6th Grade Mathematics - orange.k12.nj.us



2nd Grade Mathematics

Unit 2 Curriculum Map

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Table of Contents

|I. |Unit Overview |p. 2 |

|II. |Common Core Standards |p. 3 |

|III. |MIF Lesson Structure |p. 13 |

|IV. |Transition Lesson Structure |p. 16 |

|V. |MIF Pacing Guide |p. 17 |

|VI. |Pacing Calendar |p. 22 |

|VII. |Unit 2 Math Background |p. 24 |

|VIII. |Transition Guide References |p. 25 |

|IX. |PARCC Assessment/Clarification Statements |p. 26 |

|X. |Connections to the Mathematical Practices |P. 27 |

|XI. |Visual Vocabulary |p. 29 |

|XII. |Potential Students Misconceptions |p. 32 |

|XIII. |Assessment Framework |p. 34 |

|XIV. |Performance Tasks Assessments |p. 35 |

|XV. |Performance Tasks Scoring Rubric |p. 45 |

|XVI. |Resources |p. 47 |

Unit Overview

|Unit 2: Chapters 7, 10, 13, 14 |

|In this Unit Students will |

|Chapter 7 – Metric Measurement of Length: |

|estimate and measure medium and short lengths using the standard metric units of meters (m) and centimeters (cm). |

|use the meter stick and centimeter ruler to illustrate length as a concept of measure to determine how long or short and object is. |

|determine that the length of the curved lines can be measured with the help of a piece of string which is placed along the curved line and then measured|

|with a ruler. |

|reinforce children’s understanding of length, children are taught to draw lines of specific lengths. |

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|Chapter 10 – Mental Math and Estimation: |

|estimate and measure medium and short lengths using the standard metric units of meters (m) and centimeters (cm). |

|discover that the standard units of measure provide a basis for the comparison of lengths. |

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|Chapter 13 – Customary Measurement of Length: |

|estimate and measure the lengths of objects using a foot ruler. |

|measure how long or short an object is. |

|discover that foot is for measuring bigger objects and the inch is for measuring small objects. |

|draw lines of specific lengths and be able to measure the lines with precision. |

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|Chapter 14 – Time: |

|read time based on the position of the minute hand on the clock and that the minute hand tells the number of minutes after the hour. |

|use skip-counting strategy to tell how many minutes have passed, and how to read and write time in hours and minutes using numeral and words. |

|use the key terms, A.M. and P.M. to show morning, afternoon or night. |

|order events by time. |

|determine how much time has elapsed. |

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|Essential Questions |

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|Why do we use standard measurement tools to measure things? |

|What are some units of measurements? |

|When do you use the centimeter ruler and meter sticks to measure things? |

|Which measuring tool do you use for which object? |

|How do you decide when to use the standard versus the metric system? |

|When is it appropriate to use estimation instead of exact numbers? |

|How do I make a reasonable estimate? |

|Why is time important? |

|How do we use clocks to tell time? |

|Enduring Understandings |

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|If you need to measure things there are measuring tools to help you. |

|Specific measuring tools are used for specific purposes or objects. |

|It is useful to be precise in your measurement sometime. |

|Sometime it is okay to estimate your measurement. |

|In some situations using an estimate can be useful. |

|Telling time is an essential life skill. |

|Common Core State Standards – Chapter 7: Metric Measurement of Length |

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

| |and measuring tapes. |

|Second Graders build upon their non-standard measurement experiences in First Grade by measuring in standard units for the first time. Using both |

|customary (inches and feet) and metric (centimeters and meters) units, Second Graders select an attribute to be measured (e.g., length of classroom), |

|choose an appropriate unit of measurement (e.g., yardstick), and determine the number of units (e.g., yards). As teachers provide rich tasks that ask |

|students to perform real measurements, these foundational understandings of measurement are developed: |

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

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

|(iteration). |

|( Understand the relationship between the size of a unit and the number of units needed (compensatory principal). Thus, the smaller the unit, the more |

|units it will take to measure the selected attribute. |

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|When Second Grade students are provided with opportunities to create and use a variety of rulers, they can connect their understanding of non-standard |

|units from First Grade to standard units in second grade. For example: |

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|By the end of Second Grade, students will have also learned specific measurements as it relates to feet, yards and meters: |

|( There are 12 inches in a foot. |

|( There are 3 feet in a yard. |

|( There are 100 centimeters in a meter |

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

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

|focus on the attribute being measured and the measuring process. As students estimate, the student has to consider the size of the unit- helping them to|

|become more familiar with the unit size. In addition, estimation also creates a problem to be solved rather than a task to be completed. Once a student |

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

|measurement. |

|Example: |

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

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

|Teacher: Measure it and see. |

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

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

| |standard length unit. |

|Second Grade students determine the difference in length between two objects by using the same tool and unit to measure both objects. Students choose |

|two objects to measure, identify an appropriate tool and unit, measure both objects, and then determine the differences in lengths. |

|Example: |

|Teacher: Choose two pieces of string to measure. How many inches do you think each string is? |

|Student: I think String A is about 8 inches long. I think string B is only about 4 inches long. It’s really short. |

|Teacher: Measure to see how long each string is. Student measures. What did you notice? |

|Student: String A is definitely the longest one. It is 10 inches long. String B was only 5 inches long. I was close! |

|Teacher: How many more inches does your short string need to be so that it is the same length as your long string? Student: Hmmm. String B is 5 inches. |

|It would need 5 more inches to be 10 inches. 5 and 5 is 10. |

|2.MD.5 |Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, |

| |e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent|

| |the problems. |

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

|unit of measurement in these problems. Equations may vary depending on students’ interpretation of the task. Notice in the examples below that these |

|equations are similar to those problem types in Table 1 at the end of this document. |

|Example: In P.E. class Kate jumped 14 inches. Mary jumped 23 inches. How much farther did Mary jump than Kate? Write an equation and then solve the |

|problem. |

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|2.MD.6 |Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the |

| |numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. |

|Building upon their experiences with open number lines, Second Grade students create number lines with evenly spaced points corresponding to the numbers|

|to solve addition and subtraction problems to 100. They recognize the similarities between a number line and a ruler. |

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

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|Student A: I used a number line. I started at 27. I broke up 19 into 10 and 9. That way, I could take a jump of 10. I landed on 17. Then I broke the 9 |

|up into 7 and 2. I took a jump of 7. That got me to 10. Then I took a jump of 2. That’s 8. So, there are 8 students now on the bus. |

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|Student B: I used a number line. I saw that 19 is really close to 20. Since 20 is a lot easier to work with, I took a jump of 20. But, that was one too |

|many. So, I took a jump of 1 to make up for the extra. I landed on 8. So, there are 8 students on the bus. |

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|Common Core State Standards - Chapter 10: Mental Math & Estimation |

|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. |

|Example: 67 + 25 = __ |

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|Example: 63 – 32 = __ |

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

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

|Example: 43 + 34 + 57 + 24 = __ |

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|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. |

|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. 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. |

|Example: 354 + 287 = __ |

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|2.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. |

|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. 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. |

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|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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|Example: Within the same hundred |

|What is 10 more than 218? |

|What is 241 – 10? |

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|Example: Across hundreds |

|293 + 10 = ☐ |

|What is 10 less than 206? |

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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. |

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

|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. |

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

| |taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and|

| |equations with a symbol for the unknown number to represent the problem. |

|Second Grade students extend their work with addition and subtraction word problems in two major ways. First, they represent and solve word problems |

|within 100, building upon their previous work to 20. In addition, they represent and solve one and two-step word problems of all three types (Result |

|Unknown, Change Unknown, Start Unknown). Please see Table 1 at end of document for examples of all problem types. |

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

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|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. |

|As second grade students solve one- and two-step problems they use manipulatives such as snap cubes, place value materials (groupable and pre-grouped), |

|ten frames, etc.; create drawings of manipulatives to show their thinking; or use number lines to solve and describe their strategies. They then relate |

|their drawings and materials to equations. By solving a variety of addition and subtraction word problems, second grade students determine the unknown |

|in all positions (Result unknown, Change unknown, and Start unknown). Rather than a letter (“n”), boxes or pictures are used to represent the unknown |

|number. For example: |

|2.OA.2 |Fluently add and subtract within 20 using mental strategies. |

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

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|Second Graders internalize facts and develop fluency by repeatedly using strategies that make sense to them. When students are able to demonstrate |

|fluency they are accurate, efficient, and flexible. Students must have efficient strategies in order to know sums from memory. |

|2.MD.6 |Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the |

| |numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. |

|Building upon their experiences with open number lines, Second Grade students create number lines with evenly spaced points corresponding to the numbers|

|to solve addition and subtraction problems to 100. They recognize the similarities between a number line and a ruler. |

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

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|Student A: I used a number line. I started at 27. I broke up 19 into 10 and 9. That way, I could take a jump of 10. I landed on 17. Then I broke the 9 |

|up into 7 and 2. I took a jump of 7. That got me to 10. Then I took a jump of 2. That’s 8. So, there are 8 students now on the bus. |

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|Student B: I used a number line. I saw that 19 is really close to 20. Since 20 is a lot easier to work with, I took a jump of 20. But, that was one too |

|many. So, I took a jump of 1 to make up for the extra. I landed on 8. So, there are 8 students on the bus. |

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|M : Major Content S: Supporting Content A : Additional Content |

MIF 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 |

| |PreTest (Assessm’t Bk) |prerequisite understanding |

| |Recall Prior Knowledge | |

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

|of readiness of the upcoming chapter |Student Materials |repair student misunderstandings and vocabulary prior to the |

| |Student Book (Quick Check); Copy of the Pre|pre-test ; Students write Quick Check answers on a separate |

| |Test; Recall prior Knowledge |sheet of paper |

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| | |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 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, |Digi |majority is addressed through the hands-on, constructivist |

|each 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 | |

| |Student Book |Small Group w/Teacher circulating among groups |

| |Guided Learning Pages |Revisit Concrete and Model Drawing; Reteach |

| |Hands-on Activity |Teacher spends majority of time with struggling learners; |

| | |some time with on level, and less time with advanced groups |

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

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

| |Let’s Practice |group work and is used as formative assessment; Students |

|A formal formative assessment |Student Book |not ready for the Workbook will use Reteach. The Workbook |

| |Let’s Practice |is continued as Independent Practice. |

| |Differentiation Options |Manipulatives CAN be used as a communications tool as |

| |All: Workbook |needed. |

| |Extra Support: Reteach |Completely Independent |

| |On Level: Extra Practice |On level/advance learners should finish all workbook pages.|

| |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 Extra Practice) |students fully understand the concepts (as additional |

| | |practice) |

| | |Reteach Homework (issued to struggling learners) should be |

| | |checked the next day |

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

| |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 |

| |Student Workbook |graded/scored. |

| |Put on Your Thinking Cap |The Chapter Review/Test can be completed |

| |Assessment Book |Individually (e.g. for homework) then reviewed in class |

| |Test Prep |As a ‘mock test’ done in class and doesn’t count |

| | |As a formal, in class review where teacher walks students |

| | |through the questions |

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| | |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) |

|Concrete, Pictorial, Abstract | |

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|Task(s)/Text Resources |Activity/Description |

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MIF Pacing Guide

Key: Major Clusters, Supporting Clusters, Additional Clusters

|Activity |Description |CCSS |Est.Time |Lesson Notes |

| | | |(# of blocks) | |

|Chapter 7, Chapter Opener – Recall Prior |Centimeter rulers and metersticks can be |2.NBT.5, |1 block |After administering the Pre-test for this |

|Knowledge, Quick Check & Pre-Test 7 |used to measure and compare how long and |2.MD.1-6 | |chapter, use the data to form small math |

|(Student Book pgs. 193-195) |how tall things are. | | |groups to differentiate the instruction. |

|Lesson 1 – Measuring in Meters (Student |Use a meterstick to estimate and measure |2.MD.1, 2.MD.3 |1 block |Put children in small groups. Give each |

|Book pgs. 196-199) |length. | | |group a meterstick. Have children estimate |

| | | | |and measure various items around the room |

| | | | |or school. Have children record and compare|

| | | | |their findings. |

|Lesson 2 – Comparing Lengths in Meters |•Compare lengths. |2.MD.4 |1 block |You may want to have children work with a |

|(Student Book pgs. 200-204) |•Find the difference in lengths of | | |partner. Have partners find and compare the|

| |objects. | | |length of items around the room or school. |

| | | | |Encourage them to use the vocabulary words |

| | | | |in their discussion. |

|Lesson 3 – Measuring Lengths in |•Use a centimeter ruler to measure length.|2.MD.1, 2.MD.3 |2 blocks |You may want to have children work in |

|Centimeters (Student Book pgs. 205-214) | | | |pairs. Give each pair a centimeter ruler |

| |•Draw a line of given length. | | |and a list of common items on their desk to|

| | | | |measure. |

|Lesson 4 – Comparing Lengths in |•Use a centimeter ruler to measure and |2.MD.1, 2.MD.4 |1 block |You may want to teach this lesson as three |

|Centimeters (Student Book pgs. 215-219) |compare lengths of objects. | | |mini-lessons: measuring lengths of objects |

| |•Find the difference in centimeters in | | |in centimeters, comparing the lengths of |

| |lengths of objects. | | |the objects, and finding the difference in |

| | | | |centimeters between the lengths of the |

| | | | |objects. |

|Lesson 5 – Real World Problems: Metric |•Solve one-step and two-step problems |2.MD.5, 2.MD.6 |1 block |You may want to have children work in |

|Length (Student Book pgs. 220-224) |involving length. | | |groups of two or three. Give each group |

| |•Draw models to solve real-world problems.| | |paper strips (or strips of construction |

| | | | |paper) in two different colors to use as |

| | | | |bar models. Have one partner duplicate the |

| | | | |problem on paper strips and ask the others |

| | | | |in the group to solve the problem. |

|Math Journal Chapter 7 (Student Book A |This section allows children to reflect on|2.MD.1, 2.MD.3 |¼ block |Teacher will specifically show the proper |

|pgs. 210) |their observations and understanding of | | |technique for measuring with a centimeter |

| |the measurements of lengths in | | |ruler. |

| |centimeters. | | | |

|Put on Your Thinking Cap |Thinking Skills |2.MD.5, 2.MD.6 |¼ block | |

|(Student Book A pg. 225) |•Deduction •Sequencing | | | |

| |Problem Solving Strategies | | | |

| |•Look for pattern(s) | | | |

| |•Use guess and check | | | |

|Put on Your Thinking Cap | | |¼ block |Students should work independently to |

|(Student WorkBook A pgs. 183-184) | | | |critically think how to problem solve to |

| | | | |use the strategies to deduce and sequence. |

|Chapter 7 Review / Test |Reinforce and consolidate chapter skills |2.NBT.2, |1 block |Use rubric 1 to score the Extended Response|

| |and concepts. |2.MD.1-6 | |Questions as an Authentic Assessment |

|Test Prep 7 | | |1 block | |

|Total Time | | |Blocks: 9 ¾ | |

|Chapter 10, Chapter Opener – Recall Prior|Mental math can be used when an exact |2.NBT.5, |1 block |After administering the Pre-test for this |

|Knowledge, Quick Check & Pre-Test 10 |answer is needed. Estimation can be used |2.NBT.6, 2.NBT.7| |chapter, use the data to form small math |

|(Student Book pgs. 1-5) |when an exact answer is not needed. |2.NBT.8, | |groups to differentiate the instruction. |

| | |2.NBT.9, 2.OA.1,| | |

| | |2.OA.2, 2.MD.6 | | |

|Lesson 1 – Meaning of Sum (Student Book |Relate ‘sum’ to the addition operation. |2.NBT.6, |1 block |You may want to have children work in |

|pgs. 6-7) | |2.NBT.9, 2.OA.1,| |pairs. Give each pair paper strips to use |

| | |2.OA.2 | |as bar models. Have one partner duplicate |

| | | | |the problem on a paper strip by drawing a |

| | | | |line and writing the number sentence on the|

| | | | |strip. Have the other partner work out the |

| | | | |answer. Children can switch roles and |

| | | | |repeat the activity. |

|Lesson 2 – Mental Addition (Student Book |Add numbers with up to 3-digits mentally |2.NBT.7, |2 blocks |You can teach this lesson as a series of |

|pgs. 8-16) |with and without regrouping. |2.NBT.8, 2.NBT.9| |six mini-lessons, each focusing on one of |

| | | | |the mental addition strategies: add 10, add|

| | | | |the ones, add 10 then subtract the extra |

| | | | |ones, add the tens, add 100 then subtract |

| | | | |the extra tens, and add the hundreds. |

|Lesson 3 – Meaning of Difference (Student|Relate ‘difference’ to the subtraction |2.NBT.8, |1 block |You may want to have children circle the |

|Book pgs. 17-19) |operation. |2.NBT.9, 2.OA.1,| |greater number in each situation. Remind |

| | | | |children that the next step would be to |

| | | | |subtract the number that is less. Drawing |

| | | | |bar models is also a very good way to |

| | | | |assess whether children comprehend the |

| | | | |concept of subtraction. |

|Lesson 4 – Mental Subtraction (Student |Subtract up to 3-digit numbers mentally |2.NBT.5, |2 blocks |You can teach this lesson as a series of |

|Book pgs. 20-27) |with and without regrouping. |2.NBT.7, 2.NBT.9| |six mini-lessons, each focusing on one of |

| | | | |the mental subtraction strategies: subtract|

| | | | |10 and then add the extra ones (for 2- and |

| | | | |3-digit numbers), subtract the ones, |

| | | | |subtract the tens, subtract 100 then add |

| | | | |the extra tens, and subtract the hundreds. |

|Lesson 5 – Rounding Numbers to Estimate |•Use a number line to round numbers to the|2.NBT.5, |2 blocks |You may want to teach this lesson as a |

|(Student Book pgs. 28-38) |nearest ten. |2.NBT.6, | |series of mini-lessons involving rounding |

| |•Use rounding to estimate sums and |2.NBT.9, 2.MD.6 | |numbers, rounding to estimate and check |

| |differences. | | |sums, and rounding to estimate and check |

| |•Estimate to check reasonableness of | | |differences. |

| |answers. | | | |

|Math Journal Chapter 10 (Student Book B |This section allows children to reflect on|2.NBT.7, |¼ block |Use various addition/subtraction strategies|

|pg. 16) |and apply their understanding of mental |2.NBT.8, 2.NBT.9| |to solve. |

| |addition/subtraction to a specific | | | |

| |addition/subtraction sentence | | | |

|Math Journal Chapter 10 (Student Book B | |2.NBT.7, |¼ block | |

|pg. 27) | |2.NBT.8, 2.NBT.9| | |

|Math Journal Chapter 10 (Student Book B |This section allows children to reflect on|2.NBT.5, |¼ block |Use the nearest ten strategy to estimate |

|pg. 38) |and reinforce their understanding of the |2.NBT.6, | |sums and differences. |

| |rounding to the nearest ten strategy to |2.NBT.9, 2.MD.6 | | |

| |estimate sums and differences. | | | |

|Put on Your Thinking Cap |Thinking Skills | |¼ block |Students should work independently to |

|(Student Book B pg. 39) |•Deduction •Identifying patterns and | | |critically think how to problem solve to |

| |relationships Problem Solving Strategy | | |use the nearest ten strategy to estimate |

| |•Simplify the problem | | |sums and differences. |

|Chapter 10 Review / Test |Reinforce and consolidate chapter skills |2.NBT.5, |1 block |Use rubric 1 to score the Extended Response|

| |and concepts. |2.NBT.6, 2.NBT.7| |Questions as an Authentic Assessment |

| | |2.NBT.8, | | |

| | |2.NBT.9, 2.OA.1,| | |

| | |2.OA.2, 2.MD.6 | | |

|Test Prep 10 | | |1 block | |

|Total Time | | |Blocks: 12 | |

|Chapter 13, Chapter Opener – Recall Prior|Rulers can be used to measure and compare |2.MD.1, 2.MD.2, |1 block |After administering the Pre-test for this |

|Knowledge, Quick Check & Pre-Test 13 |how long and how tall things are. |2.MD.3 | |chapter, use the data to form small math |

|(Student Book pgs. 102-104) | |2MD.4, 2.MD.5, | |groups to differentiate the instruction. |

| | |2.MD.6, 2.OA.1,| | |

| | |2.NBT.7 | | |

|Lesson 1 – Measuring in feet (Student |Use a ruler to estimate and measure |2.MD.1, 2.MD.3 |1 block |You may want to teach this lesson as two |

|Book pgs. 105-108) |length. | | |mini-lessons: one on using a ruler to |

| | | | |estimate length, and another on using a |

| | | | |ruler to measure length. |

|Lesson 2 – Comparing Lengths in Feet |•Compare lengths. •Find the difference in |2.MD.1, 2.MD.4 |1 block |You may want to teach this lesson as two |

|(Student Book pgs. 109-112) |lengths of objects. | | |mini- lessons: one lesson about comparing |

| | | | |lengths, and another lesson about finding |

| | | | |the difference in lengths of objects. |

|Lesson 3 – Meaning in Inches (Student |•Use a ruler to measure length to the |2.MD.1, 2.MD.3 |1 block |You may want to consider teaching this |

|Book pgs. 113-119) |nearest inch. | | |lesson as two mini-lessons: one on |

| |•Draw parts of lines of given lengths. | | |measuring to the nearest inch and another |

| | | | |on drawing parts of lines of given lengths |

|Lesson 4 – Comparing Lengths in Inches & |•Use an inch ruler to measure and compare |2.MD.1, 2.MD.2, |1 block |You may wish to teach this lesson as two |

|Feet (Student Book pgs. 120-125) |lengths. |2.MD.4 | |mini-lessons: one on using a ruler to |

| |•Find the difference in lengths of objects| | |measure lengths of objects, and another on |

| |in inches. | | |comparison of lengths of objects. |

| |•Measure the same objects in inches and | | | |

| |feet. | | | |

| |•Understand how measurements relate to the| | | |

| |size of units. | | | |

|Lesson 5 – Real World Problems: Customary|•Solve one- and two-step problems |2.MD.5, 2.MD.6, |1 block |You may want to consider teaching this |

|Lengths (Student Book pgs. 126-130) |involving length. •Draw bar models to |2.OA.1 | |lesson as two mini-lessons: one on using |

| |solve real-world problems | | |bar models to solve one-step problems, and |

| | | | |another on using bar models to solve |

| | | | |two-step problems. |

|Put on Your Thinking Cap |Thinking Skills •Classifying •Comparing | |¼ block |This problem-solving exercise requires |

|(Student Book B pg. 131) |•Deduction •Sequencing •Analyzing parts &| | |children to apply deductive reasoning |

| |whole | | |skills. The exercise may be completed |

| |•Identifying patterns and relationships | | |individually or in groups. |

| |Problem Solving Strategies | | | |

| |•Guess &check | | | |

| |•Use a diagram •Solve part of the problem | | | |

|Put on Your Thinking Cap | | |¼ block | |

|(Student Workbook B pg. 93-94) | | | | |

|Chapter 13 Review / Test |Reinforce and consolidate chapter skills |2.MD.1, 2.MD.2, |1 block |Use rubric 1 to score the Extended Response|

| |and concepts. |2.MD.3 | |Questions as an Authentic Assessment |

| | |2MD.4, 2.MD.5, | | |

| | |2.MD.6, 2.OA.1,| | |

| | |2.NBT.7 | | |

|Test Prep 13 | | |1 block | |

|Total Time | | |Blocks: 8 ½ | |

|Chapter 14, Chapter Opener – Recall Prior|Time of day can be shown in different |2.NBT.2, |1 block |After administering the Pre-test for this |

|Knowledge, Quick Check & Pre-Test 14 |ways. |2.NBT.8, 2.MD.7 | |chapter, use the data to form small math |

|(Student Book pgs. 134-136) | | | |groups to differentiate the instruction. |

|Lesson 1 – The Minute Hand (Student Book |Use the minute hand to show and tell the |2.MD.7 |1 block |Use a clock to practice skip counting by 5s|

|pgs. 137-140) |number for every five minutes after the | | | |

| |hour. | | | |

|Lesson 2 – Reading & Writing Time |Show and tell time in hours and minutes. | |1 block |You may want to teach this lesson as two |

|(Student Book pgs. 141-145) | | | |mini-lessons: one on reading time and the |

| | | | |other on writing time. |

|Lesson 3 – Using A.M. & P.M. (Student |•Use A.M. and P.M. to show morning, | |1 block |You may wish to teach this lesson as two |

|Book pgs. 146-153) |afternoon, or night. | | |mini-lessons: one on using A.M. and P.M., |

| |•Order events by time. | | |and the other on ordering events by time. |

|Lesson 4 – Elapsed Time (Student Book |Determine how much time has passed. | |1 block |Practice having children show the time on |

|pgs. 154-160) | | | |their clocks |

|Math Journal Chapter 14 (Student Book B |This section reinforces children’s | |¼ block |Practice working on order of events |

|pgs. 150) |understanding of the order of events and | | | |

| |the use of A.M. and P.M. | | | |

|Put on Your Thinking Cap |Thinking Skills •Deduction •Identifying | |¼ block |This problem-solving exercise requires |

|(Student Book B pg. 161 |patterns and relationships Problem Solving| | |children to analyze pictures and deduce |

| |Strategy | | |whether the events match the time indicated|

| |• Making suppositions | | |on the clock |

|Chapter 14 Review / Test |Reinforce and consolidate chapter skills |2.NBT.2, |1 block |Use rubric 1 to score the Extended Response|

| |and concepts. |2.NBT.8, | |Questions as an Authentic Assessment |

| | |2.MD.7 | | |

|Test Prep 14 | | |1 block | |

|Total Time | | |Blocks: 7 ½ | |

|Grand Total Time | | |Blocks: 37 ¾ | |

Pacing Calendar

|November 2015 |

|Sun |

|Sun |Mon |Tue |Wed |

Pacing Calendar

|January 2016 |

|Sun |Mon |Tue |Wed |Thu |Fri |Sat |

|3 |4Book 2B. Chapter 13: |5 |6 |7 |8 |9 |

| |Customary Measurement of | | | | | |

| |Length. Chapter Opener, | | | | | |

| |Recall Knowledge, Pre-Test| | | | | |

|FEBRUARY 2016 |

|Sun |

|Transition Topic: Mental Math and Estimation |

|Chapter 4 |Objective |Additional Reteach Support |Additional |Teacher Edition Support |

|Pre Test Items | | |Extra Practice Support | |

|Items 4-5 |Mentally add a one-digit |1B pp. 95-96, 99 |Lesson 14.1 |1B Chapter 14 Lesson 1 |

| |number to a two-digit number | | | |

| |Mentally add a two-digit |1B pp. 97-98, 100 |Lesson 14.1 |1B Chapter 14 Lesson 1 |

| |number to tens. | | | |

|Items 6-7 |Mentally subtract a one-digit |1B pp. 101-102, 104 |Lesson 14.2 |1B Chapter 14 Lesson 2 |

| |number from a two-digit number| | | |

|Item 8 |Find the missing numbers in a |1B pp. 41, 43, 50 |Lesson 12.3 |1B Chapter 12 Lesson 3 |

| |pattern. | | | |

|Item 11 |Solve real-world (subtraction)|1A pp. 143-146 |Lesson 8.3 |1B Chapter 19 Lesson 4 |

| |problems. | | | |

|Item 12 |Solve real-world (addition) |1B pp. 87-89 |Lesson 13.6 |1B Chapter 19 Lesson 4 |

| |problems. | | | |

| |Mentally subtract tens from a |1B pp. 103-104 |Lesson 14.2 |1B Chapter 14 Lesson 2 |

| |two-digit number. | | | |

PARCC Assessment Evidence/Clarification Statements

|CCSS |Evidence Statement |Clarification |Math Practices |

|2.MD.1 |Measure the length of an object by selecting and using |i) Length may be measured in whole units within the same |MP.5 |

| |appropriate tools such as rulers, yardsticks, meter |measurement system using metric or U.S. customary. | |

| |sticks, and measuring tapes. |ii) Units are limited to those found in 2.MD.3. | |

|2.MD.2 |Measure the length of an object twice, using length units |i) Tasks should be limited to whole units within the same |MP.5 |

| |of different lengths for the two measurements; describe |measurement system. ii) Units are limited to those found in | |

| |how the two measurements relate to the size of the unit |2.MD.3 iii) Example: Student measures the length of a table in| |

| |chosen. |inches and in feet and notes that the number of feet is less | |

| | |than the number of inches because an inch is smaller than a | |

| | |foot. Therefore, it takes more inch units than foot units to | |

| | |measure the table’s length. | |

|2.MD.3 |Estimate lengths using units of inches, feet, centimeters,|i) Rulers are not used to estimate. |MP.5, MP.6 |

| |and meters. | | |

|2.MD.4 |Measure to determine how much longer one object is than |i) Length may be measured in whole units within the same |MP.5, MP. 6 |

| |another, expressing the length difference in terms of a |measurement system using metric or U.S. customary. | |

| |standard length unit. |Ii) Units are limited to those in 2.MD.3. | |

|2.MD.5 |Use addition and subtraction within 100 to solve word |i) Tasks may include measurements in whole units within the |MP.1, MP.2, MP.4 |

| |problems involving lengths that are given in the same |same measurement system using metric or U.S. customary. | |

| |units, e.g., by using drawings (such as drawings of |ii) Problems may be one or two-step. iii) For one-step | |

| |rulers) and equations with a symbol for the unknown number|problems, all problem situations and all of their subtypes and| |

| |to represent the problem. |language variants may be included but 50% of tasks should | |

| | |include the most difficult problem subtypes and language | |

| | |variants. | |

| | |iv) For two-step problems, the most difficult problem subtypes| |

| | |and language variants should not be included. The majority of| |

| | |the two-step problems involve single-digit addends. | |

| | |v) Subtraction and addition are emphasized beyond 20 but | |

| | |within 100. At least 75% of the tasks must focus on addition | |

| | |and subtraction greater than 20. | |

| | |* For more information see CCSS Table 1, p. 88 and the OA | |

| | |Progression | |

Connections to the Mathematical Practices

|1 |Make sense of problems and persevere in solving them |

| |Mathematically proficient students in Second Grade examine problems and tasks, can take 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-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: 2 5 + 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 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. |

Visual Vocabulary

|Visual Definition |

|The terms below are for teacher reference only and are not to be memorized by students. Teachers should first present these concepts to students with |

|models and real life examples. Students should understand the concepts involved and be able to recognize and/or use them with words, models, pictures, |

|or numbers. |

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Potential Student Misconceptions

Chapter 7 – Metric Measurement of Length:

➢ Some children may only include objects that are less than one meter on their chart. Encourage children to include objects that are both short and long.

➢ Some children may have difficulty understanding what is being asked. Help children look for key words such as longer than and shorter than as well as the objects so children know what is being compared.

➢ Some children will still have trouble aligning the ruler. Demonstrate how to align the left end of the ruler with the left end of the object being measured. Have children practice alignment.

➢ Some children may confuse meters and centimeters. Display and label a centimeter ruler and a meter stick for children to observe.

➢ Some children may choose the wrong operation. Remind children to read each word problem carefully and understand what is being asked before they begin trying to solve the problem.

Chapter 10 – Mental Math and Estimation:

➢ Some children may add incorrectly. Remind them to read the problem carefully and to review their addition.

➢ Some children may not perform step 2 in the mental subtraction strategies. They might think they have completed the mental work after completing step 1. Guide children to check if their answer is reasonable.

➢ Some children may add instead of subtract. Remind them that the phrase find the difference means to subtract.

➢ Some children may forget to perform all the steps in their mental subtraction strategies. They might think they have completed the solution after just the first step. Remind them to check their answers to see if they are reasonable.

➢ Some children may round incorrectly. Remind children that 5 is the deciding digit. Any digit less than five in the ones place is rounded down to the nearest ten. If the digit in the ones place is 5 or greater, it is rounded up to the next ten.

Chapter 13 – Customary Measurement of Length:

➢ Some children may only include objects that are less than a foot long in their chart. Encourage children to include objects that are less a foot long, about one foot, and more than a foot long.

➢ Some children may have difficulty understanding what is being asked. Guide them to look for key words such as much longer and much shorter to help them comprehend the problem. Drawing models is also a good way to aid comprehension.

➢ Some children may not remember to start measuring from 0 on the ruler. Have children highlight or pace a sticker at the 0 reading on their ruler to help them remember. Have children practice alignment of objects against the 0 marking.

➢ Some children may forget to subtract to find the length of objects placed at non-zero start points. Remind children that when measuring, objects need to align with the zero end of the ruler. Have children highlight or place a sticker at the 0 reading on their ruler to help them remember.

➢ Some children may stop after solving the first step in two-step problems. Remind children to reread the question and see if the answer makes sense.

Chapter 14 – Time:

➢ Some children may not ski-count correctly. Consider having a chart that shows the clock face number and its corresponding five-minute number. This will help those children who have difficulty relating the numbers to time.

➢ Some children may confuse the hour and minute hands. Remind them that the hour hand is always shorter than the minute hand.

➢ Some children may confuse A.M. with P.M. Tell them that A comes before P in the alphabet, so A starts the day – from just after midnight to just before noon.

➢ Some children may confuse before with after. Use a number line to help children understand the concepts of before and after.

Assessment Framework

|Unit 2 Assessment / Authentic Assessment Framework |

|Assessment |CCSS |Est. Time |Format |Graded? |

|Pre-Test – Chapter 7 |2.MD.1, 2.MD.4, 2.MD.5, 2.MD.6 |1 Block |Individual |No |

|Authentic Assessment 5 – Metric word |2.MD.1, 2.MD.4, 2.MD.5, 2.MD.6 |1 Block |Individual |Yes |

|problems | | | | |

|Chapter 7 Quiz – Metric Measurement of Length|Maintains 1.MD.1, 1.MD.2 |1-2 Blocks |Individual |Yes |

|((Two types of Quizzes – long or short – you |2.MD.1, 2.MD.3, 2.MD.4, 1.MD.5 | | | |

|choose) | | | | |

|Mini Assessment – Chapter 7 Review/Test |2.MD.1, 2.MD.4, 2.MD.5, 2.MD.6 |1 Block |Individual |No |

|Test Prep - Chapter 7 |2.MD.1, 2.MD.4, 2.MD.5, 2.MD.6 |1 Block |Individual |Yes |

|Pre-Test – Chapter 10 |2.OA.1, 2.OA.2, 2.NBT.5, 2.NBT.6, 2.NBT.7, |1 Block |Individual |No |

| |2.NBT.8, 2.NBT.9, 2.MD.6 | | | |

|Authentic Assessment 2 – Addition word |2.OA.1, 2.OA.2, 2.NBT.5, 2.NBT.6, 2.NBT.7, |1 Block |Individual |Yes |

|problems |2.NBT.8, 2.NBT.9, 2.MD.6 | | | |

|Chapter 10 Quiz – Mental Math and Estimation |2.MD.5, 2.MD.7 |1-2 Blocks |Individual |Yes |

|Length (Two types of Quizzes – long or short|Previews 3.NBT.1 | | | |

|– you choose) | | | | |

|Mini Assessment – Chapter 10 Review/Test |2.OA.1, 2.OA.2, 2.NBT.5, 2.NBT.6, 2.NBT.7, |1 Block |Individual |No |

| |2.NBT.8, 2.NBT.9, 2.MD.6 | | | |

|Test Prep - Chapter 10 |2.OA.1, 2.OA.2, 2.NBT.5, 2.NBT.6, 2.NBT.7, |1 Block |Individual |Yes |

| |2.NBT.8, 2.NBT.9, 2.MD.6 | | | |

|Pre-Test – Chapter 13 |2.OA.1, 2.NBT.7, 2.MD1, 2.MD.3, 2.MD.4 |1 Block |Individual |No |

|Authentic Assessment 5– Addition word |2.OA.1, 2.NBT.7, 2.MD1, 2.MD.3, 2.MD.4 |1 Block |Individual |Yes |

|problems | | | | |

|Chapter 13 Quiz - Customary Measurement of |2.MD.1, 2.MD.3, 2.MD.4, 2.MD.5 |1-2 Blocks |Individual |Yes |

|Length (Two types of Quizzes – long or short | | | | |

|– you choose) | | | | |

|Mini Assessment – Chapter 13 Review/Test |2.OA.1, 2.NBT.7, 2.MD1, 2.MD.3, 2.MD.4 |1 Block |Individual |No |

|Test Prep - Chapter 13 |2.OA.1, 2.NBT.7, 2.MD1, 2.MD.3, 2.MD.4 |1 Block |Individual |Yes |

|Pre-Test – Chapter 14 |2.NBT.2, 2.NBT.8, 2.MD7 |1 Block |Individual |No |

|Authentic Assessment 6 – Addition word |2.NBT.2, 2.NBT.8, 2.MD7 |1 Block |Individual |Yes |

|problems | | | | |

|Chapter 14 Quiz – Time (Two types of Quizzes|2.MD.7 |1-2 Blocks |Individual |Yes |

|– long or short – you choose) | | | | |

|Mini Assessment – Chapter 14 Review/Test |2.NBT.2, 2.NBT.8, 2.MD7 |1 Block |Individual |No |

|Test Prep - Chapter 14 |2.NBT.2, 2.NBT.8, 2.MD7 |1 Block |Individual |Yes |

Performance Tasks – Authentic Assessments

2.MD.1, 2.MD.4, 2.MD.5, 2.MD.6

1. Lisa is 130 cm tall. Nina is 5 cm shorter than Lisa. How tall is Nina?

2. A building is 80 meters tall. A flagpole on top of it is 25 meters tall. How high is the top of the flagpole from the ground?

3. Jimmy is 145 centimeters tall. Eddy is 10 centimeters taller. How tall is Eddy?

4. Make up your own (addition) word problem using meters as the units.

5. Make up your own (subtraction) word problem using centimeters as the units.

Answers to Chapter 7 Authentic Assessment 3:

1. 130 cm – 5 cm = 125 cm Nina’s Height

130 cm

|Lisa |

?

|Nina |

130 – 5 = 125 cm Nina’s Height

2. 80 + 25 = 105 m

80 m 25 m

|Building |Flagpole |

80 m + 25 m = 80 + 20 + 5 = 100 + 5 = 105 m Tall

3.

145 cm

|Jimmy |

? 10 cm

|Eddy |

145 cm + 10 cm = 155 cm Eddy’s Height

4. Students response will vary

5. Students response will vary

Performance Tasks – Authentic Assessments

2.OA.1, 2.OA.2, 2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.8, 2.NBT.9, 2.MD.6

Solve. Use mental math.

Then, use estimation to check that your answers are reasonable.

1. If you go to Shop Rite and buy a gallon of milk for $4.59. Then, you go to Pathmark and noticed that a gallon of milk cost $3.69. How much money could you had saved if you would have purchased the milk from Pathmark?

2. Steven has 100 books. Karen has 232 books. What is the difference of the number books Karen has than Steven? How many books do they have altogether?

3. Doug buys a toy car for $25 and a toy truck for $46. Find the sum for both items.

________________ + ________________ = __________________

Check: _____________ + ______________ = _______________

Is the answer reasonable? Explain. ___________________________________

________________________________________________________________

________________________________________________________________

4. Make up your own problem and determine if your answer is reasonable.

5. Make up your own problem and determine if your answer is reasonable.

Answers to Chapter 10 Authentic Assessment 1:

1. $4.59 - $3.69 = $.90 (could have saved)

Reasonable: $4.60 – 3.70 = 90 Got the same number when I estimated.

2. 232 – 100 = 132 (Karen has 132 more books than Steven)

Reasonable: 230 – 100 = 130 Answer is reasonable since it is close to the

Actual answer.

3. $25 + 46 = $71

Check: 30 + 50 = 80 Answer is reasonable since it is close.

4. Responses will vary.

5. Responses will vary.

Performance Tasks – Authentic Assessments

1. A piece of wire 200 inches long. Michael cut off 75 inches of this wire. What is the length of the wire that is left?

2. Karen runs 50 feet one day. She runs 75 feet the next day. She runs 25 feet on the third day. How many feet does she run all together?

3. Dave paints 10 feet of a hallway wall. Sue paints 20 feet of the same hallway wall. Doug paints the remainder 15 feet of the hallway wall. What is the total amount of wall space painted?

4. McDonalds is 10 feet down the street. It was a nice day so you wanted to walk there. You walked 6 feet so far. How many more feet must you walk in order to get to McDonalds?

5. How wide do you think (estimate) the book 1 and book 1. What is the measurement?

Now measure the width of the book 2. What is the measurement?

Should you measure both books in inches or feet?

What is the difference of the two objects? Which is longer?

Answers to Chapter 13 Authentic Assessment 4:

1. |----------------------------200 inches---------------|

|Wire | |

|-- 75 inches-|

Cut off

200 – 75 = 100 + 100 - 75 =

100 + 25 = 125 inches left

2. Karen

50 ft 75 ft 25 ft

| Day 1 |Day 2 |Day 3 |

50 + 75 + 25 =

50 + 50 + 25 + 25 =

100 + 50 = 150 ft

3. Dave

10 ft 20 ft 15 ft

| | | |

10 + 20 + 15 =

10 + 20 + 10 + 5 =

40 + 5 = 45 ft

4. |----------------------- 10 ft --------------------------|

| | |

6 ft

10 – 6 = 4 ft

5. Students responses vary.

Performance Tasks – Authentic Assessments

1. Draw Ten twenty-five on the analog and digital clocks.

Is this time A.M. or P.M. if the sun is not shining? __________

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2. Look at problem 1. If you went to bed thirty-five minutes later, what time did you go to bed. Draw the time on both the analog and digital clocks.

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3. Make up your own story and time (use both digital and analog clocks).

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4. Look at your problem 3. If you did something 2 hours later what time would it be?

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5. Look at your problem 4. If you did something 3 hours and 30 minutes later what time would it be now?

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Answers to Chapter 14 Authentic Assessment 5:

1.

2.

3. Students responses vary.

4. Students responses vary.

5. Students responses vary.

performance Tasks – Authentic Assessments

Performance Task Scoring Rubric 1

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| | | |

| |PLD |Genesis Conversion |

|Rubric Scoring |PLD 5 |100 |

| |PLD 4 |89 |

| |PLD 3 |79 |

| |PLD 2 |69 |

| |PLD 1 |59 |

| | | |

Performance Task Scoring Rubric 2:

|Level 5: Distinguished Command |Level 4: Strong Command |Level 3: Moderate Command |Level 2: Partial Command |Level 1: No Command |

|Student gives all 5 correct answers. |Student gives all 5 correct |Student gives all 4 correct |Student gives 3 correct answers. |Student gives less |

| |answers. |answers. | |than 3 correct |

|Clearly constructs and communicates a | | |Constructs and communicates an |answers. |

|complete response based on |Clearly constructs and communicates|Constructs and communicates a |incomplete response based on | |

|explanations/reasoning using the: |a complete response based on |complete response based on |explanations/reasoning using the: |The student shows no |

|properties of operations |explanations/reasoning using the: |explanations/reasoning using the: |properties of operations |work or |

|relationship between addition and |properties of operations |properties of operations |relationship between addition and |justification. |

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

| |subtraction |subtraction |relationship between multiplication| |

|Response includes an efficient and |relationship between multiplication|relationship between multiplication|and division | |

|logical progression of steps. |and division |and division |Response includes an incomplete or | |

| |Response includes a logical |Response includes a logical but |illogical progression of steps. | |

| |progression of steps |incomplete progression of steps. | | |

| | |Minor calculation errors. | | |

Resources

Common Core Tools:







Achieve the Core:



Manipulatives:







Helpful Websites

Singapore Math Source - has shared news, information, resources and more regarding the world’s best elementary math curriculum.



IllustrativeMath Project - We collaborate at , sharing carefully vetted resources for teachers and teacher leaders to give our children an understanding of mathematics and skill in using it. We provide expert guidance to states, districts, curriculum writers, and assessment writers working to improve mathematics education.



IXL - This site list all of the skills students learn in second grade! These skills are organized into categories, and you can move your mouse over any skill name to view a sample question. To start practicing, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!



North Carolina Department of Public Instruction - K-2 Formative Instructional and Assessment Tasks for the Common Core State Standards in Mathematics



Georgia K-5 Math Support



- is dedicated to providing educators across New York State with real-time, professional learning tools and resources to support educators in reaching the State’s vision for a college and career ready education for all students.

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ORANGE PUBLIC SCHOOLS

OFFICE OF CURRICULUM AND INSTRUCTION

OFFICE OF MATHEMATICS

GUIDED LEARNING

DIRECT ENGAGEMENT

PRE TEST

ADDITIONAL PRACTICE

INDEPENDENT PRACTICE

POST TEST

Chater 6: Show me your skills with Division (Authentic Assessment 2) [Use Rubric 2]

Chapter 7: Show me your skills with Metric Measurement (Authentic Assessment 3) [Use Rubric 2]

Chapter 10: Mental Math and Estimation (Authentic Assessment 4) [Use Rubric 2]

Chapter 13: Customary Measurement (Authentic Assessment 4) [Use Rubric 2]

Chapter 14: Time (Authentic Assessment 5) [Use Rubric 2]

101. udents responses vary...

tic Assessment):

ing 3 hours and 30 minutes later what time would it be now? 25

11 00

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