6th Grade Mathematics - Orange Board of Education



1st Grade Mathematics

Unit 2 Curriculum Map:

Table of Contents

|I. |Unit Two Overview |p. 2 |

|II. |MIF Lesson Structure |p. 8 |

|III. |Transition Lesson Structure |p. 10 |

|IV. |Unit One Pacing Guide |p. 11 |

|V. |Pacing Calendar |p. 17 |

|VI. |Assessment Framework |p. 20 |

|VII. |Transition Guide References |p. 22 |

|VIII. |PARCC Assessment Evidence/Clarification Statements |p. 23 |

|IX. |Connections To Mathematical Practices |p. 25 |

|X. |Potential Student Misconceptions |p. 27 |

|XI. |Chapter Quizzes |p. 30 |

|XII. |Resources |p. 36 |

Unit Overview

|Unit 2: Chapters 7-8, 12, 13, 14 |

|In this Unit Students will |

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|learn how to count, read and write numbers within 20. (Chapter 7) |

|learn to recognize the numbers 11 to 20 as 1 group of ten and particular numbers of ones (Chapter 7) |

|compare numbers using the concepts of greatest and least (Chapter 7) |

|recognize and make increasing and decreasing number patterns (Chapter 7) |

|learn more strategies for addition and subtraction as they solve problems that include numbers between 10 and 20. (Chapter 8) |

|Use the concepts of place value when they add or subtract by grouping the two-digit number as a 10 and ones. (Chapter 8) |

|Count, compare and order numbers to 40 (Chapter 12) |

|utilize the standard vertical form for addition and subtraction of numbers to 40 (Chapter 13) |

|use place value charts to correctly align the digits and to record the regrouping process. (Chapter 13) |

|learn and apply strategies to do addition and subtraction mentally (Chapter 14) |

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|Essential Questions |

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|How are number words and numerals connected to the quantities they represent? |

|How do we use place value? |

|How can I apply counting skills to identify the value for a category? |

|What does it look like to count, compare and order numbers to 40? |

|How can a place-value chart help with determining number patterns? |

|What does it mean to align the digits of a number in a place value chart to record regrouping? |

|How can the Associative Property of Addition and number bonds help in adding three 1-digit numbers? |

|Why are doubles facts helpful with mental math? |

|Enduring Understandings |

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|Pictorial representations of concrete objects can help when counting to 20. |

|The numbers from 10-19 are 1 group of ten and particular number of ones. |

|Strategies for adding and subtracting are grouping into a ten and ones, number bonds, and using doubles facts. Numbers can be compared using |

|words like greater than, more than, less than. |

|Whole numbers can be added and subtracted with or without regrouping. |

|Number bonds help you to add and subtract mentally. |

|Common Core State Standards |

|1.NBT.1 |Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of |

| |objects with a written numeral. |

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|Count on from a number ending at any number up to 120. |

|Recognize and explain patterns with numerals on a hundreds chart. |

|Understand that the place of a digit determines its value. For example, students recognize that 24 is different from and less than 42.) |

|Explain their thinking with a variety of examples. |

|Read and write numerals to 120. |

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|Students extend the range of counting numbers, focusing on the patterns evident in written numerals. This is the foundation for thinking about |

|place value and the meaning of the digits in a numeral. Students are also expected to read and write numerals to 120. |

|l.NBT.2a |10 Can be thought of as a bundle of ten ones – called a “ten.” |

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|Given objects such as counters, linking cubes, or ten frames, students bundle or group 10 ones to make a ten. |

|Develop vocabulary to refer to a group of 10 as 1 ten. |

|Differentiate between 1 ten (a bundle) and 10 ones. |

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|Students begin to unitize or consider 10 ones as a group or unit called a ten. Rather than seeing 10 individual cubes, they can link those cubes|

|and make a group of 1 ten. |

|1.NBT.2b |The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. |

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|Students build on previous work in kindergarten (K.NBT.A.1) where they composed and decomposed numbers from 11 to 19 into 10 ones and some more |

|ones. This standard expects that students will understand that the 10 ones, from their previous experiences, are now thought of as a bundle or |

|group of 10. It is a unit, that is, 1 ten. Through experiences using a variety of materials such as ten frames, bundling straws, and linking |

|cubes, students see a teen number, such as 16, as 1 ten plus 6 ones. |

|Given a number of objects between 11 and 19, group them into 1 group of ten and some ones. |

|Describe the grouping, using place value language. |

|1.NBT.3 |Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with |

| |the symbols >, =, and , = and with their real meaning. Rather than use aids such as alligators or Pac-Man, it may help students who confuse the symbols to think that the open end of the symbol is always closest to the greater number and the closed end is always pointed to the lesser number. It is also important to give students opportunities to change the order of the numbers to see how it impacts the symbols and their meaning.

- 1.NBT.C.4

Students who do not know basic facts may be inaccurate computing with two-digit numbers. As those students continue to work on facts, physical models will help in adding accurately. Be sure that all students have ample experience with adding physical models on place value charts, counting on by benchmark numbers (tens and ones), using a hundreds chart, and using ten frames as appropriate. Make explicit connections among written physical models, strategies, and written formats.

- 1.NBT.C.5

Since understanding the concept of 10 more or 10 less leads to understanding additional place value concepts, students who depend on counting or using their fingers have not met this standard. Students who cannot determine 10 more or 10 less than a number from 1 to 100 need more experience with concrete materials, such as linking cubes or bundles of straws. Finding patterns on the hundreds chart is also helpful, but the language can be confusing for some students.

- 1.NBT.C.6

Some students may subtract the digits in the tens place but ignore the digits in the ones place. Ask them to describe what they are subtracting in terms of place value. For example, in subtracting 70-40, students should say they are taking 4 tens from 7 tens (or 7 tens minus 4 tens). Have them put concrete models on the place value chart and then subtract or physically remove the 4 tens from the 7 tens. They describe the difference as 3 tens. Ask them how to write 3 tens (30) and how many ones are in that number. They should explain why there are 0 ones and why it is necessary to put the digit 0 in the ones place.

Chapter 7 Quiz _____/10

Name ______________________________ Date ________________________

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|1. There are _______ bananas. |2. There are _______________ pigs. |

|[pic] |[pic] |

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|3. There are _______ cars. |4. There are _______ dvds. |

|[pic] |[pic] |

| |6. Write 14 in words. |

|5. There are ____________ leaves. | |

|[pic] |______________________________________ |

|7. Write the number 17 in words. | |

|____________________________________ |8. 15 = 1 ten and __________ ones |

| |10. Write the numbers from least to greatest. |

|9. 19 is ________ tens and 9 ones |16, 17, 13, 10 |

| |________, ________, ________, ________ |

Chapter 8 Quiz _____/10

Name ______________________________ Date ________________________

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|1. 6 + 7 = 6 + 6 + 1 6 + 7 = _____ |2. Make a 10 to add. Write the numbers that belong in the bond. |

| |[pic] |

|[pic] | |

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|3. 8 + 7 = 10 + 5 8 + 7 = __________ |4. Make a 10 to add. Write the numbers that belong in the bond. |

|[pic] |[pic] |

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|5. 4 + 5 = ? 4 + 5 = 4 + __________ + 1 |6. 6 + 8 = ? 6 + 8 = 6 + _____ + 2 |

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|7. 17 – 7 = __________ |8. Make a 10 to subtract. Write the numbers that belong in the bond. |

| |[pic] |

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|9. 20 – 5 = __________ |10. Write the numbers that belong in the bond. |

| |[pic] |

| |[pic] |

Chapter 12 Quiz _____/10

Name ______________________________ Date ________________________

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|1. ________ is between 29 and 31. |2. _________ comes just before 30. |

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|3. _________ comes just after 37. |4. _________ is between 38 and 40. |

|5. Write the number twenty-six. |6. Write the number thirty-eight. |

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|_______________________ |_________________________ |

|7. 28 in words is |8. 39 in words is |

|_____________________________ |_______________________________ |

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|9. The number is __________ |10. Write the missing number in the place value chart to make fifteen. |

| |[pic] |

|[pic] | |

Chapter 13 Quiz _____/10

Name ______________________________ Date ________________________

|1. |2. |

|[pic] |[pic] |

|3. |4. [pic] |

|4 + 36 = __________ | |

|5. |6. |

|[pic] |[pic] |

|7. |8. |

|[pic] |[pic] |

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|9. [pic] |10. |

| |[pic] |

|____________________ | |

Chapter 14 Quiz _____/10

Name ______________________________ Date ________________________

|1. Add mentally |2. Add mentally. |

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|7 + 6 = __________ |5 + 8 = __________ |

|3. Add mentally. |4. Add mentally. |

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|7 + 8 = __________ + __________ + 1 |5 + 6 = 5 + __________ + 1 |

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|5. Add mentally. |6. Add mentally. |

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|6 + 9 = __________ |27 + 6 = __________ |

|7. Add mentally. |8. Add mentally. |

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|5 + 33 = __________ |26 + 9 = __________ |

|9. Add mentally. |10. Add mentally. |

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|22 + 10 = __________ |20 + 18 = __________ |

Extensions and Sources

Online Resources

Think Central



Common Core Tools







Achieve the Core



Manipulatives







Problem Solving Resources

Illustrative Math Project



The site contains sets of tasks that illustrate the expectations of various CCSS in grades K–8 grade and high school. More tasks will be appearing over the coming weeks. Eventually the sets of tasks will include elaborated teaching tasks with detailed information about using them for instructional purposes, rubrics, and student work.

Inside Mathematics



Inside Mathematics showcases multiple ways for educators to begin to transform their teaching practices. On this site, educators can find materials and tasks developed by grade level and content area.

Engage NY

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Sample Balance Math Tasks



Georgia Department of Education



Georgia State Educator have created common core aligned units of study to support schools as they implement the Common Core State Standards.

Kindergarten:

1st Grade:

Formative Assessment :

Number Talks and Multi-grade Resources:

OHIO













Gates Foundations Tasks



Minnesota STEM Teachers’ Center



Singapore Math Tests K-12



Math Score:

Math practices and assessments online developed by MIT graduates.



Massachusetts Comprehensive Assessment System

doe.mass.edu/mcas/search

Performance Assessment Links in Math (PALM)

PALM is currently being developed as an on-line, standards-based, resource bank of mathematics performance assessment tasks indexed via the National Council of Teachers of Mathematics (NCTM).



Mathematics Vision Project



NCTM



Assessment Resources

o *Illustrative Math:

o *PARCC:

o NJDOE: (username: model; password: curriculum)

o DANA:

o New York:

o *Delaware:

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ORANGE PUBLIC SCHOOLS

OFFICE OF CURRICULUM AND INSTRUCTION

OFFICE OF MATHEMATICS

PRE TEST

DIRECT ENGAGEMENT

GUIDED LEARNING

INDEPENDENT PRACTICE

ADDITIONAL PRACTICE

POST TEST

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