6th Grade Mathematics
1st Grade Mathematics
Addition and Subtraction Within 20
Unit 1 Curriculum Map: September 8th- November 9th, 2016
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First Grade Unit 1 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. |First Grade Unit I NJSLS |p. 16 |
|X. |Eight Mathematical Practices |p. 28 |
|XI. |Ideal Math Block |p. 30 |
|XII. |Math Workstations |p. 31 |
|XIII. |Math In Focus Lesson Structure |p. 34 |
|XIX. |Ideal Math Block Planning Template |p. 37 |
|XX. |Planning Calendar |p. 40 |
|XXI. |Instructional and Assessment Framework |p. 42 |
|XXII. |Performance Tasks |p. 46 |
|XXIII. |PLD Rubric |p. 49 |
|XXIV. |Data Driven Instruction |p. 50 |
|XXV. |Math Portfolio Expectations |p. 53 |
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
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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:
1.OA.1
Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
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 (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Learning Goal(s):
Students will use multiple representations to solve multi-step addition and/or subtraction situations (1.OA.1) and explain the connection between various solution paths (1.OA.6).
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 |…getting there |…that’s it |WOW! | |
| |1 |2 |3 |4 | |
|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 |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 and say what I did and why I| |
|or | | | |did it. | |
|Write | | |I can write or talk about why I did it. | | |
| |I am not able to draw or show my |I can draw, but not show my thinking; |I can draw and show my thinking |I can draw, show and talk about my | |
|Draw |thinking. |or | |thinking. | |
|or | |I can show but not draw my thinking; | | | |
|Show | | | | | |
| | | | | | |
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.
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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:
o place value,
o properties of operations, and/or
o 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.
K-2 CONCEPT MAP
|First Grade Unit I |
|In this Unit Students will: |
| |
|1.OA.1-8 |
| |
|Solve addition and subtraction situations involving: |
|Adding to, |
|Taking From , |
|Putting Together, |
|Taking Apart, and |
|Comparing situations. |
| |
|Apply the following problem solving strategies |
|Use of objects and/or drawings |
|Counting On |
|Making Ten |
|Decomposing Numbers |
|Properties of Operations |
|Relationship between Addition and Subtraction |
| |
|1.NBT.1 |
| |
|Count to 120 starting at any number less than 120 |
|Reade and write numerals |
|Represent number of objects with a written numeral |
| |
| |
|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 |
|1.OA.1 | |
| |Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in |
| |all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. |
| |
|First grade students extend their experiences in Kindergarten by working with numbers to 20 to solve a new type of problem situation: Compare (See Table 1 at end of document for examples of all problem types). In a |
|Compare situation, two amounts are compared to find “How many more” or “How many less”. |
| |
| |
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|New Jersey Student Learning Standards: Operations and Algebraic Thinking |
|1.OA.2 |Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20. |
| |
|First Grade students solve multi-step word problems by adding (joining) three numbers whose sum is less than or equal to 20, using a variety of mathematical representations. |
| |
|Example: |
|Mrs. Smith has 4 oatmeal raisin cookies, 5 chocolate chip cookies, and 6 gingerbread cookies. How many cookies does Mrs. Smith have? |
| |
|Student A: |
|I put 4 counters on the Ten Frame for the oatmeal raisin cookies. Then, I put 5 different color counters on the ten frame for the chocolate chip cookies. Then, I put another 6 color counters out for the gingerbread |
|cookies. Only one of the gingerbread cookies fit, so I had 5 leftover. Ten and five more makes 15 cookies. Mrs. Smith has 15 cookies. |
| |
|[pic] |
|Student B: |
|I used a number line. First I jumped to 4, and then I jumped 5 more. That’s 9. I broke up 6 into 1 and 5 so I could jump 1 to make 10. Then, I jumped 5 more and got 15. Mrs. Smith has 15 cookies. |
|[pic] |
| |
|Student C: |
|I wrote: 4 + 5 + 6 = 1. I know that 4 and 6 equals 10, so the oatmeal raisin and gingerbread equals 10 cookies. |
|Then I added the 5 chocolate chip cookies. 10 and 5 is 15. So, Mrs. Smith has 15 cookies. |
|New Jersey Student Learning Standards: Operations and Algebraic Thinking |
|1.OA.3 |Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 |
| |+ 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) Students need not use formal terms for these |
| |properties. |
|Elementary students often believe that there are hundreds of isolated addition and subtraction facts to be mastered. However, when students understand the commutative and associative properties, they are able to use|
|relationships between and among numbers to solve problems. First Grade students apply properties of operations as strategies to add and subtract. Students do not use the formal terms “commutative” and associative”. |
|Rather, they use the understandings of the commutative and associative property to solve problems. |
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|Students use mathematical tools and representations (e.g., cubes, counters, number balance, number line, 100 chart) to model these ideas. |
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|Commutative Property Examples: Cubes |
|A student uses 2 colors of cubes to make as many different combinations of 8 as possible. |
|When recording the combinations, the student records that 3 green cubes and 5 blue cubes |
|equals 8 cubes in all. In addition, the student notices that 5 green cubes and 3 blue cubes also equals 8 cubes. |
| |
| |
|Associative Property Examples: |
|Number Line: 1 = 5 + 4 + 5 |
|Student A: First I jumped to 5. Then, I jumped 4 more, so I landed on 9. Then I jumped 5 more and landed on 14. |
|[pic] |
|Student B: I got 14, too, but I did it a different way. First I jumped to 5. Then, I jumped 5 again. That’s 10. |
|Then, I jumped 4 more. See, 14! |
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|Mental Math: There are 9 red jelly beans, 7 green jelly beans, and 3 black jelly beans. How many jelly beans are there in all? |
|Student: “I know that 7 + 3 is 10. And 10 and 9 is 19. There are 19 jelly beans.” |
| |
|1.OA.4 |Understand subtraction as an unknown-addend problem |
| |
|First Graders often find subtraction facts more difficult to learn than addition facts. By understanding the relationship between addition and subtraction, First Graders are able to use various strategies described |
|below to solve subtraction problems. |
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|For Sums to 10 |
| |
|*Think-Addition: |
|Think-Addition uses known addition facts to solve for the unknown part or quantity within a problem. When students use this strategy, they think, “What goes with this part to make the total?” The think-addition |
|strategy is particularly helpful for subtraction facts with sums of 10 or less and can be used for sixty-four of the 100 subtraction facts. Therefore, in order for think-addition to be an effective strategy, |
|students must have mastered addition facts first. |
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|For example, when working with the problem 9 - 5 = (, First Graders think “Five and what makes nine?”, rather than relying on a counting approach in which the student counts 9, counts off 5, and then counts what’s |
|left. When subtraction is presented in a way that encourages students to think using addition, they use known addition facts to solve a problem. |
| |
|Example: 10 - 2 = ( |
|Student: “2 and what make 10? I know that 8 and 2 make 10. So, 10 - 2 = 8.” |
| |
|For Sums Greater than 10 |
|The 36 facts that have sums greater than 10 are often considered the most difficult for students to master. Many students will solve these particular facts with Think-Addition (described above), while other students|
|may use other strategies described below, depending on the fact. Regardless of the strategy used, all strategies focus on the relationship between addition and subtraction and often use 10 as a benchmark number. |
| |
|*Build Up Through 10: |
|This strategy is particularly helpful when one of the numbers to be subtracted is 8 or 9. Using 10 as a bridge, either 1 or 2 are added to make 10, and then the remaining amount is added for the final sum. |
| |
|Example: 15 -9 = ( |
|Student A: “I’ll start with 9. I need one more to make 10. Then, I need 5 more to make 15. That’s 1 and 5- so it’s 6. 15 0 9 = 6.” |
| |
|Student B: “I put 9 counters on the 10 frame. Just looking at it I can tell that I need 1 more to get to 10. Then I need 5 more to get to 15. So, I need 6 counters.” |
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|[pic] |
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|*Back Down Through 10 |
|This strategy uses take-away and 10 as a bridge. Students take away an amount to make 10, and then take away the rest. It is helpful for facts where the ones digit of the two-digit number is close to the number |
|being subtracted. |
| |
|Example: 16 – 7 = 1 |
|Student A: “I’ll start with 16 and take off 6. That makes 10. I’ll take one more off and that makes 9. 16 – 7 = 9.” |
| |
|Student B: “I used 16 counters to fill one ten frame completely and most of the other one. Then, I can take these 6 off from the 2nd ten frame. Then, I’ll take one more from the first ten frame. That leaves 9 on the|
|ten frame.” |
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|[pic] |
|1.OA.5 |Relate counting to addition and subtraction |
| |
|When solving addition and subtraction problems to 20, First Graders often use counting strategies, such as counting all, counting on, and counting back, before fully developing the essential strategy of using 10 as |
|a benchmark number. Once students have developed counting strategies to solve addition and subtraction problems, it is very important to move students toward strategies that focus on composing and decomposing number|
|using ten as a benchmark number, as discussed in 1.OA.6, particularly since counting becomes a hindrance when working with larger numbers. By the end of First Grade, students are expected to use the strategy of 10 |
|to solve problems. |
| |
|Counting All: Students count all objects to determine the total amount. |
| |
|Counting On & Counting Back: Students hold a “start number” in their head and count on/back from that number. |
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|Example: 15 + 2 = 1 |
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|Example: 12 – 3 = 1 |
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|[pic] |
|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 (e.g., knowing that 8 + 4 = 12, one|
| |knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). |
| |
|In First Grade, students learn about and use various strategies to solve addition and subtraction problems. When students repeatedly use strategies that make sense to them, they internalize facts and develop fluency|
|for addition and subtraction within 10. When students are able to demonstrate fluency within 10, they are accurate, efficient, and flexible. First Graders then apply similar strategies for solving problems within |
|20, building the foundation for fluency to 20 in Second Grade. |
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|Developing Fluency for Addition & Subtraction within 10 |
|Example: Two frogs were sitting on a log. 6 more frogs hopped there. How many frogs are sitting on the log now? |
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|[pic] |
|Add and Subtract within 20 |
|Example: Sam has 8 red marbles and 7 green marbles. How many marbles does Sam have in all? |
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|[pic] |
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|Example: There were 14 birds in the tree. 6 flew away. How many birds are in the tree now? |
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|[pic] |
|1.OA.7 |Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are |
| |true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. |
| | |
| |
|In order to determine whether an equation is true or false, First Grade students must first understand the meaning of the equal sign. This is developed as students in Kindergarten and First Grade solve numerous |
|joining and separating situations with mathematical tools, rather than symbols. Once the concepts of joining, separating, and “the same amount/quantity as” are developed concretely, First Graders are ready to |
|connect these experiences to the corresponding symbols (+, -, =). Thus, students learn that the equal sign does not mean “the answer comes next”, but that the symbol signifies an equivalent relationship that the |
|left side ‘has the same value as’ the right side of the equation. |
| |
|When students understand that an equation needs to “balance”, with equal quantities on both sides of the equal sign, they understand various representations of equations, such as: |
|• an operation on the left side of the equal sign and the answer on the right side (5 + 8 = 13) |
|• an operation on the right side of the equal sign and the answer on the left side (13 = 5 + 8) |
|• numbers on both sides of the equal sign (6 = 6) |
|• operations on both sides of the equal sign (5 + 2 = 4 + 3). |
| |
|Once students understand the meaning of the equal sign, they are able to determine if an equation is true (9 = 9) or false (9 = 8). |
|1.OA.8 | |
| |Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true |
| |in each of the equations 8 + ? = 11, 5 = _ – 3, 6 + 6 = _. |
|First Graders use their understanding of and strategies related to addition and subtraction as described in 1.OA.4 and 1.OA.6 to solve equations with an unknown. Rather than symbols, the unknown symbols are boxes or|
|pictures. |
| |
|Example: Five cookies were on the table. I ate some cookies. Then there were 3 cookies. How many cookies did I eat? |
|Student A: What goes with 3 to make 5? 3 and 2 is 5. So, 2 cookies were eaten. |
|Student B: Fiiivee, four, three (holding up 1 finger for each count). 2 cookies were eaten (showing 2 fingers). |
|Student C: We ended with 3 cookies. Threeeee, four, five (holding up 1 finger for each count). 2 cookies were eaten (showing 2 fingers). |
| |
|Example: Determine the unknown number that makes the equation true. 5 - 1 = 2 |
|Student: 5 minus something is the same amount as 2. Hmmm. 2 and what makes 5? 3! So, 5 minus 3 equals 2. |
|Now it’s true! |
|1.NBT.1 |Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. |
| |
|Count on from a number ending at any number up to 120. |
|Recognize and explain patterns with numerals on a hundreds chart. |
|Understand that the place of a digit determines its value. For example, students recognize that 24 is different from and less than 42.) |
|Explain their thinking with a variety of examples. |
|Read and write numerals to 120. |
| |
|Students extend the range of counting numbers, focusing on the patterns evident in written numerals. This is the foundation for thinking about place value and the meaning of the digits in a numeral. Students are |
|also expected to read and write numerals to 120. |
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 workstations 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.
[pic][pic]
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 |Problem Solving Lab |Fluency |Math |Small Group Instruction |
| |Lab | |Lab |Journal | |
|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 |Teacher Materials |Recall Prior Knowledge (RPK) can take place just before the |
|Assessing Prior Knowledge |Quick Check |pre-tests are given and can take 1-2 days to front load |
| |Pre-Test (Assessment Book) |prerequisite understanding |
| |Recall Prior Knowledge | |
|The Pre Test serves as a diagnostic test of| |Quick Check can be done in concert with the RPK and used to |
|readiness of the upcoming chapter |Student Materials |repair student misunderstandings and vocabulary prior to the |
| |Student Book (Quick Check); Copy of |pre-test ; Students write Quick Check answers on a separate sheet |
| |the Pre Test; Recall prior Knowledge |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 |Teacher Edition |The Warm Up activates prior knowledge for each new lesson |
|Teach/Learn |5-minute warm up |Student Books are CLOSED; Big Book is used in Gr. K |
| |Teach; Anchor Task |Teacher led; Whole group |
|Students are directly involved in making | |Students use concrete manipulatives to explore concepts |
|sense, themselves, of the concepts – by |Technology |A few select parts of the task are explicitly shown, but the |
|interacting the tools, manipulatives, each |Digi |majority is addressed through the hands-on, constructivist |
|other, and the questions | |approach and questioning |
| |Other |Teacher facilitates; Students find the solution |
| |Fluency Practice | |
|Guided Learning and Practice |Teacher Edition |Students-already in pairs /small, homogenous ability groups; |
|Guided Learning |Learn |Teacher circulates between groups; Teacher, anecdotally, captures |
| | |student thinking |
| |Technology | |
| |Digi | |
| | |Small Group w/Teacher circulating among groups |
| |Student Book |Revisit Concrete and Model Drawing; Reteach |
| |Guided Learning Pages |Teacher spends majority of time with struggling learners; some |
| |Hands-on Activity |time with on level, and less time with advanced groups |
| | |Games and Activities can be done at this time |
| | | |
|Independent Practice |Teacher Edition |Let’s Practice determines readiness for Workbook and small |
| |Let’s Practice |group work and is used as formative assessment; Students not |
|A formal formative | |ready for the Workbook will use Reteach. The Workbook is |
|assessment |Student Book |continued as Independent Practice. |
| |Let’s Practice |Manipulatives CAN be used as a communications tool as needed. |
| | |Completely Independent |
| |Differentiation Options |On level/advance learners should finish all workbook pages. |
| |All: Workbook | |
| |Extra Support: Reteach | |
| |On Level: Extra Practice | |
| |Advanced: Enrichment | |
| Extending the Lesson |Math Journal | |
| |Problem of the Lesson | |
| |Interactivities | |
| |Games | |
| Lesson Wrap Up |Problem of the Lesson |Workbook or Extra Practice Homework is only assigned when |
| |Homework (Workbook , Reteach, or |students fully understand the concepts (as additional |
| |Extra Practice) |practice) |
| | |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 End of Chapter |
|and Post Test |Chapter Review/Test |Test Prep. Put on your Thinking Cap prepares students for |
| |Put on Your Thinking Cap |novel questions on the Test Prep; Test Prep is graded/scored. |
| | |The Chapter Review/Test can be completed |
| |Student Workbook |Individually (e.g. for homework) then reviewed in class |
| |Put on Your Thinking Cap |As a ‘mock test’ done in class and doesn’t count |
| | |As a formal, in class review where teacher walks students |
| |Assessment Book |through the questions |
| |Test Prep | |
| | |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) |
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|Task(s)/Text Resources |Activity/Description |
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IDEAL MATH BLOCK LESSON PLANNING TEMPLATE
|CCSS &| |
|OBJ:(s| |
|) | |
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| | |
| | |
| |Fluency: | |
| |1.OA.6 | |
| |1.NBT.1 | |
| |Strategy: | |
| | | |
| |Tool(s): | |
|Math |Launch | |
|In | | |
|Focus/| | |
|EnGage| | |
|NY | | |
| |Exploration | |
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| |Independent Practice | |
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|Differ|Small Group Instruction | |
|entiat| | |
|ion: | | |
|Math | | |
|Workst| | |
|ations| | |
| |Tech. Lab | |
| |Problem Solving Lab | |
| |CCSS: | |
| |1.OA.1 | |
| |1.OA.2 | |
| |1.NBT.4 | |
| | | |
| | | |
| |Fluency Lab | |
| |1.OA.6 | |
| |1.NBT.5 | |
| |1.NBT.6 | |
| | | |
| |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 |23 |
|MIF Ch.1 Test Prep | | | |SGO |
|& | | | |Diagnostic (BOY) |
|MIF Ch.1 | | | |Assessment |
|Performance Task | | | | |
|26 |27 |28 |29 |30 |
October 2016
|Monday |Tuesday |Wednesday |Thursday |Friday |
|3 |4 |5 |6 |7 |
| | | | | |
| |Math Workstations: |Math Workstations: |Math Workstations: | |
| |SGO |SGO |SGO | |
| |Performance Tasks |Performance Tasks |Performance Tasks | |
|10 |11 |12 |13 |14 |
| | | |MIF Ch.2 Test Prep | |
| | | |& | |
| | | |MIF Ch.2 | |
| | | |Performance Task | |
|17 |18 |19 |20 |21 |
| |Math Workstations: |Math Workstations: |Math Workstations: | |
| |SGO |SGO |SGO | |
| |Fluency Assessments |Fluency Assessments |Fluency Assessments | |
|24 |25 |26 |27 |28 |
| | | |MIF Ch.3 Test Prep | |
| | | |& | |
| | | |MIF Ch.3 | |
| | | |Performance Task | |
|31 | | | | |
Planning Calendar November 2016
|Monday |Tuesday |Wednesday |Thursday |Friday |
| |1 |2 |3 |4 |
|7 |8 |9 |10 |11 |
| | |EnGageNY Module 1 | | |
| | |Mid-Module Assessment | | |
| | |END OF MP | | |
|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 |
First Grade Unit 1 Instructional and Assessment Framework
|Recommended |Activities |CCSS |Notes |
|September 8-9, 2016 |Math In Focus Ch.1 Opener | |Routines/Procedures |
| |Introduction to Math Workstations, and | |Ask 3 Then Me; |
| |Notebook Expectations | |Math Talk Moves; |
|September 12-30, 2016 |Math In Focus: Numbers to 10 and Number Bonds |
| |EnGageNY Module 1: Sums and Differences to 10: Mental Math Strategies. |
|September 12, 2016 |Math In Focus Ch. 1 Lesson 1 |1.NBT.1 |Math In Focus: |
| |Counting to 10 |.4 | |
| | |.6 |Access Assessments |
| | | |Pre-Test |
| | | |Chapter Review |
| | | |Test Prep |
| | | |Performance Tasks |
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| | | |EnGageNY Modules |
| | | |provided by Math Department; |
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| | | |10/4 - 10/6/2016 |
| | | |Administer |
| | | |SGO Assessments |
| | | |during the last 20 minutes of the |
| | | |math block. |
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| | | |10/18 -10/20/2016 |
| | | |Administer |
| | | |SGO Assessments |
| | | |during the last 20 minutes of the |
| | | |math block. |
|September 13, 2016 |Math In Focus Ch. 1 Lesson 2 | | |
| |Comparing Numbers | | |
|September 14, 2016 |Math In Focus Ch. 1 Lesson 2 | | |
| |Comparing Numbers | | |
|September 15, 2016 |Math In Focus Ch. 1 Lesson 3 | | |
| |Making Number Patterns | | |
| September 16, 2016 |Math In Focus Ch. 1 | | |
| |Put On Your Thinking Cap | | |
| |Chapter Wrap Up & Chapter Review | | |
|September 19, 2016 |Math In Focus Ch. 1 Test Prep | | |
| |Math In Focus Ch. 1 Performance Task | | |
|September 20, 2016 |EnGageNY Module 1 Lesson 1 |1.OA.1 1.OA.5 | |
| |Analyze and describe embedded numbers (to 10) using 5-groups and number | | |
| |bonds. | | |
|September 21, 2016 |EnGageNY Module 1 Lesson 2 | | |
| |Reason about embedded numbers in varied configurations using number bonds. | | |
|September 22, 2016 |EnGageNY Module 1 Lesson 3 |1.OA.1 1.OA.5 | |
| |See and describe numbers of objects using 1 more within 5-group | | |
| |configurations | | |
|September 23, 2016 |First Grade SGO Diagnostic Assessment | | |
|September 26, 2016 |EnGageNY Module 1 Lesson 4 |1.OA.1 1.OA.5 | |
| |Represent put together situations with number bonds. Count on from one |1.OA.6 | |
| |embedded number or part to totals of 6 and 7, and generate all addition | | |
| |expressions for each total. | | |
|September 27, 2016 |EnGageNY Module 1 Lesson 5 | | |
| |Represent put together situations with number bonds. Count on from one | | |
| |embedded number or part to totals of 6 and 7, and generate all addition | | |
| |expressions for each total. | | |
|September 28, 2016 |EnGageNY Module 1 Lesson 6 |1.OA.1 1.OA.5 | |
| |Represent put together situations with number bonds. Count on from one |1.OA.6 | |
| |embedded number or part to totals of 8 and 9, and generate all expressions | | |
| |for each total. | | |
|September 29, 2016 |EnGageNY Module 1 Lesson 7 | | |
| |Represent put together situations with number bonds. Count on from one | | |
| |embedded number or part to totals of 8 and 9, and generate all expressions | | |
| |for each total. | | |
|September 30, 2016 |EnGageNY Module 1 Lesson 8 | | |
| |Represent all the number pairs of 10 as number bonds from a given scenario, | | |
| |and generate all expressions equal to 10. | | |
| |EnGageNY Module 1 Lesson 9 | | |
|October 3, 2016 |Solve add to with result unknown and put together with result unknown math | | |
| |stories by drawing, writing equations, and making statements of the solution | | |
|October 4, 2016 |EnGageNY Module 1 Lesson 10 | | |
| |Solve put together with result unknown math stories by drawing and using | | |
| |5-group cards | | |
| |Math Workstations: | | |
| |Administer SGO Performance Task: Grapes | | |
| |EnGageNY Module 1 Lesson 11 | | |
|October 5, 2016 |Solve add to with change unknown math stories as a context for counting on by| | |
| |drawing, writing equations and making statements of the solution | | |
| |Math Workstations: | | |
| |Administer SGO Performance Task: Cats | | |
|October 6, 2016 |EnGageNY Module 1 Lesson 12 | | |
| |Solve add to with change unknown math stories using 5-group cards | | |
| |Math Workstations: | | |
| |Administer SGO Performance Task: Flowers | | |
|October 7, 2016 |Math In Focus Ch.2 Opener |1.OA.3 | |
| |Introduction to Math Workstations |1.OA.6 | |
| |Math In Focus Ch.2 Lesson 1 | | |
|October 10, 2016 |Number Bonds | | |
| |Math In Focus Ch.2 Lesson 1 | | |
|October 11, 2016 |Number Bonds | | |
| |Math In Focus Ch. 2 | | |
|October 12, 2016 |Put On Your Thinking Cap | | |
| |Chapter Wrap Up & Chapter Review | | |
| |Math In Focus Ch. 2 Test Prep | | |
|October 13, 2016 |Math In Focus Ch. 2 Performance Task | | |
|October 14, 2016 |EnGageNY Module 1 Lesson 13 |1.OA.5 1.OA.8 | |
| |Tell put together with result unknown, add to with result unknown and add to |1.OA.6 | |
| |with change unknown stories from equations | | |
|October 17, 2016 |EnGageNY Module 1 Lesson 14 | | |
| |Count on up to 3 more using numeral and 5-group cards and fingers to track | | |
| |the change | | |
| |EnGageNY Module 1 Lesson 15 | | |
|October 18, 2016 |Count on up to 3 more using numeral and 5-group cards and fingers to track | | |
| |the change | | |
| |Math Workstations: | | |
| |Administer SGO Fluency Assessments | | |
|October 19, 2016 |EnGageNY Module 1 Lesson 16 | | |
| |Count on to find the unknown part in missing addend equations | | |
| |Math Workstations: | | |
| |Administer SGO Fluency Assessments | | |
| |Math In Focus Ch.3 Opener |1.OA.1 | |
|October 20, 2016 |Math Workstations |1.OA.3 | |
| |Math Workstations: |1.OA.5 | |
| |Administer SGO Fluency Assessments |1.OA.6 | |
| | |1.OA.7 | |
| | |1.OA.8 | |
|October 21, 2016 |Math in Focus Ch. 3 lesson 1 | | |
| |Ways to add | | |
|October 24, 2016 |Math in Focus Ch. 3 lesson 2 | | |
| |Making Addition Stories | | |
|October 25, 2016 |Math in Focus Ch.3 lesson 3 | | |
| |Real World Problems | | |
|October 26, 2016 |Math In Focus Ch. 3 | | |
| |Put On Your Thinking Cap | | |
| |Chapter Wrap Up & Chapter Review | | |
|October 27, 2016 |Math in Focus Ch. 3 Test Prep | | |
| |Math In Focus Ch. 3 Performance Task | | |
|October 28, 2016 |EnGageNY Module 1 Lesson 17 |1.OA.3 | |
| |Understand meaning of equal sign by pairing equivalent expressions and |1.OA.6 | |
| |constructing true number sentences |1.OA.7 | |
|October 31, 2016 |EnGageNY Module 1 Lesson 18 | | |
| |Understand the meaning of the equal sign by pairing equivalent expressions | | |
| |and constructing true number sentences | | |
|November 1, 2016 |EnGageNY Module 1 Lesson 19 | | |
| |Represent the same story scenario with addends repositioned (commutative | | |
| |property) | | |
|November 2, 2016 |EnGageNY Module 1 Lesson 20 | | |
| |Apply the commutative property to count on from a larger addend | | |
|November 3, 2016 |EnGageNY Module 1 Lesson 21 |1.OA.3 | |
| |Visualize and solve doubles and doubles plus 1 |1.OA.6 | |
| | |1.OA.7 | |
|November 4, 2016 |EnGageNY Module 1 Lesson 22 | | |
| |Make use of repeated reasoning on the addition chart by solving and analyzing| | |
| |problems | | |
|November 7, 2016 |EnGageNY Module 1 Lesson 23 | | |
| |Look for and make use of structure on the addition chart by looking for and | | |
| |coloring problems with the same total. | | |
|November 8, 2016 |EnGageNY Module 1 Lesson 24 | | |
| |Practice to build fluency with fact to 10 | | |
|November 9, 2016 |EnGageNY Module 1 Mid-Module Assessment | | |
New Jersey Student Learning Standards
First Grade Mathematics
Fluency Benchmark 1: Automaticity
Student Name: ________________________________ School: ___________________ Teacher: _____________________
BENCHMARK I: FLUENCY WITHIN 10 (10 minutes)
|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 | |
Score: _____/ 40
New Jersey Student Learning Standards
First Grade Mathematics
Student Fluency Progress Monitoring Tool
NJSLS: 1.OA.6: Add and subtract within 20 (fluently within 10).
Student Name: _________________________________________ School: ___________________ Teacher: ___________________
Student Conference Note:
Student: Shade in each box upon mastery of fact.
Teacher: Enter the date mastery was achieved for each fact in the upper left corner.
AUTOMATICITY
Addition Facts within 10
|10 |9 |
|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 distinguished levels |Student work shows strong levels of |Student work shows moderate levels of |Student work shows partial understanding |Student work shows little understanding |
|of understanding of the mathematics. |understanding of the mathematics. |understanding of the mathematics. |of the mathematics. |of the mathematics. |
| | | | | |
|Student constructs and communicates a |Student constructs and communicates a |Student constructs and communicates a |Student constructs and communicates an |Student attempts to constructs and |
|complete response based on |complete response based on |complete response based on |incomplete response based on student’s |communicates a response using the: |
|explanations/reasoning using the: |explanations/reasoning using the: |explanations/reasoning using the: |attempts of explanations/ reasoning using|Tools: |
|Tools: |Tools: |Tools: |the: |Manipulatives |
|Manipulatives |Manipulatives |Manipulatives |Tools: |Five Frame |
|Five Frame |Five Frame |Five Frame |Manipulatives |Ten Frame |
|Ten Frame |Ten Frame |Ten Frame |Five Frame |Number Line |
|Number Line |Number Line |Number Line |Ten Frame |Part-Part-Whole Model |
|Part-Part-Whole Model |Part-Part-Whole Model |Part-Part-Whole Model |Number Line |Strategies: |
|Strategies: |Strategies: |Strategies: |Part-Part-Whole Model |Drawings |
|Drawings |Drawings |Drawings |Strategies: |Counting All |
|Counting All |Counting All |Counting All |Drawings |Count On/Back |
|Count On/Back |Count On/Back |Count On/Back |Counting All |Skip Counting |
|Skip Counting |Skip Counting |Skip Counting |Count On/Back |Making Ten |
|Making Ten |Making Ten |Making Ten |Skip Counting |Decomposing Number |
|Decomposing Number |Decomposing Number |Decomposing Number |Making Ten |Precise use of math vocabulary |
|Precise use of math vocabulary |Precise use of math vocabulary |Precise use of math vocabulary |Decomposing Number | |
|Response includes an efficient and | | |Precise use of math vocabulary |Response includes limited evidence of the|
|logical progression of mathematical |Response includes a logical progression |Response includes a logical but incomplete| |progression of mathematical reasoning and|
|reasoning and understanding. |of mathematical reasoning and |progression of mathematical reasoning and |Response includes an incomplete or |understanding. |
| |understanding. |understanding. |illogical progression of mathematical | |
| | |Contains minor errors. |reasoning and understanding. | |
|5 points |4 points |3 points |2 points |1 point |
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[1].
• 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.
• A 2-pocket folder for each Student Assessment Portfolio is recommended.
• All Student Assessment Portfolio entries should be scored and recorded in Genesis as an Authentic Assessment grade (25%)[2].
• 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…
_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
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Resources
Engage NY
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Common Core Tools
Achieve the Core
Manipulatives
Illustrative Math Project :
Inside Mathematics:
Sample Balance Math Tasks:
Georgia Department of Education:
Gates Foundations Tasks:
Minnesota STEM Teachers’ Center:
Singapore Math Tests K-12:
:
-----------------------
[1] The Mathematics Department will provide guidance on task selection, thereby standardizing the process across the district and across grades/courses.
[2] The Mathematics Department has propagated gradebooks with appropriate weights.
-----------------------
ORANGE PUBLIC SCHOOLS
OFFICE OF CURRICULUM AND INSTRUCTION
OFFICE OF MATHEMATICS
(Pictures)
(Manipulatives)
(Written)
(Real Life Situations)
(Communication)
1st & 2nd Grade Ideal Math Block
Essential Components
15-20 min.
5 min.
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.
EXIT TICKET (DOL): Individual
Students complete independently; Used to guide instructional decisions;
Used to set instructional goals for students;
SUMMARY: Whole Group
Lesson Closure: Student Reflection; Real Life Connections to Concept
MATH WORKSTATIONS:
Pairs / Small Group/ Individual
DIFFERENTIATED activities designed to RETEACH, REMEDIATE, ENRICH student’s understanding of concepts.
Small Group
Instruction
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.
INDEPENDENT PRACTICE: Individual
Math In Focus Let’s Practice, Workbook, Reteach, Extra Practice, Enrichment
LAUNCH: Whole Group
Anchor Task: Math In Focus Learn
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:
• ________________________________________________________________________________________________________________________________________________
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