1 !Grade!! Math!UnitGuide! - Jackson County School District Core/Pacing Guides... · 1st Grade Math! Grade 1 Subject Math # of Units Timeline UNIT CURRICULUM MAP Unit%1:%Exploring%quantities%to%99%

1st Grade

Math Unit Guide

2014-‐2015

Jackson County School District Year At A Glance 1st Grade Math

Unit 1 Exploring Quantities to 99 8 Days Unit 2 Using place value to read, write, represent, and compare numbers 10 Days Unit 3 Understanding ten ones make a ten 20 Days Unit 4 Developing addition and subtraction strategies 10 Days Unit 5 Telling and writing time to the hour 5 Days Unit 6 Using data to add and subtract within 20 12 Days Unit 7 Extending strategies for solving addition and subtraction problems 15 Days Unit 8 Distinguishing attributes of shapes 8 Days Unit 9 Composing and drawing shapes 8 Days Unit 10 Applying properties of operations to solve problems 10 Days Unit 11 Telling and writing time to the half hour 5 Days Unit 12 Adding multiples of ten 10 Days Unit 13 Using understanding of place value to add and subtract 10 Days Unit 14 Interpreting and using symbols in numeric expressions and comparisons 10 Days Unit 15 Ordering and comparing lengths 5 Days Unit 16 Measuring lengths with non-‐standard units 10 Days Unit 17 Finding equal shares of shapes 5 Days Unit 18 Demonstrating proficiency in addition and subtraction situations 10 Days

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1st Grade Math

Grade 1 Subject Math # of Units

Timeline

UNIT CURRICULUM MAP Unit 1: Exploring quantities to 99 Suggested number of days: 8

Learning Targets Notes/Comments Unit Materials and Resources

Unit Overview:

This unit is focused on counting and writing two-‐digit numbers. This unit provides student opportunities to practice making groups of ten to efficiently represent and count objects. Common Core State Standards for Mathematical Content

Number and Operations in Base Ten – 1.NBT A. Extend the counting sequence. 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.

Common Core State Standards for Mathematical Practice 6. Attend to precision.

7. Look for and make use of structure.

1.NBT.1.1 Count from a given number to 120. 1.NBT.1.2 Read from a given number to 120. 1.NBT.1.3 Write from a given number to 120. 1.NBT.1.4 Look at a number of objects from 0-‐120 and write the correct numeral to represent that number of objects.

The focus of this unit is numbers within 99. 1.NBT.A.1 will be repeated in unit 8, in which the number range will be extended to 120. In this unit students can focus on the uniformity of how tens and ones change as you count larger quantities.

In this unit students recognize and apply number patterns (MP.7) and communicating this understanding precisely in reading, writing, and representing numbers (MP.6).

CCSS 1st Grade Math Flip Book: http://katm.org/wp/wpcontent/uploads/flipbooks/1stFLIPpdf2.pdf Bridges 1st Grade CCSS Math: http://catalog.mathlearningcenter.org/files/pdfs/B1SUPCCSS-‐B_1211w.pdf Oregon City 1st Grade CCSS Math: http://www.orecity.k12.or.us/staff/curriculum_resources/mathematics/first_grade Yuureka CCSS Math Resources: http://www.yuureka.com/resources-‐1/common-‐core K-‐5 Teaching Resources: www.k-‐5mathteachingresources.com 1st Grade Homework Resource: www.mathworksheetsland.com CCSS 1st Grade Interactive Math: www.mathplayground.com www.adaptedmind.com www.ixl.com

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Vocabulary Essential Questions • Ones • Tens • Grouping • Fact families • Left/Right • Numerals • Doubles • Counting On • Represent • Objects • Precision

• Why do we need to be able to count objects? • Why do we need to be able to read and write number words? • How can lots of objects be counted quickly? • How can I start at any given number and continue counting? • How far can I count? What patterns do I notice • If I start at zero and write my numbers in order how far can I go?

Formative Assessment Strategies

• Choral Response: In response t o a cue, all students respond verbally at the same time. The response can be either to answer a question or to repeat something the teacher has said.

• White Board-‐Draw it: Teachers gives prompt question and students draw what they understand. Example: What symbols can I use to show a number is greater than or less than another number?

• Anecdotal Records: Take short notes during a lesson or circulate the classroom and observe students as they work to check for learning. The teacher should reflect on a specific aspect of the learning (sorts geometric shapes correctly) and adjust instruction as needed.

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Unit 2: Using place value to read, write, represent, and compare numbers Suggested number of days: 10


Unit Overview:

In this unit students extend their understanding from unit 1, to a larger number range. Students apply the structure of teen numbers to reason about larger quantities and their relative magnitude. Common Core State Standards for Mathematical Content

Number and Operations in Base Ten – 1.NBT A. Extend the counting sequence. 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.

B. Understand place value. 2. Understand that the two digits of a two-‐digit number represent amounts of tens and ones. Understand the following as special cases: c. The numbers 10, 20, 30, 40, 50, 60, 70,

80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

3. Compare two two-‐digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols », =, and <.

1.NBT.1.1 Count from a given number to 120. 1.NBT.1.2 Read from a given number to 120. 1.NBT.1.3 Write from a given number to 120. 1.NBT.1.4 Look at a number of objects from 0-‐120 and write the correct numeral to represent that number of objects. 1.NBT.2c.1 Demonstrate that 10, 20, 30, 40, 50, 60, 70, 80, 90 represent a certain number of tens bundles and zero ones units. 1.NBT.3.1 Compare two, 1 digit numbers using symbols >,<, or = 1.NBT.3.2 Compare two, 2 digit numbers using symbols >,<, or =. 1.NBT.3.3 I can use <,>, or = to compare two digit numbers.

Comments 1.NBT.A.1 involves relating the structure of numbers 0-‐20 to the numbers 100-‐120.

In this unit 1.NBT.B.3 focuses on students using comparative language to describe numerical comparisons. Mathematical comparison symbols (< and >) will be introduced in Unit 13.

CCSS 1st Grade Math Flip Book: http://katm.org/wp/wp-‐content/uploads/flipbooks/1stFLIPpdf2.pdf Bridges 1st Grade CCSS Math: http://catalog.mathlearningcenter.org/files/pdfs/B1SUPCCSS-‐B_1211w.pdf Oregon City 1st Grade CCSS Math: http://www.orecity.k12.or.us/staff/curriculum_resources/mathematics/first_grade Yuureka CCSS Math Resources: http://www.yuureka.com/resources-‐1/common-‐core K-‐5 Teaching Resources: www.k-‐5mathteachingresources.com 1st Grade Homework Resource: www.mathworksheetsland.com CCSS 1st Grade Interactive Math: www.mathplayground.com www.adaptedmind.com www.abcya.com www.ixl.com

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Common Core State Standards for Mathematical Practice

2. Reason abstractly and quantitatively.


Students continue to explore the structure of place value (MP.7); namely that the two digits of a two-‐digit number represent amounts of tens and ones and that to compare numbers relies on their relative magnitudes. Students make sense of the relationships between the numerals and the quantities (MP.2).

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Vocabulary Essential Questions • Count • Number • Numerals • Represent • Objects • Digits • Two-‐digit • Compare • Demonstrate • Bundles • Zero • Units

• How can I start at any given number and continue counting? • How far can I count? What patterns do I notice • If I start at zero and write my numbers in order how far can I go? • How can I represent a number using tens and ones with objects and symbols? • How can I tell if one number is greater than, less than, or equal to another number?



• Pop Sickle Stick-‐Pop Quiz: Students demonstrate understanding and mastery of skills and concepts. Have each student’s name on a Popsicle stick in a cup. Draw random names to answer questions.

• Anecdotal Records: Take short notes during a lesson or circulate the classroom and observe students as they work to check for learning. The teacher should reflect on a specific aspect of the learning (sorts geometric shapes correctly) and adjust instruction as needed.

• Fist To Five: Students show number of fingers on a scale, with 1 being lowest and 5 the highest. Ask, “How well do you feel you know this information?” 1. I can teach it to others 2. I can do it alone 3. I need some help 4. I could use more practice 5. I am just beginning to learn

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Unit 3: Understanding ten ones make a ten Suggested number of days: 20


Unit Overview:

In Kindergarten students have gained familiarity with making groups of ten ones. This unit develops a more abstract understanding of place value, viewing 2-‐ digit numbers as tens and ones. This understanding of place value supports counting on and making ten strategies that students use to become more efficient in addition and subtraction situations. Common Core State Standards for Mathematical Content

0perations and Algebraic Thinking -‐ 1.0A C. Add and subtract within 20. 6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 -‐ 4 = 13 -‐ 3 -‐ 1 = 10 -‐ 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 -‐ 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Number and 0perations in Base Ten -‐ 1.NBT B. Understand place value. 2. Understand that the two digits of a two-‐digit number represent amounts of tens and ones. Understand the following as special cases:

a. 10 can be thought of as a bundle of ten ones -‐ called a "ten."

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

1.OA.6.1 Identify the greater number when given two numbers. 1.OA.6.2 Solve addition problems by identifying the greater number and counting on. 1.OA.6.3 Solve addition facts to 10 within a given time frame to build fluency. 1.OA.6.4 Solve addition problems by making 10 and then counting on. 8+2=10 plus 4 more 8+6=___ 1.OA.6.5 Add and subtract using fact families in various ways. 7+3=___, 3+___=10 1.OA.6.6 Add using doubles and doubles plus or minus 1. 8+7=___, 1+7+7=___ 1.OA.6.7 Solve subtraction facts to 10 within a given time frame to build fluency 1.OA.6.8 Solve mixed addition and subtraction problems within 20. 1.NBT.2.1 Identify place value of a digit in a given 2 digit number. 1.NBT.2a.1 Represent a 2 digit number with units and bundles. 1.NBT.2b.1 Demonstrate that numbers 11-‐19 are made up of a tens bundle and a certain number of ones units. (through use of manipulatives, drawing, or verbal explanation)

Comments In this unit the focus in 1.0A.C.6 is on counting on and making ten.

1.0A.C.6 is repeated in several units to provide multiple opportunities to learn and practice all of the different strategies. In each of these units, new strategies will be introduced to expand students' proficiency in addition and subtraction to work towards fluency.

CCSS 1st Grade Math Flip Book: http://katm.org/wp/wpcontent/uploads/flipbooks/1stFLIPpdf2.pdf Bridges 1st Grade CCSS Math: http://catalog.mathlearningcenter.org/files/pdfs/B1SUPCCSS-‐B_1211w.pdf Oregon City 1st Grade CCSS Math: http://www.orecity.k12.or.us/staff/curriculum_resources/mathematics/first_grade Yuureka CCSS Math Resources: http://www.yuureka.com/resources-‐1/common-‐core K-‐5 Teaching Resources: www.k-‐5mathteachingresources.com 1st Grade Homework Resource: www.mathworksheetsland.com CCSS 1st Grade Interactive Math: www.mathplayground.com www.adaptedmind.com www.abcya.com www.ixl.com

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Common Core State Standards for Mathematical Practice 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others.

Students will progress from concrete to pictorial to more abstract reasoning (MP.2). This includes the habit of listening to others and responding (MP.3).

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Vocabulary Essential Questions • Add • Plus • Counting On • Making Ten • Subtract • Minus • Two-‐Digit Number • Represent • Tens • Ones • Bundle of Ten • Fluency • Fact families • Doubles • Place Value • Manipulatives • Compose

• What strategies can I use to add numbers quickly? • How can I use “counting on” strategy to solve addition problems? • How can I use fact families to help me solve addition and subtraction problems? • How can I represent a number using tens and ones with objects and symbols?


• Questioning: Asking questions periodically throughout lesson that give students opportunity for deeper thinking and provide teachers with insight into the degree and depth of student understanding adjusting instruction as needed.

• White Board-‐Draw it: Teachers gives prompt question and students draw what they understand. Example: What symbols can I use to show a number is greater than or less than another number?

• Think-‐Pair-‐Share: Teacher gives direction to students. Students formulate individual response, and then turn to a partner to share their answers. Teacher calls on several random pairs to share their answers with the class.

• Exit Ticket: Exit cards are written student responses to questions posed at the end of a class or learning activity or at the end of a day.

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Unit 4: Developing addition and subtraction strategies Suggested number of days: 10


Unit Overview:

In this unit the focus is on "put Together/Take Apart" problems with unknown addends. These problem types give students the opportunity to see subtraction as the opposite of addition in a different way than as reversing the action. Counting on strategies reinforce that subtraction is an unknown addend problem, which help students view subtraction as being just as easy as addition and emphasizes the relation between subtraction and addition. Common Core State Standards for Mathematical Content

0perations and Algebraic Thinking -‐ 1.0A B. Understand and apply properties of operations and the relationship between addition and subtraction.

3. Apply properties of operations as strategies to add and subtract.3

Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) NOTE:3 Students need not use formal terms for these properties.

4. Understand subtraction as an unknown-‐addend problem. For example, subtract 10 -‐ 8 by finding the number that makes 10 when added to 8.

C. Add and subtract within 20. 6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use

1.OA.3.1 Identify math terms addends, sum, and difference. 1.OA.3.2 Rearrange addends to create turnaround facts. (commutative property) 1.OA.3.3 Explain that I can add in any order to find the sum of three addends. 1.OA.3.4 Apply properties of addition and subtraction. 1.OA.4.1 Use addition to solve a subtraction problem. Exp. 10-‐8=__ Say 8+ ___ = 10 1.OA.6.1 Identify the greater number when given two numbers. 1.OA.6.2 Solve addition problems by identifying the greater number and counting on.

Comments 1.0A.B.3 is repeated in unit 15 to add the associative property to students' repertoire.

In this unit the focus in 1.0A.C.6 is on the relationship between addition and subtraction. This


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strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 -‐ 4 = 13 -‐ 3 -‐ 1 = 10 -‐ 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 -‐ 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).


3. Construct viable arguments and critique the reasoning of others.


1.OA.6.3 Solve addition facts to 10 within a given time frame to build fluency. 1.OA.6.4 Solve addition problems by making 10 and then counting on. 8+2=10 plus 4 more 8+6=___ 1.OA.6.5 Add and subtract using fact families in various ways. 7+3=___, 3+___=10 1.OA.6.6 Add using doubles and doubles plus or minus 1. 8+7=___, 1+7+7=___ 1.OA.6.7 Solve subtraction facts to 10 within a given time frame to build fluency. 1.OA.6.8 Solve mixed addition and subtraction problems within 20.

standard is repeated in units 9 and 18 to provide multiple opportunities to learn and practice all of the different strategies. In each of these units, new strategies will be introduced to expand students' proficiency in addition and subtraction to work towards fluency.

It is important for students to construct viable arguments (MP.3) because in order for students to develop this conceptual understanding, they need to be given the opportunity to explain how they know a strategy works. Exploring structure of problem types facilitate the development of more sophisticated strategies (MP.7).

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Vocabulary Essential Questions • Properties of Operations • Strategies • Add • Addition • Counting On • Making Ten • Addend • Subtract • Subtraction • Rearrange • Relationship • Properties of addition • Properties of subtraction • Greater • Less • Fluency • Solve • Doubles • Fact Families

• What happens to the answer if I change the order of the numbers I am adding? • When I am adding more than two numbers, what strategies can I use to make my

work easier? • What strategies can I use to solve a subtraction problem? • What strategies can I use to add numbers quickly? • How can I identify the greater number? How does this help me when adding two

numbers together? • How does knowing fact families help me build fluency when adding and subtracting?


• White Board-‐Draw it: Teachers gives prompt question and students draw what they understand. Example: What symbols can I use to show a number is greater than or less than another number.

• Yes/No Cards: Teacher asks students if they know meaning of vocab words or math terms. Call out a word, students hold up (prepared to give meaning), students hold up no teacher takes note to inform instruction.



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Unit 5: Telling and writing time to the hour Suggested number of days: 5


Unit Overview:

This is students' first experience in the classroom telling and writing time. In this unit students are not doing any operations with time. Students identify the different parts of the clock, making connections between these parts and the time in hours. Common Core State Standards for Mathematical Content

Measurement and Data – 1.MD B. Tell and write time. 3. Tell and write time in hours and half-‐hours using analog and digital clocks.

Common Core State Standards for Mathematical Practice 5. Use appropriate tools strategically. 6. Attend to precision.

1.MD.3.1 Identify the parts of a clock. (hour hand, minute hand, and second hand) 1.MD.3.2 Tell the difference between analog and digital clocks. 1.MD.3.3 Tell time to the hour using analog and digital clocks. 1.MD.3.4 Tell time to the ½ hour using analog and digital clocks. 1.MD.3.5 Write the time correctly in hours and ½ hours using the colon correctly.

Comments The focus of 1.MD.B.3 in this unit is telling time in hours. Students will extend this skill to telling time to the half hour in unit 10.

Precisely communicating the roles of the different components of the clock is the focus of this unit (MP.5, MP.6).


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Vocabulary Essential Questions • Analog Clock • Digital Clock • Appropriate Tools • Hour hand • Minute Hand • Second hand • Colon

• How do I tell time using a digital clock? • How do I tell time using an analog clock? • What do the different hands on an analog clock stand for? • How do I write the time?



• Exit Tickets Exit Ticket: Exit cards are written student responses to questions posed at the end of a class or learning activity or at the end of a day.


• Yes/No Cards: Teacher asks students if they know meaning of vocab words or math terms. Call out a word, students hold up (prepared to give meaning), students hold up no teacher

takes note to inform instruction.

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Unit 6: Using data to add and subtract to 20 Suggested number of days: 12


Unit Overview:

In this unit students build on the strategies and problem types with which they are familiar with from Kindergarten, extending the number range to 20. The data work in this unit provides a context for students to make important connections to addition and subtraction. Common Core State Standards for Mathematical Content

0perations and Algebraic Thinking – 1.0A A. Represent and solve problems involving addition and subtraction. 1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 2 NOTE: 2 See Glossary, Table 1.

C. Add and subtract within 20. 5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Measurement and Data – 1.MD C. Represent and interpret data. 4. Organize, represent, and interpret data with up to three categories; ask and

1.OA.1.1 Define clue words 1.OA.1.2 Locate clue words to solve problems. 1.OA.1.3 Match clue words to operation symbols in a word problem. 1.OA.1.4 Name and match the operation to its symbol. 1.OA.1.5 Solve addition word problems with unknowns in all positions. 1.OA.1.6 Solve subtraction word problems with unknowns in all positions. 1.OA.1.7 Solve addition word problems within 20. 1.OA.1.8 Solve subtraction word problems within 20. 1.OA.1.9 Model/Show/Draw/Write addition of numbers less than 20 with manipulatives. 1.OA.1.10 Model/Show/Draw/Write subtraction numbers less than 20 with manipulatives. 1.OA.5.1 Relate counting to addition and subtraction. 1.OA.5.2 Use skip counting to add and subtract starting at any given number. 1.OA.5.3 Use an array of examples to show repeated addition by skip counting. 1.MD.4.1 Identify the parts of a bar graph (title, numbers, categories). 1.MD.4.2 Identify the parts of a pictograph. 1.MD.4.3 Collect data by using tally marks.

Comments 1.0A.A.1 is addressed in full in unit 9 to include all problem types.

1.MD.4 is used as a context for students to make sense of numbers and as an application in everyday


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answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.


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

4. Model with mathematics. 1 For additional information, see page 5 in the Categorical

Data progressions document.

1.MD.4.4 Collect data from up to three categories. 1.MD.4.5 Organize and represent collected data. 1.MD.4.6 Create a graph using information I have collected. 1.MD.4.7 Compare results to answer questions. 1.MD.4.8 Answer questions about collected data. 1.MD.4.9. Ask questions about collected data.

life. It can also be used as a context throughout the year. This standard will be addressed in full in unit 9 to include compare problems.

Working with data gives students an opportunity to model with mathematics (MP.4) Students use the context of data to reason through rich problem situations that encourage them to persevere when problem solving (MP.1).

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Vocabulary Essential Questions • Addition • Adding to • Putting together • Repeated Addition • Skip Counting • Subtract • Subtraction • Taking from • Taking apart • Word problems • Clue Words • Solve • Match • Objects • Organize • Represent • Collected Data • Interpret Data • Data Points • Category • Compare • Array of examples • Bar Graph • Pictograph • Tally Marks

• How can I use drawings to represent an addition problem? • How can I use drawings to represent a subtraction problem? • How can I use objects to help me add? • How can I use objects to help me subtract? • How can I use drawings to help me solve word problems? • How can I use objects to help me solve word problems? • When adding two numbers how do you decide which number to start with? • What does “=” mean in an equation? • How are adding and subtracting similar to counting? • How can I organize data using tally marks? • What is a bar graph? • What is a pictograph? • How do I create a graph using data I have collected? • How can I find out how many more or less objects are in one category verses

another?


• Graphic Organizer: Visual model that can assist students in organizing information and communicating clearly and effectively. Students can use graphic organizers to assist in decision making, collect data and help with problem solving.



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Unit 7: Extending strategies for solving addition and subtraction problems Suggested number of days: 15


Unit Overview:

In this unit data provides an authentic context for students to develop appropriate strategies to reason about and solve addition and subtraction problems. In particular, this unit introduces "compare" problems. Because compare problems are relatively difficult for students to master, this unit should provide students time to grapple with the misleading language and difficult contexts involved in these problem types. Common Core State Standards for Mathematical Content

0perations and Algebraic Thinking -‐ 1.0A A. Represent and solve problems involving addition and subtraction. 1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

C. Add and subtract within 20. 6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 -‐ 4 = 13 -‐ 3 -‐ 1 = 10 -‐ 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 -‐ 8 = 4); and creating equivalent but easier or

1.OA.1.1 Define clue words 1.OA.1.2 Locate clue words to solve problems. 1.OA.1.3 Match clue words to operation symbols in a word problem. 1.OA.1.4 Name and match the operation to its symbol. 1.OA.1.5 Solve addition word problems with unknowns in all positions. 1.OA.1.6 Solve subtraction word problems with unknowns in all positions. 1.OA.1.7 Solve addition word problems within 20. 1.OA.1.8 Solve subtraction word problems within 20. 1.OA.1.9 Model/Show/Draw/Write addition of numbers less than 20 with manipulatives. 1.OA.1.10 Model/Show/Draw/Write subtraction numbers less than 20 with manipulatives. 1.OA.6.1 Identify the greater number when given two numbers. 1.OA.6.2 Solve addition problems by identifying the greater number and counting on. 1.OA.6.3 Solve addition facts to 10 within a given time frame to build fluency. 1.OA.6.4 Solve addition problems by making 10 and then counting on. 8+2=10 plus 4 more 8+6=___ 1.OA.6.5 Add and subtract using fact families in various ways. 7+3=___, 3+___=10 1.OA.6.6 Add using doubles and doubles plus or minus 1. 8+7=___, 1+7+7=___

Comments 1.0A.A.1 is addressed in its entirety in this unit to include "compare" problems (the most difficult problem type). The other problem types should also be revisited during this unit. Students will have the opportunity to discuss how this problem type relates to the previous ones they have encountered.

1.0A.C.6 will be addressed in its entirety in unit 18 in which students are expected to demonstrate fluency.


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known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

D. Work with addition and subtraction equations. 7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 -‐ 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

Measurement and Data -‐ 1.MD C. Represent and interpret data. 4. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.


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



1.OA.6.7 Solve subtraction facts to 10 within a given time frame to build fluency 1.OA.6.8 Solve mixed addition and subtraction problems within 20. 1.OA.7.1 Decide if addition or subtraction number sentences are equal. 1.OA.7.2 Demonstrate understanding of the equal sign. 1.MD.4.1 Identify the parts of a bar graph (title, numbers, categories). 1.MD.4.2 Identify the parts of a pictograph. 1.MD.4.3 Collect data by using tally marks. 1.MD.4.4 Collect data from up to three categories. 1.MD.4.5 Organize and represent collected data. 1.MD.4.6 Create a graph using information I have collected. 1.MD.4.7 Compare results to answer questions. 1.MD.4.8 Answer questions about collected data. 1.MD.4.9. Ask questions about collected data.

1.0A.D.7 is repeated in full in unit 13 to provide the opportunity for students to reason about equality and expressions.

1.MD.C.4 is a useful context for practicing compare problem types and Level 3 strategies and provides opportunity for students to construct arguments about the context and strategies involved.

Reasoning about strategies and selecting appropriate strategies is critical to developing conceptual understanding of addition and subtraction in all situations (MP.1, MP.2, MP.3).

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Vocabulary Essential Questions • Add • Addition • Adding To • Putting Together • Counting On • Making Ten • Subtract • Subtraction • Taking From • Taking Apart • Decomposing • Comparing • Word Problems • Solve • Equations • Symbol • Unknown Number • Represent • Relationship • Clue Words • Operation • Model • Greater Number • Fluency • Fact families • Doubles • Equal Sign • Organize • Interpret Data • Categories • Data Points • Bar Graph • Pictograph • Tally Marks • Collect Data

• How do I use clue words to help me understand a word problem? • What manipulatives can I use to help me do addition and subtraction? • What different strategies can I use to check my answer for addition and subtraction? • What does the equal sign mean? • How can I determine if two sides of an equation are equal? • What strategies can I use to add and subtract quickly? • How can I organize data using tally marks? • What is a bar graph? • What do the parts of the bar graph represent? • What is a pictograph? • What do the parts of the pictograph represent? • How do I create a graph using data I have collected? • How can I find out how many more or less objects are in one category verses

another? • What questions can I ask and answer about the data I’ve collected?

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Formative Assessment Strategies • One Word Summary: Select (or invent) one word which best summarizes a topic (skip counting).

• Draw it-‐Exit Ticket or White Board: Students use drawings to represent an addition or subtraction problem.

• Fist To Five: Students show number of fingers on a scale, with 1 being lowest and 5 the highest. Ask, “How well do you feel you know this information?” 1. I can teach it to others 2. I

can do it alone 3. I need some help 4. I could use more practice 5. I am just beginning to learn

• Yes/No Cards: Teacher asks students if they know meaning of vocab words or math terms. Call out a word, students hold up (prepared to give meaning), students hold up no teacher takes note to inform instruction.

• Hand Signals: Ask students to display a designated hand signal to indicate their understanding of a specific concept, principal, or process: -‐ I understand_______ and can explain it

(e.g., thumbs up). -‐ I do not yet understand _______ (e.g., thumbs down). -‐ I’m not completely sure about _______ (e.g., wave hand).

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Unit 8: Distinguishing attributes of shapes. Suggested number of days: 5


Unit Overview:

In this unit students extend their understanding of attributes-‐e.g. orientation, size, and number of sides-‐they learned in Kindergarten to distinguish between defining attributes and non-‐defining attributes. Students need to explore various examples in different ways so that their experiences with shapes are not limited to single examples (e.g. if a student has only worked with equilateral triangles, it may be difficult for them to develop more general understandings of triangles).7 Common Core State Standards for Mathematical Content Geometry – 1.G A. Reason with shapes and their attributes. 1. Distinguish between defining attributes (e.g., triangles are closed and three-‐sided) versus non-‐ defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. Common Core State Standards for Mathematical Practice 3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure.

1.G.1.1 Identify shapes according to their characteristics that define them (number of sides, open or closed, etc.). 1.G.1.2 Identify open and closed shapes. 1.G.1.3 Build and draw identified shapes.

Comments Although building and drawing shapes can support students understanding of defining attributes, this part of 1.G.A.1 is not required until later in the year. This unit gives students opportunities to construct arguments and justify their conclusions based on defining attributes and the structure of geometric figures (MP.3, MP.7).


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Vocabulary Essential Questions • Defining Attributes • Triangles • Non-‐Defining Attributes • Orientation • Shapes • Characteristics • Open-‐Shape • Closed-‐Shape

• How can I describe basic shapes? • How can I sort different shapes? • What is the difference between an open and closed shape? • How can I draw different shapes?



• Word Sort: Given a set of vocabulary terms, students sort in to given categories or create their own categories for sorting

• Graphic Organizer: Visual model that can assist students in organizing information and communicating clearly and effectively. Students can use graphic organizers to assist in decision making, collect data and help with problem solving.

• Worksheet completed and collected for teacher to assess students for factual information, concepts and skills. There is usually a single best answer. Some quiz examples are: True/False, Matching, Multiple Choice

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Unit 9: Composing and drawing shapes Suggested number of days: 8


Unit Overview: In this unit students transition from using trial and error to applying their understanding of different attributes in order to draw and compose shapes. Composing and decomposing figures supports students' understanding of part-‐whole relationships. Common Core State Standards for Mathematical Content Geometry -‐ 1.G A. Reason with shapes and their attributes. 1. Distinguish between defining attributes (e.g., triangles are closed and three-‐sided) versus non-‐ defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

2. Compose two-‐dimensional shapes (rectangles, squares, trapezoids, triangles, half-‐circles, and quarter-‐ circles) or three-‐dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.4 NOTE: 4Students do not need to learn formal names such as "right rectangular prism." Common Core State Standards for Mathematical Practice 2. Reason abstractly and quantitatively. 4. Model with mathematics.

1.G.1.1 Identify shapes according to their characteristics that define them (number of sides, open or closed, etc.). 1.G.1.2 Identify open and closed shapes. 1.G.1.3 Build and draw identified shapes. 1.G.2.1 Create two-‐dimensional shapes. 1.G.2.2 Identify three-‐dimensional shapes. 1.G.2.3 Design/compose shapes to make a new shape. 1.G.2.4 Separate/Decompose shapes from a given shape. 1.G.2.5 Create new shapes from the combined shape. 1.G.2.6 Compose trapezoids, half-‐circles, and quarter circles. 1.G.2.7 Compose rectangular prisms, right circular cones, and right circular cylinders.

Comments Students model these geometric figures (MP.4) in meaningful ways that highlight defining attributes in an abstract way (MP.2). For example, students understand that a new shape can be composed from two other shapes and can simultaneously see both the composite shape and the component shapes.3


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Vocabulary Essential Questions • Defining Attributes • Non-‐Defining Attributes • Create • Compose • Separate • Decompose • Two-‐Dimensional Shape • Triangle • Rectangle • Square • Trapezoid • Half-‐Circles • Quarter-‐Circle • Three-‐Dimensional Shape • Cube • Cone • Cylinder • Composite Shape

• How can I use defining attributes to describe shapes? • How can I use defining attributes to sort shapes? • What is the difference between a two-‐dimensional and three-‐dimensional shape? • What is a composite shape? • How can I use two shapes to create a new shape? • How can I break a shape into two halves? What happens if I break the halves in half?


• Exit Ticket: Exit cards are written student responses to questions posed at the end of a class or learning activity or at the end of a day. Can use handout with shapes to me identified by matching

• One Word Summary: Select (or invent) one word which best summarizes a topic (examples of composite shapes).

• Think-‐Pair-‐Share: Teacher gives direction to students. Students formulate individual response, and then turn to a partner to share their answers. Teacher calls on several random pairs

to share their answers with the class.

• Word Sort: Given a set of vocabulary terms, students sort in to given categories or create their own categories for sorting

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Unit 10: Applying properties of operations to solve problems Suggested number of days: 10


Unit Overview:

Throughout other units students have been building understandings of properties of operations through repeated experience with addition and subtraction. In this unit students apply these understandings to solve real-‐world and mathematical word problems. Common Core State Standards for Mathematical Content 0perations and Algebraic Thinking -‐ 1.0A A. Represent and solve problems involving addition and subtraction. 2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

B. Understand and apply properties of operations and the relationship between addition and subtraction. 3. Apply properties of operations as strategies to add and subtract. 3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) NOTE:3 Students need not use formal terms for these properties. Common Core State Standards for Mathematical Practice 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

1.OA.2.1 Add three numbers with a sum less than or equal to 20 using objects, manipulatives, or drawings. 1.OA.2.2 Write an addition equation to find the sum of three numbers less than or equal to 20. 1.OA.2.3 Solve word problems to find the sum of three whole numbers less than or equal to 20. 1.OA.3.1 Identify math terms addends, sum, and difference. 1.OA.3.2 Rearrange addends to create turnaround facts. (commutative property) 1.OA.3.3 Explain that I can add in any order to find the sum of three addends. 1.OA.3.4 Apply properties of addition and subtraction.

Comments 1.0A.B.3 is repeated here to include the associative property of addition. This unit focuses on students' understanding of the structure of addition and subtraction and use of properties in problem solving (MP.7) and applying it to their calculations (MP.8).


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Vocabulary Essential Questions • Word Problems • Whole Numbers • Add • Addition • addend • Sum • Subtract • Difference • Less than • Equal To • Objects • Manipulatives • Equations • Symbol • Unknown Number • Represent • Properties of Operations • Strategies • Turnaround Facts • Properties of Addition • Properties of Subtraction

• What strategies can I use to solve a word problem? • How can I use drawings to help me solve word problems? • How can I use symbols to help me find the unknown number in an addition or

subtraction problem? • When I am adding more than two numbers, what strategies can I use to make my

work easier? • What are turnaround facts? How can they help me solve problems quicker?



• Whip Around: Teacher poses a question or task. Students with partner or individually respond verbally or on white board then stand up. Teacher randomly calls on a student to share

answers. Students check off any items that are said and sit down when all of their ideas have been shared with the group, whether or not they were the one to share them. The teacher calls on students until they are all seated. As the teacher listens to the information shared by students, he/she can adjust instruction if need.

• Questioning: Asking questions periodically throughout lesson that give students opportunity for deeper thinking and provide teachers with insight into the degree and depth of

student understanding adjusting instruction as needed.

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Unit 11: Telling and writing time to the half hour Suggested number of days: 5


Unit Overview:

In this unit students extend their understanding of telling and writing time from unit 5 to include situations that deal with telling time to the half hour. Common Core State Standards for Mathematical Content Measurement and Data -‐ 1.MD B. Tell and write time. 3. Tell and write time in hours and half-‐hours using analog and digital clocks. Common Core State Standards for Mathematical Practice 5. Use appropriate tools strategically. 6. Attend to precision.


As in unit 5, precisely communicating the roles of the different components of the clock is the focus of this unit (MP.5, MP.6).


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Vocabulary Essential Questions • Analog Clock • Digital Clock • Appropriate Tool • Precision • Hour Hand • Minute Hand • Second Hand

• How do I tell time to the half-‐hour using a digital clock? • What do the different hands on an analog clock stand for? • How do I tell time to the half-‐hour using an analog clock? • How do I write the time to the half-‐hour?


• Worksheet completed and collected for teacher to assess students for factual information, concepts and skills. There is usually a single best answer. Some quiz examples are: True/False, Matching, Multiple Choice



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Unit 12: Adding multiples of ten Suggested number of days: 10


Unit Overview:

In this unit students build on their understanding of adding and subtracting within 20 to develop strategies for adding larger numbers. Students are also introduced to mentally adding 10. These standards are grouped together because the ability to compose a ten and the ability to add and subtract ten is a crucial understanding that can help students develop number sense and proficiency with numbers and operations. Concrete objects or drawings afford connections with written numerical work and discussions in terms of tens and ones by using activities that build number sense. Common Core State Standards for Mathematical Content

Number and Operations in Base Ten -‐ 1.NBT C. Use place value understanding and properties of operations to add and subtract. 4. Add within 100, including adding a two-‐digit number and a one-‐digit number, and adding a two-‐digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-‐digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

5. Given a two-‐digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

Common Core State Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them.

5. Use appropriate tools strategically.

1.NBT.4.1 Add a two-‐digit number to a one-‐digit number within 100 using concrete models, drawing, and strategies 1.NBT.4.2 Add 10 to a two-‐digit number. 1.NBT.4.3 Understand to add the ones place before adding the tens place. 1.NBT.4.4 Use ten units to make a bundle. 1.NBT.5.1 Discuss patterns of 10 on the hundreds chart. 1.NBT.5.2 Locate patterns of 10 on the hundreds. chart1.NBT.5.3 Practice mentally finding 10 more or 10 less. 1.NBT.5.4 Explain how to add or subtract 10 from a given number.

Comments While 1.NBT.C.4 calls for first graders to add two two-‐digit numbers (adding the tens to tens and ones to ones, which may involve composing tens), they are not expected to compute differences of two-‐digit numbers other than multiples of ten. 9

1.NBT.C.4 and 1.NBT.C.5 are repeated in later units to provide the opportunity for students to explain their reasoning.

Students should have ample time to make sense of concrete models with a focus on composing tens (MP.1, MP.5).


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Vocabulary Essential Questions • Add • Addition • Compose • Subtraction • More • Less • One-‐Digit Number • Two-‐Digit Number • Multiple • Strategies • Place Value • Properties of Operations • Mental Strategy • Units • Bundle • Patterns • Hundreds Chart

• How can knowing place values help me to add many numbers with different values? • How can I find 10 more or 10 less than a number without counting? • How can I use bundles of 10 to help me solve problems? • How can I use drawings to help me solve problems with two-‐digit numbers? • How can I use the hundreds chart to help me solve addition and subtraction

problems?


• Exit Ticket: written responses to questions the teacher poses at the end of a lesson or a class to assess student understanding of key concepts (can use a number line or hundreds chart on hand out).




• Draw it-‐Exit Ticket or White Board: Students use drawings to represent an addition or subtraction problem.

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Unit 13: Using understanding of place value to add and subtract Suggested number of days: 10


Unit Overview:

In this unit students extend their understanding from previous units to include subtraction. They are also expected to relate their strategies for addition and subtraction to written methods and explain their reasoning. Common Core State Standards for Mathematical Content

Number and Operations in Base Ten -‐ 1.NBT C. Use place value understanding and properties of operations to add and subtract. 4. Add within 100, including adding a two-‐digit number and a one-‐digit number, and adding a two-‐digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-‐digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

5. Given a two-‐digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

6. Subtract multiples of 10 in the range 10-‐90 from multiples of 10 in the range 10-‐90 (positive or zero differences), using

1.NBT.4.1 Add a two-‐digit number to a one-‐digit number within 100 using concrete models, drawing, and strategies. 1.NBT.4.2 Add 10 to a 2 digit number. 1.NBT.4.3 Understand to add the ones place before adding the tens place. 1.NBT.4.4 Use ten units to make a bundle. 1.NBT.5.1 Discuss patterns of 10 on the hundreds chart. 1.NBT.5.2 Locate patterns of 10 on the hundreds chart 1.NBT.5.3 Practice mentally finding 10 more or 10 less. 1.NBT.5.4 Explain how to add or subtract 10 from a given number. 1.NBT.6.1 Choose and tell in my own words how to subtract patterns of ten in the range 10-‐-‐90 1.NBT.6.2 Use what I know about place value to show that only the tens place changes when

Comments While 1.NBT.C.4 calls for first graders to add two two-‐digit numbers (adding the tens to tens and ones to ones, which may involve composing tens), they are not expected to compute differences of two-‐digit numbers other than multiples of ten. 12

1.NBT.C.5 is repeated here to include mentally subtracting 10 from a number.

1.NBT.C.6 calls for students to extend on their work with adding and subtracting 10 to subtracting multiples of ten.


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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 and explain the reasoning used.


6. Attend to precision.

8. Look for and express regularity in repeated reasoning.

adding/subtracting multiples of 10.

In doing the mental calculation without counting students give carefully formulated explanations for their reasoning by saying that they have one more or one less ten than before (MP.6). This relies on the students' attention to the regularity in the structure of two-‐digit numbers (MP.8).

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Vocabulary Essential Questions • Addition • Subtraction • One-‐Digit Number • Two-‐Digit Number • Multiples of 10 • Ones Place • Tens Place • Zero • Units • Bundle of Ten • Strategies • Written Method • Place Value • Properties of Operations • Relationship • Compose • Explain • Patterns • Hundreds Chart • Mental Strategy

• How does understanding place value help me add or subtract numbers with different values?

• What strategies can I use to find 10 more or 10 less than a given number? • What strategies can I use to help me add multiples of 10? • What strategies can I use to helm me subtract multiples of 10? • How can I explain the relationship between addition and subtraction? • How can I explain how to subtract using the pattern of 10? • How can I use the hundreds chart to demonstrate my understanding of the pattern

of 10?



• Anecdotal Records: Take short notes during a lesson or circulate the classroom and observe students as they work to check for learning. The teacher should reflect on a specific aspect of the learning (making and using bundles of 10 with manipulatives) and adjust instruction as needed.

• Hand Signals: Ask students to display a designated hand signal to indicate their understanding of a specific concept, principal, or process: -‐ I understand_______ and can explain it

(e.g., thumbs up). -‐ I do not yet understand _______ (e.g., thumbs down). -‐ I’m not completely sure about _______ (e.g., wave hand).

• Exit Ticket: written responses to questions the teacher poses at the end of a lesson or a class to assess student understanding of key concepts (can use a number line or hundreds chart on hand out).

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Unit 14: Interpreting and using symbols in numeric expressions and comparisons. Suggested number of days: 10


Unit Overview:

In this unit students apply their conceptual understanding of addition, subtraction, and comparison to interpret and write expressions and equations. It is important for students to make sense of the symbols involved, as well as knowing when to use them. A new concept to this unit is reasoning about whether or not equations are true or false. This unit also provides an opportunity for students to apply their understanding of the symbols while practicing their addition and subtraction strategies in different problem situations. Common Core State Standards for Mathematical Content 0perations and Algebraic Thinking -‐ 1.OA D. Work with addition and subtraction equations. 7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 -‐ 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

8. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = , -‐ 3, 6 + 6 =0.

1.OA.7.1 Decide if addition or subtraction number sentences are equal. 1.OA.7.2 Demonstrate understanding of the equal sign. 1.OA.8.1 Solve addition or subtraction equations by applying my knowledge of fact families.

Comments 1.0A.D.7 was addressed in unit 9. Students now use their understanding of the equal sign to determine whether or not equations are true or false.

1.0A.D.8 introduces the use of symbols to represent unknown quantities. Teachers may have been using some sort of symbol to represent unknown quantities in earlier units, but students to do so during this unit.


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Number and 0perations in Base Ten -‐ 1.NBT B. Understand place value. 3. Compare two two-‐digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Common Core State Standards for Mathematical Practice 2. Reason abstractly and quantitatively. 4. Model with mathematics.

1.NBT.3.1 Compare two, 1 digit numbers using symbols >,<, or = 1.NBT.3.2 Compare two, 2 digit numbers using symbols >,<, or =. 1.NBT.3.3 I can use <,>, or = to compare two digit numbers.

1.NBT.B.3 is repeated in this unit to now include the use of mathematical symbols in expressing numeric comparisons. Correctly placing the < and > symbols is a challenge for early learners.

Students will use models to justify their reasoning throughout this unit (MP.4) and will represent these concrete models with abstract symbols and expressions (MP.2).

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Vocabulary Essential Questions • Equal Sign • Equations • Addition • Subtraction • True • False • Unknown Number • Whole Number • Ones Digit • Tens Digit • Symbols • Model • Number Sentences • Demonstrate • Fact Families • Compare

• What does the equal sign mean? • How can I determine if two sides of a given equation are equal? • What strategies can I use to determine an unknown number? • How can I use pictures to explain a number sentence? • How can I use fact families to solve an addition or subtraction problem?


• White Board-‐Draw it: Teachers gives prompt question and students draw what they understand. Example: What symbols can I use to show a number is greater than or less than another number? How can I use drawings to explain my answer?

• Pop Sickle Stick-‐Pop Quiz: Students demonstrate understanding and mastery of skills and concepts. Have each student’s name on a Popsicle stick in a cup. Draw random names to

answer questions.

• Hand Signals: Ask students to display a designated hand signal to indicate their understanding of a specific concept, principal, or process: -‐ I understand_______ and can explain it (e.g., thumbs up). -‐ I do not yet understand _______ (e.g., thumbs down). -‐ I’m not completely sure about _______ (e.g., wave hand).


(Give equation and they respond <,>,=)

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Unit 15: Ordering and comparing lengths Suggested number of days: 5


Unit Overview: In this unit students explore length comparisons both directly and indirectly. They build and expand upon the direct comparison that they learned in Kindergarten to compare and order three objects directly, and then extend this to indirect comparisons through the use of a third object. This concrete experience with length comparisons supports students' understanding of number comparisons and comparison problem solving. Common Core State Standards for Mathematical Content

Measurement and Data – 1.MD A. Measure lengths indirectly and by iterating length units. 1. Order three objects by length; compare the lengths of two objects indirectly by using a third object.


3. Construct viable arguments and critique the reasoning of others. 5. Use appropriate tools strategically.

1.MD.1.1 Order 3 objects by length. 1.MD.1.2 Compare 3 objects with different lengths.

1.MD.A.1 involves measuring non-‐standard units.3

Comparison is the focus of this unit, whereas iterating length units (1.MD.A.2), is addressed in unit 16.

Students need to use the tools appropriately (MP.5), but this unit should also provide an opportunity for students to explain their reasoning about length comparisons (MP.3).


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Vocabulary Essential Questions • Length • Compare • First • Second • Third • Order • Appropriate Tools

• How can I determine how to order things by length? • How can I compare three objects with different lengths?



• Anecdotal Records: Take short notes during a lesson or circulate the classroom and observe students as they work to check for learning. The teacher should reflect on a specific aspect

of the learning (measuring objects) and adjust instruction as needed.


• Worksheet completed and collected for teacher to assess students for factual information, concepts and skills. There is usually a single best answer. Some quiz examples are:

True/False, Matching, Multiple Choice

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Unit 16: Measuring lengths with non-‐standard units Suggested number of days: 10


Unit Overview:

This unit lays the groundwork for the use of standard measurement units in Grade 2 and the general concept of length. They learn about the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal-‐sized units). Common Core State Standards for Mathematical Content

Measurement and Data -‐ 1.MD A. Measure lengths indirectly and by iterating length units. 2. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-‐size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.




1.MD.2.1 Use non-‐standard units to measure length. 1.MD.2.2 Use standard units to measure to length. (inches, centimeters)

Comments Giving students opportunities to use and select appropriate tools (MP.5) and justify and critique strategies for measurement (MP.3) supports conceptual understanding of measurement rather than just procedural skills.


40

Vocabulary Essential Questions • Whole Number • Multiple • Length • Longer • Shorter • Same-‐Size • Span • Appropriate Tools • Measure • Non-‐standard Unit • Standard Unit

• How can I decide what tool to use to measure the length of something? • What tools can I use to measure something? What objects can I use? • How can I record my findings when I measure things?


• Admit ticket-‐White Board: Teacher asks question at start of lesson, students write or give verbal answer. Teacher assesses overall class understanding of previous lesson taught and adjusts current lesson accordingly.


• Whip Around: Teacher poses a question or task. Students with partner or individually respond verbally or on white board then stand up. Teacher randomly calls on a student to share answers. Students check off any items that are said and sit down when all of their ideas have been shared with the group, whether or not they were the one to share them. The teacher calls on students until they are all seated. As the teacher listens to the information shared by students, he/she can adjust instruction if need.

41

Unit 17: Finding equal shares of shapes Suggested number of days: 5


Unit Overview:

In this unit, students partition shapes into equal shares. The focus is fair shares and equal area to support initial understandings of properties such as congruence and symmetry in area-‐not to discuss fractions. The terms "halves, fourths, and quarters" name the amount of area that is represented to describe the part-‐whole relationship. Fraction notation is first used in Grade 3. Common Core State Standards for Mathematical Content

Geometry -‐ 1.G A. Reason with shapes and their attributes. 3. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Common Core State Standards for Mathematical Practice 3. Construct viable arguments and critique the reasoning of others.

1.G.3.1 Identify equal parts of a shape. 1.G.3.2 Describe the parts of a shape with the terms half, fourth, and quarter. 1.G.3.3 Break apart circles and rectangles into two or four equal parts. 1.G.3.4 Place the parts back together to make a whole.

Comments Students construct arguments to support their own partitioning, but also distinguish correct reasoning from that which is flawed (MP.3).


42

Vocabulary Essential Questions • Partition • Shape • Circles • Rectangles • Whole • Equal Parts • Equal Shares • Break Apart • Halves • Fourths • Quarters • Half of • Fourth Of • Quarter Of • Create • Compose • Decompose

• How do I divide a shape into equal parts? • How do I break apart a shape into halves? How do demonstrate putting the pieces

back together to make a whole? • How do I break apart a shape into four equal parts? How do I model putting the

pieces back together to make a whole?


• Exit Ticket: written responses to questions the teacher poses at the end of a lesson or a class to assess student understanding of key concepts (can use geometric shapes to be identified by fill in the blank or matching on hand out).


• Pop Sickle Stick-‐Pop Quiz: Students demonstrate understanding and mastery of skills and concepts. Have each student’s name on a Popsicle stick in a cup. Draw random names to

answer questions.

• Word Sort: Given a set of vocabulary terms (geometric shapes) students sort in to given categories or create their own categories for sorting

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Unit 18: Demonstrating proficiency in addition and subtraction situations Suggested number of days: 10


Unit Overview:

In this unit students apply their understanding from the entire year to demonstrate fluency in addition and subtraction. They should have experienced ample opportunities to practice the various problem types using strategies based on place value, properties of operations, and the relationship between addition and subtraction. Common Core State Standards for Mathematical Content 0perations and Algebraic Thinking -‐ 1.0A A. Represent and solve problems involving addition and subtraction. 1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

1.OA.1.1 Define clue words 1.OA.1.2 Locate clue words to solve problems. 1.OA.1.3 Match clue words to operation symbols in a word problem. 1.OA.1.4 Name and match the operation to its symbol. 1.OA.1.5 Solve addition word problems with unknowns in all positions. 1.OA.1.6 Solve subtraction word problems with unknowns in all positions. 1.OA.1.7 Solve addition word problems within 20. 1.OA.1.8 Solve subtraction word problems within 20. 1.OA.1.9 Model/Show/Draw/Write addition of numbers less than 20 with manipulatives. 1.OA.1.10 Model/Show/Draw/Write subtraction numbers less than 20 with manipulatives.

Comments


44

C. Add and subtract within 20. 6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 -‐ 4 = 13 -‐ 3 -‐ 1 = 10 -‐ 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 -‐ 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Common Core State Standards for Mathematical Practice 3. Construct viable arguments and critique the reasoning of others. 8. Look for and express regularity in repeated reasoning.

1.OA.6.1 Identify the greater number when given two numbers. 1.OA.6.2 Solve addition problems by identifying the greater number and counting on. 1.OA.6.3 Solve addition facts to 10 within a given time frame to build fluency. 1.OA.6.4 Solve addition problems by making 10 and then counting on. 8+2=10 plus 4 more 8+6=___ 1.OA.6.5 Add and subtract using fact families in various ways. 7+3=___, 3+___=10 1.OA.6.6 Add using doubles and doubles plus or minus 1. 8+7=___, 1+7+7=___ 1.OA.6.7 Solve subtraction facts to 10 within a given time frame to build fluency. 1.OA.6.8 Solve mixed addition and subtraction problems within 20.

1.0A.C.6 is finalized in this unit to include creating equivalent but easier or known sums as a strategy for solving addition and subtraction problems.

Students will select, justify, and explain their strategies in addition and subtraction situations (MP.3). Students find shortcuts by using numerical reasoning to effectively add and subtract (MP.8).

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Vocabulary Essential Questions • Addition • Adding To • Putting Together • Subtraction • Taking From • Taking Apart • Solve • Word Problems • Comparing • Unknowns • Positions • Equation symbol • Represent

• How do I write an equation to represent an addition problem? • How can using manipulatives help me add or subtract? • What strategies can I use to help me add and subtract quickly? • How can I use drawings to help me solve addition and subtraction problems quickly?


• White Board-‐Draw it: Teachers gives prompt question and students draw what they understand. Example: Students use drawings to solve addition and subtraction problems?

• Anecdotal Records: Take short notes during a lesson or circulate the classroom and observe students as they work to check for learning. The teacher should reflect on a specific aspect of the learning (making and using bundles of 10 with manipulatives) and adjust instruction as needed.



• Pop Quiz: Students demonstrate understanding of a concept or skill such as skip counting using a hundreds chart. Can use sheet protectors and dry erase markers. Can use white boards or popsicle stick strategy.

Key: Major Clusters; Supporting Clusters; Additional Clusters

FIRST GRADE CRITICAL AREAS OF FOCUS CRITICAL AREA OF FOCUS #1 Developing understanding of addition, subtraction, and strategies for addition and subtraction within 20 Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Students understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children build their understanding of the relationship between addition and subtraction. Operations and Algebraic Thinking 1.OA Represent and solve problems involving addition and subtraction.

1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Understand and apply properties of operations and the relationship between addition and subtraction.

3. Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

4. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.

Add and subtract within 20. 5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use

mental strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Work with addition and subtraction equations. 7. Understand the meaning of the equal sign, and determine if equations involving addition and

subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

8. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 +? = 11, 5 = – 3, 6 + 6 = .


FIRST GRADE CRITICAL AREAS OF FOCUS

CRITICAL AREA OF FOCUS #1, CONTINUED

Number and Operations in Base Ten 1.NBT

Use place value understanding and properties of operations to add and subtract. 4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-

digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

6. Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), 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 and explain the reasoning used.


FIRST GRADE CRITICAL AREAS OF FOCUS CRITICAL AREA OF FOCUS #2 Developing understanding of whole number relationships and place value, including grouping in tens and ones Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10. They compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they understand the order of the counting numbers and their relative magnitudes

Number and Operations in Base Ten 1.NBT Extend the counting sequence.

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.

Understand place value. 2. Understand that the two digits of a two-digit number represent amounts of tens and ones.

Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones—called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven,

eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven,

eight, or nine tens (and 0 ones). 3. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the

results of comparisons with the symbols >, =, and <.


FIRST GRADE CRITICAL AREAS OF FOCUS

CRITICAL AREA OF FOCUS #3 Developing understanding of linear measurement and measuring lengths as iterating length units Students develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal-sized units) and the transitivity principle for indirect measurement.

Measurement and Data 1.MD

Measure lengths indirectly and by iterating length units. 1. Order three objects by length; compare the lengths of two objects indirectly by using a third

object. 2. Express the length of an object as a whole number of length units, by laying multiple copies of a

shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

Tell and write time. 3. Tell and write time in hours and half-hours using analog and digital clocks.

Represent and interpret data. 4. Organize, represent, and interpret data with up to three categories; ask and answer questions

about the total number of data points, how many in each category, and how many more or less are in one category than in another.


FIRST GRADE CRITICAL AREAS OF FOCUS CRITICAL AREA OF FOCUS #4 Reasoning about attributes of, and composing and decomposing geometric shapes Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build understanding of part-whole relationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for measurement and for initial understandings of properties such as congruence and symmetry.

Geometry 1.G

Reason with shapes and their attributes. 1. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-

defining attributes (e.g., color, orientation, overall size); build and draw shapes that possess defining attributes.

2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

3. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Bailey Educational Group

Common Core State Standards “I Can Statements” 1st Grade Mathematics

CCSS Key: Operations and Algebraic Thinking (OA) Number and Operations in Base Ten (NBT) Measurement and Data (MD) Geometry (G)

Common Core State Standards for Mathematics (Outcome Based)

I Can Statements (Concepts & Skills)

I Can: 1.OA.1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 2

I Can: 1.OA.1.1 Define clue words 1.OA.1.2 Locate clue words to solve problems. 1.OA.1.3 Match clue words to operation symbols in a word problem. 1.OA.1.4 Name and match the operation to its symbol. 1.OA.1.5 Solve addition word problems with unknowns in all positions. 1.OA.1.6 Solve subtraction word problems with unknowns in all positions. 1.OA.1.7 Solve addition word problems within 20. 1.OA.1.8 Solve subtraction word problems within 20. 1.OA.1.9 Model/Show/Draw/Write addition of numbers less than 20 with manipulatives. 1.OA.1.10 Model/Show/Draw/Write subtraction numbers less than 20 with manipulatives.

1.OA.2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

1.OA.2.1 Add three numbers with a sum less than or equal to 20 using objects, manipulatives, or drawings. 1.OA.2.2 Write an addition equation to find the sum of three numbers less than or equal to 20. 1.OA.2.3 Solve word problems to find the sum of three whole numbers less than or equal to 20.

1.OA.3. Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) 3Students need not use formal terms for these properties

1.OA.3.1 Identify math terms addends, sum, and difference. 1.OA.3.2 Rearrange addends to create turnaround facts. (commutative property) 1.OA.3.3 Explain that I can add in any order to find the sum of three addends. 1.OA.3.4 Apply properties of addition and subtraction.

1.OA.4. Understand subtraction as an unknown-addend problem. For example, subtract 1 0 – 8 by finding the number that makes 10 when added to 8.

1.OA.4.1 Use addition to solve a subtraction problem. Exp. 10-8=__ Say 8+ ___ = 10



I Can: 1.OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

I Can: 1.OA.5.1 Relate counting to addition and subtraction. 1.OA.5.2 Use skip counting to add and subtract starting at any given number. 1.OA.5.3 Use an array of examples to show repeated addition by skip counting.

1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

1.OA.6.1 Identify the greater number when given two numbers. 1.OA.6.2 Solve addition problems by identifying the greater number and counting on. 1.OA.6.3 Solve addition facts to 10 within a given time frame to build fluency. 1.OA.6.4 Solve addition problems by making 10 and then counting on. 8+2=10 plus 4 more 8+6=___ 1.OA.6.5 Add and subtract using fact families in various ways. 7+3=___, 3+___=10 1.OA.6.6 Add using doubles and doubles plus or minus 1. 8+7=___, 1+7+7=___ 1.OA.6.7 Solve subtraction facts to 10 within a given time frame to build fluency. 1.OA.6.8 Solve mixed addition and subtraction problems within 20.

1.OA.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

1.OA.7.1 Decide if addition or subtraction number sentences are equal. 1.OA.7.2 Demonstrate understanding of the equal sign.

1.OA.8. Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ☐ – 3, 6 + 6 = ☐.

1.OA.8.1 Solve addition or subtraction equations by applying my knowledge of fact families.

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.

1.NBT.1.1 Count from a given number to 120. 1.NBT.1.2 Read from a given number to 120. 1.NBT.1.3 Write from a given number to 120. 1.NBT.1.4 Look at a number of objects from 0-120 and write the correct numeral to represent that number of objects.



I Can: 1.NBT.2. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones —

called a “ten.” b. The numbers from 11 to 19 are composed of a

ten and one, two, three, four, five, six, seven, eight, or nine ones.

c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

I Can: 1.NBT.2.1 Identify place value of a digit in a given 2 digit number. 1.NBT.2a.1 Represent a 2 digit number with units and bundles. 1.NBT.2b.1 Demonstrate that numbers 11-19 are made up of a tens bundle and a certain number of ones units. (through use of manipulatives, drawing, or verbal explanation) 1.NBT.2c.1 Demonstrate that 10, 20, 30, 40, 50, 60, 70, 80, 90 represent a certain number of tens bundles and zero ones units.

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 <.

1.NBT.3.1 Compare two, 1 digit numbers using symbols >,<, or = 1.NBT.3.2 Compare two, 2 digit numbers using symbols >,<, or =. 1.NBT.3.3 I can use <,>, or = to compare two digit numbers.

1.NBT.4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

1.NBT.4.1 Add a two-digit number to a one-digit number within 100 using concrete models, drawing, and strategies. 1.NBT.4.2 Add 10 to a 2 digit number. 1.NBT.4.3 Understand to add the ones place before adding the tens place. 1.NBT.4.4 Use ten units to make a bundle.

1.NBT.5. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

1.NBT.5.1 Discuss patterns of 10 on the hundreds chart. 1.NBT.5.2 Locate patterns of 10 on the hundreds chart. 1.NBT.5.3 Practice mentally finding 10 more or 10 less 1.NBT.5.4 Explain how to add or subtract 10 from a given number.

1.NBT.6. Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), 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 and explain the reasoning used.

1.NBT.6.1 Choose and tell in my own words how to subtract patterns of ten in the range 10—90. 1.NBT.6.2 Use what I know about place value to show that only the tens place changes when adding/subtracting multiples of 10.



I Can: 1.MD.1. Order three objects by length; compare the lengths of two objects indirectly by using a third object.

I Can: 1.MD.1.1 Order 3 objects by length. 1.MD.1.2 Compare 3 objects with different lengths.

1.MD.2. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

1.MD.2.1 Use non-standard units to measure length. 1.MD.2.2 Use standard units to measure to length. (inches, centimeters)

1.MD.3. Tell and write time in hours and half-hours using analog and digital clocks.


1.MD.4. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

1.MD.4.1 Identify the parts of a bar graph (title, numbers, categories). 1.MD.4.2 Identify the parts of a pictograph. 1.MD.4.3 Collect data by using tally marks. 1.MD.4.4 Collect data from up to three categories. 1.MD.4.5 Organize and represent collected data. 1.MD.4.6 Create a graph using information I have collected. 1.MD.4.7 Compare results to answer questions. 1.MD.4.8 Answer questions about collected data. 1.MD.4.9. Ask questions about collected data.

1.G.1. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

1.G.1.1 Identify shapes according to their characteristics that define them (number of sides, open or closed, etc.). 1.G.1.2 Identify open and closed shapes. 1.G.1.3 Build and draw identified shapes.



I Can: 1.G.2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.4 4Students do not need to learn formal names, such as “right rectangular prism”.

I Can: 1.G.2.1 Create two-dimensional shapes. 1.G.2.2 Identify three-dimensional shapes. 1.G.2.3 Design/compose shapes to make a new shape. 1.G.2.4 Separate/Decompose shapes from a given shape. 1.G.2.5 Create new shapes from the combined shape. 1.G.2.6 Compose trapezoids, half-circles, and quarter circles. 1.G.2.7 Compose rectangular prisms, right circular cones, and right circular cylinders.

1.G.3. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

1.G.3.1 Identify equal parts of a shape. 1.G.3.2 Describe the parts of a shape with the terms half, fourth, and quarter. 1.G.3.3 Break apart circles and rectangles into two or four equal parts. 1.G.3.4 Place the parts back together to make a whole.

Common Core “Shifts” in Mathematics There are six shifts in Mathematics that the Common Core requires of us if we are to be truly

aligned with it in terms of curricular materials and classroom instruction. Shift 1 - Focus Teachers use the power of the eraser and significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards so that students reach strong foundational knowledge and deep conceptual understanding and are able to transfer mathematical skills and understanding across concepts and grades. Shift 2 - Coherence Principals and teachers carefully connect the learning within and across grades so that, for example, fractions or multiplication spiral across grade levels and students can build new understanding onto foundations built in previous years. Teachers can begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning. Shift 3 - Fluency Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions (found in the attached list of fluencies) such as multiplication tables so that they are more able to understand and manipulate more complex concepts. Shift 4 - Deep Understanding Teachers teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of core math concepts by applying them to new situations, as well as writing and speaking about their understanding. Shift 5 – Application Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations. Teachers in content areas outside of math, particularly science, ensure that students are using math – at all grade levels – to make meaning of and access content. Shift 6 - Dual Intensity Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity. Teachers create opportunities for students to participate in “drills” and make use of those skills through extended application of math concepts. The amount of time and energy spent practicing and understanding learning environments is driven by the specific mathematical concept and therefore, varies throughout the given school year.

Standards for Mathematical Practice

1

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

The Standards: 1. Make sense of problems and persevere in solving them.



4. Model with mathematics.


6. Attend to precision.


8. Look for and express regularity in repeated reasoning.

1. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

2. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

3. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects,

Standards for Mathematical Practice

2

drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

4. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

5. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

6. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

7. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well-remembered 7 x 5 + 7 x 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

8. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x +1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

CCSS Standards for Mathematical Practice

Questions for Teachers to Ask 1.Make sense of problems and persevere in

solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics

Teachers ask: • What is this problem asking? • How would you describe the problem in

your own words? • Could you try this with simpler numbers?

Fewer numbers? • How could you start this problem? • Would it help to create a diagram? Make

a table? Draw a picture? • How is ___’s way of solving the problem

like/different from yours? • Does your plan make sense? Why or why

not? • What are you having trouble with? • How can you check this?

Teachers ask: • What does the number ____ represent in

the problem? • How can you represent the problem with

symbols and numbers? • Create a representation of the problem.

Teachers ask: • How is your answer different than

_____’s? • What do you think about what _____ said? • Do you agree? Why/why not? • How can you prove that your answer is

correct? • What examples could prove or disprove

your argument? • What do you think about _____’s

argument? • Can you explain what _____ is saying? • Can you explain why his/her strategy

works? • How is your strategy similar to _____? • What questions do you have for ____? • Can you convince the rest of us that your

answer makes sense? *It is important that the teacher poses tasks that involve arguments or critiques

Teachers ask: • Write a number sentence to describe this

situation. • How could we use symbols to represent

what is happening? • What connections do you see? • Why do the results make sense? • Is this working or do you need to change

your model? *It is important that the teacher poses tasks that involve real world situations

5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

Teachers ask: • How could you use manipulatives or a

drawing to show your thinking? • How did that tool help you solve the

problem? • If we didn’t have access to that tool, what

other one would you have chosen?

Teachers ask: • What does the word ____ mean? • Explain what you did to solve the problem. • Can you tell me why that is true? • How did you reach your conclusion? • Compare your answer to _____’s answer • What labels could you use? • How do you know your answer is

accurate? • What new words did you use today? How

did you use them?

Teachers ask: • Why does this happen? • How is ____ related to ____? • Why is this important to the problem? • What do you know about ____ that you

can apply to this situation? • How can you use what you know to

explain why this works? • What patterns do you see? *deductive reasoning (moving from general to specific)

Teachers ask: • What generalizations can you make? • Can you find a shortcut to solve the

problem? How would your shortcut make the problem easier?

• How could this problem help you solve another problem?

*inductive reasoning (moving from specific to general)

Documents

1 !Grade!! Math!UnitGuide! - Jackson County School District Core/Pacing Guides... · 1st Grade Math! Grade 1 Subject Math # of Units Timeline UNIT CURRICULUM MAP Unit%1:%Exploring%quantities%to%99%