# Kindergarten Math Curriculum Course Description and Philosophy Text Reference:

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1 Kindergarten Math Curriculum Course Description and Philosophy How do numbers and math affect our daily lives? What types of problems can be solved by understanding numbers and math concepts? Through inquiry, discussion, and experiences found in the Kindergarten Math curriculum, students will begin to construct the knowledge needed to develop a strong foundation for mathematical concepts that they will use throughout their lives. In the Kindergarten curriculum, students make discoveries about math in the world around them and the role that numbers play in many of our daily activities. Through, stories, art projects, and hands-on experiences, students develop their number sense. Learning to recognize and write numbers to 100 is taught in many of the daily, which are supported by hands-on activities, number stories, computer activities, and Smartboard. Children are encouraged to explore and expand on the basic concept of numbers to 100, through applicable skills, such as reading a calendar, measuring, counting the days of school, and various other counting experiences. In addition, the children are recognizing, comparing, and ordering numbers 0 to 100, understanding addition and subtraction, as well as, composing and decomposing numbers. They then delve into exploring measurement, sorting, classifying, counting, and categorizing data. Lastly, they will discover how to describe the position and location of shapes, as well as analyzing, comparing, identifying, and composing of shapes. The Envisions Kindergarten Math Program covers a sequential development of skills by providing many practical experiences that can be found in various math centers, group, projects, and Smartboard activities, which help students make real-life connections to mathematical concepts. Using a variety of teacher tools and techniques, we evaluate our students based on the Envisions Kindergarten Math Program. Observation of student participation in projects, learning centers, and written tests provide feedback about the understanding and conceptual development that takes place within the classroom. The students demonstrate their mathematical understanding through interactive Smartboard with corresponding activities that require manipulatives and critical thinking skills. They also use Quick Check assessments for each lesson, practice and enrichment worksheets, topic tests, as well as, standardized testing. The series also offers support through a math diagnosis system for at risk learners. The journey through the Envisions Kindergarten Math program helps to develop the concepts needed to transition learners from the concrete to the symbolic level, which helps to build a strong foundation for mathematical understanding. Text Reference: Pearson Education Inc., Envision Math Common Core, 2012, Saddle River, NJ/USA Murphy, Stuart J., MathStart series, HarperCollins publishers, 2005, New York, NY / USA Khan Academy s Common Core Mapping for Kindergarten Written 2013

2 Unit I: Counting and Cardinality Essential Question: What are some ways that numbers and counting affect our daily lives? Objectives: Students will be able to: Number Uses, Classification, and Representation: Numbers are used for different purposes, and numbers can be classified and represented in different ways. Use manipulatives to represent, count, order, and compare numbers 0 to 100 Recognize number names and count the sequence. Write numbers 0 to 100. Identify the number of objects in a group regardless of their arrangement Identify each unique symbol that goes with each number word Numbers and the Number Line: The set of real numbers is infinite and ordered. Whole numbers, integers, and fractions are real numbers. Each real number can be associated with a unique point on the number line. Use number line to locate numbers Identify numbers by locating its unique point on the number line. Recognize that the distance between any two consecutive whole numbers on a given number line is always the same The Base-Ten Numeration System: The base-ten numeration system is a scheme for recording numbers using digits 0-9, groups of ten, and place value. Use 5 and 10 frames to represent numbers Find patterns on a hundreds chart Identify missing numbers on a hundreds chart (numbers are written in a specific sequence on a hundreds chart Build decade numbers by counting in groups of ten Comparison and Relationships: Numbers, expressions, measures, and objects can be compared and related to other numbers, expressions, measures, and objects in different ways. Use manipulatives to discover relationships between numbers, as well as compare numbers to one another Compare groups of objects to discover whether the groups have the same, more, or less than one another Use counting to identify numbers that are 1 more, 1 fewer, 2 more, and 2 fewer Use the number 5 and 10 as a benchmark to compare numbers Pattern, Relations, and Functions: Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways. For some relationships, mathematical expressions and equations can be used to describe how members of one set are related to members of a second set. Use a hundred chart to recognize patterns when counting by 2s, 5s, and 10s Use benchmarks to estimate quantities of groups Practices, Processes, and Proficiencies: Mathematics content and practices can be applied to solve problems.

3 Use real-life experiences and physical materials to construct meanings for numbers, as well as solve problems Solve problems by using objects to act out the actions in the problem Solve problems by identifying elements that repeat in a predictable way Solve problems by reasoning about conditions in the problem Topic/Content Skills Topic 1: #s 1-5 Topic 2: Comparing and Ordering 0 to 5 Topic 3: #s 6-10 Topic 4: Comparing and Ordering Numbers 0 to 10 Topic 5: Numbers to 20 Topic 6: Numbers to 100 Assessment Resources Instructional Method Quick Check for Topic Activity Whole Class each specific Pages (Problem- lesson and lesson Based Learning and discussion Topic Tests Visual Learning) Topic Activity Electronic Quick Check Pages with (SmartBoard) Assessments corresponding Quizzes, Review EnVisions online Smartboard lesson & Enrichment lesson materials and manipulatives Weekly homework Math workbooks Small group In-class Daily Common Core review and assignment Review Pages assistance Math Center Kits Math Centers Direct observation Hands-On Class Participation Math Start Books Activities Math center Read-Alouds participation and Tech Infusion Interactive Math Story Animated Introduction to each Problem-Based Interactive Learning Activities on Smartboard (used with manipulatives) Visual Learning Activities on Smartboard Starfall.com Math Games ABCya.com Math Activities Computer Lab Activities and Projects Common Core K.CC.2 K.CC.3 K.CC.4 K.CC.4.a K.CC.4.b K.CC.4.c K.CC.5 K.CC.6 K.CC.7 K.OA.1 Differentiated Learning Activities Students work at their own level to complete various hands-on activities such as centers, interactive, projects, and worksheets. Literature-based units allow students to listen, interact, and contribute to class discussions and develop math skills individually. Math Centers are used to allow for individualized growth. Math games provide opportunities for students to learn from one another, at their own pace, and in an exciting format. A great example of a game is Mingle & Count: A Game of Number Sense. CCSS Math.K.CC.B.4b Teaching Channel video Let's Count! Learning Numbers in Multiple Ways illustrates how one can teach about counting and ordering numbers in multiple ways. CCSS: Math.K.CC.B.4b 21 st Century Skills/Critical Thinking Each Topic provides one or two problem solving that deal with real-life situations and ask the students to problem solve by using real examples and skills that they face in their own lives. The variety of technological aspects in the program prepares students for the future by teaching them how to use technology in an academic setting, as well as for a purpose.

4 Unit II: Operations and Algebraic Thinking Essential Question: Why is it important to be able to add, subtract, compose, and decompose numbers? What areas of my life would this assist me in? Objectives: Students will be able to: Equivalence: Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value. Show a number in more than one way through various combinations of other numbers Operation Meanings and Relationships: There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers, and each operation is related to other operations. Join parts to make a whole Use the addition expression that uses the plus sign (+) as well as the word and Read, understand, write, and create number sentences using + and = to show parts of a whole Separate parts from a whole and take parts of a group away to represent subtraction Compare two quantities to find how much more/less one quantity is than the other Represent a subtraction sentence using the minus sign (-) by separating, taking away, and using comparison situations Read, understand, write, and create number sentences using and = to show subtraction situations Practices, Processes, and Proficiencies: Mathematics content and practices can be applied to solve problems. Depict information from a problem by using a picture or diagram to understand and solve the problem Solve subtraction problems by using objects to act out the actions in the problem Solve problems by making, reading, and analyzing a graph Topic/Content Skills Topic 7: Understanding Addition Topic 8: Understanding Subtraction Topic 9: Composing and Decomposing Numbers to 10 Assessment Resources Instructional Method Quick Check for Topic Activity Whole Class each specific Pages (Problem- lesson and lesson Based Learning and discussion Topic Tests Visual Learning) Topic Activity Electronic Quick Check Pages with (SmartBoard) Assessments corresponding Lesson Quizzes, EnVisions online Smartboard lesson Review, and lesson materials and manipulatives Enrichment work Math workbooks Small group Weekly homework Daily Common Core review and In-class Review Pages assistance assignment Math Center Kits Math Centers Hands-On Direct observation Math Start Books Activities Tech Infusion Interactive Math Story Animated Introduction to each Problem-Based Interactive Learning Activities on Smartboard (used with manipulatives) Visual Learning Activities on Smartboard Starfall.com Math Games ABCya.com Math Activities Computer Lab Activities and Projects Common Core K.OA.1 K.OA.2 K.OA.3 K.OA.4 K.OA.5 K.MD.3

5 Participation in Math center participation and Read-Alouds Differentiated Learning Activities Students work at their own level to complete various hands-on activities such as centers, interactive, projects, and worksheets. Literature-based units allow students to listen, interact, and contribute to class discussions and develop math skills individually. Math Centers are used to allow for individualized growth. Math games provide opportunities for students to learn from one another, at their own pace, and in an exciting format. One example is the Teaching Channel video Quick Images: Visualizing Number Combinations which helps students use quick images to identify combinations of 8. CCSS: Math.K.OA.A.1 Math.K.OA.A.3 Ethical Decision Making/Character Education Student participation in discussions, read-alouds, and interactive teach students to converse in a polite manner, wait for their turn, as well as share their thoughts and opinions with their classmates in an accepting learning environment. Math Centers and Games help students develop sharing, turn-taking, and sportsman ship qualities. In addition, they learn how to work with one another for the common interest of learning mathematic concepts and assisting one another in their learning, Sustainability Students will learn that addition and subtraction skills help students understand real-life situations where they can contribute to sustainability in their environment. They will be able to gage how much or little of supplies, food items, toys, etc that they need for various real-life situations. Once students understand how to add, subtract, and estimate numbers, they will be able to make more educated decisions on their necessities in life in order to reduce waste. Unit III: Number and Operations in Base Ten Essential Question: Why is it important to work with numbers and gain and understanding of foundations and place value? How does learning these skills help us problem solve in our daily lives? Objectives: Students will be able to: Represent 11, 12, and 13 as the composition of 10 plus 1, 2, and 3. Write number sentences the represent the above composition. Use manipulative counters and a ten-frame to represent 11, 12, and 13. Represent 14, 15, and 16 as the composition of 10, plus 4, 5, and 6. Write number sentences that will represent the above composition. Use manipulative counters and a ten-frame to represent 14, 15, and 16. Represent 17, 18, and 19 as the composition of 10, plus 7, 8, and 9.

6 Write number sentences that will represent the above composition. Use manipulative counters that will represent 17, 18, and 19. Use drawings and number sentences to identify patterns on the first two rows of the hundreds chart. Compose and decompose numbers by writing an equation or drawing, displaying understanding. Use objects to create sets to 19. Use manipulatives to show many ways to create sets of 19. By using ten frames, children visualize the relationships between ten and teen numbers, thus understanding that a teen number is 10 plus some more. Represent the decomposition of 11, 12 and 13 as ten ones and additional ones. Create drawings and write equations that represent the decomposition of 11, 12, and 13 as ten ones and some additional ones. Use manipulatives and/or counters with the ten frames to record representation. Represent the decomposition of 14, 15, and 16 as one ten and four, five or six ones. Create drawings and write equations that represent the decomposition of 14, 15, and 16 as one ten and four, five or six ones. Use manipulatives and /or counters with the ten frames to record representation. Make drawings and write number sentences that represent the decomposition of 17, 18 and 19 into ten and 7, 8, or 9 ones. Create drawings and write equations that represent the decomposition of 17, 18, and 19 into ten and 7, 8, and 9 ones. Use manipulatives and/or counters with the ten frames to record representation. Topic/Content Skills Topic 10-1: Making 11, 12 & 13 Topic 10-2: Making 14, 15 & 16 Topic 10-3: Making 17, 18 & 19 Topic 10-4: Look for a pattern Topic 11-1: Creating sets to 19 Topic 11-2: Parts of 11, 12 & 13 Topic 11-3: Parts of 14, 15 & 16 Assessment Resources Instructional Method Quick Check for Topic Activity Whole Class each specific Pages (Problem- lesson and lesson Based Learning and discussion Topic Tests Visual Learning) Topic Activity Electronic Quick Check Pages with (SmartBoard) Assessments corresponding Lesson Quizzes, EnVisions online Smartboard lesson Review, and lesson materials and manipulatives Enrichment work Math workbooks Small group Weekly homework Daily Common Core review and In-class Review Pages assistance assignment Math Center Kits Math Centers Hands-On Direct observation Math Start Books Activities Participation in Read-Alouds Math center participation and Tech Infusion Interactive Math Story Animated Introduction to each Problem-Based Interactive Learning Activities on Smartboard (used with manipulatives) Visual Learning Activities on Smartboard Starfall.com Math Games ABCya.com Math Activities Computer Lab Activities and Projects NJCCCS K.NBT.1 Topic 11-4:

7 Parts of 17, 18 &19 Topic 11-5: Look for a pattern Differentiated Learning Activities There are many opportunities to differentiate instruction for all learners. This can be done using learning centers and games to extend learning. These centers are geared to the topics covered and can be simplified or intensified depending on the ability of the learner. Math journal activities can also be used to individualize instruction as well as being used as a way to see progression of skills, thus driving instruction for that particular learner. For learners who may struggle, you may want to number counters as a way of understanding the order in a more concrete way. Benchmarks such as these will help the child move toward using counters that are not numbered. Ethical Decision Making/Character Education Discuss with students about sharing ideas and that it is important to learn to problem solve in all areas of life. Also discuss concepts such as the importance of structure and using tools to help you in your daily lives. Development of social skills are continuously in progress as students work together in math centers and completing projects using math materials 21 st Century Skills Critical Thinking After viewing the Teaching Channel video, Beyond Fingers: Place Value & the Numbers 11-19, the teacher will help students Understand the numbers as 10 ones and some further one. In this activity, students 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 (such as 18 = ); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones Unit IV: Measurement and Data Essential Question: Some questions can be answered by collecting, analyzing and measuring objects and data. How can we then take this information we have gathered and apply it to solving problems in our daily lives and in what form will this data be presented and analyzed? Objectives: Students will be able to: Recognize and describe measurable attributes of objects Children will uses objects in the classroom to compare and contrasted their differences and similarities These comparisons can be recorded in a variety of forms ( i.e. pictures, words, graphs or pictograph) Children will learn the vocabulary that accompanies this topic Directly compare objects by length and height Children will use objects in the classroom to compare and order them by length and height These comparisons can be recorded in a variety of forms (i.e. pictures, words, graphs or pictograph) Children will learn the vocabulary that accompanies this topic Compare objects by capacity and weight

8 Children will compare containers in the classroom by their capacity and weight Children will use their estimation skills to reason and deduce both capacity and weight Children will learn the vocabulary that accompanies this topic Attributes can be used to identify same and different. Children will identify same and different by the attributes of color, shape, size and kind Objects can be sorted by one or many attributes in the same or different ways Children will sort objects by one attribute such as color, shape, size or kind Children will sort the same set in different ways Children will use more than one attribute to sort a set of objects using logical reasoning skills Data can be collected and represented using different types of graphs Children will make and read a real graph Children will make and read a pictograph Children will be able to interpret the findings of such graphs and make observations Children will be able to verbalize and explain the findings of such graphs Topic/Content Skills Topic: 12-1 Describing objects with more than one attribute Topic: 12-2 Comparing objects by length and height Topic: 12-3 Comparing capacities and comparing by weight Topic: 13-1 Same and Different Topic: 13-2 Sorting Assessment Resources Instructional Method Quick Check for Topic Activity Whole Class each specific Pages (Problem- lesson and lesson Based Learning and discussion Topic Tests Visual Learning) Topic Activity Electronic Quick Check Pages with (SmartBoard) Assessments corresponding Lesson Quizzes, EnVisions online Smartboard lesson Review, and lesson materials and manipulatives Enrichment work Math workbooks Small group Weekly homework Daily Common Core review and In-class Review Pages assistance assignment Math Center Kits Math Centers Hands-On Direct observation Math Start Books Activities Participation in Read-Alouds Math center Graphing and table participation and making projects Tech Infusion Interactive Math Story Animated Introduction to each Problem-Based Interactive Learning Activities on Smartboard (used with manipulatives) Visual Learning Activities on Smartboard Starfall.com Math Games ABCya.com Math Activities Computer Lab Activities and Projects Common Core K.MD.A.1 K.MD.A.2 K.MD.B.3

9 by one or more than one attribute in the same or different ways Topic: 13-3 Graphing Differentiated Learning Activities This topic lends itself to many types of learners. It is easy to differentiate by using graphs and tables to demonstrate comparisons. Learners who need more concrete examples can use pictographs to explain findings as well as using actual objects. There are also opportunities to pair up learners or engage in small group activities to work cooperatively in a group to solve problems in this area. Ethical Decision Making/Character Education - Student participation in discussions, read-alouds, and interactive teach students to converse in a polite manner, wait for their turn, as well as share their thoughts and opinions with their classmates in an accepting learning environment. Math Centers and Games help students develop sharing, turn-taking, and sportsman ship qualities. In addition, they learn how to work with one another for the common interest of learning mathematic concepts and assisting one another in their learning, 21 st Century Skills Critical Thinking - When children write equations, they are forming abstract sentences that they can apply to limitless situations. For children to use this mathematical power, they must be able to take situations and problems from their world and connect them to symbols and numbers in mathematical terms. To mathematize situations, young children must have many experiences and guidance in reasoning abstractly and quantitatively. Sustainability This area of mathematics is an area that all learners will encounter their whole lives. Comparing lengths and weights, graphing, looking at different attributes of objects is a part of our daily lives whether it be in school, work or a home setting. As students grow and move into the work force they may be using graphing as an opportunity to explain changes, growth or decline of products or some other work related explanations they will need to make. They will then have to use these demonstrations to prove points they will need to make. Unit V: Geometry Essential Question: How can children create opportunities to explore the geometric world in which they live, to make observations and construct relationships about shape and space, and to solve problems in a special context? Objectives: Students will be able to: Identify rectangles, squares, circles, triangles, and hexagons Children will identify and describe listed shapes Children will be able to replicate listed shapes Children will solve problems by using objects Identify solid and three-dimensional figures

10 Children will identify cones, cylinders, and spheres and relate them to real-life objects Identify flat surfaces of solid figures Children will identify three-dimensional figures and describe the shape of flat surfaces Children will examine, trace, and describe flat surfaces of solid figures Children will solve problems by using objects Position and Location of shapes Children will describe an object as inside or outside of a given place Children will describe an object as above, below, or on a given object Children will place shapes over, under and on a surface Children will describe an object as in front of, behind, next to and beside Children will use their positional vocabulary to act our and solve problems Left and Right Children will describe an object as left and right of a given object Children will distinguish between their right and left hand Children will use their positional vocabulary to act out and solve problems Same size and same shape Children will recognize that shapes can be combined to make other shapes Children will identify solid figures that roll, stack and/or slide on a flat surface Children will identify figures that are the same size and the same shape Comparing and building with solid figures Children will identify solid figures that roll, stack and/or slide on a flat surface Children will make shapes by combining 2 solid figures Children will build three-dimensional shapes using solid figures Children will use logical reasoning to solve problems Topic/Content Skills Topic 14-1 Recognizing Rectangles, Squares, Circles, Triangles, and Hexagons Topic 14-2 Assessment Resources Instructional Method Quick Check for Topic Activity Whole Class each specific Pages (Problem- lesson and lesson Based Learning and discussion Topic Tests Visual Learning) Topic Activity Electronic Quick Check Pages with (SmartBoard) Assessments corresponding Lesson Quizzes, EnVisions online Smartboard lesson Review, and lesson materials and manipulatives Tech Infusion Interactive Math Story Animated Introduction to each Problem-Based Interactive Learning Activities on Smartboard (used with manipulatives) Visual Learning Activities on Smartboard Common Core K.G.A.1 K.G.A.2 K.G.A.3 K.G.B.4 K.G.B.5 K.G.B.6

11 Solid Figures Topic 14-3 Flat Surfaces and Solid Figures Topic 15-1 Inside and Out Above, Below and On Topic 15-2 In Front of and Behind Enrichment work Weekly homework In-class assignment Direct observation Participation in Math center participation and End of year standardized testing Math workbooks Daily Common Core Review Pages Math Center Kits Math Start Books Small group review and assistance Math Centers Hands-On Activities Read-Alouds Starfall.com Math Games ABCya.com Math Activities Computer Lab Activities and Projects Topic 15-2 Left and Right Topic 16-1 Same Size, Same Shape, Making Shapes and other Shapes Topic 16-2 Comparing and Building Solid Figures Differentiated Learning Activities - There are many opportunities to differentiate instruction for all learners. This can be done using learning centers and games to extend learning. These centers are geared to the topics covered and can be simplified or intensified depending on the ability of the learner. Math journal activities can also be used to individualize instruction as well as being used as a way to see progression of skills, thus driving instruction for that particular learner. For learners who may struggle, you may want to use actual shapes as a way of understanding and connecting to the concept in a more concrete way. Benchmarks such as these will help the child move toward using counters that are not numbered. Ethical Decision Making/Character Education - This concept lends itself to pairing children together to find shapes, draw shapes and discuss shapes in and out of the classroom. Children can work on cooperative learning skills in all classes. 21 st Century Skills Critical Thinking After viewing the Teaching Channel video, Counting Objects and Ordering Numbers, the teacher will foster critical thinking with his or her Kindergarteners by having them count and order numbers with and without a number line. CCSS: Math.K.CC.A.3

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