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for ematics Introduction is a digital, K through 5 teaching and planning tool that integrates key subject areas around core critical thinking, creative thinking, and academic success skills. The following document shows how content within Forward aligns to the Common Core State Standards for ematics. This document contains references located within one of four program parts and specific weeks. Program Philosophy Forward is a digital K through 5 planning and teaching platform that integrates the subject areas around core critical thinking, creative thinking, and academic success skills. The outcome of this integration is accelerated student learning, setting students on a path to college and career readiness in elementary school. Program Organization To promote the development of critical thinking, creative thinking, and academic success skills, Forward challenges students to uncover the big ideas, answer essential questions, and build enduring understandings. Thinking and Academic Success Skills Research supports that students who are successful in their academic careers learn more than just facts. They have a certain set of skills called Thinking and Academic Success Skills that enable them to learn and thrive in almost any setting. Critical thinking includes the skills of analysis, synthesis, and evaluation. Creative thinking includes fluency, flexibility, originality, and elaboration. Academic success includes collaboration, effort/motivation/persistence, intellectual risk taking, and metacognition. Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved
for ematics Table of Contents Counting and Cardinality...1 Operations and Algebraic Thinking...8 Number and Operations in Base Ten...9 Measurement and Data...10 Geometry...12 Copyright 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved
for ematics Counting and Cardinality K.CC Know number names and the count sequence. 1. Count to 100 by ones and by tens. 1.1 Count and represent numerical information 1.1 Count a collection of objects 1.9 Count using one-to-one correspondence 1.9 PVA Task: Sort and count shoes 1.9 Count objects 2.1 Teacher Support: Counting to 100 2.3 Worksheet: Pick a Plant 2.9 Count and represent numbers up to 100 2.9 Animation: Counting to 100 2.9 Count and manipulate cubes to express numerals up to 100 2.9 Worksheet: Hundred Chart 1.4 Worksheet: Collect Data 2.6 Ask and answer animal life cycles Instruction: Do the! Count Social Studies 1.4 Identify attributes of the American flag 2. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). 2.1 Count forward beginning from a given number 2.2 Play a before-or-after number game 2.2 Teacher Support: Identifying Numbers, Before, After, and Between 2.8 Count forward from a given number 2.9 Count and manipulate cubes to express numerals up to 100 4.1 Teacher Support: Using the Number Line 4.7 Represent numbers from 12-19, count on, and describe a number as 10 and some more ones 1
for ematics 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). 1.1 Count and write numerals to represent quantities 1.1 Count and represent numerical information. 1.1 Count, compare, and record numerals 1.4 Represent, describe and record weather data 1.9 Count objects 2.1 Count objects and represent the related quantities using numerals and pictures 2.2 Write and count items in a line 2.3 Animation: Counting, Reading, and Writing 3.6 Professional Development: Representing Numbers to 10 in a Variety of Ways 4.1 Record number sentences to represent different arrangements of 7 counters 4.3 Worksheet: Danny Sings Instruction: Do the! Count 2
for ematics Count to tell the number of objects. 4. Understand the relationship between numbers and quantities; connect counting to cardinality. 1.1 Count and write numerals to represent quantities 1.1 Count and represent numerical information. 1.1 Count, compare, and record numerals 1.4 Represent, describe and record weather data 1.9 Count using one-to-one correspondence 2.1 Reinforce the relationship between numbers and quantities and connect counting to cardinality 2.1 Professional Development: Understanding Counting and Cardinality 2.1 Count the quantity of construction materials and build them into a different formation 23. Arrange a set of blocks in different ways, understanding that the quantity does not change 2.7 Perform actions a number of times to demonstrate quantity 2.9 PBA Task: Share predictions about quantity 4.6 Count out quantities of counters and examine composing relationships through 19 1.4 Worksheet: Collect Data 2.6 Ask and answer animal life cycles Instruction: Do the! Count Social Studies 1.4 Identify attributes of the American flag 3
for ematics 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. 1.1 Count and write numerals to represent quantities 1.1 Teacher Support: Importance of the Attendance Routine 1.1 Count, compare, and record numerals 1.1 Count a collection of objects 1.9 Count using one-to-one correspondence 1.9 PVA Task: Sort and count shoes 1.9 Count objects 2.1 Professional Development: Understanding the Stages of Counting 2.1 Teacher Support: Counting to 100 2.3 Worksheet: Pick a Plant 2.4 Additional Resources: Beginning Number Concepts 2.9 Count and represent numbers up to 100 2.9 Animation: Counting to 100 2.9 Count and manipulate cubes to express numerals up to 100 4.6 Count out quantities of counters and examine composing relationships through 19 1.4 Worksheet: Collect Data 2.6 Ask and answer animal life cycles Instruction: Do the! Count Social Studies 1.4 Identify attributes of the American flag 4
for ematics 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. 1.1 Count and write numerals to represent quantities 1.1 Count and represent numerical information. 1.1 Count, compare, and record numerals 1.1 Count a collection of objects 1.4 Represent, describe and record weather data 2.1 Reinforce the relationship between numbers and quantities and connect counting to cardinality 2.1 Count the quantity of construction materials and build them into a different formation 2.3 Arrange a set of blocks in different ways, understanding that the quantity does not change 2.7 Perform actions a number of times to demonstrate quantity 4.6 Count out quantities of counters and examine composing relationships through 19 1.4 Worksheet: Collect Data 2.6 Ask and answer animal life cycles Instruction: Do the! Count Social Studies 1.4 Identify attributes of the American flag 5
for ematics c. Understand that each successive number name refers to a quantity that is one larger. 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. 1.1 Count and write numerals to represent quantities 1.1 Count, compare, and record numerals 1.1 Count a collection of objects 1.4 Represent, describe and record weather data 1.9 Count using one-to-one correspondence 2.4 Animation: More, Fewer, Same As 2.4 Professional Development: Comparing Sets of Objects 2.4 Teacher Support: Comparison Tasks 2.4 Teacher Support: The Concepts of More and Less (fewer) 3.2 Animation: More Comparing by Height 3.2 Animation: More Comparing Objects by Length 3.4 Professional Development: Comparing Sets of Objects 4.1 Teacher Support: More than 5, Less than 5 4.3 Game: 2 More at the Music Store 4.3 Worksheet: Stories about Comparing 4.5 Teacher Support: More or Fewer 1.4 Worksheet: Collect Data 2.6 Ask and answer animal life cycles 1.1 Count and write numerals to represent quantities 1.1 Count, compare, and record numerals 1.1 Count a collection of objects 1.4 Represent, describe and record weather data 2.2 Write and count items in a line 2.4 Worksheet: How Many Beans 2.7 Worksheet: How Many Turtles 4.3 Teacher Support: How Many Fingers 4.5 Worksheet: How Many Buttons 4.8 Teacher Support: How Many Social Studies 1.4 Identify attributes of the American flag 6
for ematics Compare numbers. 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. 1.1 Count, compare, and record numerals 1.5 Collect, count, and compare data 1.5 Represent, count, and compare survey responses 1.9 Animation: More, fewer, and same as- Extra Support 2.4 compare sets of object to reinforce concepts of greater than, less than, and equal to 2.4 Compare sticks of cubes to reinforce concepts of greater than, less than, and equal to 2.4 Play a game to reinforce concepts of greater than, less than, and equal to 2.6 String beads to create a necklace with more, fewer, or an equal amount of beads as a sample 2.8 compare a random numeral with another to decide if it is greater than, less than, or equal to 4.1 Identify whether a set of objects is greater than, less/fewer than, or equal to 10 4.1 Identify whether a set of objects is greater than, less/fewer than, or equal to 5 4.1 Teacher Support: More than 4, Less than 5 4.1 Worksheet: Comparing Numbers to 10 4.1 Worksheet: Comparing Numbers to 5 4.2 Worksheet: Play a Game 7. Compare two numbers between 1 and 10 presented as written numerals. 1.1 Count and write numerals to represent quantities 1.1 Count, compare and record numerals 2.1 Count objects and represent the related quantities using numerals and pictures 2.5 Compare two numbers between one and ten presented as written numerals 2.8 Compare a random numeral with another to decide if it is greater than, less than, or equal to 2.8 Teacher Support: Show Then Change 7
for ematics Operations and Algebraic Thinking K.OA Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. 1. Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. 2.1 Worksheet: Helping Hands 2 2.2 Worksheet: Look and See 1 2.6 Teacher Support: Number Necklaces 2.7 Paint a picture to represent a given number as combinations of different pairs of numbers 2.7 Worksheet: How Many Turtles 2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. 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 = 2 + 3 and 5 = 4 + 1). 2.4 How Many Beans 2.7 Worksheet: How Many Turtles 2.7 Worksheet: Use Numbers to Tell 2.9 Represent numbers as a combination of two quantities 2.9 Worksheet: Try Together 4.2 Represent addition and subtraction with objects 4.2 Identify and record addition sentences for sums through 10 4.3 Teacher Support: Finding Sums 4.3 Animation: Stories About Take Away 4.3 Addition and subtraction by acting out situations 4.4 Worksheet: Finding Sums 4.5 Add (within10) and compare two sums 4.5 Worksheet: Neighbor Sums 4.1 Instruction: Five Little Monkeys 4.1 Worksheet: Monkey Problems 2.6 Create arrangements of counters to represent a number in different ways 2.6 Create arrangements of cups to represent a given number in different ways 4.1 Animation: Writing Number Sentences for 6 and 7 4.1 Decompose and represent 6 color tiles using colors and number sentences 4.1 Worksheet: Making 4 and 5 4.2 Worksheet: Making 6 and 7 4.5 Worksheet: Writing number Sentences for 8 and 9 8
for ematics 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. 2.2 Worksheet: Look and See 1 2.3 Worksheet: Ten-Frame Mat 4.2 Represent addition and subtraction with objects 4.2 Identify and record addition sentences for sums through 10 5. Fluently add and subtract within 5. 2.4 How Many Beans 2.7 Worksheet: How Many Turtles 2.7 Worksheet: Use Numbers to Tell 2.9 Represent numbers as a combination of two quantities 2.9 Worksheet: Try Together 4.2 Represent addition and subtraction with objects 4.2 Identify and record addition sentences for 4.3 Teacher Support: Finding Sums 4.3 Animation: Stories About Take Away 4.3 Addition and subtraction by acting out situations 4.4 Worksheet: Finding Sums 4.5 Worksheet: Neighbor Sums 4.1 Instruction: Five Little Monkeys 4.1 Worksheet: Monkey Problems Number and Operations in Base Ten K.NBT Work with numbers 11 19 to gain foundations for place value. 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 2.3 Represent quantities from 11 to 19, composition or decomposition by a drawing or decomposing quantities into tens and ones equation (e.g., 18 = 10 +8); understand that 2.3 Arrange numbers in tens and ones to these numbers are composed of ten ones and count and write numbers through 20 one, two, three, four, five, six, seven, eight, or 2.4 Count greater quantities of objects, nine ones. decomposing quantities into tens and ones 4.6 Compose and decompose numbers from 11 to 19 into ten and some more ones 4.6 Compose and decompose numbers from 11 to 19 using connecting cubes 4.6 Decompose numbers in a recipe from 11 to 19 into ten and some more ones 4.8 Teacher Support: How to Decompose Numbers 11 to 19 9
for ematics Measurement and Data K.MD Describe and compare measurable attributes. 1. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. 3.1 Lesson Guide: Comparing and Describing Measureable Attributes 3.1 Reader: Help Us Measure 1.6 Measure our feet 4.1 Measure Solids 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. 1.2 Describe and compare attribute blocks 1.2 Teacher Support: Suggestions for a Sorting and Classifying Center 1.4 Sort and count pattern blocks 3.1 Reader: When Bob Shops 3.1 Teacher Support: Line Up the Family 3.1 Teacher Support: Taller Than Teddy 3.1 Teacher Support: The Language of 3.2 Teacher Support: I m Thinking of Something 3.3 Teacher Support: Suggestions for a Measurement Center 4.9 Compare objects based on weight 1.6 Measure our feet 1.9 Identify and describe local tree attributes 2.5 Compare animal babies to their parents 10
for ematics Classify objects and count the number of objects in each category. 3. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. 1.3 Describe and compare objects by a single attribute 1.4 Sort and count pattern blocks 1.4 Collect, sort, and organize data using illustrations 1.4 Collect, sort, and record data 1.4 Teacher Resource: Discussing Data Using Think-Pair-Share 1.5 Professional Development: Collecting and Graphing Data 1.5 Graphic Organizer: Square Tile Graph 1.9 Sort and count shoes 1.1 Compare attributes of objects 1.4 Teacher Support: Collect Data 1.5 Compare attributes 2.3 Seek information about plants 2.7 Share data about plant growth Reading 2.8 Sort objects into logical categories 2.8 Animation: Picture It! Classify and Categorize 11
for ematics Geometry K.G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). 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. 1.1 Describe location or position of objects 1.1 Describe position or location of tiles in an arrangement 1.2 Describe location of objects using directional and positional words 1.2 Describe objects and their locations 1.2 Use directional and positional words 2.7 Teacher Support: Positions 3.5 Identify and describe 3-dimensional shapes in the environment 3.4 Instruction: What Do You See 3.4 Animation: Circles 3.9 Use informal language to describe the attributes of shapes Social Studies 2.7 Use location words to find objects 2.7 Use location words to describe and identify a location 2.9 PBA Task: Represent physical locations in different ways 2. Correctly name shapes regardless of their orientations or overall size. 1.2 Describe and compare attribute blocks 1.2 Teacher Support: Explore Attribute Blocks 2.2 Worksheet: Tangram Puzzle 3.4 Animation: Circles, Hexagon, Rectangles, Squares, Triangles 3.4 Teacher Support: Animal Shapes 3.4 Teacher Support: Cookie Fun 3.4 Teacher Support: Review Circles, Triangles, and four-sided Shapes 3.4 Teacher Support: Shaping Up 3.5 Worksheet: Traffic Signs Have Geometric Shapes 3.5 Use informal language to describe similarities and differences of two-dimensional 12
for ematics 3. Identify shapes as two-dimensional (lying in a plane, flat ) or three dimensional ( solid ). 3.4 Compose smaller two-dimensional shapes to form a hexagon 3.4 Compose two-dimensional shapes to form larger shapes 3.4 Use informal language to describe parts of two-dimensional shapes 3.4 Represent two-dimensional in different sizes and orientation 3.4 Use different combinations of twodimensional shapes to compose a large triangle 3.5 Describe and identify three-dimensional shapes by their texture and visual description 3.5 Identify and describe three-dimensional in the environment 3.5 Animation: Building With Solid Figures 3.5 Animation: Solid Figures Analyze, compare, create, and compose shapes. 4. Analyze and compare two- and threedimensional shapes, in different sizes and orientations, using informal language to describe 3.4 Use informal language to describe parts of their similarities, differences, parts (e.g., two-dimensional shapes number of sides and vertices/ corners ) and 3.9 Use informal language to describe the other attributes (e.g., having sides of equal attributes of shapes length). 3.9 Use informal mathematics vocabulary to compare and contrast shapes 5. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. 3 Professional Development: Composing and Decomposing Shapes 3.4 Animation: Making Shapes From Other Shapes 3.6 Animation: Building with Solid Figures 3.8 Build rectangular prisms with connecting cubes 3.8 Use knowledge of objects characteristics to build things 13
for ematics 6. Compose simple shapes to form larger shapes. For example, Can you join these two triangles with full sides touching to make a rectangle? 2.2 Worksheet: Tangram Puzzle 3 Professional Development: Composing and Decomposing Shapes 3.4 Animation: Making Shapes From Other Shapes 3.4 Worksheet: Making Shapes From Other Shapes 1, 2 3.4 Animation: Problem Solving: Use Objects 3.4 Compose smaller two-dimensional shapes to form a hexagon 3.4 Compose two-dimensional shapes to form larger shapes 3.4 Use different combinations of twodimensional shapes to compose a large triangle 3.6 Animation: Building with Solid Figures 14