# SCOPE & SEQUENCE. Kindergarten, First Grade, and Second Grade. Skills and Activities

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1 SCOPE & SEQUENCE Kindergarten, First Grade, and Second Grade Skills and Activities

2 INNOVATIVE LEARNING CONCEPTS INC. creators of TOUCHMATH TouchMath materials were first published in Innovative Learning Concepts Inc. s publications may not be reproduced or disseminated in any way, or stored in any database or retrieval system, without written permission of the publisher. However, limited permission is granted to reproduce only the blackline activity masters solely for noncommercial educational use with students in a single classroom or a single home, and for no other purpose. TouchMath, TouchNumerals and The Alphabet of Mathematics are registered trademarks of Innovative Learning Concepts Inc. Touch2Learn, TouchPoint, TouchShapes, TouchMath Tutor, TouchStar, TouchTunes, StepNumerals and Innovative Learning Concepts are trademarks of Innovative Learning Concepts Inc. of Colorado Springs, CO. Innovative Learning Concepts Inc Mark Dabling Blvd., Colorado Springs, CO Toll Free: Fax: Web: Printed in the United States of America

3 SCOPE AND SEQUENCE (K 2) Table of Contents Introduction... 2 Number Sense (Counting & Cardinality) Representation and Comparison of Numbers Addition and Subtraction Multiplication Measurement Data Geometry Notes

4 SCOPE AND SEQUENCE (K 2) INTRODUCTION: TouchMath Scope and Sequence TouchMath offers three presentations of the scope and sequence. One is a comprehensive exhibit of clusters, standards, skills, and activities. Another is a simplified version, including the clusters, standards, and skills. A third demonstrates the clusters, standards, and activities. All presentations are designed to clearly outline the scaffolding of the content in the new TouchMath K 2 Program. The Common Core State Standards outline the journey to success in learning mathematics. This journey is outlined in detail in the scope and sequence. It is organized by clusters (topics), standards (broad skills or outcomes), skills (more specific skills or objectives), and activities (step-by-step skills or approaches to ensure achievement of the skills). The activities and skills combine to create the standards. The standards relate directly to the Common Core State Standards. The skills define the content; the activities define the approach. Scaffolding is evident through review of this document, designed to address each step of the developmental process for students to learn to use numbers to compute, reason, and think. Problem solving with numbers is the end result. The scaffolding is two-fold: content and approach. The content in the skills is task-analyzed and broken down into small-size chunks that are often needed for learners requiring intervention and/or special education. The approach incorporates kinesthetic, visual, and abstract techniques. Both the content and approach are scaffolded to build success for learners and pave the road for independence in working with numbers. The TouchMath approach is natural, based on the most basic mathematical skill: counting. Counting and cardinality are consistently reinforced as students build number sense and apply understanding in operations with numbers. Spatial sense is developed in measurement and geometry, where the step-by-step approach is again scaffolded. Flexibility in instruction is also inherent in the approach. As students demonstrate the need for fewer and larger chunks of skills, many of the activities can be eliminated or combined. The program can be easily adapted for students with a variety of learning styles and developmental levels. The scope and sequence can be used to chart the course for students in primary classrooms in general education, in intervention programs, and in IEPs for special education learners. The thorough analysis of skills makes it an easy tool for teachers to use to ensure the steps needed to learn mathematics. The various presentations of this tool provide options for teachers and administrators to determine the level of the content and approach that meets the needs of individual learners Mark Dabling Boulevard Colorado Springs, CO 80918

5 Number Sense (Counting and Cardinality) Count Numbers to 100 Count 1 to 100 Count to 10 Count 10 to 20 Count 21 to 30 Count 31 to 40 Count 41 to 50 Count 51 to 60 Count 61 to 70 Count 71 to 80 Count 81 to 90 Count 91 to 100 Count from any number Count Numbers to 120 Count 1 to 120 Count 70 to 90 Count 70 to 100 Count 100 to 110 Count 110 to 120 Count from any number Count Numbers to 1,000 Count 1 to 1,000 Count from any number Count numbers for each hundred Practice odd and even numbers within each hundred Skip Count Count to 100 by fives and tens Count to 50 by tens Count to 100 by tens Count to 100 by fives Count to 1,000 by hundreds Count within hundreds by fives and tens Skip count to find unknowns Count to 1,000 by hundreds

6 SCOPE AND SEQUENCE (K 2) Number Sense (Counting and Cardinality) cont d Read and Write Numbers Read numbers in sequence Name numbers before and after given numbers Name numbers after, between, and before a given number(s) Identify missing numbers in sequence Identify numbers out of order Read number words Read number words in sequence Read number words in flow charts Write numbers Trace numbers Write numbers 0 20 Write numbers Write numbers 0 1,000 Fill in missing numbers Write number words and numerals in sequence Integrate writing number names into finding missing numbers in sequence Apply understanding in writing numerals from number names in flow charts Mark Dabling Boulevard Colorado Springs, CO 80918

7 Representation and Comparison of Numbers Represent Numbers with Manipulatives Represent numbers to 100 with objects Answer how many objects are represented using manipulatives Associate groups of objects to numbers Use matching and counting strategies to represent numbers Represent numbers 10 to 20 using objects Represent numbers 0 to 20 using objects Represent numbers to 100 using objects Represent Numbers with Manipulatives, Pictures, and TouchPoints Represent numbers to 100 with objects and pictures Use TouchPoints to reinforce counting for numbers 1 to 5 Use TouchPoints to reinforce counting for numbers 6 to 9 Demonstrate the correct Touching and Counting Patterns Associate manipulatives, pictures, and TouchPoints to represent quantities Represent quantities in multiple ways Apply understanding of counting to quantities Represent numbers 0 to 5 using objects and pictures Represent numbers 6 to 9 using objects and pictures Represent number 10 using objects and pictures Represent numbers 10 to 15 using objects and pictures Represent numbers 16 to 20 using objects and pictures Represent numbers 10 to 20 using objects and pictures Represent numbers 10 to 20 using objects and pictures Represent numbers 0 to 20 using objects and pictures Represent numbers to 100 using objects and pictures Demonstrate bundles of 10 and additional ones using objects and pictures Use bundles of straws, beads on a string, and connecting cubes to represent numbers using objects and pictures Demonstrate that 10 is a bundle of ten ones and a hundred is a bundle of 10 tens using objects and pictures Represent numbers to 120 with objects and pictures Represent numbers with objects and arrays of dots Represent numbers to 1,000 using models and pictures Demonstrate hundred, tens, and ones using models and pictures Use models and pictures of Base 10 blocks to represent three digit numbers Demonstrate that 10 is a bundle of ten ones and a hundred is a bundle of 10 tens using models and pictures

8 SCOPE AND SEQUENCE (K 2) Representation and Comparison of Numbers cont d Represent Numbers with Pictures and TouchPoints Represent one-digit numbers with pictures and TouchPoints Represent one-digit numbers with TouchPoints Transfer pictures to numerals (pictorial TouchPoints) to represent numbers Relate pictorial TouchPoints to TouchPoints to represent numbers Associate one-digit numbers with multiple representations Represent numbers 10 to 20 with pictures Correspond numbers 10 to 15 to quantities in pictures Correspond numbers 16 to 20 to quantities in pictures Match different representations of numbers Represent numbers to 120 with pictures Represent numbers with arrays of dots Identify numerals for dot representations Represent Numbers with Manipulatives, Pictures, Place Value Charts, and Numerals Represent 0 to 1,000 with manipulatives, drawings, pictures of Base 10 models, and place value charts Compose and decompose numbers into a ten and some additional ones using objects and drawings Represent 0 to 100 with manipulatives, pictures of Base 10 models, and place value charts Apply pictorial representations of numbers to place value charts Use place value charts and numerals to represent numbers Match multiple representations of numbers Relate models, pictures, and place value charts to represent numbers Represent 0 to 1,000 with pictures of Base 10 models and place value charts Represent hundreds, tens, and ones using pictures, place value charts, and numerals Represent each multiple of 100 using pictures, place value charts, and numerals Represent 100 to 1,000 using place value Represent numbers with unknowns in place value charts Use expanded place value Match compact numerals to identified place value Use expanded notation to reflect place value Relate all forms of numbers: compact numerals, expanded forms, and number names Identify compact numbers from written word place values Find mystery numbers based on understanding of place value Match representations of numbers using words, mystery numbers, compact numerals, place value, and expanded notation Mark Dabling Boulevard Colorado Springs, CO 80918

9 Representation and Comparison of Numbers cont d Compare Numbers Compare quantities using pictures and numbers Identify more using pictures Identify less using pictures Identify equal using pictures Make mixed comparisons using pictures Compare quantities using numbers Compare two-digit numbers using models and pictures Demonstrate comparisons using models and pictures Use place value charts and numerals to make comparisons Compare three-digit numbers using place value Compare numbers using place value and expanded notation Use symbols >, =, or < to compare numbers Relate > with more or greater than Relate = with equal to Relate < with less or less than Use symbols to make mixed comparisons

13 Addition and Subtraction cont d Subtract Using Manipulatives, Pictures, and TouchPoints Recognize taking parts from the whole Use models, drawings, and TouchPoints to subtract Show subtraction as taking away a part from the whole Match models to numerals to subtract Use drawings to explain subtraction Demonstrate that subtraction begins with the whole Apply counting strategies to subtraction problems Use fingers to represent the problem Count groups of objects to find the difference Demonstrate subtraction with TouchPoints on both numbers Use TouchPoints to count and find the difference Relate subtraction to counting backward using TouchPoints Use backward counting as a subtraction strategy Apply using TouchPoints on the subtrahend only Show a subtraction problem using an equation Demonstrate subtraction with TouchPoints Write missing addends in boxes Match expressions to differences Identify true or false and select correct answers in subtraction Select correct answers from two to four choices in subtraction Solve subtraction word problems Use pictures to solve word subtraction problems Use rebus and controlled vocabulary to solve subtraction word problems Read one-step subtraction word problems Write number sentences for subtraction word problems Write word problems for subtraction number sentences

14 SCOPE AND SEQUENCE (K 2) Addition and Subtraction cont d Subtract Using Manipulatives, Pictures, and TouchPoints Find differences within 10 as the minuend Subtract using minuends within 5 Use counters to show the subtraction problem Master subtracting fluently with minuends within 5 Subtract using minuends within 10 Recognize multiple representations of subtraction problems Use pictures to show subtraction problems Apply strategies to subtract using TouchPoints Decompose 10 into pairs of addends Master subtracting fluently using minuends within 10 Use blacking out to show objects being taken away Use crossing out to show objects being taken away Use boxes for unknowns in subtraction Use other symbols for unknowns in subtraction Find differences within 20 as the minuend Apply TouchPoints as tactile of visual cues to subtract Cross out dots for missing addends (unknowns) to count backward Find differences within 13 as the minuend Find differences within 20 as the minuend Use Ten Frames to demonstrate subtracting tens and ones Say the minuend and use TouchPoints to subtract the subtrahend Master subtracting fluently within Mark Dabling Boulevard Colorado Springs, CO 80918

15 Addition and Subtraction cont d Subtract Using Place Value, Properties of Operations, and Strategies Subtract using place value Use place value charts to subtract Compare differences using place value Recognize and apply Base 10 blocks to subtraction of two-digit numbers Regroup a ten to 10 ones using models and pictures Use place value charts, visual cues, and TouchPoints to subtract ones from ones and tens from tens Subtract two-digit numbers using place value charts, TouchPoints, and visual cues Use place value and indicators of where to begin (visual cues) Regroup hundreds to compose tens using models and pictures Use place value charts, visual cues, and TouchPoints to subtract ones from ones, tens from tens, and hundreds from hundreds Subtract three-digit numbers using place value charts and visual cues Find differences with minuends within 100 Find differences with minuends within 50 Subtract using a 50 chart Subtract a one-digit number from a two-digit number (no regrouping) Subtract a two-digit number from a two-digit number (no regrouping) Find differences with minuends within 100 Subtract using a 100 chart Subtract using strategies Use place value charts, TouchPoints, and visual cues to subtract Apply patterns in subtraction Find missing addends Subtract multiples of 10 to one-digit numbers Subtract multiples of 10 to two-digit numbers Subtract multiples of 100 to two-digit numbers

18 SCOPE AND SEQUENCE (K 2) Multiplication Multiply Using Equal Groups of Objects Sort concrete objects and pictures into equal groups to multiply Sort concrete objects into equal groups to multiply Relate the objects to pictures in multiplication Correlate the objects with the pictorial TouchPoints on the numbers to multiply Use the pictures as TouchPoints on the numbers to multiply Skip count using TouchPoints to multiply Show multiplication problems as repeated addition of the same number Show multiplication as equal groups of 2 Show multiplication as equal groups of 3 Show multiplication as equal groups of 4 Show multiplication as equal groups of 5 Show multiplication as equal groups of 2, 3, 4, and 5 Apply understanding of multiplication in solving word problems Draw pictures to represent multiplication word problems Use arrays to show multiplication Transfer learning from objects and pictures to arrays of dots to multiply Transfer from pictorial TouchPoints to TouchPoints to multiply Ring equal groups of dots in arrays to show multiplication Skip count without TouchPoints to multiply Tell multiplication word problems from pictures Skip count to find missing numbers in sequences for multiplication Relate skip counting to equal groups of objects to multiply Solve multiplication word problems and draw pictures to represent them Mark Dabling Boulevard Colorado Springs, CO 80918

19 Multiplication cont d Multiply Using Odd and Even Numbers Find odd and even numbers to demonstrate multiplication Use pairs of objects to find odd and even numbers Use pairs in pictures to find odd and even numbers Match groups of pictures of objects to even (or odd) numbers Identify numbers 1 to 10 as even or odd to use for multiplication Find pairs and two equal addends to demonstrate multiplication Write multiplication problems as two equal addends from pictures Show multiplication problems as the sum of two equal addends Write multiplication problems using x as the multiplication symbol Demonstrate the commutative property of multiplication Identify numbers 11 to 25 as even or odd to find pairs of equal addends Show multiplication using various means Draw arrays of dots to represent multiplication problems Use pictures to solve multiplication word problems Use drawings and equations to solve multiplication word problems Multiply by 2, 3, 4, and 5 (up to 5 x 5) using pictures, equal addends, arrays of dots, and multiplication equations Match models and strategies to products Relate addition and multiplication equations Solve multiplication word problems that require both multiplication and addition or subtraction

20 SCOPE AND SEQUENCE (K 2) Measurement Describe and Compare Measurable Attributes of Objects Describe attributes using pictures Describe lengths of objects using nonstandard units and informal language Describe weights of objects using sink and float Describe length and weight of a single object Compare attributes using pictures Compare lengths of objects in pictures Compare weights of objects in pictures Compare length and weight of an object to another object to see which object has more of or less of Mark Dabling Boulevard Colorado Springs, CO 80918

21 Measurement cont d Learn about Length Measure line length Measure line lengths using paperclips Measure physical objects using paperclips and other units (e.g., lengths of string) Measure pictorial objects using various tools Demonstrate end to end measurement with no gaps and no overlaps Demonstrate that the number of same length units is the measurement of length of an object Cut out and use various length units to measure objects Use various length units to measure pictorial objects Order three objects by length Compare lengths of two objects indirectly with a third object Select the tool to measure length Learn about the ruler standard (customary) measurement Find that a ruler equals 12 inches or one foot Demonstrate how to measure with and read the measurement using a ruler Measure line lengths up to 12 inches to the nearest number of whole length units Identify objects that can be measured with a ruler (up to 12 inches) Use the customary abbreviation for inches and feet Learn about the yardstick Find that a yardstick equals three feet Demonstrate how to measure with and read the measurement using a yardstick to the nearest number of whole length feet Demonstrate how to read the measurement using a yardstick for feet and inches Identify objects that can be measured with a yardstick Use the customary abbreviation for yards Learn about the tape measure Find that the tape measure shows markings for inches and feet Demonstrate how to measure with and read the measurement using a tape measure for lengths greater than three feet Identify objects that can be measured with a tape measure Learn about the metric ruler (metric measurement) Find that a metric ruler equals ~30 centimeters Measure line lengths up to 30 centimeters to the nearest number of whole length units Use the customary abbreviation for centimeters Identify objects that can be measured with a metric ruler

23 Measurement cont d Tell Time Tell and write times in hours and half hours Identify hour and minute hand on an analog clock Identify each hour on an analog clock by tracing the hands Fill in missing hours on an analog clock Match digital time to analog time Recognize five-minute intervals on an analog clock Skip count by fives to 60 Identify each five-minute interval between 12:00 and 1:00 Match analog time to digital time Say and write each half hour for a 12 hour period Draw hands for each half hour on an analog clock Match half hours on an analog clock to a digital clock Write the hours on an analog clock and identify digital time Write the digital time for half hours on analog clocks Tell and write times to the nearest five minutes, using a.m. and p.m. Understand a 24 hour day Trace the hands on an analog clock and the corresponding time on a digital clock Identify a.m. and p.m. activities Relate a.m. and p.m. activities to personal experiences Identify each five-minute interval between 11:30 a.m. and 12:30 p.m. Tell time to the nearest five minutes Associate time on analog and digital clocks with personal experiences Select the analog clock that reflects the time associated with an activity Demonstrate telling time to the nearest five minutes with a.m. and p.m. Find elapsed time Find elapsed time one to two hours later Find elapsed time one to two hours earlier

24 SCOPE AND SEQUENCE (K 2) Measurement cont d Learn about Money Identify coins and one dollar bill Match the front and back of coins Read and write the coin and one dollar bill names Demonstrate the value of the coins and one dollar bill using and \$ Know the purpose of the decimal point in the representation with \$ Count the values of multiple coins Count the value of same type coins using skip counting Compare values of multiple same type coins (e.g., 8 nickels compared to 8 dimes) Match multiple same type coins to their values using and \$ Count values of mixed coins with the coin values arranged from greatest to least Count values of mixed coins with the coin values arranged randomly Identify the coins for given values Find one dollar using coins of multiple values Match values of mixed coins and dollars Solve word problems related to money Apply understanding in word problems related to money Use patterns and/or missing addends and/or subtraction to solve word problems related to money Mark Dabling Boulevard Colorado Springs, CO 80918

25 Data Represent Data Classify objects by measurable attributes Sort, classify, and count objects by length Sort, classify, and count objects by weight Classify objects by length and weight Represent data on graphs Sort and classify pictures by cutting and pasting on 2 x 5 graphs Sort and classify pictures by cutting and pasting on graphs up to 3 x 6 Record data on vertical and horizontal graphs Create 4 x 10 pictorial graphs from given data Construct bar graphs from given data Generate measurement data by measuring lengths of objects Use non-standard, customary, and metric measurements for data Record the measurement data in a table Represent data onto line plots Transfer data from tables to line plots Generate and record data Measure objects with a picture of a centimeter ruler (up to 15 cm) Record lengths of objects as whole number units Interpret Data Answer questions about the data in graphs and line plots Ask and answer questions about data on graphs Identify the number of data points on graphs Select answers from four choices about the graphs Select the graph that represents given data Order the data in graphs and line plots from least to greatest Interpret the data in the line plots Find differences in line lengths represented in the line plots Answer questions about the measurement data that was generated

26 SCOPE AND SEQUENCE (K 2) Geometry Learn 2-D and 3-D Shapes Describe 2-D and 3-D shapes in the environment Describe relative positions of objects (e.g., over/under) Describe shapes by kind of line and number of sides or edges and corners Distinguish between 2-D and 3-D shapes Compare 2-D and 3-D shapes for similarities and differences Identify common shapes in the environment that are made up of various shapes Define 2-D and 3-D shapes Define shapes: circle, triangle, rectangle, square, sphere, cone, cube, and cylinder Distinguish each shape from other shapes in pictures Match each shape in pictures regardless of size, color, or orientation Name each shape by its defining attributes Match each shape to an object in the environment Describe similarities and differences of 2-D shapes Describe similarities and differences of 3-D shapes Describe similarities and differences of 2-D and 3-D shapes Define shapes: rhombus, trapezoid, hexagon, and 3-D rectangle (right rectangular prism) Identify parallel, intersecting, and perpendicular lines Demonstrate that lines are combined to make shapes Distinguish between open and closed shapes Learn that the number of edges and corners define the shape Define each shape by the number of edges and corners Read, trace, and write the names of shapes Match the names of shapes to their defining attributes Associate names with shapes Demonstrate that color, size, and orientation do not define the shape Match shapes of different sizes and orientations Identify the number and kind of sides and angles (e.g., equal, different) Manipulate 3-D shape models Identify the number of faces, edges, and corners on 3-D shapes Apply understanding of 2-D shapes to 3-D shapes Distinguish shapes with three sides and three angles: triangles (equilateral, right, isosceles, and irregular) Distinguish shapes with four sides and four angles (quadrilaterals): squares, rhombuses, rectangles, parallelograms, and trapezoids Distinguish pentagons, hexagons, octagons, nonagons, and decagons Match shapes, shape names, and definitions Mark Dabling Boulevard Colorado Springs, CO 80918

27 Geometry cont d Learn 2-D and 3-D Shapes Compose 2-D and 3-D shapes Compose larger 2-D shapes from smaller shapes using manipulatives Compose larger 2-D shapes from smaller shapes using cutting and pasting Build 3-D shapes from readily available materials Compose larger 3-D shapes from smaller shapes using cutting and pasting (with guidance) Cut and paste parts of shapes to make each shape Cut a shape into parts and assemble them to make the shape Cut and paste parts of shapes to simulate making actual 3-D shapes Cut and paste parts of various 3-D shapes to match to the shapes Compose new shapes of different sizes of a given shape Compose new shapes of different sizes of different shapes Draw shapes using a ruler to connect dots Draw shapes with no guides Learn about Area Partition rectangles into same-size squares (readiness for area) Follow dotted lines, then gray lines, then dots to be connected to partition same-size squares Use vertical and horizontal orientations of partitioned rectangles with same-size squares Create two, four, and six same-size squares in rectangles Create eight and nine same-size squares in rectangles Create ten and twelve same-size squares in rectangles Identify true or false for statements about the number of same-size squares in given numbers of rows and columns in rectangles Learn about Fractional Parts of Shapes Partition rectangles and circles into equal squares (readiness for fractions) Divide rectangles and circles into two, three, and four equal shares Shade the identified equal share in rectangles and circles, trace the fraction word name, and associate the fraction Connect dots using a ruler to divide rectangles and circles into equal parts Identify the fraction for the shaded part in rectangles and circles Match partitioned rectangles and circles to the fraction and to the fraction word names (e.g., one-third, a third of, three-thirds, one whole) Draw the identified fractional part of rectangles Recognize that equal shares of identical wholes using circles and rectangles need not have the same shape

28 TouchMath Teacher Notes Mark Dabling Boulevard Colorado Springs, CO 80918

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