The Mathematics Curriculum and Pacing. EnVision K-5

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1 The Mathematics Curriculum and Pacing EnVision K-5

2 Mathematics Curriculum - Kindergarten Suggested Blocks of Instruction: 12 days /September Topic: 1-One to Five Objectives/CPI s/standards /Enduring Materials/Assessment Know number names and the count sequence. How does counting tell you how 1.1 Counting 1,2, and 3 K.CC.3. Write numbers from 0 to 20. Represent a many? 1.2 Counting 1,2,3 in Different number of objects with a written numeral 0-20 (with How can you use objects to solve a 1.3 Reading and Writing 1,2, and 3 0 representing a count of no objects). problem? 1.4 Counting 4 and Counting 4 and 5 in Different Count to tell the number of objects. Enduring Arrangements 1.6 Reading and Writing 4 and 5 K.CC.4. Understand the relationship between Counting tells how many are in a set, 1.7 Use Objects numbers and quantities; connect counting to regardless of their arrangement or the cardinality. order in which they were counted. Web Site Resources: The last number said when counting a 4a. When counting objects, say the number names in set is the total. Counting is the standard order, pairing each object with one and cumulative. only one number name and each number name with There is a unique symbol that goes one and only one object. with each number word. 4b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Topic Test K.CC.5. Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1 20, count out that many objects.

3 Mathematics Curiculumn Kindergarten Suggested Blocks of Instruction: 12 days /September/October Topic: 2-Comparing & Ordering Numbers 0 to 5 Objectives/CPI s/standards /Enduring Materials/Assessment Know number names and the count sequence. How does using one to one correspondence help you 2.1 More, Fewer, and Same as K.CC.3. Write numbers from 0 to 20. compare two sets of objects? and 2 More Represent a number of objects with a How can we use objects to show the number sequence and 2 Fewer written numeral 0-20 (with 0 from 0 to 5? 2.4 The Number 0 representing a count of no objects). 2.5 Reading and Writing 0 Enduring 2.6 As Many, More, and Fewer Count to tell the number of objects. 2.7 Ordering Number 0-5 If you compare two groups of objects and the number of 2.8 Ordinal Numbers Through K.CC.4. Understand the relationship objects match, the groups have the same number of Fifth between numbers and quantities; objects. If one group has items left over, that group has 2.9 Use Objects connect counting to cardinality. more. The other group has fewer objects. 1 more than or 2 more than expresses the relationship 4c. Understand that each successive between two groups of objects. Web Site Resources: number name refers to a quantity that is 1 fewer than or 2 fewer than expresses the relationship one larger. between two groups of objects. Zero is a number that tells how many objects there are Compare numbers. when there are none. If you compare two groups of objects and the number of K.CC.6. Identify whether the number of objects match, the groups have the same number of Daily Quick Check objects in one group is greater than, less objects. If you compare two groups and one group has Masters than, or equal to the number of objects in items left over, that group has more. The other group another group, e.g., by using matching has fewer objects. and counting strategies. There is a specific order to the set of whole numbers. Topic Test Zero is a number that tells how many objects there are when there are none. Basic FactTest t Numbers can be used to tell order (ordinal numbers). Positions/order in a row can be found by counting,and d ordinal names are similar to number names.

4 10 Days /October Mathematics Curriculum - Kindergarten Topic: 3-Six to Ten Objectives/CPI s/standards /Enduring Materials/Assessment Know number names and the count sequence. How can you be sure you are counting 3.1 Counting 6 and 7 K.CC.3. Write numbers from 0 to 20. Represent a correctly? 3.2 Reading and Writing 6 and 7 number of objects with a written numeral 0-20 How do you use counting to tell how many 3.3 Counting 8 and 9 (with 0 representing a count of no objects). objects are in a set? 3.4 Reading and Writing 8 and Counting 10 Count to tell the number of objects. Enduring 3. 6 Reading and Writing Look for a Pattern K.CC.4. Understand the relationship between Counting tells how many are in a set no numbers and quantities; connect counting to matter which order the numbers are Web Site Resources: cardinality. counted. The last number said when counting a set is the total. 4a. When counting objects, say the number names There is a unique symbol that goes with in the standard order, pairing each object with one each number word. and only one number name and each number Some problems can be solved by identifying name with one and only one object. elements that repeat in a predictable way. 4b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their Topic Test arrangement or the order in which they were counted. K.CC.5. Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1 20, count out that many objects.

5 Mathematics Curriculum Kindergarten Suggested Blocks of Instruction: 13 Days /November/December Topic: 4-Comparing and Ordering Numbers 0 to 10 Objectives/CPI s/standards /Enduring Materials/Assessment Know number names and the count sequence. 4.1 Comparing Numbers Through 10 How do you know which number is 4.2 Comparing Numbers to 5 K.CC.2. Count forward beginning from a given greater than another? 4.3 Comparing to 10 number within the known sequence (instead of How can you use a number line to help More having to begin at 1). count from 0 to 10? Fewer More Count to tell the number of objects Fewer Enduring 4. 8 Ordering Numbers Through 10 Compare numbers. 4.9 Ordering Numbers on a Number Line In a pair of numbers, the number that Use Objects K.CC.6. Identify whether the number of objects in shows more is greater. The number that one group is greater than, less than, or equal to the number of objects in another group, e.g., by shows fewer is less. You can use 5 as a benchmark to compare using matching and counting strategies.1 numbers. You can use 10 as a benchmark to K.CC.7. Compare two numbers between 1 and 10 presented as written numerals. compare numbers. 1 more than, 1 fewer than, 2 more than, and 2 fewer than expresses a relationship between two numbers. There is a specific order to the set of whole numbers. Numbers can be shown by a unique point on the number line. The distance between any two consecutive whole numbers on a given number line is always the same. Web Site Resources: Topic Test

6 8 days /December Mathematics Curriculum - Kindergarten Topic: 5 - Numbers to 20 Objectives/CPI s/standards /Enduring Materials/Assessment Know number names and the count sequence. How can numbers to 20 be counted, read, and written? 5.1 Counting, Reading and Writing K.CC.2. Count forward beginning from a given number within the known sequence (instead of 5.2 Counting, Reading and Writing 13,14 having to begin at 1). 5.3 Counting, Reading and Writing 16 and 17 Enduring 5.4 Counting, Reading and Writing 18, 19 Count to tell the number of objects. and 20 There is a unique symbol that goes with 4b. Understand that the last number name each number word. said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. 5.5 Use Logical Reasoning Web Site Resources: Topic Test

7 9 days / December/January Mathematics Curriculum Kindergarten Topic: 6-Numbers to 100 Objectives/CPI s/standards /Enduring Materials/Assessment Know number names and the count sequence. How can numbers from 1 to 100 be counted 6.1 Counting to 30 K.CC.1. Count to 100 by ones and by tens. using a hundred chart? 6.2 About How Many? When you count by 2 s and 10 s on a hundred 6.3 Counting to 100 Count to tell the number of objects. chart, what patterns do you see? 6.4 Counting Groups of 10 K.CC.5. Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1 20, count out that many objects. Enduring Counting tells how many are in a set no matter which order the objects are counted. The last number said when counting a set is the total. Counting is cumulative. Numbers are counted and written in a specific sequence on a hundred chart. The decade numbers are built on groups of ten. The oral names are similar but not the same as the number of tens counted. Counting patterns (numerical and visual) can be seen on a hundred chart. 6.5 Patterns on a Hundred Chart 6.6 Look for a Pattern Web Site Resources: Topic Test

8 10 days /January Mathematics Curriculum - Kindergarten Topic: 7-Understanding Addition Objectives/CPI s/standards /Enduring Materials/Assessment Understand addition as putting together and adding to, and understand subtraction as taking apart and taking How does moving two groups of objects 7.1 Stories about Joining from. together help you know how many objects 7.2 More Joining there are in all? 7.3 Joining Grouos K.OA.1. Represent addition and subtraction What do you find out when you join two 7.4 Using the Plus Sign with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal groups, or two parts of a whole? 7.5 Finding Sums 7.6 Addition Sentences explanations, expressions, or equations. Enduring 7.7 Draw a Picture K.OA.2. Solve addition and subtraction word Joining parts to make a whole is one Web Site Resources: problems, and add and subtract within 10, e.g., interpretation of addition. by using objects or drawings to represent the Joining groups can be shown in an addition problem. expression that uses the plus sign (+). Joining parts to make a whole is one K.OA.5. Fluently add and subtract within 5. interpretation of addition. Addition number sentences using + and = can be used to show parts of a whole. Topic Test

9 11 days /January / February Mathematics Curriculum - Kindergarten Topic: 8-Understanding Subtraction Objectives/CPI s/standards Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. K.OA.1. Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. K.OA.2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. K.OA.5. Fluently add and subtract within 5. /Enduring How does moving an object, or objects, to the side of a group of objects help you know how many objects are left? What types of situations involve subtraction? Enduring Separating parts from a whole is one interpretation of subtraction. Taking part of a group away is one interpretation of subtraction. Comparing two quantities to find how much more/less one quantity is than the other is one interpretation of subtraction. Separating, take away, and comparison subtraction situations can be shown in a subtraction expression that uses the minus sign (-). Some separating, take away, and comparison situations can be represented and solved using subtraction. Subtraction number sentences using and = can be used to show subtraction situations. Materials/Assessment 8.1 Stories About Separating 8.2 Stories About Take Away 8.3 Stories About Comparing 8.4 Act It Out 8.5 Using the Minus Sign 8.6 Finding Differences 8.7 Subtraction Sentences 8.8 Use Objects Web Site Resources: Topic Test

10 12 days / February/March Mathematics Curriculum Kindergarten Topic: 9-More Addition and Subtraction Objectives/CPI s/standards /Enduring Materials/Assessment Understand addition as putting together and adding to, and understand subtraction as taking apart and taking Why can you show the same number 9.1 Making 4 and 5 from. of objects in different ways? 9.2 Writing Number Sentences for 4 and 5 How can the parts of a number be 9.3 Making 6 and 7 K.OA.3. Decompose numbers less than or equal written as a number sentence? 9.4 Writing Numbers Sentences for 6 and 7 to 10 into pairs in more than one way, e.g., by 9.5 Making 8 and 9 using objects or drawings, and record each Enduring 9. 6 Writing Number Sentences for 8 and 9 decomposition by a drawing or equation (e.g., Making 10 = and 5 = 4 + 1). There is more than one way to show a 9. 8 Writing Number Sentences for 10 number. K.OA.4. For any number from 1 to 9, find the Joining parts to make a whole is one Web Site Resources: number that makes 10 when added to the given interpretation of addition. Addition number, e.g., by using objects or drawings, and number sentences using + and = can record the answer with a drawing or equation. be sued to show parts of a whole. Describe and compare measurable attributes. K.MD.3. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. Topic Test

11 7 days /March Mathematics Curriculum - Kindergarten Topic: 10-Composing Numbers 11 to 19 Objectives/CPI s/standards /Enduring Materials/Assessment Work with numbers to gain foundations for place value. How can you add 1 ten and some ones to 10.1 Making 11,12, and 13 K.NBT.1. Compose and decompose numbers make numbers from 11 to 19? 10.2 Making 14,15 and 16 from 11 to 19 into ten ones and some further What strategies can you use to find the 10.3 Making 17,18 and 19 ones, e.g., by using objects or drawings, and number of objects in a set greater than 10.4 Look for a Pattern record each composition or decomposition by a 10? drawing or equation (such as 18 = ); understand that these numbers are composed Web Site Resources: of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. Enduring Numbers from can be represented as the sum of 10 and some more. Topic Test

12 8 days /March Mathematics Curriculum - Kindergarten Topic: 11-Decomposing Numbers 11 to 19 Objectives/CPI s/standards /Enduring Materials/Assessment Work with numbers to gain foundations for place value. How can we break the numbers 11 to Creating Sets to 19 K.NBT.1. Compose and decompose numbers into parts? 11.2 Parts of 11,12, and 13 from 11 to 19 into ten ones and some further 11.3 Parts of 14,15, and 16 ones, e.g., by using objects or drawings, and Enduring 11.4 Parts of 17, 18, and 19 record each composition or decomposition by a 11.5 Look for a Pattern drawing or equation (such as 18 = ); There is more than one way to show a understand that these numbers are composed number. of ten ones and one, two, three, four, five, six, The numbers 11, 12, and 13 can be Web Site Resources: seven, eight, or nine ones. decomposed as the sum of ten and some ones. The number 11 is decomposed to the sum of , the number 12 is decomposed to , and the number 13 is decomposed to The numbers 14, 15, and 16 can be decomposed as the sum of ten and some ones. The number 14 is decomposed to , the number 15 is decomposed to , and the number 16 is decomposed to Topic Test The number 17, 18, and 19 can be decomposed as a ten and some ones. The number 17 is decomposed to , the number 18 is decomposed , and the number 19 is decomposed to

13 11 days /April Objectives/CPI s/standards Describe and compare measurable attributes. K.MD.1. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. K.MD.2. Directly compare two objects with a measurable attribute in common, to see which object has more of / less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. Mathematics Curriculum Kindergarten Topic: 12-Measurement /Enduring Enduring How can you describe the attributes of an object? How can you make a good guess to try to solve a problem? Objects have measurable attributes such as length, capacity, and weight that can be compared and described. Objects can be compared by length. Objects can be compared by height. Comparing by height is similar to comparing by length. Objects can be compared by capacity. Objects can be compared by weight. Materials/Assessment 12.1 Describing Objects by More Than One Attribute 12.2 Comparing by Length 12.3 More Comparing Objects by Length 12.4 Try, Check, and Revise 12.5 Comparing by Height 12.6 More Comparing Objects by Height 12.7 Comparing Capacities 12.8 Comparing by Weight Web Site Resources: Topic Tests

14 10 days /April/May Mathematics Curriculum - Kindergarten Topic: 13-Sorting, Classifying, Counting, and Categorizing Data Objectives/CPI s/standards /Enduring Materials/Assessment Classify objects and count the number of objects in each category. What does looking at the color, shape, 13.1 Same and Different K.MD.3. Classify objects into given categories; and size of objects help you know 13.2 Sorting by One Attribute count the numbers of objects in each category about them? 13.3 Sorting the Same Set in Different Ways and sort the categories by count. What are some ways to sort objects? Sorting by More Than One Attribute 13.5 Use Logical Reasoning Enduring Attributes can be used to compare objects. Attributes can be sued to sort a group of objects. Attributes such as color, shape, or size can be sued to sort the same set of objects in different ways. A set of objects can be sorted according to a combination of attributes Real Graphs 13.7 Picture Graphs Web Site Resources: Topic Test Basic Facts Tests

15 11 days / May Mathematics Curriculum - Kindergarten Topic: 14-Identifying & Describing Shapes Objectives/CPI s/standards Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). K.G.2. Correctly name shapes regardless of their orientations or overall size. K.G.3. Identify shapes as two-dimensional (lying in a plane, flat ) or three-dimensional /Enduring What do you look for when you describe and match shapes? How can you describe the flat surfaces of solids? Enduring A rectangle has four sides and four corners. A square has four sides and four corners. All the sides of a square are the same length. A circle is round and does not have any corners. All triangles have three sides but can have different configurations of sides and angles. A hexagon is a shape with six sides and six corners. Three-dimensional or solid figures have length, width, and height. Many everyday objects closely approximate standard geometric solids. Flat surfaces of many solid figures have specific shapes. Materials/Assessment 14.1 Rectangles 14.2 Squares 14.3 Circles 14.4 Triangles 14.5 Hexagons 14.6 Solid Figures 14.7 Flat Surfaces of Solids Figures 14.8 Use Objects Web Site Resources: Topic Test

16 8 days / May/June Mathematics Curriculum - Kindergarten Topic:15- Position & Location of Shapes Objectives/CPI s/standards /Enduring Materials/Assessment Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). K.G.1. Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. How can you describe where something is using the words above, below or on? Enduring The position of objects can be determined in relation to surrounding objects and described using words Inside and Outside 15.2 Above, Below, and On 15.3 In Front of and Behind Left and Right Act It Out Web Site Resources: Topic Test

17 8 days / June Mathematics Curriculum - Kindergarten Topic: 16- Analyzing, Comparing, and Composing Shapes Objectives/CPI s/standards /Enduring Materials/Assessment Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). How do you know when shapes are exactly 16.1 Same Size, Same Shape the same? 16.2 Making Shapes from Other Shapes Analyze, compare, create, and compose What three-dimensional shapes can you 16.3 Comparing Solid Figures shapes. make using solid figures? 16.4 Building with Solid Figures 16.5 Use Logical Reasoning K.G.4. Analyze and compare two- and threedimensional shapes, in different sizes and Enduring Web Site Resources: orientations, using informal language to describe their similarities, differences, parts Shapes in the plane can be the same size (e.g., number of sides and vertices/ corners ) and other attributes (e.g., having sides of equal and shape. Shapes can be combined to make other length). shapes. Solid figures can be compared in different K.G.5. Model shapes in the world by building ways. Some solid figures can be compared shapes from components (e.g., sticks and clay by their flat surfaces (faces) and vertices balls) and drawing shapes. (corners). Solid figures can be combined to make K.G.6. Compose simple shapes to form larger other solid figures. Topic Test shapes. For example, Can you join these two triangles with full sides touching to make a rectangle?

18 15 days /September Mathematics Curriculum Grade 1 Topic: 1-Understanding Addition Objectives/CPI s/standards /Enduring Materials/Assessment Represent and solve problems involving addition and subtraction. What are ways to think about addition? 1.1 Spatial Pattern for Number to 10 1.OA.1. Use addition and subtraction within Making 6 & 7 to solve word problems involving situations of Enduring 1.3 Making 8 adding to, taking from, putting together, taking 1.4 Making 9 apart, and comparing, with unknowns in all The number of objects in some patterned 1.5 Introducing Addition Expressions & positions, e.g., by using objects, drawings, and arrangements can be recognized without Number Sentences equations with a symbol for the unknown counting. 1.6 Stories about Joining number to represent the problem. Numbers 6, 7, 8, and 9 can be can be 1.7 Adding in any Order broken into parts of the whole in 1.8 Use Objects Understand and apply properties of different ways. operations and the relationship between Parts of a whole is one interpretation of Web Site Resources: addition and subtraction. addition. Addition number sentences can be used to show parts of a whole. 1.OA.3. Apply properties of operations as Joining parts to make a whole is one strategies to add and subtract.2 Examples: If = 11 is known, then = 11 is also known. interpretation of addition. Addition number sentences can be used to show (Commutative property of addition.) To add 2 + joining situations , the second two numbers can be added to Two numbers can be added in any order. make a ten, so = = 12. (Associative property of addition.) Topic Test

19 Mathematics Curriculum Grade 1 Suggested Blocks of Instruction: 14 days / October Objectives/CPI s/standards Represent and solve problems involving addition and subtraction. 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. Understand and apply properties of operations and the relationship between addition and subtraction. 1.OA.4.Understand subtraction as an unknownaddend problem. For example, subtract 10 8 by finding the number that makes 10 when added to 8. Add and subtract within 20. Add and subtract within 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., = = = 14); decomposing a number leading to a ten (e.g., = = = 9); using the relationship between addition and subtraction (e.g., knowing that = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 1 3). Work with addition & subtraction equations. 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, = 2 + 5, = Topic: 2-Understanding Subtraction /Enduring What are ways to think about subtraction? Enduring A missing part of a whole can be found when the whole and the other part are known. A missing part of a whole is one interpretation of subtraction. Subtraction number sentences can be used to show a missing part subtraction situation. Taking away parts from a whole is one interpretation of subtraction. Subtraction number sentences can be sued to show takingaway subtraction situations. Comparing two quantities to find how much more/less one quantity is than the other is one interpretation of subtraction. Subtraction number sentences can be sued to show comparison subtraction situations. Finding a missing part of a whole is one interpretation of subtraction. Subtraction number sentences can be used to show missing part subtraction situations. There are different interpretations of subtraction. Addition and subtraction have an inverse relationship. The difference can be written at the beginning or end of an subtraction sentence, as long as the number or expression on each side of the equal sign are the same amount. Materials/Assessment 2.1 Finding Missing Parts of 6 & Finding Missing Parts of Finding Missing Parts of Introducing Subtraction Expression and Number Sentences 2.5 Stories about Taking Away 2.6 Stories about Comparing 2.7 Stories about Missing Parts 2.8 All Kinds of Subtraction Stories 2.9 Connecting Addition & Subtraction 2.10 Connecting Models & Symbol 2.11 Act it out Web Site Resources: Topic Test

20 Mathematics Curriculum Grade 1 Suggested Blocks of Instruction: 9 days /October Topic: 3-Five and Ten Relationships Objectives/CPI s/standards /Enduring Materials/Assessment Represent and solve problems involving addition and subtraction. How can numbers up to 10 be shown 3.1 Representing Numbers on a Ten-Frame Understand and apply properties of using 5 and some more? 3.2 Recognizing Numbers on a Ten-Frame operations and the relationship between 3.3 Parts of 10 addition and subtraction. 3.4 Finding Missing Parts of 10 Enduring 3.5 Make a Table 1.OA.4. Understand subtraction as an unknown-addend problem. For example, Numbers to 10 can be represented on a Web Site Resources: subtract 10 8 by finding the number that ten-frame using 5 and 10 as makes 10 when added to 8. Add and subtract benchmarks. within 20. The number 10 can be broken into parts of the whole in different ways. Add and subtract within 20. A missing part of a whole can be found 1.OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 1.OA.6. Add and subtract within 20, showing fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., = = = 1 4); decomposing a number leading to a ten (e.g., 13 4 = = 10 1 = 9); using the relationship between addition and subtraction (e.g., knowing that = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 13). when the whole and the other part are known. Topic Test

21 Mathematics Curriculum Grade 1 Suggested Blocks of Instruction: 14 days /November Objectives/CPI s/standards Represent and solve problems involving addition and subtraction. 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. Understand and apply properties of operations and the relationship between addition and subtraction. 1.OA.3. Apply properties of operations as strategies to add and subtract.2 Examples: If = 11 is known, then = 11 is also known. (Commutative property of addition.) To add , the second two numbers can be added to make a ten, so = = 12. (Associative property of addition.) 1.OA.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. Add and subtract within OA.5. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 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., = = = 14); decomposing a number leading to a ten (e.g., = = 10 1 = 9); using the relationship between addition and subtraction (e.g., knowing that = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 13). Topic: 4-Addition & Subtraction Facts to 12 /Enduring : What strategies can be used to find addition & subtraction facts? Enduring Represent and solve problems involving addition and subtraction. Understand and apply properties of operations and the relationship between addition and subtraction. Work with addition and subtraction equations. Add and subtract within 20. Materials/Assessment 4.1 Adding with 0,1,2 4.2 Doubles 4.3 Near Doubles 4.4 Facts with 5 on a Ten-Frame 4.5 Making 10 on a Ten-Frame 4.6 Subtracting 0,1,2 4.7 Thinking Addition 4. 8 Thinking Addition to 8 to Subtract 4.9 Thinking Addition to 12 to Subtract 4.10 Draw a Picture and Write a Number Sentence Web Site Resources: Daily Quick Check Master End of module performance assessment Portfolio assessment

22 13 days / December Objectives/CPI s/standards Represent and solve problems involving addition and subtraction. 1.OA.1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.OA.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. 1.OA.3. Apply properties of operations as strategies to add and subtract.2 Examples: If = 11 is known, then = 11 is also known. (Commutative property of addition.) To add , the second two numbers can be added to make a ten, so = = 12. (Associative property of addition.) Add and subtract within OA.6. Add and subtract within 20, demonstrating fluency for adding & subtracting within 10. Use strategies such as counting on; making ten (e.g., = = = 14); decomposing a # leading to a ten (e.g., = = 10 1 = 9); using the relationship between addition and subtraction (e.g., knowing that = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 13). Mathematics Curriculum Grade 1 Topic: 5-Addition Facts to 20 /Enduring What strategies can be used to find addition facts? Enduring Doubles facts can be associated with memorable real-world situations. Basic addition facts that are near doubles can be found using a related doubles fact. Some addition facts can be found by changing to an equivalent fact with 10. Addition facts involving 9 can be changed to an equivalent fact with 10. Addition facts involving 8 can be changed to an equivalent fact with 10. Three numbers can be added in any order and the sum will be the same. Numbers can be grouped in different ways to solve word problems with three addends. Materials/Assessment 5.1 Doubles 5.2 Doubles Plus Doubles Plus Two Question Problems 5.5 Making 10 to Add 5.6 Making 10 to Add Making 10 to Add Adding Three Numbers 5.9 Word Problems with Three Addends Web Site Resources: Daily Quick Check Master End of module performance assessment Portfolio assessment

23 Mathematics Curriculum Grade 1 Topic: 6-Subtraction Facts to 20 Suggested Blocks of Instruction: 10 days / January Objectives/CPI s/standards /Enduring Materials/Assessment Represent and solve problems involving addition and subtraction. 1.OA.1. Use addition and subtraction within 20 to solve What strategies can be used to find 6.1 Making 10 to Subtract word problems involving situations of adding to, taking subtraction facts? 6.2 More Making 10 to Subtract from, putting together, taking apart, and comparing, with 6.3 Using Related Facts unknowns in all positions, e.g., by using objects, 6.4 Fact Families drawings, and equations with a symbol for the unknown Enduring 6.5 Using Addition to Subtract number to represent the problem. 6.6 Subtraction Facts Subtraction facts with teen numbers 6.7 Draw a Picture and Write a Number Understand and apply properties of operations can be simplified by making use of the Sentence and the relationship between addition and number s relationships to 10. subtraction. Addition and subtraction have an Web Site Resources: 1.OA.4. Understand subtraction as an unknown-addend inverse relationship. The inverse problem. For example, subtract 10 8 by finding the relationship between addition and number that makes 10 when added to 8. Add and subtract subtraction can be sued to find within 20. subtraction facts; every subtraction fact has a related addition fact. Add and subtract within OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use Daily Quick Check Master strategies such as counting on; making ten (e.g., = = = 14); decomposing a number leading to a ten (e.g., = = 10 1 = 9); using the End of module performance relationship between addition and subtraction (e.g., assessment knowing that = 12, one knows 12 8 = 4); and Portfolio assessment creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 13). Work with addition and subtraction equations. 1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating three whole

24 9 days /January Mathematics Curriculum Grade 1 Topic: 7- Counting & Number Patterns to 120 Objectives/CPI s/standards /Enduring Materials/Assessment Extend the counting sequence. 1.NBT.1. Count to 120, starting at any number What patterns do you notice when you count 7.1 Making Numbers 11 to 19 less than 120. In this range, read and write forward from 1 through 100? 7.2 Using Numbers 11 to 19 numerals and represent a number of objects 7.3 Counting by 10s to 120 with a written numeral. Enduring 7.4 Counting on a Hundred Chart 7.5 Using Skip Counting Understand place value. Numbers can be used to tell how many Look for a Pattern Counting and place-value patterns can be seen on a hundred chart. A hundred chart Web Site Resources: 1.NBT.2. Understand that the two digits of a two-digit number represent amounts of tens shows numbers in order in rows and and ones. Understand the following as special columns. cases: Numbers 11 through 20 can be shown as a group of 10 up to 10 more. The decade numbers are built on groups of 2b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. 2c. 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). ten. The but the oral names are similar, not same as the number of tens counted. Skip counting can be used to find the total number of objects in a collection of equal groups. Topic Tests Basic Facts Tests

25 9 days /January / February Mathematics Curriculum Grade 1 Topic: 8- Tens & Ones Objectives/CPI s/standards /Enduring Materials/Assessment Extend the counting sequence. Understand place value. How can numbers 10 and higher be shown, 8.1 Counting with Groups of 10 and counted, read, and written? Leftovers 1.NBT.2. Understand that the two digits of a 8.2 Numbers Made with Tens two-digit number represent amounts of tens Enduring 8.3 Tens and Ones and ones. Understand the following as special 8.4 Expanded Form cases: Numbers can be used to tell how many. 8.5 Ways to Make Numbers Sets of 10 can be perceived as single entities. 8.6 Make an Organized List 2a. 10 can be thought of as a bundle of ten ones In a standard numeral, the tens are written called a ten. to the left of the ones. Web Site Resources: The decade numbers to 100 are built on 2c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, groups of ten. When there are only tens, 90 refer to one, two, three, four, five, six, seven, counting by 10s can be sued to find how eight, or nine tens (and 0 ones). many there are in all. When objects are grouped in sets of 10 and leftovers (ones), counting the groups of ten and adding ones tells how many there are in all. Numbers greater than 10 can be represented as the sum of the tens and the ones. Topic Tests Numbers greater than 10 can be named in more than one way and have the same value. Basic Facts Tests

26 7 days / February Mathematics Curriculum Grade 1 Topic: 9-Comparing & Ordering Numbers to 100 Objectives/CPI s/standards /Enduring Materials/Assessment Extend the counting sequence. 1.NBT.1. Count to 120, starting at any number less How can numbers to 100 be compared More, 1 Less, 10 More, 10 Less than 120. In this range, read and write numerals and and ordered? 9.2 Making Numbers on a Hundred Chart represent a number of objects with a written 9.3 Comparing Numbers with >,<, and = numeral. Enduring 9.4 Ordering Three Numbers 9.5 Making an Organized List Understand place value. 1 more, 1 less, 10 more, 10 less express a relationship between two numbers. Web Site Resources: 1.NBT.3. Compare two two-digit numbers based on Place value can be used to compare meanings of the tens and ones digits, recording the and order numbers. results of comparisons with the symbols >, =, and <. Ordering 3 or more numbers is similar to comparing 2 numbers because each Use place value understanding and number must be compared to each of properties of operations to add and subtract. the other numbers. Numbers can be represented on a 1.NBT.4. Add within 100, including adding a two- hundred chart digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using Topic Tests 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 twodigit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 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. Basic Facts Tests

27 9 days / February / March Mathematics Curriculum Grade 1 Topic: 10-Adding with Tens & Ones Objectives/CPI s/standards /Enduring Materials/Assessment Use place value understanding and properties of operations to add and subtract. What are ways to add with tens and ones? 10.1 Adding Groups of Adding Tens on a Hundred Chart 1.NBT.4. Add within 100, including adding a Enduring 10.3 Adding Tens to Two-Digit Numbers two-digit number and a one-digit number, and 10.4 Using Mental Math to Add Tens adding a two-digit number and a multiple of 10, using concrete models or drawings and Adding groups of 10 is similar to adding numbers less than Adding to a Two-Digit Number 10.6 Draw a Picture and Write a Number strategies based on place value, properties of When adding tens to a two-digit number, Sentence operations, and/or the relationship between only the tens digit changes. addition and subtraction; relate the strategy to There is more than one way to do a mental Web Site Resources: a written method and explain the reasoning calculation. Techniques for doing addition used. Understand that in adding two-digit calculations mentally involve changing the numbers, one adds tens and tens, ones and numbers or the expression so the ones; and sometimes it is necessary to compose calculation is easy to do mentally. a ten. The traditional algorithm for adding a two- digit number and a two-digit number starts by adding ones. Sometimes 10 ones need to be regrouped as 1 ten. Then the tens are added. Topic Tests

28 8 days / March Mathematics Curriculum Grade 1 Topic: 11- Subtracting with Tens & Ones Objectives/CPI s/standards /Enduring Materials/Assessment Use place value understanding and properties of operations to add and subtract. What are ways to subtract two digit 11.1 Subtracting Groups of 10 numbers? 11.2 Subtracting Tens on a Hundred Chart 1.NBT.6. Subtract multiples of 10 in the range 11.3 Subtracting Tens from Two-Digit from multiples of 10 in the range Enduring Numbers (positive or zero differences), using concrete 11.4 Using Mental Math to Subtract Tens models or drawings and strategies based on Subtracting groups of 10 is similar to 11.5 Subtracting from a Two-Digit Number place value, properties of operations, and/or subtracting numbers less than Draw a Picture and Write a Number the relationship between addition and When subtracting tens from a two-digit Sentence subtraction; relate the strategy to a written number, only the tens digit changes. method and explain the reasoning used. There is more than one way to do a Web Site Resources: mental calculation. Techniques for Pearsonsuccessnet.com doing subtraction calculations mentally involve changing the numbers or the expression so the calculation is easy to do mentally. The traditional algorithm for subtracting a one-digit number from a two-digit number starts by subtracting ones. Sometimes 1 ten needs to be renamed as 10 ones before subtracting. Topic Tests Then the tens are subtracted.

29 8 days / March / April Mathematics Curriculum - Grade 1 Topic: 12-Length Objectives/CPI s/standards /Enduring Materials/Assessment Measure lengths indirectly and by iterating length units. How can objects be measured, compared, and ordered by length? 12.1 Comparing and Ordering by Length 12.2 Indirect Measurement 12.3 Using Units to Estimate and 1.MD.1. Order three objects by length; compare the lengths of two objects indirectly by using a third object. Enduring Measure Length 12.4 More Measuring Length 1.MD.2. Express the length of an object as a Objects can be compared and ordered by 12.5 Use Reasoning whole number of length units, by laying length Measuring Using Different Units multiple copies of a shorter object (the length Two objects can be compared indirectly by unit) end to end; understand that the length comparing both to a third object. Web Site Resources: measurement of an object is the number of Measurement is a process of comparing a same-size length units that span it with no gaps unit to the object being measured. The or overlaps. Limit to contexts where the object length of any object can be used as a being measured is spanned by a whole number measurement unit length. of length units with no gaps or overlaps. Different units can be used to measure length. Topic Test

30 6 days / April Topic: 13-Time Mathematics Curriculum Grade 1 Objectives/CPI s/standards /Enduring Materials/Assessment Measure lengths indirectly and by iterating length units. How can clocks and schedules be read and 13.1 Understanding the Hour and Minute Tell and write time. used? Hands 13.2 Telling and Writing Time to the 1.MD.3. Tell and write time in hours and Enduring Hour half-hours using analog and digital clocks Telling and Writing Time to the Half The hour hand tells the hour, and the minute Hour hand tells the number of minutes after the Use Data from a Table hour. Time to the hour can be shown on an analog Web Site Resources: clock or on a digital clock and can be written in two ways: _ o clock or _:00. Time can be given to the half hour. Topic Test

31 10 days / May Mathematics Curriculum Grade 1 Topic: 14- Using Data to Answer Questions Objectives/CPI s/standards /Enduring Materials/Assessment Represent and interpret data. 1.MD.4. Organize, represent, and interpret How can graphs be used to show data and 14.1 Using Data from Real Graphs data with up to three categories; ask and answer questions? 14.2 Using Data from Picture Graphs answer questions about the total number of Using Data from Bar Graph data points, how many in each category, and how many more or less are in one Enduring Collecting Data Using Tally Marks Making Real Graphs category than in another. Each type of graph is most appropriate 14.6 Making Reap Graphs for certain kinds of data Making Picture Graphs Real graphs, picture graphs, and bar graphs make it easy to compare data. Web Site Resources: Tally charts are useful in recording and organizing some kinds of data. In a real graph, real objects are arranged in a particular way to make comparisons. The key for a pictograph determines the Topic Readiness Test number of pictures needed to represent Teacher observation each number in a set of data. Topic Test

32 Mathematics Curriculum Gradee 1 Suggested Blocks of Instruction: 13 days / May Topic: 15-Geometry Objectives/CPI s/standards /Enduring Materials/Assessment Reason with shapes and their attributes. How can shapes and solids be described, 1.G.1. Distinguish between defining attributes compared, and used to make other 15.1 Identifying Plane Shapes (e.g., triangles are closed and three-sided) shapes? 15.2 Make an Organized List versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw Enduring Properties of Plane Shapes Building with Shapes shapes to possess defining attributes. Many everyday objects are close Making new Shapes from Shapes approximations of standard plane 15.6 Identifying Solids Figures 1.G.2. Compose two-dimensional shapes shapes Flat Surfaces and Vertices (rectangles, squares, trapezoids, triangles, half- Plane shapes have many properties that 15.8 Sorting Solid Figures circles, and quarter-circles) or three- make them different from one another Building with Solid Figures dimensional shapes (cubes, right rectangular Many plane shapes can be described by Use Reasoning prisms, right circular cones, and right circular their sides and vertices. cylinders) to create a composite shape, and Plane shapes can be combined to make Web Site Resources: compose new shapes from the composite new plane shapes. shape.1 Many everyday objects closely approximate standard geometric solids. Many solid figures are comprised of flat surfaces and vertices. Attributes can be sued to sort solid figures. Many sets of solid figures can be sorted in more than one way. Solid figures can be combined to make other solid figures. Topic Test

33 Mathematics Curriculum Grade 1 Suggested Blocks of Instruction: 6 days / May / June Topic: 16-Fractions of Shapes Objectives/CPI s/standards /Enduring Materials/Assessment Reason with shapes and their attributes. How can you divide a shape into equal 16.1 Making Equal Parts 1.G.3. Partition circles and rectangles into two parts? 16.2 Describing Equal Parts of Whole Objects and four equal shares, describe the shares 16.3 Making Halves and Fourths of Rectangles using the words halves, fourths, and quarters, Enduring and Circles and use the phrases half of, fourth of, and 16.4 Draw a Picture quarter of. Describe the whole as two of, or A region can be divided into equal-sized four of the shares. Understand for these parts in different ways. Equal-sized parts of Web Site Resources: examples that decomposing into more equal a region have the same area but not shares creates smaller shares. necessarily the same shape. Topic Test

34 13 days / September Mathematics Curriculum Grade 2 Topic: 1 - Understanding Addition and Subtraction Objectives/CPI s/standards Represent and solve problems involving addition and subtraction. 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. /Enduring What are some ways to think about addition and subtraction? Enduring Parts of a whole is one interpretation of addition. Addition number sentences can be used to show parts of a whole. Joining parts to make a whole is one interpretation of addition. Addition number sentences can be used to show joining parts of a whole. Separating parts from a hole and comparison are two interpretations of subtraction. Subtraction number sentences can be used to show separating parts from a hole or comparison subtraction situations. Addition and subtraction have an inverse relationship. The inverse relationship between addition and subtraction can be used to find subtraction facts; every subtraction fact has a related addition fact. Materials/Assessment 1.1 Writing addition number sentences 1.2 Stories about joining 1.3 Writing subtraction number sentences 1.4 Stories about separating 1.5 Stories about comparing 1.6 Connecting addition & subtraction 1.7 Use objects for solving problems Web Site Resources: Topic Test

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