   | 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)  |
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| | 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 | | | | |
| | 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 | | | | | | |
| | 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 | | | | |
| | 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). | | | | | | | | | | |
| | Standard 2: | Use number notation and place value up to 25. | K.2a | Understand that numbers 1 through 9 represent “ones.” | | | | | | | | | | |
| | 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.” | | | | | | | | | | |
| | 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 | | | | | | |
| | 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 | | |
| | 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. | | | | | | | | | | |
| | 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 | | |
| | 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 |
| | 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 | | | | | | | | |
| | 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 | | | | |
| | 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 |
| | 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 | | | | | | | | |
| | 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. | | | | | | | | | | |
| | 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. | | | | | | | | | | |
| | 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 | | | | | | | | |
| | Standard 5: | Compose and decompose numbers 2 through 10. | K.5b | Recognize 6 through 10 as a five and some ones. | | | | | | | | | | |
| | 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 |
| | 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. | | | | | | | | | | |
| | 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 | | | | | | | | |
| | 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 | | | | | | | | |
| | 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 | | | | | | |
| | 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 | | | | | | | | |
| | 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 | | | | | | | | |
| | 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 | | | | | | |
| | 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 | | | | | | |
| | 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 | | | | |
| | 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 | | | | | | | | |
| | 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 | | | | | | |
| | 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. | | | | | |
| | 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. | | | | | |
| | 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. | | | | | |
| | 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 | | | | | | | | |
| | 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 | |
| | 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 | | | |
| | 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. | | |
| | 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 | | | | | | |
| | 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. | | | | | |
| | 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. | | | | | |
| | 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 | | | |
| | 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 | | | | | | | | |
| | 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 | | | | | |
| | 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. | | | | | |
| | 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 | | | |
| | 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 | | | |
| | 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 | | | |
| | 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 | | | | | | |
| | 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. | | | | | |
| | 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 | | | | | | | | |
| | 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 | | | | | | | | |
| | 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. | | | | | |
| | 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. | | | | | |
| | 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 | | | | | |
| | 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 | | | | | | |
| | 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 | | | |
| | 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 | | | |
| | 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 | | | |
| | 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 | | | |
| | 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 | | | |
| | 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 | | | | | | | | | |
| | 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 | | | | | | | | | |
| | 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 | | | | | | | | | |
| | 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 | | | | | | | | | |
| | 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 | | | |
| | 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 | | | |
| | 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 | | | |
| | 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; | | | |
| | 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, | | | | |