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Grade Standard # Standard Description Sub Point # Sub Point Description Book/ Unit Investigation Book/ Unit (2) Investigation (2) Book/ Unit (3) Investigation (3) Book/ Unit (4) Investigation (4) Book/ Unit (5) Investigation (5) Count = 3 Kindergarten Standard 1:  Count objects through 30 and use numbers to express quantity. K.1a    Count up to 30 objects and tell how many there are in the counted group of objects. Counting Ourselves and Others How Many Are We? Collecting Counting and Measuring Counting Books Collecting Counting and Measuring Taking Inventory Kindergarten Standard 1:  Count objects through 30 and use numbers to express quantity. K.1b    Count up to 30 objects in groups of 2, 5 and 10. Number Games and Story Problems Twos, Fives, and Tens Coins, Coupons, and Combinations Groupings by Twos, Fives, and Tens Kindergarten Standard 1:  Count objects through 30 and use numbers to express quantity. K.1c    Read aloud and write the numerals 1 to 30 and match numerals with the numbers used in counting. Counting Ourselves and Others Mathematical Teaching In Kindergarten Counting Jar Mathematical Thinking In Kindergarten Attendance Building Number Sense Counting Kindergarten Standard 1:  Count objects through 30 and use numbers to express quantity. K.1d    Recognize and use correctly numerical adjectives (e.g. first, fourth, last). Kindergarten Standard 2:  Use number notation and place value up to 25. K.2a    Understand that numbers 1 through 9 represent “ones.” Kindergarten Standard 2:  Use number notation and place value up to 25. K.2b    Understand that numbers 11 through 25 consist of one or two “tens” and some “ones.” Kindergarten Standard 2:  Use number notation and place value up to 25. K.2c    Count to 100 by tens. Number Games and Story Problems Twos, Fives, and Tens Coins, Coupons, and Combinations Groupings by Twos, Fives, and Tens Kindergarten Standard 3: Compare numbers up to 30 and sets of up to 10 objects. K.3a    Compare sets of ten or fewer objects and identify which are equal to, more than, or less than others. Collecting Counting and Measuring Comparing Towers Collecting Counting and Measuring Counting and Comparing Collecting Counting and Measuring Least To Most Exploring Numbers Building Number Sense Kindergarten Standard 3: Compare numbers up to 30 and sets of up to 10 objects. K.3b    Place numbers 1 through 10 in their correct sequence. Kindergarten Standard 3: Compare numbers up to 30 and sets of up to 10 objects. K.3c     Compare numbers up to 30 (e.g. which is/has more?  Which is/has fewer?  Which is/has less?) Collecting Counting and Measuring Comparing Towers Collecting Counting and Measuring Counting and Comparing Collecting Counting and Measuring Least To Most Mathematical Thinking at Grade 1 Exploring Numbers Kindergarten Standard 4: Understand addition as putting together and subtraction as breaking apart for totals equal to or less than 10. K.4a    Understand add as “put together” and solve addition problems with numbers less than 10. How many In All? Six Tiles How many In All? Story Problems How many In All? Blue and Red Crayons Mathematical Thinking at Grade 1 Exploring Numbers Building Number Sense Addition and Subtraction Kindergarten Standard 4: Understand addition as putting together and subtraction as breaking apart for totals equal to or less than 10. K.4b    Understand subtract as “break apart” or “take away” and solve subtraction problems using numbers between 1 and 10. Building Number Sense Addition and Subtraction Kindergarten Standard 4: Understand addition as putting together and subtraction as breaking apart for totals equal to or less than 10. K.4c    Add and subtract single digit numbers who total (or difference) is between 1 and 10. Mathematical Thinking at Grade 1 Exploring Numbers Building Number Sense Building Numbers in Different Ways Building Number Sense Addition and Subtraction Kindergarten Standard 4: Understand addition as putting together and subtraction as breaking apart for totals equal to or less than 10. K.4d    Solve problems, make drawings, and create illustrative stories involving addition and subtraction of numbers between 1 and 10. How many In All? Story Problems How many In All? Story Problems How many In All? Blue and Red Crayons Mathematical Thinking at Grade 1 Exploring Numbers Building Number Sense Addition and Subtraction Kindergarten Standard 4: Understand addition as putting together and subtraction as breaking apart for totals equal to or less than 10. K.4e    Be able to write expressions (e.g. 5 + 2 or 7 – 3) to represent situations involving addition or subtraction of numbers less than 10. Building Number Sense Addition and Subtraction Kindergarten Standard 4: Understand addition as putting together and subtraction as breaking apart for totals equal to or less than 10. K.4f     Use the commutative property to reduce the number of addition facts that must be learned. Kindergarten Standard 4: Understand addition as putting together and subtraction as breaking apart for totals equal to or less than 10. K.4g    Use addition facts to solve subtraction problems. Kindergarten Standard 5: Compose and decompose numbers 2 through 10. K.5a Understand that numbers greater than 2 can be decomposed in several different ways. Collecting Counting and Measuring Six Tiles Kindergarten Standard 5: Compose and decompose numbers 2 through 10. K.5b Recognize 6 through 10 as a five and some ones. Kindergarten Standard 6: Compare the length, weight and capacity of objects. K.6a Make direct comparisons between objects (e.g. recognize which is shorter, longer, taller, lighter, heavier, or holds more). Collecting Counting and Measuring Comparing Towers Collecting Counting and Measuring Least To Most Bigger Taller Heavier Smaller Weighing and Balancing Bigger Taller Heavier Smaller Filling Bigger Taller Heavier Smaller Measuring Length Kindergarten Standard 6: Compare the length, weight and capacity of objects. K.6b Recognize that length, weight, and capacity are preserved when objects are decomposed and recomposed. Kindergarten Standard 6: Compare the length, weight and capacity of objects. K.6c Recognize tools used to measure length, weight and capacity. Bigger Taller Heavier Smaller Weighing and Balancing Kindergarten Standard 7: Recognize and use words that represent periods of time. K.7a Recognize day, night, morning, afternoon, evening, yesterday, today, tomorrow. Mathematical Thinking In Kindergarten Calendar Kindergarten Standard 7: Recognize and use words that represent periods of time. K.7b Recognize the role of clocks or calendars in measuring and keeping track of time. Mathematical Thinking at Grade 1 Calendar Mathematical Thinking In Kindergarten Daily Schedule Kindergarten Standard 7: Recognize and use words that represent periods of time. K.7c Identify daily landmark times such as bedtime or lunch time. Mathematical Thinking In Kindergarten Daily Schedule Kindergarten Standard 8: Create, explore and describe shapes K.8a Identify common shapes such as rectangles, circles and triangles. Making Shapes and Building Blocks 2D shapes Around Us Kindergarten Standard 8: Create, explore and describe shapes K.8b Make compound pictures by putting together simple geometric shapes. Making Shapes and Building Blocks Exploring Shapes With the Computer Making Shapes and Building Blocks Making Shapes and Building Blocks Kindergarten Standard 9: Identify, sort and classify objects. K.9a Sort by attribute and identify objects that do not belong in a particular group. Counting Ourselves and Others What Did You Eat for Lunch? Counting Ourselves and Others Collecting Data About Our Class Kindergarten Standard 10: Create, describe and extend simple patterns. K.10a Use repeating, growing and shrinking patterns. Pattern Trains and Hopscotch Paths Exploring Patterns Pattern Trains and Hopscotch Paths What Comes Next? Pattern Trains and Hopscotch Paths Pattern Borders 1st Grade Standard 1: Understand and use number notation and place value up to 100. 1.1a Count to 100 by ones and tens, and relate these number words to groups of tens and ones. Number Games and Story Problems Investigation 2, sessions 6-8 and 10-12 1st Grade Standard 1: Understand and use number notation and place value up to 100. 1.1b Read and write numbers up to 100 in numerals and in words. Building Number Sense Investigation 3, sessions 1 and 2 Number Games and Story Problems Investigation 2, sessions 6-8 1st Grade Standard 1: Understand and use number notation and place value up to 100. 1.1c Recognize the place value of numbers (hundreds, tens & ones). Coins, Coupons and Combinations(2nd Grade) Investigation 4, sessions 2-4 and daily class routine with # of the day Putting Together and Taking Apart(2nd Grade) All of Investigation 1, specifically sessions 1 and 2 emphasize the strategy of manipulating numbers. Place Value is taught as a daily routine of manipulating numbers with addition and subtraction. 1st Grade Standard 2: Compare numbers up to 100 and arrange them in numerical order. 1.2a Arrange numbers in increasing and decreasing order. Building Number Sense Investigation 3, sessions 1 and 2 Note that students do not anything in decreasing order. 1st Grade Standard 2: Compare numbers up to 100 and arrange them in numerical order. 1.2b Locate numbers up to 100 on the number line. Building Number Sense Investigation 3, sessions 1 and 2, and 5-7 Number Games and Story Problems Investigation 2, sessions 6-8 In both units using the 100's chart instead of number line. 1st Grade Standard 2: Compare numbers up to 100 and arrange them in numerical order. 1.2c Compare two or more sets of objects in terms of the difference in the number of elements. Mathematical Thinking at Grade 1 Investigation 2, sessions 1-3 1st Grade Standard 3: Understand how to add, subtract, compose and decompose numbers up to 100. 1.3a Use efficient methods to add and subtract numbers to 100, and to solve associated word problems. Building Number Sense Investigation 1, sessions 1,2, 7-9; all of Investigation 2; Investigation 3, sessions 5-7; all of Investigation 4 Number Games and Story Problems All of Investigation 1; Investigation 2, sessions 1-8 and 10-12; all of Investigation 3 Methods are used for quantities up to 40. Putting Together and Taking Apart(2nd Grade) All of Investigation 2; All of Investigation 4; Investigation 5, sessions 1, 4, 5, and 7 Coins, Coupons and Combinations (2nd Grade) All of Investigation 3 1st Grade Standard 3: Understand how to add, subtract, compose and decompose numbers up to 100. 1.3b Understand how to compose and decompose numbers up to 100. Building Number Sense Investigation 1, sessions 1,2 and 5-9; all of Investigation 2; Investigation 3, sessions 1,2, 5-7; all of investigation 4 Number Games and Story Problems All of Investigation 1; Investigation 2, sessions 1-8 and 10-12; all of Investigation 3 Putting Together and Taking Apart(2nd Grade) All of Investigation 3; All of Investigation 4; Investigation 5, sessions 2 and 3 1st Grade Standard 3: Understand how to add, subtract, compose and decompose numbers up to 100. 1.3c Recognize that adding and subtracting are inverse operations. Number Games and Story Problems Investigation 1, sessions 2-9; all of Investigation 3 Inverse operations not explicitly taught, but briefly covered and encouraged. Putting Together and Taking Apart(2nd Grade) All of Investigation 3 The entire unit emphasizes that students can use both addition and subtraction to solve the same problem. 1st Grade Standard 3: Understand how to add, subtract, compose and decompose numbers up to 100. 1.3d Create drawings, stories and equations to illustrate addition and subtraction of numbers smaller than 100. Building Number Sense Investigation 2, sessions 1, 2 and 6-8; all of Investigation 4 Number Games and Story Problems All of Investigation 1; Investigation 2, sessions 1, 2, 4-8, and 10-12; all of Investigation 3 1st Grade Standard 3: Understand how to add, subtract, compose and decompose numbers up to 100. 1.3e Understand how to use groups of tens and ones to add numbers greater than ten. Number Games and Story Problems Investigation 1, sessions 2-9; Investigation 2, sessions 10-12; all of Investigation 3 Strategy not explicitly taught, but often encouraged in the Spring to find friendly 10 combinations. 1st Grade Standard 3: Understand how to add, subtract, compose and decompose numbers up to 100. 1.3f Solve verbal problems by using diagrams, numbers and symbolic expressions. Building Number Sense Investigation 4, sessions 1 and 2 Number Games and Story Problems Investigation 3, sessions 1 and 2 Students express the verbal idea while the teacher records responses. 1st Grade Standard 4: Measure length, weight, capacity and time. 1.4a Use rulers, scales and containers to measure and compare the dimensions, weight and capacity (volume) of classroom objects. Bigger, Taller, Heavier, Smaller All of Investigations 1, 2 and 3 Note that students do not use rulers rather, non-standard units of measure (pencils, cubes, hands, feet). From Paces to Feet (2nd Grade) All of Investigation 2; All of Investigation 3; All of Investigation 4 1st Grade Standard 4: Measure length, weight, capacity and time. 1.4b Compare lengths, weights and capacities of pairs of objects. Bigger, Taller, Heavier, Smaller All of Investigation 1; Investigation 2, sessions 2-7; all of Investigation 3 1st Grade Standard 4: Measure length, weight, capacity and time. 1.4c Tell time from analog (round) clocks in half-hour intervals. Not covered in 1st Grade Investigations 1st Grade Standard 5: Count, add and subtract money up to $100.00. 1.5a Tell the different denominations of coins and notes. Number Games and Story Problems Investigation 2, session 3 Money is only counted up to one dollar and only penny, nickel, dime and quarter and used. 1st Grade Standard 5: Count, add and subtract money up to $100.00. 1.5b Tell the amount of money in cents up to $1 and in dollars up to $100. Number Games and Story Problems Investigation 2, session 3 The unit works with coins only. Putting Together and Taking Apart(2nd Grade) Investigation 2, sessions 5 and 6 1st Grade Standard 5: Count, add and subtract money up to $100.00. 1.5c Add and subtract money; in cents only; in dollars only (within the scope of Standard 1.3). Number Games and Story Problems Investigation 2, session 3 Money is only added. Mathematical Thinking at Grade 3 Investigation 2, sessions 5-7 1st Grade Standard 5: Count, add and subtract money up to $100.00. 1.5d Solve word problems using addition and subtraction of money; in cents only; in dollars only. Number Games and Story Problems Investigation 2, sheet 14 Cents are added up to 10 cents. Mathematical Thinking at Grade 3 Investigation 2, sessions 5-7 1st Grade Standard 6: Make picture graphs of measurements and use them to pose and solve problems. 1.6a Explain the meaning of picture graphs. Survey Questions and Secret Rules Investigation 2, sessions 1-6; Investigation 3, sessions 1 and 2; Investigation 4, sessions 2 and 3 Mathematical Thinking at Grade 1 Investigation 5, sessions 3-6 1st Grade Standard 6: Make picture graphs of measurements and use them to pose and solve problems. 1.6b Make picture graphs from collected or given data. Survey Questions and Secret Rules Investigation 2, sessions 1, 2 and 5-6; Investigation 3, session 1; Investigation 4, sessions 2-5 Mathematical Thinking at Grade 1 Investigation 5, sessions 3 and 4 Students use manipulatives and then transfer to a picture graph. 1st Grade Standard 7: Recognize, describe, draw and manipulate two-dimensional figures. 1.7a Identify circle, triangle, square and rectangle. Quilt Squares and Block Towns Investigation 1, session 1, 3-6, and 11-15; Investigation 2, sessions 1, 2, 4-6 and 7; Investigation 3, sessions 1-5 1st Grade Standard 7: Recognize, describe, draw and manipulate two-dimensional figures. 1.7b Sort objects by shape and size. Quilt Squares and Block Towns Investigation 1, sessions 11 and 12; all of Investigation 2; Investigation 3, sessions 1-5 1st Grade Standard 7: Recognize, describe, draw and manipulate two-dimensional figures. 1.7c Describe and draw shapes resulting from rotation and flips of simple two-dimensional figures. Quilt Squares and Block Towns Investigation 1, sessions 3-15 Students draw 3-D shapes and flipping takes place on the computer program. 1st Grade Standard 8: Recognize and extend simple patterns. 1.8a Sort objects and create and describe patterns by number, shapes, sizes, rhythms or colors. Survey Questions and Secret Rules All of Investigation 1; Investigation 2, sessions 3-6; Investigation 3, sessions 1 and 2; Investigation 4, sessions 2 and 3 Mathematical Thinking at Grade 1 Investigation 1, sessions 2-4; Investigation 2, sessions 2 and 3; all of Investigation 3; Investigation 4, session 5; all of Investigation 5 Continues throughout all 1st grade investigation units. Number Games and Story Problems-number patterns.  Quilt Squares and Block Towns-shapes and colors.  Bigger, Taller, Heavier, Smaller-sizes.  Mathematical Thinking at Grade 1-rhythms and colors. 1st Grade Standard 8: Recognize and extend simple patterns. 1.8b Distinguish between repeating and growing patterns. Mathematical Thinking at Grade 1 Investigation 3, sessions 1 and 2; Investigation 4, session 5 Number Games and Story Problems Investigation 2, sessions 2 and 9 Mathematical Thinking at Grade 1-repeating patterns.  Number Games and Story Problems-growing patterns 1st Grade Standard 8: Recognize and extend simple patterns. 1.8c Identify and describe the next element in simple repeating patterns. Mathematical Thinking at Grade 1 Investigation 3, sessions 1 and 2; Investigation 4, session 5 Number Games and Story Problems Investigation 2, sessions 2 and 9 2nd Grade Standard 1: Understand and use number notation and place value up to 1000. 2.1a Count to 1000 by ones, tens and hundreds. Putting Together and Taking Apart Investigation 2 Coins, Coupons, and Combinations Investigation 2 Mathematical Thinking at Grade 3 Investigation 1 Only to 100 2nd Grade Standard 1: Understand and use number notation and place value up to 1000. 2.1b Read and write numbers up to 1000 in numerals and in words. Coins, Coupons, and Combinations Investigation 4 Mathematical Thinking at Grade 3 Investigation 1 Only to 100 2nd Grade Standard 1: Understand and use number notation and place value up to 1000. 2.1c Recognize the place value of numbers (hundreds, tens & ones). Coins, Coupons, and Combinations Classroom Routines: Today's Number Putting Together and Taking Apart Investigation 5 and Classroom Routines: Today's Number Up to 200 2nd Grade Standard 1: Understand and use number notation and place value up to 1000. 2.1d Understand and utilize the relative values of the different number places. Classroom Routines: How Many Pockets covers Estimating     MTG3:Teacher Note  page 46 2nd Grade Standard 1: Understand and use number notation and place value up to 1000. 2.1e Compare numbers up to 1000. Coins, Coupons, and Combinations Investigation 4 Putting Together and Taking Apart Investigation 2 Mathematical Thinking at Grade 3 Investigation 1 Up to 100 2nd Grade Standard 2: Know how to locate numbers on the number line. 2.2a Know that on the number line larger numbers are located to the right and smaller numbers are located to the left. Lynn Kuske Lesson 2nd Grade Standard 2: Know how to locate numbers on the number line. 2.2b Know how to locate zero on the number line. Lynn Kuske Lesson 2nd Grade Standard 2: Know how to locate numbers on the number line. 2.2c Use number line pictures and manipulatives to illustrate the actions of adding and subtracting. Lynn Kuske Lesson 2nd Grade Standard 2: Know how to locate numbers on the number line. 2.2d Know how to place -1, -2, -3, … on the number line as mirror images of 1, 2, 3 … with respect to zero. Lynn Kuske Lesson 2nd Grade Standard 3: Understand how to add and subtract numbers up to 1000 and solve related word problems. 2.3a Understand how to efficiently add and subtract two- and three-digit numbers. Coins, Coupons, and Combinations Investigation 3  Investigation 4 Putting Together and Taking Apart Investigation 1, 2, 3, 4, and 5 Mathematical Thinking at Grade 3 Investigation 2      Investigation 4 Up to 100 2nd Grade Standard 3: Understand how to add and subtract numbers up to 1000 and solve related word problems. 2.3b Understand that subtracting is the inverse of adding, and use this inverse to solve problems. Putting Together and Taking Apart Investigation 3 Mathematical Thinking at Grade 3 Investigation 3 Coins, Coupons, and Combinations Investigation 3 a+b=c needs to be explicitly taught; Traditional Algorithm needs to be taught when appropriate; See CCC page 102 teacher note;  PTTA pg 32-34 Teacher Note  2nd Grade Standard 3: Understand how to add and subtract numbers up to 1000 and solve related word problems. 2.3c Solve word problems of more than one step that use numbers with three or fewer digits. Putting Together and Taking Apart Investigation 3   Investigation 5 Coins, Coupons, and Combinations Investigation 3   Investigation 4 Does not include 3 digit problems; Some problems with irrelevant information but don't have problems with insufficient information 2nd Grade Standard 3: Understand how to add and subtract numbers up to 1000 and solve related word problems. 2.3d Add and subtract mentally with ones, tens and hundreds. Putting Together and Taking Apart Investigation 5 Mathematical Thinking at Grade 3 Investigation 1 Only 2 digit numbers, no 3 digit numbers; Mental Math in the Primary (several lessons), Classroom Routines from 3rd Grade; 2nd Grade Standard 3: Understand how to add and subtract numbers up to 1000 and solve related word problems. 2.3e Create stories, drawings, and equations to illustrate arithmetic problems with unknowns of various types. Putting Together and Taking Apart Investigation 1, 2, 4, and 5 Coins, Coupons, and Combinations Investigation 1, 3, 2nd Grade