# BREATHITT COUNTY SCHOOLS KINDERGARTEN MATH CURRICULUM

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1 Weeks 1-2 Instructional Emphasis: Counting and Cardinality Topic 1: One to Five K.CC.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Counting to tell the number of objects. K.CC.4: Understand the relationship between numbers and quantities; connect counting to cardinality. a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. b. 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. 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. Big Ideas: Essential Questions: 1-1, 1-2, 1-4, 1-5: Counting tells how many are in a set, regardless of their arrangement or the order in which they were counted. The last number said when counting a set is the total. Counting is cumulative. How does counting tell how many? (1-1) How can you tell just by looking how many objects there are in a group? (1-2) Why is writing the number 1, 2, or 3 important? (1-3) 1-3, 1-6: There is a unique symbol that goes with each number word. 1-7: Some problems can be solved by using objects to act out the actions in the problem. Why is the last number you say important when counting a set of objects? (1-4) How can you recognize different arrangements of 4 or 5 objects? (1-5) Why is writing the numbers 4 and 5 important? (1-6) How can you use objects to solve a problem? (1-7) Lesson 1: Counting 1, 2, and 3 one, two, three, count Lesson 2: Counting 1, 2, and 3 in Different Arrangements Lesson 3: Reading and Writing 1, 2, and 3 number Lesson 4: Counting 4 and 5 four, five Lesson 5: Counting 4 and 5 in Different Arrangements Children will use objects to represent and count the quantities 1, 2, and 3. Children will identify whether a particular set includes 1, 2, or 3 objects, regardless of Children will recognize and write the numerals that describe the quantities 1, 2, and 3. Children will use objects to represent and count the quantities 4 and 5. Children will identify whether a particular set includes 4 or 5 objects. 1

2 Count 3; Compare Quantities K.CC.4.a; K.CC.5 how the objects are arranged. Count 2; Count 3 K.CC.4.a; K.CC.5 Number Cards 0-11 (Teaching Tool 5) Count 1; Count 3; Count 2 K.CC.4.a; K.CC.4; K.CC.5 Count 2; Count and Trace the Number 3; Count 3 K.CC.4.a; K.CC.5 Use Numbers to Tell How Many; Count 5 K.CC.4.a; K.CC.5 I can use objects to represent and count the quantities 1, 2, and 3. I can identify whether a particular set includes 1, 2, or 3 objects, regardless of how the objects are arranged. I can identify and write the numerals that describe the quantities 1, 2, and 3. I can use objects to represent and count the quantities 4 and 5. I can identify whether a particular set includes 4 or 5 objects. Assessment Assessment Assessment Assessment Assessment Topic 1 Introduction Lesson 6: Reading and Writing 4 and 5 Lesson 7: : Use Objects 2

3 Children will recognize and write numerals that describe the quantities 4 and 5. Number Cards 1-5 (Teaching Tool 5) Count 1; Count 3; Count 2 Children will solve problems by using objects. Tape Count 2; Count and Read 4; Count 3 K.CC.3; K.CC.4; K.CC.5 K.CC.5; K.CC.4.b I can identify and write I can solve problems by numbers that describe using objects. the quantities 4 and 5. Assessment Assessment Topic 1 Assessment Weeks 3-4 Instructional Emphasis: Counting and Cardinality Topic 2: Comparing and Ordering 0 to 5 3

4 K.CC.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Counting to tell the number of objects. K.CC.4: Understand the relationship between numbers and quantities; connect counting to cardinality. b. 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. c. Understand that each successive number name refers to a quantity that is one larger. 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. Comparing numbers. K.CC.6: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Note: Include groups with up to ten objects.) Big Ideas: 2-1: If you compare two groups of objects and number of objects match, the groups have the same number of objects. If one group has items left over, that group has more. The other group has fewer objects. 2-2: 1 more than or 2 more than expresses the relationship between two groups of objects. 2-3: 1 fewer than or 2 fewer than expresses the relationship between two groups of objects. 2-4, 2-5: Zero is a number that tells how many objects there are when there are none. 2-6: If you compare two groups of objects and the number of objects match, the groups have the same number of objects. If you compare two groups and one group has items left over, that group has more. The other group has fewer objects. 2-7: There is a specific order to the set of whole numbers. Zero is a number that tells how many objects there are when there are none. 2-8: Numbers can be used to tell order (ordinal numbers). Positions/order in a row can be found by counting, and ordinal names are similar to number names. 2-9: some problems can be solved by using objects to act out the actions in the problem. Lesson 1: Lesson 2: More, Fewer, and Same 1 and 2 More Lesson 3: 1 and 2 Fewer Essential Questions: How does using one-to-one correspondence help you compare two sets of objects? (2-1) How can you tell whether a group has 1 more or 2 more? (2-2) How can you tell whether a group has 1 fewer or 2 fewer? (2-3) What number would you use to show no objects, or none? (2-4) What number would you use to show no object, or none? (2-5) How does matching objects in two groups of objects help you know which group has more, fewer, or as many as the other group? (2-6) How can you use objects to show the number sequence 0 to 5? (2-7) How can you describe the order of five things in a row? (2-8) How can you use connecting cubes to solve a problem? (2-9) Lesson 4: The Number 0 Lesson 5: Reading and Writing 0 4

5 As more (than), fewer (than), same as, same number of, column, row Children will use one-toone correspondence to compare objects and decide whether one group has more, fewer, or the same number as the other group. Connecting Cubes Use Numbers to Tell How Many; Count Objects K.CC.6 I can use one-to-one correspondence to compare objects and decide whether one group has more, fewer, or the same number as the other group. 1 more (than), 2 more (than) Children will recognize and identify a group of objects that has 1 more or 2 more than another group. Connecting Cubes Writing Practice 4, 5, 0 (Teaching Tool 13) Identify More Than, Less Than; Use Numbers to Tell How Many K.CC.6 I can identify and identify a group of objects that has 1 more or 2 more than another group. 1 fewer (than), 2 fewer (than) Children will recognize and identify a group of objects that has 1 fewer or 2 fewer than another group Connecting Cubes Use Numbers to Tell How Many; Identify 2 More K.CC.6 I can identify and identify a group of objects that has 1 fewer or 2 fewer than another group. zero, none Children will understand that zero means none. Count Objects; Use Numbers to Tell How Many; Identify Ways to Make 5 K.CC.3 I can identify and write the number zero and demonstrate the fact that zero means none. Children will recognize and write the numeral that describes the quantity of 0. Number Cards 0-5 (Teaching Tool 5) Writing Practice 4, 5, 0 (Teaching Tool 13) Identify Ways to Make 5; Count Objects K.CC.3; K.CC.4; K.CC.5 I can identify and write the numeral that describes the quantity of 0. Assessment Assessment Assessment Assessment Assessment Topic 2 Introduction 5

6 Lesson 6: As Many, More, and Fewer as many Children will use one-toone correspondence to compare two groups and determine whether one group has more, fewer, or as many as the other group. Connecting Cubes Count Objects; Compare Quantities K.CC.6 Lesson 7: Ordering Numbers 0 to 5 order Children will use objects to order numbers 0 to 5 in sequence. 12 Connecting Cubes Number Cards 0-5 (Teaching Tool 5) Glue Count Objects; Identify 1 Fewer K.CC.4c Lesson 8: Ordinal Numbers Through Fifth first, second, third, fourth, fifth Children will use words first through fifth to identify ordinal positions. Number Cards 1-5 (Teaching Tool 5) Blunt-Tipped Scissors Glue Use Numbers to Tell How Many; Use Language such as 1 More Than and 1 Fewer Than; Write Numbers Lesson 9: : Use Objects fewest, most Children will use objects to show the number in each group, order the number of objects in each group, and identify the group that has the most or fewest number of objects. Connecting Cubes (red, green, blue, yellow, purple, orange) Identify Ordinal Positions; Identify ways to Make 5 6

7 I can use one-to-one correspondence to compare two groups. I can use objects to order numbers 0 to 5 in sequence. K.CC.4; K.CC.4c I can use words first through fifth to identify ordinal positions. K.CC.6; K.CC.4.b; K.CC.4.c I can use objects to show the number in each group. I can determine whether one group has more, fewer, or as many as the other group. I can order the number of objects in each group that has the most or fewest number of objects. Assessment Assessment Assessment Assessment Topic 2 Assessment 7

8 Weeks 5-6 Instructional Emphasis: Counting and Cardinality Topic 3: Six to Ten K.CC.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Counting to tell the number of objects. K.CC.4: Understand the relationship between numbers and quantities; connect counting to cardinality. a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. b. 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. c. Understand that each successive number name refers to a quantity that is one larger. 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. Big Ideas: 3-1, 3-3, 3-5: 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. 3-2, 3-4, 3-6: There is a unique symbol that goes with each number word. 3-7: Some problems can be solved by identifying elements that repeat in a predictable way. Lesson 1: Counting 6 and 7 six, seven Children will use objects to represent and count the quantities of 6 and 7. Lesson 2: Reading and Writing 6 and 7 Children will recognize and write the numerals that describe the quantities 6 and 7. Essential Questions: How can you be sure you are counting correctly? (3-1) Why is writing the number 6 or 7 important? (3-2) What does the last number you say when counting a set of objects tell you? (3-3) When can you write the number 8 to show how many items are in a group? (3-4) How do you use counting to tell how many objects are in a set? (3-5) Which number can you use to show there are 10 items in a group? Can you use any other number to show 10 items? (3-6) How can you predict what comes next in a growing pattern? (3-7) Lesson 3: Counting 8 and 9 eight, nine Children will use objects to represent and count 8 and 9. Lesson 4: Reading and Writing 8 and 9 Children will recognize and write numerals that describe the quantities 8 and 9. (per child) Lesson 5: Counting 10 ten Use objects to represent and count the quantity 10. (per child) 8

9 Counting to 5; Drawing 1 Fewer K.CC.4b; K.CC.5 I can use objects to represent and count the quantities of 6 and 7. Topic 3 Introduction Lesson 6: Reading and Writing 10 Number Cards 1-7 (from Teaching Tool 5) Five-Frame Mat (Teaching Tool 7) Identify Numbers; Count 6; Show 1 Fewer Item K.CC.3; K.CC.4; K.CC.5 I can identify and write the numbers that describe 6 and 7. BREATHITT COUNTY SCHOOLS Five-Frame Mat (Teaching Tool 7) Ten-Frame Mat (8) Counting 7; Counting 4; Count and Write Numbers K.CC.4b; K.CC.5 I can use objects to represent and count 8 and 9. Number Cards for 1-9 (Teaching Tool 5) Count 5; Match 0 to a Set with 0 Objects; Count 9 K.CC.3; K.CC.4; K.CC.5 I can identify and write the numbers that describe the quantities 8 and 9. Ten-Frame Mat (Teaching Tool 8) Use Cubes to Order Numbers from 1 to 5; Recognize 8; 2 More K.CC.4b; K.CC.5 I can use objects to count the quantity of 10. Assessment Assessment Assessment Assessment Assessment Children will recognize Lesson 7: : Look for a Pattern growing pattern 9

10 and write the numeral that describes the quantity of 10. (per child) Number Cards 1-10 (from Teaching Tool 5) Count 8; Recognize the Number 10; Reading and Writing 9 K.CC.3; K.CC.4; K.CC.5 I can identify and write the numerals that describe 8, 9 and 10. Assessment Children will solve problems by identifying growing patterns and predicting what comes next. Connecting Cubes Counting to 5; Counting to 8 K.CC.4b; K.CC.4.a; K.CC.4.c I can solve problems by identifying growing patterns and predicting what comes next. Assessment Topic 3 Assessment 10

11 Weeks 7-8 Instructional Emphasis: Counting and Cardinality Topic 4: Comparing and Ordering Numbers 0 to 10 K.CC.2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1). K.CC.4: Understand the relationship between numbers and quantities; connect counting to cardinality. c. Understand that each successive number name refers to a quantity that is one larger. K.CC.6: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Note: Include groups with up to ten objects.) K.CC.7: Compare two numbers between 1 and 10 presented as written numerals. K.OA.1: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (Note: Drawings need not show details, but should show the mathematics in the problem -- this applies wherever drawings are mentioned in the Standards.) Big Ideas: Essential Questions: 4-1: In a pair of numbers, the number that shows more How do you know which number is greater than is greater. The number that shows fewer is less. 4-2: You can use 5 as a benchmark to compare numbers. 4-3: You can use 10 as a benchmark to compare numbers. 4-4: 1 more than expresses a relationship between two numbers. 4-5: 1 fewer expresses a relationship between two numbers. 4-6: 2 more than expresses a relationship between two numbers. 4-7: 2 fewer than expresses a relationship between two numbers. 4-8: There is a specific order to the set of whole numbers. 4-9: 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. 4-10: some problems can be solved by using objects to act out the actions in a problem. Lesson 1: Lesson 2: Comparing Numbers Comparing Numbers to Through 10 5 Lesson 3: Counting Numbers to 10 another? (4-1) How can you use 5 as a benchmark to compare numbers? (4-2) How can you tell if a number is less than 10? (4-3) How can you find the number that is 1 more than another number? (4-4) How can you find the number that is 1 fewer than another number? (4-5) How can you find the number that is 2 more than another number? (4-6) How can you find the number that is 2 fewer than another number? (4-7) Which numbers do you know that come after 5? (4-8) How can you use a number line to help count from 0 to 10? (4-9) How do you use counters to solve a problem? (4-10) Lesson 4: 1 More Lesson 5: 1 Fewer 11

12 greater, less Children will compare two numbers using sets of objects and one-toone correspondence to determine which number is greater and which is less. Use Numbers to Describe How Many; Count Objects; One Fewer K.CC.6; K.CC.7 I can compare two numbers using sets of objects and one-to-one correspondence to determine which number is greater and which is less. Given a number from 0-5, children will tell if the number is greater or less than 5. Number Cards 1-11 (Teaching Tool 5) Count Objects; Use Numbers to Describe How Many K.CC.6; K.CC.7 I can identify numbers greater or less than 5 Given a number or set from 0-12, children will decide if the number is greater or less than 10. Count Objects; Identify Number Order; Compare Sets K.CC.6; K.CC.7 I can count objects (1-12) and identify if the number is greater or less than 10. Children will use counting to identify a number that is 1 more than another number. Count Objects; Compare Numbers to 5 K.CC.6; K.CC.7; K.OA.1 I can use objects to count one more. Children will use counting to identify a number that is 1 fewer than another number. Number Cards 0-10 (Teaching Tool 5) Compare Quantities; Use Numbers to Tell How Many K.CC.6; K.CC.7; K.OA.1 I can use objects to count one fewer. Assessment Assessment Assessment Assessment Assessment Topic 4 Introduction 12

13 and Enrichment Lesson 6: 2 More Children will use counting to identify a number that is 2 more than another number. Count Objects; Compare Quantities K.CC.6; K.CC.7; K.OA.1 I can use counting to identify a number that is 2 more than another number. Lesson 7: 2 Fewer Children will use counting to identify a number that is 2 fewer than another number. Compare Quantities; Count How Many K.CC.6; K.CC.7; K.OA.1 I can use counting to identify a number that is 2 fewer than another number. Lesson 8: Ordering Numbers Through 10 Children will order numbers from 0 through 10 in sequence. Number Cards 1-10 (Teaching Tool 5) Glue Blunt-tipped Scissors Use Numbers to Tell How Many; Compare Quantities K.CC.2; K.CC.4.c I can order numbers 0 through 10 in sequence. Lesson 9: Ordering Numbers on a Number Line order, number line, forward, backward Children will use a number line to count numbers 0 to 10 in order. Number Cards 1-10 (from Teaching Tool 5) Glue Same As; Reading and Writing 6 K.CC.2 I can use a number line to count numbers 0 to 10 in order. Lesson 10: : Use Objects Children will solve problems by using counters to show 1 more and 2 more. Counters or Teaching Tool 32 Count Objects; Count Up; Draw Objects to Show How Many K.CC.7 I can solve problems by using counters to show 1 more and 2 more than. 13

14 Assessment Assessment Assessment Assessment Assessment and Enrichment Topic 4 Assessment 14

15 Weeks 9-10 Instructional Emphasis: Counting and Cardinality Topic 5: Numbers to 20 K.CC.2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1). K.CC.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). K.CC.4: Understand the relationship between numbers and quantities; connect counting to cardinality. b. 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. Big Ideas: Essential Questions: 5-1, 5-2, 5-3, 5-4: There is a unique When should you write the number 11 to tell about a set of objects? symbol that goes with each number word. 5-5: Some problems can be solved by reasoning about conditions in the problem. Lesson 1: Counting, Reading, and Writing 11 and 12 eleven, twelve Children will recognize and write the numerals that describe the quantities 11 and 12. (per child) Lesson 2: Counting, Reading, and Writing 13, 14, and 15 thirteen, fourteen, fifteen Children will recognize and write the numerals that describe the quantities 13, 14, and 15. The number 12? (5-1) When can you use the number 13 to tell about a set of objects? The number 14? The number 15? (5-2) What do the numbers 16 and 17 tell you about sets of objects? (5-3) When can you use the number 18 to tell about a set of objects? Can you use the number words nineteen or twenty to tell about the same set of objects? (5-4) How can you use logical reasoning to solve a problem? (5-5) Lesson 3: Counting, Reading, and Writing 16 and 17 sixteen, seventeen Children will recognize and write the numerals that describe the quantities 16 and 17. Lesson 4: Counting, Reading, and Writing 18, 19, and 20 eighteen, nineteen, twenty Children will recognize and write numerals that describe the quantities 18, 19, and 20. Lesson 5: : Use Logical Reasoning Children will solve problems by applying logical reasoning to identify missing numbers in a number sequence. Number Cubes

16 Number Cards 0-20 (Teaching Tools 5,6) Double Ten-Frame Mat (Teaching Tool 9) Identify a Group with 2 More; Use Numbers to Describe How Many; Write 8 and 9 to Match Objects K.CC.4b; K.CC.3 I can recognize and write the numerals that describe the quantities 11 and 12. Number Cards 1-15 (Teaching Tool 5, 6) Count and Identify 10; Use Numbers to Tell How Many; Identify Ordinal Positions K.CC.4b; K.CC.3 I can identify and write the numerals that describe the quantities 13, 14, and 15. Number Cards (Teaching Tool 6) Find the Greater Number; Identify Ordinal Positions; Use Numbers to Describe How Many K.CC.4b; K.CC.3 I can recognize and write the numerals that describe the quantities 16 and 17. Number Cards for (Teaching Tool 6) Double Ten-Frame (Teaching Tool 9) Compare Numbers Through 10; Identify 2 Fewer K.CC.4.b; K.CC.3 I can identify and write numerals that describe the quantities (Teaching Tool 5, 6) Identify 2 More; Count and Read 16 K.CC.2 I can solve problems by applying logical reasoning to identify missing numbers in a number sequence. Assessment Assessment Assessment Assessment Assessment Topic 5 Introduction Weeks Instructional Emphasis: Counting and Cardinality Topic 5 Assessment 16

17 Topic 6: Numbers to 100 K.CC.1: Count to 100 by ones and by tens. K.CC.2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1). K.CC.4: Understand the relationship between numbers and quantities; connect counting to cardinality. b. 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. c. Understand that each successive number name refers to a quantity that is one larger. 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. Big Ideas: Essential Questions: 6-1, 6-2: Counting tells how many are in a set no matter which order the objects are counted. The last number said when When will you count to 30 to find out about a set of objects? (6-1) counting a set is the total. Counting is cumulative. How can you estimate how many objects are in a 6-3: Numbers are counted and written in a specific sequence on a group? (6-2) hundred chart. What numbers are repeated in each column you 6-4: The decode numbers are built on groups of ten. The oral count? (6-3) names are similar but not the same as the number of tens counted. How can you count objects that are in groups of 10? (6-4) 6-5: Counting patterns (numerical and visual) can be seen on a hundred chart. When you count by 2s and 10s on a hundred chart, what patterns do you see? (6-5) 6-6: Some problems can be solved by identifying elements that repeat in a predictable way. How can you find a pattern to solve a problem? (6-6) Lesson 1: Counting to 30 Lesson 2: About How Many? Lesson 3: Counting to 100 Lesson 4: Counting Groups of 10 Lesson 5: Patterns on a Hundred Chart Children will count to 30 objects. (per child) about Children will use benchmarks to estimate quantities of groups. (per child) Connecting Cubes hundred chart, row, column Children will count and write numbers to 100 on the hundred chart. Hundred Chart (Teaching Tool 18) Children will count groups of 10, up to 10 tens, and write how many. Ten-Frame for Counting (Teaching Tool 8) count by 2s, count by 10s Children will use a hundred chart to recognize patterns when counting by 2s and 10s. 17

18 Compare Numbers to 5; 1 Fewer; Numbers to 20 K.CC.1; K.CC.2; K.CC.4.b I can count to 30 objects. Count to Represent Numbers; 2 More K.CC.5 I can use benchmarks to estimate quantities of groups. Find a Group Fewer Than 10; Identify Number That Tells 2 Fewer; Count and Read 13 K.CC.1 I can count and write numbers to 100 on the hundred chart. Connecting Cubes Describe Relative Size of Sets Using the Words Same As; Count and Read 16; Count and Write Numbers K.CC.1 I can count groups of 10, up to 10 tens, and write how many. Red, Yellow, and Blue Hundred Chart (Teaching Tool 18) Ordinal Numbers Through Fifth; Identify 1 Fewer Draw and Write 9 K.CC.1 I can use a hundreds chart to recognize patterns when counting by 2s and 10s. Assessment Assessment Assessment Assessment Assessment Topic 6 Introduction Lesson 6: : Look for a Pattern 18

19 Children will solve problems by looking for a pattern. (per child) Books Hundred Chart (Teaching Tool 18) Paper Squares Use Patterns to Count How Many; Count Objects; Make 10 in Two Different Ways K.CC.1; K.CC.2 I can solve problems by looking for a pattern.. Assessment 19

20 Topic 6 Assessment Weeks Instructional Emphasis: Operations and Algebraic Thinking Topic 7: Understanding Addition K.OA.1: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (Note: Drawings need not show details, but should show the mathematics in the problem -- this applies wherever drawings are mentioned in the Standards.) 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.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = and 5 = 4 + 1). Big Ideas: Essential Questions: 7-1, 7-2, 7-3: Joining parts to make a whole is one interpretation of addition. How does moving two groups of objects together help you know how many objects there are in all? (7-1) 7-4: Joining groups can be shown in an addition expression that uses the plus sign (+). What can you tell by looking at pictures of two groups that leave a circle around them? (7-2) 7-5, 7-6: Joining parts to make a whole is one interpretation of addition. Addition number sentences What do you find out when you join two groups, or two parts of a whole? (7-3) using + and = can be used to show parts of a whole. What symbol can you write to show joining two groups? 7-7: Information in a problem can often be shown using a (7-4) picture or diagram and used to understand and solve the problem. What symbols can you write to show adding two groups and finding the sum? (7-5) What information does an addition sentence tell you? (7-6) What do you draw to solve a problem about joining groups? (7-7) Lesson 1: Stories About Joining Lesson 2: More Joining Lesson 3: Joining Groups Lesson 4: Using the Plus Sign Lesson 5: Finding Sums number story, join, in all Children will act out number stories that Children will interpret illustrations that show joining groups and write the corresponding altogether Children will determine how many there are altogether when two add, plus sign Children will use the plus sign (+) to represent joining equal sign, sum Children will identify and use the equal sign (=); add and 20

21 involve joining two groups. Use Numbers to Tell How Many; Use Language Such as Same As; Recognize Ordinal Positions K.OA.1; K.OA.2; K.OA.5 I can act out number stories that involve joining two groups. numbers. Count and Recognize a Number of Objects; Compare Sets of Objects; Ordinal Numbers Through Fifth K.OA.1; K.OA.2; K.OA.5 I can interpret illustrations that show joining groups and write the corresponding numbers. groups are joined. Connecting Cubes of 2 Colors Count and Recognize a Number of Objects; Compare Sets of Objects; Count and Recognize a Number of Objects K.OA.1; K.OA.2; K.OA.5 I can determine how many there are altogether when two groups are joined. groups when recording addition. Joining Groups; Count Objects; Use Language Such as Fewer K.OA.1; K.OA.2; K.OA.5 I can use the plus sign (+) to represent joining groups when recording addition. write the sum. Joining Groups; Recognize and Name a Number of Objects; Determine answers to Addition Problems K.OA.1; K.OA.2; K.OA.5 I can identify and use the equal sign (=); add and write the sum. Assessment Assessment Assessment Assessment Assessment Topic 7 Introduction 21

22 Lesson 6: Addition Sentences addition, sentence Children will write and solve addition sentences to represent joining situations. Use Symbols to Show Adding; Compare Sets of Objects; Joining Groups K.OA.5; K.OA.1; K.OA.2 I can write and solve addition sentences. Lesson 7: : Draw a Picture Children will solve problems by drawing pictures about joining two groups. Solve Addition Problems; Use Language Such as Less Than; Recognize Ordinal Positions K.OA.2; K.OA.1; K.OA.5 I can solve problems by drawing pictures about joining two groups. Assessment Assessment 22

23 Topic 7 Assessment Weeks Instructional Emphasis: Operations and Algebraic Thinking Topic 8: Understanding Subtraction K.OA.1: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (Note: Drawings need not show details, but should show the mathematics in the problem -- this applies wherever drawings are mentioned in the Standards.) 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.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = and 5 = 4 + 1). Big Ideas: Essential Questions: 8-1: Separating parts from a whole is one interpretation of subtraction. How does moving an object, or objects, to the side of a group of objects help you know how many objects are 8-2: Taking part of a group away is one interpretation of subtraction. left? (8-1) How can you act out a number story about things being 8-3: Comparing two quantities to find how much more/less one quantity is than the other is one interpretation of subtraction. taken away? (8-2) How does matching one object in one group with another object in another group help you find out about two 8-4, 8-8: Some problems can be solved by using objects to act out the actions in the problem. groups? (8-3) What do you act out to solve a problem about taking away 8-5: Separating, take away, and comparison subtraction situations can be shown in a subtraction expression that uses the minus sign (-). part of a group? (8-4) What symbol can you write to show separating a part of a group? (8-5) 8-6: Some separating, take away, and comparison situations can be represented and solved using subtraction. What symbol can you write in a number sentence between the number being subtracted and the number that tells how many objects are left? (8-6) 8-7: Subtraction number sentences using and = can be used to show subtraction situations. Lesson 1: Stories About Lesson 2: Stories About Take Lesson 3: Stories About What information does a subtraction sentence tell you? (8-7) How can you use counters to solve a problem? (8-8) Lesson 4: : Act It Lesson 5: Using the Minus Sign 23

24 Separating Away Comparing Out take away left, separate Children will act out number stories that involve separating two groups. Understand Addition Problems; Use Language Such as More Than; Ordering Numbers K.OA.1; K.OA.2; K.OA.5 I can act out subtraction story problems. Children will determine how many are left when some objects in a group are taken away. Solve Addition Problems; Describe Simple Additions; Determine Answers to Addition Problems K.OA.1; K.OA.2; K.OA.5 I can identify the number of objects left in a set when some are taken away. Children will compare two groups to find how many more or fewer. Sheets of Paper Pencils Connecting Cubes Represent Addition Situations; Use Language Such as More Than and Less Than; Identify Ordinal Positions K.OA.1; K.OA.2; K.OA.5 I can compare two groups to find how many more or fewer. Children will act out and solve subtraction word problems and record the answers. Describe Simple Subtraction Problems; Determine Answers to Subtraction Problems; Show 2 Ways to Make 5 K.OA.1; K.OA.2; K.OA.5 I can act out and solve subtraction word problems and record the answers. minus sign (-), subtract Children will use the minus sign (-) to represent take away situations when recording subtraction. 6 Pencils Compare Sets of Objects; Describe Simple Subtractions; Determine Answers to Subtraction Problems K.OA.1; K.OA.2; K.OA.5 I can demonstrate how to use the minus sign (-) to represent take away situations when recording subtraction. Assessment Assessment Assessment Assessment Assessment Topic 8 Introduction 24

25 Lesson 6: Finding Differences difference Children will use the equal sign (=), subtract, and write the difference. Describe Simple Subtraction Problems; Count and Recognize a Number of Objects; Represent Subtraction Situations Lesson 7: Subtraction Sentences subtraction, sentence Children will write and solve subtraction sentences to represent take-away situations. Determine Answers to Addition Problems K.OA.5; K.OA.1; K.OA.2 Lesson 8: : Use Objects Children will solve problems by choosing addition or subtraction. Identify Ordinal Positions; Represent Subtraction Situations K.OA.2; K.OA.1 K.OA.1; K.OA.2; K.OA.5 25

26 I can use the equal sign (=) when completing a subtraction equation and write the difference. I can write and solve subtraction sentences to represent take-away situations. BREATHITT COUNTY SCHOOLS I can solve problems by choosing addition or subtraction. Assessment Assessment Assessment Topic 8 Assessment Weeks Instructional Emphasis: Operations and Algebraic Thinking Topic 9: Composing and Decomposing Numbers to 10 K.OA.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = and 5 = 4 + 1). K.OA.4: For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. K.MD.3: Classify objects or people into given categories; count the numbers in each category and sort the categories by count. (Note: Limit category counts to be less than or equal to 10.) 26

27 Big Ideas: 9-1, 9-3, 9-5, 9-7: There is more than one way to show a number. 9-2, 9-4, 9-6, 9-8: Joining parts to make a whole is one interpretation of addition. Addition number sentences using + and = can be used to show parts of a whole. 9-9: Some problems can be solved by making, reading, and analyzing a graph. Lesson 1: Making 4 and 5 whole, part Children will use objects to show 4 and 5 in two parts. Count 4; Identify 2 Fewer; Count and Write 3 Lesson 2: Writing Number Sentences for 4 and 5 Children will write number sentences to describe the decomposition of 4 or 5 into two parts. Numbers to 20; Identify 1 Fewer BREATHITT COUNTY SCHOOLS Essential Questions: Why can you show the same number of objects in different ways? (9-1) How can number sentences represent part-part-whole relationships? (9-2) How can you show a whole group of objects in a different way? (9-3) How can the parts of a number be written as a number sentence? (9-4) How can you show the same number of objects in different ways? (9-5) How can the parts of a number be represented as a number sentence? (9-6) How can you show the same number in different ways? (9-7) How can the parts of a number be represented as a number sentence? (9-8) How do you use a graph to solve a problem? (9-9) Lesson 4: Lesson 5: Writing Number Making 8 and 9 Sentences for 6 and 7 Lesson 3: Making 6 and 7 Children will use objects to show 6 and 7 in two parts. 2 More; Sort by Attributes; Ordering Numbers 0 to 5 Children will write number sentences to describe the decomposition of 6 or 7 into two parts. Counting to 3; Write Number Sentences for 5 Children will use objects to show 8 and 9 in two parts. Counting 8; Zero; Identify 2 More Than 27

28 K.OA.3 K.OA.3 K.OA.3 K.OA.3 K.OA.3 Assessment Assessment Assessment Assessment Assessment Topic 9 Introduction I can use objects to show 4 and 5 in two parts. I can write number sentences to describe the decomposition of 4 or 5 into two parts. I can use objects to show 6 and 7 in two parts. I can write number sentences to describe the decomposition of 6 or 7 into two parts. I can use objects to show 8 and 9 in two parts. Lesson 6: Writing Number Sentences for 8 and 9 Children will write number sentences that add up to 8 and 9. 2 Sets of Colored Lesson 7: Making 10 Children use objects to show 10 in two parts. (red, yellow) Ten-Frame Mat (Teaching Tool 8) Lesson 8: Writing Number Sentences for 10 Children will write number sentences that show how two numbers can add to 10. Two-Color Counters (or Teaching Lesson 9: : Make a Graph graph Children will construct graphs using real objects or pictures to answer questions. 28

29 Writing Number Sentences for 4 and 5; Writing Number Sentences for 6 and 7 K.OA.3 I can write number sentences that add up to 8 and 9. Counting 10; Counting 8; Counting 4 K.OA.4 I can use objects to show 10 in two parts. Subtraction Sentences; Writing Number Sentences for 8 and 9 K.OA.3 I can write number sentences that show how two numbers can add to 10. Making 10 in Two Parts; Counting 10; Writing 8 and 9 K.MD.3 I can construct graphs using real objects or pictures to answer questions. Assessment Assessment Assessment Assessment Topic 9 Assessment Weeks Instructional Emphasis: Numbers and Operations in Base 10 Topic 10: Composing Numbers 11 to 19 K.NBT.1: Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 +8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. 29

30 Big Ideas: 10-1, 10-2, 10-3: Numbers from can be represented as the sum of 10 and some more. 10-4: Patterns on the hundreds chart can be represented using number sentences and drawings. Lesson 1: Making 11, 12, and 13 Children will represent 11, 12, and 13 as the composition of 10 plus 1, 2, or 3. Ten-Frame (or Teaching Tool 8) Counters Paper Bags Making 7; Writing Number Sentences for 8 K.NBT.1 Lesson 2: Making 14, 15, and 16 Children will represent 14, 15, and 16 as the composition of 10 plus 4, 5, or 6. Ten Frames (or Teaching Tool 8) Counters Writing Number Sentences for 10; Making 13 K.NBT.1 Essential Questions: How can the parts of a number be represented as a number sentence? (10-1) How can the parts of a number be represented as a number sentence? (10-2) How can the parts of a number be represented as a drawing or as a number sentence with 10 as one of the parts? (10-3) What patterns are there on the first two rows of the hundred chart, and how can the patterns be represented? (10-4) Lesson 3: Lesson 4: Making 17, 18, and 19 : Look for a Pattern How many more? Children will represent 17, 18, and 19 as the composition of 10 plus Or 9. 2 Ten Frames (or Teaching Tool 8) Counters Making 15; Ordering Numbers Through 10; Identify 2 Fewer K.NBT.1 Children will use drawings and number sentences to identify patterns on the first two rows of the hundreds chart. Large Sheet of Chart Paper Glue or Tape Markers 2 Sets of Number Card Pairs (per pair) 3 Ten-Frames (or Teaching Tool 8) 30 Counters Writing Number Sentences for 10; 30

31 Making 17, 18, and 19 I can show 11, 12, and 13 as the composition of 10 plus 1, 2, or 3. I can show 14, 15, and 16 as the composition of 10 plus 4, 5, or 6. I can make number sentences with the numbers 14, 15, and 16. I can show 17, 18, and 19 as the composition of 10 plus 7, 8, or 9. K.CC.2 I can use drawings and number sentences to identify patterns on the first two rows of the hundreds chart. Assessment Assessment Assessment Assessment Topic 10 Introduction Topic 10 Assessment Weeks Instructional Emphasis: Numbers and Operations in Topic 11: Decomposing Numbers 11 to 19 Base Ten K.NBT.1: Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 +8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. 31

32 Big Ideas: 11-1: There is more than one way to show a number. 11-2: The numbers 11, 12, and 13 can be 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 : The numbers 17, 18, and 19 can be decomposed as a ten and some ones. The number 17 is decomposed to , the number 18 is decomposed to , and the number 19 is decomposed to : Some problems can be solved by identifying elements that repeat in a predictable way. Essential Questions: What strategies can you use to find the number of objects in a set greater than 10?? (11-1) How can 11, 12, and 13 be broken apart into ten ones and some more ones using a drawing and a number sentence? (11-2) How can the parts of 14, 15, and 16 be represented as 10 ones, or one ten, and some more ones? (11-3) How can the parts of 17, 18, and 19 be represented as a drawing and an equation using one ten and some more ones? (11-4) What patterns can be identified and extended to decompose numbers 11 to 19 into ten and ones? (11-5) Lesson 1: Creating Sets to 19 double ten-frame, set Children will use objects to create sets to 19. Number Cards (Teaching Tools 5, 6) Glue Count and Recognize a Lesson 2: Making 11, 12, and 13 Children will represent the decomposition of 11, 12, and 13 as ten ones and additional ones. Find 2 Equal Sets; Identify 2 Fewer; Counting Groups of 10 Lesson 3: Making 14, 15, and 16 Children will represent the decomposition of 14, 15, and 16 as one ten and four, five, or six ones. Count and Recognize a Number of Objects; Ordering Numbers; Lesson 4: Making 17, 18, and 19 Children will make drawings and write number sentences that represent the decomposition of 17, 18, and 19 into ten and 7, 8, or 9 ones. Two-Color Counters (or Teaching Connecting Cubes Lesson 5: : Look for a Pattern Children will identify patterns found in decomposing the teen numbers, including the constant of one ten and the variable number of ones. They will make drawings and write number sentences for numbers 11 to 19. Counters 32

33 Number of Objects; Use Numbers to Tell How Many K.NBT.1 K.NBT.1 Represent Addition Situations K.NBT.1 Parts of 14; Write Number Sentences for 8 K.NBT.1 Large Piece of Paper, such as Butcher Paper Count 14; Represent Addition Situations; Identify Ways to Make 7 I can use objects to create sets to 19. I can use objects to decompose 11, 12, and 13 as ten ones and additional ones. I can use objects to decompose numbers 14, 15, 16 as one ten and additional ones. I can use objects to decompose numbers 17, 18, 19 as one ten and additional ones. K.NBT.1 I can identify patterns in decomposing the teen numbers. Assessment Assessment Assessment Assessment Assessment Topic 11 Introduction Weeks Topic 11 Assessment Topic 12: Measurement Weeks Instructional Emphasis: Measurement and Data 33

34 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. Big Ideas: 12-1: Objects have measureable attributes such as length, capacity, and weight that can be compared and described. 12-2, 12-3: Objects can be compared by length. 12-4: Some problems can be solved by making a reasoned first try for what the answer might be and then, through additional reasoning, arrive at the correct answer. 12-5, 12-6: Objects can be compared by height. Comparing by height is similar to comparing by length. 12-7: Objects can be compared by capacity. 12-8: Objects can be compared by weight. Lesson 1: Describing Objects by More Than One Attribute Children will recognize and describe the measureable attributes of objects. Plastic Cup Classroom Objects Balance Cube Train Measuring Cup Lesson 2: Comparing by Length length, shorter (than), longer (than), as long as (same length as) Children will directly compare objects by length. Classroom Objects Connecting Cubes Lesson 3: More Comparing Objects by Length longest, shortest Children will compare and order objects by length. or Pencils Connecting Cubes Count Objects; Identify Essential Questions: How can you describe the attributes of an object? (12-1) What words tell how long objects are? (12-2) How can you compare the lengths of three objects? (12-3) How can you make a good guess to try to solve a problem? (12-4) What words tell how tall objects are? (12-5) How can you compare the height of three objects? (12-6) How can you tell if a container holds the same, more, or less than another? (12-7) How can you compare the weights of two objects? (12-8) Lesson 4: Lesson 5: : Try, Comparing by Height Check, and Revise Children will solve problems by comparing lengths and revising their answers. Yarn Chart Paper Tape Glue height, taller (than), as tall as Children will directly compare objects by height. Plastic Cup Connecting Cube Pencil 34

35 (Per child) Represent Addition Situations; Use Number to Tell How Many K.MD.1 I can identify and use more than one attribute to describe an object. Order Numbers to 10; Represent Subtraction Situations K.MD.2; K.MD.1 I can compare objects by length. 2 Fewer K.MD.2; K.MD.1 I can compare and order objects by length. Order Numbers to 10; Identify 2 Fewer K.MD.2 I can use problemsolving to compare and order attributes by length. Compare Quantities, Comparing by Length K.MD.2; K.MD.2 I can compare attributes by height. Assessment Assessment Assessment Assessment Assessment Topic 12 Introduction Lesson 6: More Comparing Objects by Height tallest Children will compare and order objects by Lesson 7: Comparing Capacities holds more, holds less, empty, full, most, least, capacity Lesson 8: Comparing by Weight weight, lighter (than), weighs less, heavier (than), weighs more, about the same, balance scale 35

36 height. Classroom Objects Connecting Cubes Use One-to-One Correspondence; Order Numbers K.MD.2; K.MD.1 I can compare and order items by height. Children will compare containers by their capacity. 2 Different-Sized Cups or Mugs Classroom Containers, Water Blunt-Tipped Scissors Glue Comparing Capacities (Teaching Tool 26) Measurement K.MD.2; K.MD.1 I can compare containers by how much is in them. Children will directly compare objects by weight. Balance Scale, Classroom Objects, Balls, Ordinal Position; Recognize and Extend Shape Patterns K.MD.2; K.MD.1 I can compare objects by weight. Assessment Assessment Assessment Topic 12 Assessment 36

37 Weeks Instructional Emphasis: Measurement and Data Topic 13: Sorting, Classifying, Counting, and Categorizing Data 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. K.MD.3: Classify objects or people into given categories; count the numbers in each category and sort the categories by count. (Note: Limit category counts to be less than or equal to 10.) Big Ideas: Essential Questions: 13-1: Attributes can be used to compare objects. What does looking at the color, shape, and size of 13-2: Attributes can be used to sort a group of objects. objects help you know about them? (13-1) 13-3: Attributes such as color, shape, or size can be used to What are some ways you can sort objects? (13-2) sort the same set of objects in different ways. How does looking at the colors and shapes of objects in 13-4: A set of objects can be sorted according to a a set help you sort them in two ways? (13-3) combination of attributes. How can you use what you know to solve a problem? 13-5: Some problems can be solved by reasoning about (13-5) conditions in the problem. How does making and reading a real graph help you 13-6, 13-7: Data can be collected and represented using answer questions? (13-6) different types of graphs. Graphs can be used to answer questions. How does making a graph with pictures help you answer questions? (13-7) Lesson 1: Same and Different same (alike), different Children will identify same and different by the attributes of color, shape, size, and kind. Hexagon Pattern Blocks Lesson 2: Sorting by One Attribute sort, does not belong Children will sort objects by one attribute such as color, shape, size, or kind. Blue Crayon Yellow Pencil Black Pen Lesson 3: Sorting the Same Set in Different Ways Children will sort the same set in different ways. Large Brown Bag Small Brown Bag Attribute Blocks (or Teaching Tool 36) (blue, yellow) Lesson 4: Sorting by More Than One Attribute Children will use more than one attribute to sort a set of objects. Attribute Blocks (or Teaching Tool 36) (yellow, blue) Red Construction Paper Square, Red Lesson 5: : Use Logical Reasoning sorting rule Children will solve problems by thinking logically. Attribute Blocks (blue, yellow, red) 3 Blocks 37

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