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.

85 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

86 work to ensure the accuracy of solutions.

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

87 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.

88 1st & 2nd Grade Ideal Math Block Essential Components

FLUENCY: Partner/Small Group CONCRETE, PICTORIAL, and ABSTRACT approaches to support ARITHMETIC5 min . FLUENCY and FLUENT USE OF STRATEGIES. LAUNCH: Whole Group Anchor Task: Math In Focus Learn EXPLORATION: Partner / Small Group Math In Focus Hands-On, Guided Practice, Let’s Explore INDEPENDENT PRACTICE: Individual Math In Focus Let’s Practice, Workbook, Reteach, Extra Practice, Enrichment

MATH WORKSTATIONS: Pairs / Small Group/ Individual 15-20 min. DIFFERENTIATED activities designed to RETEACH, REMEDIATE, ENRICH student’s understanding of concepts.

Small Problem Math Group Solving Journal Technology Lab Fluency Lab Instruction Lab Lab

SUMMARY: Whole Group Lesson Closure: Student Reflection; Real Life Connections to Concept

EXIT TICKET (DOL): Individual Students complete independently; Used to guide instructional decisions; 5 min. Used to set instructional goals for students;

 Place emphasis on the flow of the lesson in order to ensure the development of students’ conceptual 89 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

90 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.

91 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

Math Workstation: ______Time: ______skills and concepts.

NJSLS.:

Read Math Work Stations by Debbie Diller. ______

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

______

Objective(s): By the end of this task, I will be able to: 92

______

Task(s):

______

Exit Ticket:

______

______Math Workstation: ______Time: ______

NJSLS.:

______

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

______

MATH WORKSTATION INFORMATION CARD ______

______

Task(s):

______

Exit Ticket:

______

______Math Workstation: ______Time: ______

NJSLS.:

______

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

______

Task(s):

______

MATH WORKSTATION SCHEDULE Week of: ______DAY Technology Problem Solving Lab Fluency Math Small Group Exit Ticket: Lab Lab Journal Instruction Mon. Group ____ Group ____ Group ____ Group ____

Tues. BASED Group ____ Group ____ Group ____ Group ____ ON CURRENT Wed. Group ____ Group ____ Group ____ Group ____ OBSERVATIONAL ______DATA Thurs. Group ____ Group ____ Group ____ Group ____

Fri. Group ____ Group ____ Group ____ Group ____

______INSTRUCTIONAL GROUPING

______

94 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 Teacher Materials Recall Prior Knowledge (RPK) can take place just Assessing Prior Knowledge Quick Check before the pre-tests are given and can take 1-2 Pre-Test (Assessment days to front load prerequisite understanding Book) The Pre Test serves as a Recall Prior Knowledge Quick Check can be done in concert with the diagnostic test of readiness of RPK and used to repair student

the upcoming chapter Student Materials misunderstandings and vocabulary prior to the PRE TEST PRE Student Book (Quick pre-test ; Students write Quick Check answers Check); Copy of the Pre on a separate sheet of paper Test; Recall prior Knowledge 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 ENGAGEMENT DIRECT

95 Direct Teacher Edition The Warm Up activates prior knowledge for IndependentInvolvement/Engagement Practice 5-minuteTeacher Editionwarm up Let’seach Practicenew lesson determines readiness for Teach/Learn Teach;Let’s Practice Anchor Task WorkbookStudent Books and aresmall CLOSED; group work Big Book and is used in A formal formative asGr. formative K assessment; Students not assessmentStudents are directly involved TechnologyStudent Book readyTeacher for led; the WholeWorkbook group will use Reteach. in making sense, themselves, DigiLet’s Practice TheStudents Workbook use concrete is continued manipulatives as Independent to explore of the concepts – by Practice.concepts interacting the tools, OtherDifferentiation Options ManipulativesA few select parts CAN of be the used task as are a explicitly manipulatives, each other, FluencyAll: Workbook Practice communicationsshown, but the majority tool as needed.is addressed through and the questions Extra Support: Reteach Completelythe hands-on, Independent constructivist approach and On Level: Extra Practice Onquestioning level/advance learners should finish all Advanced: Enrichment workbookTeacher facilitates; pages. Students find the solution Guided Learning and Practice Teacher Edition Students-already in pairs /small, homogenous Guided Learning Learn ability groups; Teacher circulates between groups; Teacher, anecdotally, captures student Extending the Lesson TechnologyMath Journal thinking DigiProblem of the Lesson

Interactivities GUIDED LEARNING GUIDED StudentGames Book Small Group w/Teacher circulating among Guided Learning Pages groups Hands-on Activity Revisit Concrete and Model Drawing; Reteach Lesson Wrap Up Problem of the Lesson WorkbookTeacher spends or Extra majority Practice of Homeworktime with struggling is Homework (Workbook , onlylearners; assigned some when time students with on level,fully and less time Reteach, or Extra understandwith advanced the groupsconcepts (as additional Practice) practice)Games and Activities can be done at this time Reteach Homework (issued to struggling learners) should be checked the next day

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

Student Workbook The Chapter Review/Test can be completed INDEPENDENT PRACTICE INDEPENDENT Put on Your Thinking  Individually (e.g. for homework) then Cap reviewed in class  As a ‘mock test’ done in class and Assessment Book doesn’t count Test Prep  As a formal, in class review where teacher walks students through the questions

Test Prep is completely independent;

scored/graded

POST TEST POST POST TEST POST 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,

ADDITIONAL PRACTICE ADDITIONAL students should be doing the Put on Your Thinking Cap problems on their own

96 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:

97 CPA Strategy/Materials Ability Groupings/Pairs (by Name)

98 Task(s)/Text Resources Activity/Description

99 IDEAL MATH BLOCK LESSON PLANNING TEMPLATE

100 ) s ( : J B O

S S C DanielsonC Framework for Teaching: Domain 1: Planning Preparation

Fluency: 2.OA.2

Strategy:

Tool(s):

Y Launch N e g a G n E / s u c o F

n I Exploration h t a M

Independent Practice s

n Small Group o i t a t Instruction s k r o W

h t a M

: n o i t a i t n e r

e Tech. Lab f f i D

Problem Solving Lab 101

CCSS: 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;

102 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:

103 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;

104 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;

105 ______

Component 1F: Assessing Student Learning

Lesson Plans include:  Focus Question/Essential Understanding

 Anchor Problem

 Checks for Understanding

 Demonstration of Learning (Exit Ticket)

106 Planning Calendar September 2016

Monday Tuesday Wednesday Thursday Friday

5 6 7 8 9

12 13 14 15 16

19 20 21 22 23

EnGageNY

End of Module 1

107 Asssessment

26 27 28 29 30

SGO SGO

SGO Diagnostic (BOY) Diagnostic (BOY)

Diagnostic (BOY) Assessment Assessment

Assessment

October 2016

3 4 5 6 7

MIF Ch. 7 Test Prep

108 Performance Task

10 11 12 13 14

Math Workstations: Math Workstations: Math Workstations:

SGO SGO SGO

Performance Tasks Performance Tasks Performance Tasks

17 18 19 20 21

EnGageNY

End of Module 2

Assessment

24 25 26 27 28

Math Workstations: Math Workstations: Math Workstations:

109 SGO SGO SGO

Fluency Assessments Fluency Assessments Fluency Assessments

MIF Ch. 13 Test Prep

Performance Task

110 Planning Calendar November 2016

1 2 3 4

7 8 9 10 11

Performance Tasks

Fluency Benchmark I

END OF MP

14 15 16 17 18

111 21 22 23 24 25

28 29 30

December 2016

5 6 7 8 9

112 12 13 14 15 16

19 20 21 22 23

26 27 28 29 30

113 Grade 2 Unit 1 Instructional and Assessment Framework

Recommended Activities CCSS Notes Pacing

September 8-9, 2016 Setting Up Classroom Routines/Procedures Routines/Procedures: Introduction to Math Workstations 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 EnGageNY Module B Lesson 4 2.OA.1 EnGageNY Modules provided Make a ten to add within 20 2.OA.2 by Math Department: 2.NBT.5 Lesson Implementation: September 16, 2016 EnGageNY Module B Lesson 5 50-60 minutes Make a ten to add within 100 September 19, 2016 EnGageNY Module B Lesson 6 Continue to reinforce mental Subtract single-digit numbers from multiples of 10 within strategies: 100 Count on/Count back; Making ten/Decomposing ten; September 20, 2016 EnGageNY Module B Lesson 7 Addition and subtraction Take from ten within 20 relationships; Doubles +/- September 21, 2016 EnGageNY Module B Lesson 8 Take from ten within 100 Demonstration of Learning: Exit tickets: (5 min.) Students complete independently. September 22, 2016 EnGageNY End of Module 1 Assessment Analyze and utilize the results of exit tickets to drive

114 September 23, 2016 Math In Focus Ch. 7

Chapter Opener

Recall Prior Knowledge

Quick Check

Pre-Test

instructional decision making. Place exit tickets in Student September 26, 2016 Math In Focus Ch. 7 Lesson 1 Portfolios

Measuring in Meters

September 27, 2016 Math In Focus Ch. 7 Lesson 2

Comparing Lengths in Meters

Math Workstation: SGO Diagnostic (BOY) Assessment

115 September 28, 2016 Math In Focus Ch. 7 Lesson 3 9/27 -9/30

Administer Measuring in Centimeters

SGO Assessments Math Workstation: SGO Diagnostic (BOY) Assessment

during the last 20 minutes September 29, 2016 Math In Focus Ch. 7 Lesson 4

of the math block.

Comparing Lengths in Centimeters

Math Workstation: SGO Diagnostic (BOY) Assessment

September 30, 2016 Math In Focus Ch. 7 Lesson 5

Real World Problems: Metric Length

Math In Focus Ch. 7 EnGageNY Modules

provided by Math October 3, 2016 Problem Solving

116 Chapter Wrap-Up Department:

Lesson Implementation: October 4, 2016 Math In Focus Ch. 7 Test Prep

50-60 minutes MIF Ch. 7 Performance Task

Demonstration of Learning: EnGageNY Module 2 A Lesson 1 2.OA.1

Exit tickets: (5 min.) Connect measurement with physical units by using 2.OA.2 October 5, 2016

multiple copies of the same physical unit to measure Students complete 2.MD.1

independently. October 6, 2016 EnGageNY Module 2 A Lesson 2 2.MD.2

Analyze and utilize the Use iteration with one physical unit to measure 2.MD.3

results of exit tickets to October 7, 2016 EnGageNY Module 2 A Lesson 3 2.MD.4

117 Apply concepts to create unit rulers and measure drive instructional decision

lengths using unit rulers making.

EnGageNY Module 2 B Lesson 4 Place exit tickets in Student

2.MD.5

Measure various objects using centimeter rulers and October 10, 2016 Portfolios

2.MD.6

meter sticks

EnGageNY Module 2 B Lesson 5 Thinkcentral.com for MIF

Develop estimation strategies by applying prior October 11, 2016 materials

knowledge of length and using mental benchmarks

EnGageNY Module 2 C Lesson 6

Measure and compare lengths using centimeters and October 12, 2016

meters

118 EnGageNY Module 2 C Lesson 7

Measure and compare lengths using metric length units October 13, 2016

and non-standard length units;

EnGageNY Module 2 D Lesson 8

Solve addition and subtraction word problems using October 14, 2016

the ruler as a number line

EngageNY Module 2 D Lesson 9

Measure lengths of string using measurement tools; October 17, 2016

and use tape diagrams to represent and compare the

lengths

EngageNY Module 2 D Lesson 10

119 October 18, 2016 Apply conceptual understanding of measurement by

solving two-step word problems

120 Recommended Activities CCSS Notes

Pacing

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

121 October 24, 2016 Math In Focus Chapter 13 Lesson 2 10/24 -10/26

Comparing Lengths in Feet Administer

Math Workstations: SGO Fluency Assessments SGO Assessments

October 25, 2016 Math In Focus Chapter 13 Lesson 3 during the last 20

Measuring in Inches minutes of the math

Math Workstations: SGO Fluency Assessments block.

Comparing Lengths in Inches and Feet

Math Workstations: SGO Fluency Assessments

Real World Problems: Customary Length

122 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

November 3, 2016

123 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:

124 Blocks

Jumping Contest

125 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: ______

126 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.

127 128 129 130 Solution: ______

131 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.

Performance Task (2.MD.5)

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

133 134 135 Solution: ______

136 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)

137 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.

138 139 140 Solution: ______

141 142 2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a

(SAMPLE)

Express Yourself

Math Journal (2.MD.4)

143 What can you say about the objects below?

Use words, pictures and numbers to express your thinking.

144 145 146 147 2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a

(SAMPLE)

Measurements

Math Journal (2.MD.4)

148 What can you say about the objects below?

Use words, pictures and numbers to express your thinking.

149 150 151 152 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

5+5 9+0

12-3 11-4

153 3 23

4+6 8+1

15-6 7-3

3+7 2+7

11-3 8-6

2+8 6+3

17-12 11-8

1+9 5+4

12-6 13-9

154 11 31

0+10 4+4

9-3 14-9

5+3 6+2

11-9 13-7

1+7 0+8

9-7 15-8

7+0 1+6

15-3 16-8

155 4+3

5+2 20-11

156 Got It Not There Yet

Evidence shows that the student essentially has the target Student Second shows Grade evidence PLD ofRubric a major misunderstanding, incorrect concepts or procedure, or a

concept or big math idea. failure to engage in the task.

PLD Level 5: 100% PLD Level 4: 89% PLD Level 3: 79% PLD Level 2: 69% PLD Level 1: 59%

Distinguished command Strong Command Moderate Command Partial Command Little Command

Student work shows Student work shows strong Student work shows moderate Student work shows partial Student work shows little

distinguished levels of levels of understanding of the levels of understanding of the understanding of the understanding of the

understanding of the mathematics. mathematics. mathematics. mathematics.

mathematics.

Student constructs and Student constructs and Student constructs and Student attempts to constructs 157

Student constructs and communicates a complete communicates a complete communicates an incomplete and communicates a response

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.

159 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?

160  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.

161 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.

162 Data Analysis Form School: ______Teacher: ______Date: ______

Assessment: ______NJSLS: ______

GROUPS (STUDENT INITIALS) SUPPORT PLAN PROGRESS

MASTERED (86% - 100%):

DEVELOPING (67% - 85%):

163 INSECURE (51%-65%):

BEGINNING (0%-50%):

164 165 Student Conference Form SCHOOL: ______TEACHER: ______

Student Name: ______Date: ______

NJSLS: ACTIVITY OBSERVED:

OBSERVATION NOTES:

166 FEEDBACK GIVEN:

GOAL SET:

167 NEXT STEPS:

168 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.

169 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

170  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

1 w/Opportunity for Student Interviews .

1 The Mathematics Department will provide guidance on task selection, thereby standardizing the process across the district and across grades/courses. 171  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.

172 2  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

2 The Mathematics Department has propagated gradebooks with appropriate weights. 173 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.

174 GRADES K-2

Purging and Next-Grade Transitioning

rd During the third (3 ) 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

175 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.

176 MATHEMATICIAN: ______SCHOOL: ______TEACHER: ______DATE: ______

MATH PORTFOLIO REFLECTION FORM

PORTFOLIO ARTIFACT: ______

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

______

178 ______

______

THIS WORK ALSO SHOWS THAT I NEED TO WORK ON…

______

179 ______

______

180 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 0+19 0+18 0+17 0+16 0+15 0+14 0+13 0+12 0+11 0+10 0+9 0+8 0+7 0+6 0+5 0+4 0+3 0+2 0+1

20+0 19+0 18+0 17+0 16+0 15+0 14+0 13+0 12+0 11+0 10 +0 9+0 8+0 7+0 6+0 5+0 4+0 3+0 2+0 1+0 0+0

1+19 1+18 1+17 1+16 1+15 1+14 1+13 1+12 1+11 1+10 1+9 1+8 1+7 1+6 1+5 1+4 1+3 1+2

19+1 18+1 17+1 16+1 15+1 14+1 13+1 12+1 11+1 10+1 9+1 8+1 7+1 6+1 5+1 4+1 3+1 2+1 1+1

2+18 2+17 2+16 2+15 2+14 2+13 2+12 2+11 2+10 2+9 2+8 2+7 2+6 2+5 2+4 2+3

18+2 17+2 16+2 15+2 14+2 13+2 12+2 11+2 10+2 9+2 8+2 7+2 6+2 5+2 4+2 3+2 2+2

181 3+17 3+16 3+15 3+14 3+13 3+12 3+11 3+10 3+9 3+8 3+7 3+6 3+5 3+4

17+3 16+3 15+3 14+3 13+3 12+3 11+3 10+3 9+3 8+3 7+3 6+3 5+3 4+3 3+3

4+16 4+15 4+14 4+13 4+12 4+11 4+10 4+9 4+8 4+7 4+6 4+5

16+4 15+4 14+4 13+4 12+4 11+4 10+4 9+4 8+4 7+4 6+4 5+4 4+4

5+15 5+14 5+13 5+12 5+11 5+10 5+9 5+8 5+7 5+6

15+5 14+5 13+5 12+5 11+5 10+5 9+5 8+5 7+5 6+5 5+5

6+14 6+13 6+12 6+11 6+10 6+9 6+8 6+7

14+6 13+6 12+6 11+6 10+6 9+6 8+6 7+6 6+6

7+13 7+12 7+11 7+10 7+9 7+8 7+7

182 13+7 12+7 11+7 10+7 9+7 8+7

8+12 8+11 8+10 8+9

12+8 11+8 10+8 9+8 8+8

9+11 9+10

11+9 10+9 9+9

183 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

184 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

185 6-0 6-1 6-2 6-3 6-4 6-5 6-6

186 5-0 5-1 5-2 5-3 5-4 5-5

187 4-0 4-1 4-2 4-3 4-4

188 3-0 3-1 3-2 3-3

189 Resources

Engage NY

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

191 Common Core Tools

http://commoncoretools.me/

http://www.ccsstoolbox.com/

http://www.achievethecore.org/steal-these-tools

Achieve the Core

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

Manipulatives

192 http://nlvm.usu.edu/en/nav/vlibrary.html

http://www.explorelearning.com/index.cfm?method=cResource.dspBrowseCorrelations&v=s&id=USA-000

http://www.thinkingblocks.com/

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

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

193 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

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