6th Grade Mathematics



2nd Grade Mathematics

Unit 4 Curriculum Map:

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Table of Contents

|I. |Second Grade Unit IV |p. 2 |

|II. |Common Core State Standards |p. 4 |

|III. |Eight Mathematical Practices |p. 13 |

|IV. |IDeal Math Block |p. 16 |

|V. |Math In Focus Lesson Structure |p. 17 |

|VI. |Transition Lesson Structure |p. 19 |

|VII. |IDeal Math Block Planning Template |p. 20 |

|VIII. |Recommend Pacing Calendar |p. 22 |

|IX. |Instructional and Assessment Framework |p. 25 |

|X. |Authentic Assessments |p. 27 |

|XI. |PLD Rubric |p. 36 |

|XII. |Resources |p. 37 |

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|Second Grade Unit IV |

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|In this Unit Students will: |

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|2.OA.1 |

|Solve addition and subtraction one-step and two-step word problems involving: |

|Adding to, |

|Taking From , |

|Putting Together, |

|Taking Apart, and |

|Comparing situations. |

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|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 |

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|2.NBT.5-9 |

|Add and Subtract multiples of 10 to numbers within the range 10-100 |

|Add up to four two-digit numbers |

|Fluently Add and Subtract with 100. |

|Add and Subtract within 1000 using strategies. |

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|Mathematical Practices |

|Make sense of math task and find an entry point and a solution path for math tasks. |

|De-contextualize and contextualize mathematical math tasks. |

|Construct and critique arguments. |

|Model real-life situations. |

|Select and use appropriate mathematical tools |

|Use precise mathematical language, units of measure, and strive accuracy. |

|Look for and use patterns. |

|Express regularity in repeated reasoning |

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|Second Grade Unit IV | |

|Topics |Commons Core State Standards | |

| |2.OA.2: Fluently add and subtract within 20 using mental strategies. Know from memory all | |

|Fluency: |sums of two one digit numbers. | |

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|Ideal Math Block: | | |

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|* Fluency | | |

|(5-7 min.) | | |

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|Math | | |

|Workstation | | |

|* Fluency Lab: | | |

|(15-20 min.) | | |

| |2.NBT.5: Fluently add and subtract within 100 using strategies: | |

| |Count On/Back, | |

| |Making (Composing) Tens, | |

| |Decomposing a Number Leading to Ten, | |

| |Relationship between Addition and Subtraction, and | |

| |Equivalent (Easier) Known Sums: (Doubles, Compensation, Conservation) | |

| |2.NBT.8: Mentally add/subtract 10 or 100 to/from a given number 100-900. | |

|Addition & Subtraction |2.OA.1: Use addition and subtraction within 100 to solve one- and two-step word problems |North Carolina: 2.OA.1 |

|Situations |involving situations (15 types)of: |Math Tasks: |

| |adding to, |

| |taking from, |i.2.OA.1+Tas|

| |putting together, |ks |

| |taking apart, and | |

| |comparing, | |

| |with unknowns in all positions, | |

| |result unknown, | |

| |change unknown | |

| |start unknown (See Table 1) | |

| |e.g., by using drawings and equations with a symbol for the unknown number to represent the | |

| |problem. | |

|Problem Solving Strategies |2.NBT.6: Add up to four two-digit numbers using strategies based on place value and |North Carolina: 2.NBT.5-9 |

| |properties of operations. |Math Tasks: |

| | |

| | |i.2.NBT.5-2.|

| | |NBT.9+Tasks |

| |2.NBT.7: Add and subtract within 1000, using | |

| |concrete models or drawings and | |

| |strategies based on place value, | |

| |properties of operations, and/or | |

| |the relationship between addition and subtraction; | |

| |relate the strategy to a written method. Understand that in adding or subtracting three-digit| |

| |numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and | |

| |sometimes it is necessary to compose or decompose tens or hundreds. | |

| |2.NBT.9: Explain why addition and subtraction strategies work, using place value and the | |

| |properties of operations. | |

|Common Core State Standards: Operations and Algebraic Thinking |

|2.OA.1 |Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and |

| |comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. |

|Second Grade students extend their work with addition and subtraction word problems in two major ways. First, they represent and solve word problems within 100, building upon their previous work to 20. In |

|addition, they represent and solve one and two-step word problems of all three types (Result Unknown, Change Unknown, Start Unknown). Please see Table 1 at end of document for examples of all problem types.|

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

|[pic] |

|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. |

|Common Core State Standards: Numbers and Operations in Base Ten |

|2.NBT.5 |Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. |

|There are various strategies that Second Grade students understand and use when adding and subtracting within 100 (such as those listed in the standard). The standard algorithm of carrying or borrowing is |

|neither an expectation nor a focus in Second Grade. Students use multiple strategies for addition and subtraction in Grades K-3. By the end of Third Grade students use a range of algorithms based on place |

|value, properties of operations, and/or the relationship between addition and subtraction to fluently add and subtract within 1000. Students are expected to fluently add and subtract multi-digit whole |

|numbers using the standard algorithm by the end of Grade 4. |

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|[pic] |

|[pic] |

|2.NBT.6 |Add up to four two-digit numbers using strategies based on place value and properties of operations. |

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|Second Grade students add a string of two-digit numbers (up to four numbers) by applying place value strategies and properties of operations. |

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|[pic] |

|2.NBT.7 | |

| |Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition |

| |and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens|

| |and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. |

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|Second graders extend the work from 2.NBT. to two 3-digit numbers. Students should have ample experiences using concrete materials and pictorial representations to support their work. This standard also |

|references composing and decomposing a ten. This work should include strategies such as making a 10, making a 100, breaking apart a 10, or creating an easier problem. |

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|THE STANDARD ALGORITHM OF CARRYING OR BORROWING IS NOT AN EXPECTATION IN SECOND GRADE. |

|STUDENTS ARE NOT EXPECTED TO ADD AND SUBTRACT WHOLE NUMBERS USING A STANDARD ALGORITHM UNTIL THE END OF FOURTH GRADE. |

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|PLEASE EMPHASIZE A DEEP UNDERSTANDING OF THE FOLLOWING STRATEGIES AND TOOLS: |

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|STRATEGIES: |

|Place Value Strategy |

|Properties of Operations |

|Relationship between Addition and Subtraction |

|Composing and Decomposing a Ten |

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|TOOLS: |

|Number Bonds |

|Number Lines |

|Tape Diagrams |

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|[pic] |

|[pic] |

|[pic] |

|1.NBT.8 |Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. |

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|Second Grade students mentally add or subtract either 10 or 100 to any number between 100 and 900. |

|As teachers provide ample experiences for students to work with pre-grouped objects and facilitate discussion, second graders realize that when one adds or subtracts 10 or 100 that only the tens place or |

|the digit in the hundreds place changes by 1. |

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|As the teacher facilitates opportunities for patterns to emerge and be discussed, students notice the patterns and connect the digit change with the amount changed. |

|Opportunities to solve problems in which students cross hundreds are also provided once students have become comfortable adding and subtracting within the same hundred. |

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|[pic] |

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|This standard focuses only on adding and subtracting 10 or 100. Multiples of 10 or multiples of 100 can be explored; however, the focus of this standard is to ensure that students are proficient with adding|

|and subtracting 10 and 100 mentally. |

|1.NBT.9 |Explain why addition and subtraction strategies work, using place value and the properties of operations. |

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|Second graders explain why addition or subtraction strategies work as they apply their knowledge of place value and the properties of operations in their explanation. They may use drawings or objects to |

|support their explanation. |

|Once students have had an opportunity to solve a problem, the teacher provides time for students to discuss their strategies and why they did or didn’t work. |

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|Example: There are 36 birds in the park. 25 more birds arrive. How many birds are there? Solve the problem and show your work. |

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|[pic] |

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|Example: One of your classmates solved the problem 56 - 34 = __ by writing “I know that I need to add 2 to the number 4 to get 6. I also know that I need to add 20 to 30 to get 20 to get to 50. So, the |

|answer is 22.” Is their strategy correct? Explain why or why not? |

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|Student: I see what they did. Yes. I think the strategy is correct. They thought, ‘34 and what makes 56?’ So they thought about adding 2 to the 4 to get 6. Then, they had 36 and needed 56. So, they added 20|

|more. That means that they added 2 and 20 which is 22. I think that it’s right. |

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|Example: One of your classmates solved the problem 25 + 35 by adding 20 + 30 + 5 + 5. Is their strategy correct? Explain why or why not? |

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|Student: Well, 20 + 30 is 50. And 5 + 5 is 10. So, 50 + 10 is 60. I got 60 too, but I did it a different way. I added 25 and 25 to make 50. Then I added 5 more and got 55. Then, I added 5 more and got 60. |

|We both have 60. I think that it doesn’t matter if you add the 20 first or last. You still get the same amount. |

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 |

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| |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 |

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| |Mathematically proficient students in Second Grade make sense of quantities and relationships while solving tasks. This involves two processes- decontexualizing 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 others’ reasoning and strategies, citing similarities and differences between strategies. |

|4 |Model with mathematics |

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| |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 |

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| |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 equals 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 In Focus Lesson Structure

|LESSON STRUCTURE |RESOURCES |COMMENTS |

|Chapter Opener |Teacher Materials |Recall Prior Knowledge (RPK) can take place just before the pre-tests|

|Assessing Prior Knowledge |Quick Check |are given and can take 1-2 days to front load prerequisite |

| |Pre-Test (Assessment Book) |understanding |

| |Recall Prior Knowledge | |

|The Pre Test serves as a diagnostic | |Quick Check can be done in concert with the RPK and used to repair |

|test of readiness of the upcoming |Student Materials |student misunderstandings and vocabulary prior to the pre-test ; |

|chapter |Student Book (Quick Check); Copy of the |Students write Quick Check answers on a separate sheet of paper |

| |Pre Test; Recall prior Knowledge | |

| | |Quick Check and the Pre Test can be done in the same block (See |

| | |Anecdotal Checklist; Transition Guide) |

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| | |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 | |Students use concrete manipulatives to explore concepts |

|making sense, themselves, of the |Technology |A few select parts of the task are explicitly shown, but the majority|

|concepts – by interacting the tools, |Digi |is addressed through the hands-on, constructivist approach and |

|manipulatives, each other, and the | |questioning |

|questions |Other |Teacher facilitates; Students find the solution |

| |Fluency Practice | |

|Guided Learning and Practice |Teacher Edition |Students-already in pairs /small, homogenous ability groups; Teacher |

|Guided Learning |Learn |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 time |

| |Hands-on Activity |with on level, and less time with advanced groups |

| | |Games and Activities can be done at this time |

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|Independent Practice |Teacher Edition |Let’s Practice determines readiness for Workbook and small group work|

| |Let’s Practice |and is used as formative assessment; Students not ready for the |

|A formal formative | |Workbook will use Reteach. The Workbook is continued as Independent |

|assessment |Student Book |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 students |

| |Homework (Workbook , Reteach, or |fully understand the concepts (as additional practice) |

| |Extra Practice) |Reteach Homework (issued to struggling learners) should be checked |

| | |the next day |

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| End of Chapter Wrap Up |Teacher Edition |Use Chapter Review/Test as “review” for the End of Chapter Test Prep.|

|and Post Test |Chapter Review/Test |Put on your Thinking Cap prepares students for novel questions on the|

| |Put on Your Thinking Cap |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 through the|

| |Assessment Book |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 |

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|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 PLANNING TEMPLATE

Provides guidance during planning sessions

|CCSS & | |

|OBJ:(s) | |

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| |Fluency: | |

| |Strategy/Tool | |

| |Getting Ready | |

|Math In |Launch | |

|Focus | | |

| |Exploration | |

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| |Independent Practice | |

| |Summary | |

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| |D.O.L | |

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|Different|Small Group | |

|iation:: |Instruction | |

|Math |CCSS: | |

|Workstati| | |

|ons |OBJ: | |

| |Tech. Lab | |

| |CCSS: | |

| |Problem Solving Lab | |

| |CCSS: | |

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| |OBJ: | |

| |Fluency Lab | |

| |CCSS: | |

| |Strategy: | |

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| |Tool: | |

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| |Math Journal | |

| |CCSS: | |

| |OBJ: | |

Recommend Unit IV Pacing Calendar: APRIL

|Monday |Tuesday |Wednesday |Thursday |Friday |

| | | | |1 |

| | | | | |

|4 MP4 BEGINS |5 |6 |7 |8 |

|11 |12 |13 |14 |15 |

|18 |19 |20 |21 |22 |

|25 |26 |27 |28 |29 |

MAY

|Monday |Tuesday |Wednesday |Thursday |Friday |

|2 |3 |4 |5 |6 |

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|9 |10 |11 |12 |13 |

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|16 |17 |18 |19 |20 |

|23 |24 |25 |26 |27 |

|30 |31 | | | |

JUNE

|Monday |Tuesday |Wednesday |Thursday |Friday |

| | |1 |2 |3 |

| | | | | |

|6 |7 |8 |9 |10 |

|13 |14 |15 |16 |17 |

|20 |21 |22 |23 |24 |

| |MP4 ENDS | | | |

|27 |28 |29 |30 | |

Instructional and Assessment Framework

Administer Assessments during Small Group Instruction Math Workstation.

Use Diagnostic and Observational Data to Map Instructional Pacing.

|Activities |CCSS |Notes |

|Re-Teach: |2.OA.1 |Place emphasis on students’ ability |

|MIF Ch. 4: Lesson 1 | |to show their understanding using: |

|Using Part-Part-Whole in Addition and Subtraction | |Place Value Strategy |

| | |Composing Tens Decomposing to Tens; |

| | |Bar Models |

| | |Number Bonds |

| | |Open Number Lines |

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| | |Use MIF Supplemental Materials: |

| | |Re-Teach, Extra Practice, |

| | |Enrichment, |

| | |Performance Tasks |

|Re-Teach: | | |

|MIF Ch. 4: Lesson 2 | | |

|Adding On and Taking Away Sets | | |

|Re-Teach: | | |

|MIF Ch. 4: Lesson 3 | | |

|Comparing Two Sets | | |

|Re-Teach: | | |

|MIF Ch. 4: Lesson 4 | | |

|Real World Problems: | | |

|Two Step Problems | | |

|Assessment: 2.OA.1 |2.OA.1 |Curriculum Guide |

|EnGageNY Module 4 Topic A Lesson 5 |2.OA.1 |Provided by |

|Solve One- and Two-Step Word Problems using Place Value |2.NBT.5 |Math Department |

| |2.NBT.7 |Lesson Implementation: |

| | |50-60 minutes |

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| | |Exit tickets: (5 min.) |

| | |Students complete independently. |

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| | |Place exit tickets in Student |

| | |Portfolios |

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|EnGageNY Module 4 Topic B Lesson 8 | | |

|Use Drawings to Represent Composition | | |

|EnGageNY Module 4 Topic B Lesson 9 and 10 | | |

|Use Drawings to Add Two-Digit to Three-Digit Addends | | |

|EnGageNY Module 4 Topic C Lesson 13 | | |

|Use Drawings to Represent Subtraction with and without Decomposition | | |

|EnGageNY Module 4 Topic C Lesson 14 and 15 | | |

|Represent subtraction with and without Decomposition when there is a Three-Digit Minuend | | |

|EnGageNY Module 4 Topic C Lesson 16 | | |

|Solve one- and two-step word problems using place value | | |

|EnGageNY Module 4 Topic D Lesson 17 |2.NBT.8 | |

|Mental Math Strategies: Composition: 10 tens as 1 Hundred and 10 ones as 1 ten | | |

|EnGageNY Module 4 Topic D Lesson 20 and 21 |2.OA.1 | |

|Use Drawings to Represent Addition; |2.NBT.5 | |

|Relate Drawing to Written Method | | |

|EnGageNY Module 4 Topic D Lesson 22 |2.OA.1 | |

|Solve Addition with Up To Four Addend |2.NBT.6 | |

|Assessment 2.NBT.5-8 | |Curriculum Guide |

|EnGageNY Module 4 Topic F Lesson 29 |2.NBT.9 |Provided by |

|Use and Explain the Totals Using Words, Math Drawings, and Numbers | |Math Department |

| | |Lesson Implementation: |

| | |50-60 minutes |

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| | |Exit tickets: (5 min.) |

| | |Students complete independently. |

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| | |Place exit tickets in Student |

| | |Portfolios |

|EnGageNY Module 4 Topic F Lesson 30 |2.NBT.9 | |

|Compare Totals Below to Bew Groups as Written Methods | | |

|EnGageNY Module 4 Topic F Lesson 31 |2.OA.1 | |

|Solve Two-Step Word Problems | | |

|Assessment 2.NBT.9 |2.NBT.9 |Curriculum Guide |

|Ch. 8 MIF Pre-Assessment: Mass |2.OA.1 |Think |

| |2.NBT.7 | |

|Chapter 8 Opener | | |

|Lesson 1: measuring in Kilograms | | |

|Lesson 2: Comparing Mass in Kilograms | | |

|Lesson 3: Measuring in Grams | | |

|Lesson 4: Comparing Mass in Grams | | |

|Lesson 5: Real-World Problems: Mass | | |

|Put On Your Thinking Cap | | |

|Chapter 8 Review/Test & Chapter Wrap Up | | |

|Chapter 8 MIF Assessment: Mass | | |

|Ch. 9 Pre-Assessment: Volume | |Think |

| |2.OA.1 | |

| |2.NBT.7 | |

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|Chapter 9 Opener | | |

|Lesson 1: Getting to Know Volume | | |

|Lesson 2: Measuring in Liters | | |

|Lesson 3: Real World Problems: Volume | | |

|Put On Your Thinking Cap | | |

|Chapter 9 Review/Test & Chapter Wrap Up | | |

|Chapter 9 MIF Assessment: Volume | | |

SECOND GRADE UNIT IV

Assessment: 2.OA.1

Name Date

Solve the problem. Write an equation using a symbol for the unknown.

Use words, numbers or pictures to explain your reasoning.

1. Some baseball cards were on the table. Sam took 42 baseball cards. Then there were 26 baseball cards on the table. How many baseball cards were on the table before?

2. Erick has 32 glass marbles and 21 steel marbles. How many marbles does Erick have?

3. Nevaeh had some jewels. She gave 11 jewels to her sister. Now Nevaeh has 79 jewels. How many jewels did Nevaeh have to start with?

4. Sally saw horses in a field. She counted 10 horses. Some horses were brown, some horses were gray, and some horses were black. How many brown, gray, and black horses did she see? Find as many different combinations as you can. Write an equation for each combination.

5. Olivia has 45 sparkle markers. Makayla has 28 sparkle markers. How many more sparkle markers does Olivia have than Makayla?

6. Evan has 20 fewer raisins than Kayla. Kayla has 31 raisins. How many raisins does Evan have?

7. Luke has 5 fewer books than Josh. Luke has 7 books. How many books does Josh have?

8. The zoo had 7 cows and some horses in the big pen. There were 15 animals in the big pen. Then 4 more horses ran into the big pen. How many horses are there now?

9. Pam has 17 cards of animals from Africa. She has some cards from other continents. All together she has 90 cards. How many cards are from other continents?

10. The blue team has 5 more girls than the red team. The red team has 18 girls. How many girls are on the blue team?

SECOND GRADE UNIT IV

Diagnostic Assessment: 2.OA.1

Addition and Subtraction Situations

|Question # |Situation Type |

|1 |Take From-Start Unknown |

|2 |Put Together/Take Apart- Total Unknown |

|3 |Add To-Start Unknown |

|4 |Put Together/Take Apart- Both Addends Unknown |

|5 |Compare-Difference Unknown |

|6 |Compare-Smaller Unknown |

|7 |Compare Bigger Unknown |

|8 |Take From-Change Unknown |

|9 |Add To-Change Unknown |

|10 |Compare-Bigger Unknown |

Note:

Students can use words, numbers or pictures to explain your reasoning.

• Place Value Strategy

• Chip Model

• Base Ten Blocks

• Bar Models

• Number Bonds

Focus on student’s ability to develop an equation to support each situation type.

Does the equation support the visual representation?

Reminder:

Some situation types can be supported by addition and subtraction depending on the solution path the student has chosen.

SECOND GRADE UNIT IV

Diagnostic Assessment: 2.NBT.5-9

Name Date

Brooke and Regina both have some base ten blocks.

1. If they combine their blocks, how much do they have altogether? _____________________

2. When Mary adds her blocks to Brooke’s and Regina’s blocks they have 700 blocks.

How many blocks did Mary have? ________________________________________________

3. Label each as true or false. Use a place value strategy to show how you know.

a. 23 – 14 = 14 + 23 _________________

b. 45 – 19 = 22 + 4 _________________

c. 93 – 56 = 84 – 37 __________________

d. 8 ones + 5 tens = 85 __________________

4. Sarah solved the word problem below.

a. Explain why Sarah’s addition strategy worked.

b. There are 18 fewer cats than birds. How many birds are in Cuddle’s Pet Shop? Use another place value strategy to find the answer. Show your work.

5. Solve:

a. Find the solution and model how you found your answer.

|87 + 56 = |Model: |

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|38 + 68 + 71 + 12 = |Model: |

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b. Solve and explain your answer using place value.

|91 – 24 = |154 + 27 = |

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|105 – 42 = |86 + 45 = |

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c. Susan and James solved 125 + 32 in different ways. Explain why both ways are correct.

|Susan’s Way: |James’s Way: |

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|Explanation: |Explanation: |

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1. Second Grade PLD Rubric

|Got It |Not There Yet |

|Evidence shows that the student essentially has the target concept or big math idea. |Student shows evidence of a major misunderstanding, incorrect concepts or procedure, or a 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 |

|Clearly constructs and communicates as a |Clearly constructs and communicates a |Constructs and communicates a complete |Constructs and communicates an incomplete |The student work shows little |

|complete response based on |complete response based on |response based on explanations/reasoning |response based on student’s attempts of |understanding of the mathematics. Student|

|explanations/reasoning using the: |explanations/reasoning using the: |using the: |explanations/reasoning using the: |attempts to construct and communicates a |

|Properties of operations |Properties of operations |properties of operations |properties of operations |response using the: |

|Relationship between addition and |relationship between addition and |relationship between addition and |relationship between addition and |properties of operations |

|subtraction |subtraction |subtraction |subtraction |relationship between addition and |

|Understanding of base ten system |grade appropriate strategies |understanding of base ten system |understanding of base ten system |subtraction |

|grade appropriate strategies |use of math vocabulary |grade appropriate strategies |grade appropriate strategies |understanding of base ten system |

|precise use of math vocabulary |Response includes a logical progression of|Response includes a logical but incomplete|Response includes an incomplete or |grade appropriate strategies |

|Response includes an efficient and logical|mathematical reasoning and understanding. |progression of mathematical reasoning and |illogical progression of mathematical |Response includes limited evidence of the |

|progression of mathematical reasoning and | |understanding. Contains minor errors. |reasoning and understanding. |progression of mathematical reasoning and |

|understanding. | | | |understanding. |

|5 points |4 points |3 points |2 points |1 point |

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| |PLD |Genesis Conversion |

|Rubric Scoring |PLD 5 |100 |

| |PLD 4 |89 |

| |PLD 3 |79 |

| |PLD 2 |69 |

| |PLD 1 |59 |

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:

Kindergarten:

1st Grade:

Gates Foundations Tasks:

Minnesota STEM Teachers’ Center:

Singapore Math Tests K-12:

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ORANGE PUBLIC SCHOOLS

OFFICE OF CURRICULUM AND INSTRUCTION

OFFICE OF MATHEMATICS

GETTING READY: Whole Group

Morning Routine

Do Now; Homework Review;

EXPLORATION: Partner / Small Group

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

INDEPENDENT PRACTICE: Individual

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

CENTERS/STATIONS:

Pairs / Small Group/ Individual

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

Technology

Lab

Small Group

Instruction

Problem

Solving

Fluency Lab

Math

Journal

1st & 2nd Grade Ideal Math Block

Essential Components

FLUENCY: Partner/Small Group

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

SUMMARY: Whole Group

Lesson Closure: Student Reflection;

Real Life Connections to Concept

DEMONSTRATION OF LEARNING

Students complete independently;

Used to guide instructional decisions;

Used to set instructional goals for students

5-7 min.

5-7 min.

15-20 min.

5-7 min.

50-60 min.

LAUNCH: Whole Group

Anchor Task: Math In Focus Learn

PRE TEST

DIRECT ENGAGEMENT

GUIDED LEARNING

POST TEST

ADDITIONAL PRACTICE

POST TEST

POST TEST

INDEPENDENT PRACTICE

ADDITIONAL PRACTICE

CHAPTER 17: GRAPHS AND LINE PLOTS

RE-TEACH CHAPTER 4: ADDITION AND SUBTRACTION

ENGAGENY LESSONS 2.OA.1, 2.NBT.5-9

ENGAGENY LESSONS 2.OA.1, 2.NBT.5-9

ENGAGENY LESSONS 2.OA.1, 2.NBT.5-9

ENGAGENY LESSONS 2.OA.1, 2.NBT.5-9

CHAPTER 8: MASS

CHAPTER 8: MASS

CHAPTER 9: VOLUME

Explain your reasoning with drawings, words, and/or numbers.

Explain your reasoning with drawings, words, and/or numbers.

There are 47 cats in Cuddle’s Pet Shop. There are 29 more dogs than cats. How many dogs are in Cuddle’s Pet Shop?

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