Embedded Files
First Grade mathematics is about
- Developing understanding of addition, subtraction, and strategies for addition and subtraction within 20
- Developing understanding of whole number relationships and place value, including grouping in tens and ones
- Developing understanding of linear measurement and measuring lengths as iterating length units
- Reasoning about attributes of, and composing and decomposing geometric shapes.
Second Grade mathematics is about
- Extending understanding of base-ten notation
- Building fluency with addition and subtraction
- Using standard units of measure
- Describing and analyzing shapes
Module 1: Place Value, Comparison, Addition and Subtraction to 40
Module 1: Place Value, Comparison, Addition and Subtraction to 40
(35 Hours)
(35 Hours)
Standards
1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones—called a “ten.” c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
1.NBT.3 Compare two two-digit numbers based on meaning of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
1.NBT.6 Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Overview
Students study, organize, and manipulate numbers within 40. They compare quantities and begin using the symbols for greater than (>) and less than (<). Addition and subtraction of tens is another focus of this module as is the use of familiar strategies to add two-digit and single-digit numbers within 40. Near the end of the module, the focus moves to new ways to represent larger quantities and adding like place value units as students add two-digit numbers.
This unit is a combination of 3 separate FIRST GRADE units. Second grades may need additional extensions (higher numbers, represent in multiple ways, solve fluently, etc) . All materials for all three modules are linked below.
Unit Vocab
A ten (a group, or unit, consisting of 10 items)
Ones (individual units, 10 of which become a ten)
> (greater than)
< (less than)
Place value (quantity represented by a digit in a particular place within a number)
Topic A: Addition Word Problems under 10
Topic A: Addition Word Problems under 10
Standards
1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart and comparing, with unknowns in all positions, e.g., by using objects, drawings and equations with a symbol for the unknown number to represent the problem.
1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Overview
Students develop a more robust understanding of addition word problems, moving beyond the Kindergarten problem types (K.OA.2) by reviewing put together with result unknown and add to with result unknown problems, and then moving to the more complex change unknown version of the earlier problem types.
Lessons **Everything is a clickable link***
Lesson: “Add To” With Change Unknown: A Context For Counting On
Lesson: “Put Together” and “Add To” With Result and Change Unknown
Topic B: Subtraction Word Problems under 10
Topic B: Subtraction Word Problems under 10
Standards
1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart and comparing, with unknowns in all positions, e.g., by using objects, drawings and equations with a symbol for the unknown number to represent the problem.
1.OA.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8
Overview
Focuses on students understanding the meaning of subtraction as it relates to addition and provides students with rich experiences connecting subtraction to their solid foundation of addition (1.OA.4), using various word problem types (1.OA.1).
Lessons **Everything is a clickable link***
Lesson: “Add To” With Change Unknown: Math Stories with Drawings
Lesson: “Take From” With Change Unknown: Math Stories With Drawings
Lesson: “Put Together/Take Apart” With Addend Unknown: Math Stories
Topic Quiz *click*
Topic C: Counting on or Making Ten to Solve
Topic C: Counting on or Making Ten to Solve
Standards
1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart and comparing, with unknowns in all positions, e.g., by using objects, drawings and equations with a symbol for the unknown number to represent the problem.
1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20.
1.OA.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8
1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10
Overview
Result/Total Unknown Problems With problems that always include at least two numbers that yield 10 when added together
Lessons **Everything is a clickable link***
Lesson: Word Problems With Three Addends, Two Of Which Make Ten
Lesson: Associative And Commutative Properties To Make Ten With Three Addends
Topic Quiz 1 (first half of unit)
Topic Quiz 2 (first half of unit)
Topic D: Tens and Ones
Topic D: Tens and Ones
Standards
1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones—called a “ten.” c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
Overview
This topic opens where students study, organize, and manipulate numbers within 40. Having worked with creating a ten and some ones in the previous topic, students now recognize multiple tens and ones. Students use fingers, linking cubes, dimes, and pennies to represent numbers to 40 in various ways—from all ones to tens and ones (1.NBT.2). They use a place value chart to organize units. The topic closes with the identification of 1 more, 1 less, 10 more, and 10 less as students learn to add or subtract like units
Lessons
Topic E: Comparisons of Paris of Two-Digit Numbers
Topic E: Comparisons of Paris of Two-Digit Numbers
Standards
1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones—called a “ten.” c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used
Overview
Students compare quantities and begin using the symbols for greater than (>) and less than (<) (1.NBT.3). Students demonstrate their understanding of place value when they recognize that 18 is less than 21 since 2 tens already have a greater value than 1 ten 8 ones.
Lessons
Topic F: Addition and Subtraction of Tens
Topic F: Addition and Subtraction of Tens
Standards
1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
1.NBT.6 Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Overview
Topic F focuses on addition and subtraction of tens (1.NBT.4, 1.NBT.6). Having used concrete models in previous topics to represent 10 more and 10 less, students now recognize that just as 3 + 1 = 4, 3 tens + 1 ten = 4 tens. With this understanding, students add and subtract a multiple of 10 from another multiple of 10.
Lessons
Topic G: Addition of Tens or Ones to a Two-Digit Number
Topic G: Addition of Tens or Ones to a Two-Digit Number
Standards
1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
Overview
Students use familiar strategies to add two-digit and single-digit numbers within 40. Students apply the Level 2 strategy of counting on and use the Level 3 strategy of making ten, this time making the next ten (1.NBT.4). For instance, when adding 28 + 5, students break 5 into 2 and 3 so that 28 and 2 can make the next ten, which is 30, or 3 tens, and then add 3 to make 33.
Lessons
Topic H: Varied Problem Types within 20
Topic H: Varied Problem Types within 20
Standards
1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Overview
Students consider new ways to represent larger quantities when approaching put together/take apart with total or addend unknown and add to with result or change unknown word problems. Students begin labeling drawings with numerals and eventually move to tape diagrams to represent the problems pictorially (1.OA.1). Throughout this topic, students continue developing their skills with adding single-digit and double-digit numbers (introduced in Topic D) during fluency activities.
Lessons
Topic I: Addition of Tens and Ones to a Two-Digit Number
Topic I: Addition of Tens and Ones to a Two-Digit Number
Standards
1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones—called a “ten.” c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
Overview
The final topic focuses on adding like place value units as students add two-digit numbers. The topic begins with interpreting two-digit numbers in varied combinations of tens and ones (e.g., 34 = 34 ones = 3 tens 4 ones = 2 tens 14 ones = 1 ten 24 ones). This flexibility in representing a given number prepares students for addition with regrouping (e.g., 12 + 8 = 1 ten 10 ones = 2 tens or 18 + 16 = 2 tens 14 ones = 3 tens 4 ones). To close the module, students add pairs of numbers with varied sums in the ones place to support flexibility in thinking.
Lessons
Module 2: Measuring
Module 2: Measuring
(10 hours)
(10 hours)
Standards
1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.
1.MD.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes
Overview
This module begins by extending students’ kindergarten experiences with direct length comparison to indirect comparison whereby the length of one object is used to compare the lengths of two other objects. Longer than and shorter than are taken to a new level of precision by introducing the idea of a length unit. Students then explore the usefulness of measuring with similar units. Students engage in activities designed to deepen their conceptual understanding of measurement, using metric units, and to relate addition and subtraction to length.
This unit is a combination of both FIRST GRADE and SECOND GRADE units. First graders are expected to explore and gain exposure to standard measuring. Second graders are expected to master it.
Unit Vocab
Benchmark (e.g., “round” numbers like multiples of 10) Endpoint (point where something begins or ends)
Estimate (an approximation of a quantity or number)
Hash mark (marks on a ruler or other measurement tool)
Meter (standard unit of length in the metric system)
Meter stick or strip (tool used to measure length)
Number line Overlap (extend over, or cover partly)
Ruler (tool used to measure length)
Centimeter (standard length unit within the metric system)
Centimeter cube (pictured right, also used as a length unit in this module)
Centimeter ruler (measurement tool using length units of centimeters)
Data (collected information)
Endpoint (the end of an object, referenced when aligning for measurement purposes)
Height (measurement of vertical distance of an object)
Length unit (measuring the length of an object with equal-sized units)
Topic A: Standard Length Units
Topic A: Standard Length Units
Standards
1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.
1.MD.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
Overview
Centimeter cubes are laid alongside the length of an object as students learn that the total number of cubes laid end to end with no gaps or overlaps represents the length of that object (1.MD.2).
Lessons **All clickable links***
Lesson 4: Length and Centimeter Cubes
Slide Deck
Topic Quiz *click*
Topic B: Non-standard and Standard Length Units
Topic B: Non-standard and Standard Length Units
Standard
1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.MD.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
Overview
This topic explores the usefulness of measuring with similar units. Students measure the same objects using two different non-standard units, toothpicks and small paper clips, simultaneously to measure one object and answer the question, “Why do we measure with same-sized length units?” (1.MD.2)
Lesson
Topic C: Understanding Concepts about the Ruler
Topic C: Understanding Concepts about the Ruler
Standards
2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes
Overview
In Lesson 1, students relate length to physical units by measuring various objects with multiple centimeter cubes, creating a mental benchmark for the centimeter. In Lesson 2, they apply their knowledge of using centimeter cubes to measure by moving from repeated physical units to the iteration of one physical unit. This enables them to internalize their understanding of a length unit as the amount of space between one end of the cube and the other (or space between hash marks). Thus, they begin moving from the concrete to the conceptual. Finally, in Lesson 3, students apply knowledge of known measurements to create unit rulers using one centimeter cube. This deepens the understanding of distance on a ruler and the ruler as a number line.
Lesson
Topic D: Measure and Estimate Length Using Different Measurement Tools
Topic D: Measure and Estimate Length Using Different Measurement Tools
Standard
2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes
Overview
Students build skills in measuring, learning that length is a segment of a line. They learn about benchmark measurements and estimate length using those benchmarks.
Lessons
Module 3: Place Value, Add, and Subtract to 100
Module 3: Place Value, Add, and Subtract to 100
(22 hours)
(22 hours)
Standards
1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
1.NBT.2 Understand that the two digits in a two-digit number represent amounts of tens and ones. Understand the following special cases: a. 10 can be thought of as a bundle of ten ones—called a “ten.” c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. 1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
1.NBT.4 Add within 100, including adding a two‐digit number and a one‐digit number, and adding a two‐digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two‐digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
1.NBT.6 Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s
2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
Overview
This module begins by extending students’ kindergarten experiences with direct length comparison to indirect comparison whereby the length of one object is used to compare the lengths of two other objects. Longer than and shorter than are taken to a new level of precision by introducing the idea of a length unit. Students then explore the usefulness of measuring with similar units. Students engage in activities designed to deepen their conceptual understanding of measurement, using metric units, and to relate addition and subtraction to length.
This unit is a combination of both FIRST GRADE and SECOND GRADE units. First graders are expected to master addition, subtraction, and comparison to 100. Second graders are expected to master it to 1000.
Unit Vocab
Base ten numerals (e.g., a thousand is 10 hundreds, a hundred is 10 tens, starting in Grade 3 a one is 10 tenths, etc.)
Expanded form (e.g., 500 + 70 + 6)
Hundreds place (e.g., the 5 in 576 is in the hundreds place)
One thousand (1,000)
Place value or number disk (pictured)
Standard form (e.g., 576)
Unit form (e.g., 5 hundreds 7 tens 6 ones)
Word form (e.g., five hundred seventy-six)
Topic A: Numbers to 120
Topic A: Numbers to 120
Standards
1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
1.NBT.2 Understand that the two digits in a two-digit number represent amounts of tens and ones. Understand the following special cases: a. 10 can be thought of as a bundle of ten ones—called a “ten.” c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. 1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
Overview
Count and write numbers to 120 using numerals and unit form. Students extend their understanding of and skill with tens and ones to numbers to 100 in Topic B (1.NBT.2). For example, they mentally find 10 more, 10 less, 1 more, and 1 less (1.NBT.5) and compare numbers using the symbols >, =, and < (1.NBT.3). They then count and write numbers to 120 (1.NBT.1) using both standard numerals and the unit form.
Lessons
Topic B: Addition to 100 Using Place Value
Topic B: Addition to 100 Using Place Value
Standards
1.NBT.4 Add within 100, including adding a two‐digit number and a one‐digit number, and adding a two‐digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two‐digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
1.NBT.6 Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Overview
Add pairs of two-digit numbers to sums within 100. Students apply all of their place value and Level 3 strategy knowledge to add pairs of two-digit numbers to sums within 100. To this point, students have only added pairs of two-digit numbers within 40. They now extend their skills and strategies to larger pairs, such as 36 + 57, using all of the same methods.
Lessons
Lesson 15: Ones Digits’ Sum Greater Than 10 -Drawing and Recording the Total
Lesson 16: Ones Digits’ Sum Greater Than 10 - Drawing and Recording the Ten
Lesson 17: Ones Digits’ Sum Greater Than 10 - Drawing and Recording the Ten (Continued)
Topic C: Understanding Place Value Units of One, Ten and a Hundred
Topic C: Understanding Place Value Units of One, Ten and a Hundred
Standards
2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s
Overview
Students practice counting by ones and skip-counting by tens and hundreds, Students learn the structure of multiples of ten and a hundred. Students practice counting by ones and skip-counting by tens and hundreds, counting efficiently and effectively.
Lessons
Topic D: Three-Digit Numbers in Unit, Standard, Expanded, and Word Form
Topic D: Three-Digit Numbers in Unit, Standard, Expanded, and Word Form
Standards
2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form
Overview
Students continue bundling units, analyzing benchmark numbers. They work with three-digit numbers, expressing them in unit and word form and on the place value chart. Students continue counting and practice moving fluidly between the word form, unit form, standard form, and expanded form.
Lessons
Topic E: Comparing 2 Three-Digit Numbers
Topic E: Comparing 2 Three-Digit Numbers
Standards
2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
Overview
Students use the number disks to make comparisons. They learn more about “more than” and “less than” and their relation to addition and subtraction. Students compare and order three-digit numbers.
Lessons
Topic F: Finding 1, 10, and 100 More or Less
Topic F: Finding 1, 10, and 100 More or Less
Standards
2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s
Overview
Students continue counting up and down using the “more than” and “less than” concepts, focusing on using their words to make statements about values.
Lessons
Module 4: Addition and Subtraction to 1000
Module 4: Addition and Subtraction to 1000
(35 hours)
(35 hours)
Standards
2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.
2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
2.NBT.8 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
Overview
Students develop place value strategies to fluently add and subtract within 100 and develop conceptual understanding of addition and subtraction of multi-digit numbers within 1000. Students continue renaming place value units.
This unit is a combination of SECOND GRADE units. First graders may need additional scaffolding as they are only expected to master addition, subtraction, and comparison to 100. Second graders are expected to master it to 1000.
Unit Vocab
Algorithm (a step-by-step procedure to solve a particular type of problem)
Compose (e.g., to make 1 larger unit from 10 smaller units)
Decompose (e.g., to break 1 larger unit into 10 smaller units)
Equation (two expressions with an equal sign between them; that is, an equation is a statement that two expressions are equal; however, there is no guarantee that the statement is true)
New groups below (show newly composed units on the line below the appropriate place in the addition algorithm)
Simplifying strategy (e.g., to solve 299 + 6, think 299 + 1 + 5 = 300 + 5 = 305)
Topic A: Strategies for Composing A Ten *Standard Algorithm*
Topic A: Strategies for Composing A Ten *Standard Algorithm*
Standards
2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
Overview
Students apply their understanding of place value strategies to the addition algorithm, moving from horizontal to vertical notation.
Lessons
Lesson 6: Manipulatives Representing Composition of 10 Ones as 1 Ten
Lesson 7: Relate Addition Using Manipulatives to a Written Vertical Method
Lesson 8: Math Drawings Representing Composition and Relating Drawings to Written Method
Lesson 9: Math Drawings Representing Composition When Adding Two- and Three-Digit Addends
Lesson 10: Math Drawings Representing Composition When Adding Two- and Three-Digit Addends
Topic B: Strategies for Decomposing a Ten *Standard Algorithm*
Topic B: Strategies for Decomposing a Ten *Standard Algorithm*
Standards
2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
Overview
Students apply their understanding of place value strategies to the subtraction algorithm, moving from concrete to pictorial to abstract.
Lessons
Lesson 12: Relate Manipulative Representations to a Written Method
Lesson 13: Math Drawings Representing Subtraction With and Without Decomposition
Lesson 14: Represent Subtraction When There is a Three-Digit Minuend
Lesson 15: Represent Subtraction When There is a Three-Digit Minuend (Continued)
Lesson 16: Solve One- and Two-Step Problems Using Place Value Strategies
Topic C: Strategies Composing Tens and Hundreds within 200
Topic C: Strategies Composing Tens and Hundreds within 200
Standards
2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.
2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
2.NBT.8 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
Overview
Students extend the base ten understanding developed to numbers within 200. Students use place value disks on a place value chart to represent addition with the composition of 1 ten and 1 hundred. Students relate manipulatives to the vertical form, recording compositions as new groups below. Students move from concrete to pictorial as they use math drawings to represent compositions of 1 ten and 1 hundred. Students now have multiple strategies for composing and decomposing numbers, and they use properties of operations (i.e., the associative property) to add numbers in an order that is easiest to compute.
Lessons
Topic D: Strategies for Decomposing Tens and Hundreds within 200
Topic D: Strategies for Decomposing Tens and Hundreds within 200
Standards
2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
Overview
This topic begins with an extension of mental math strategies learned in first grade, when students learned to subtract from the ten by using number bonds. They return to this strategy to break apart three-digit minuends and subtract from the hundred. Students use place value disks on a place value chart to represent subtraction and develop an understanding of decomposition of tens and hundreds. Students move toward the abstract when they model decompositions on their place value charts while simultaneously recording the changes in the vertical form.
Lessons
Lesson 24: Manipulatives With Decompositions: 1 Hundred as 10 Tens
Lesson 25: Relate Manipulative Representations to a Written Method
Lesson 26: Math Drawings Representing Subtraction With Up to Two Decompositions
Lesson 27: Subtract From 200, From Numbers With Zeros in Tens Place
Lesson 28: Subtract From 200, From Numbers With Zeros in Tens Place (Continued)
Topic E: Strategies for Adding and Subtracting within 1000
Topic E: Strategies for Adding and Subtracting within 1000
Standards
2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
2.NBT.8 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
Overview
Students practice the simplifying strategies they learned with numbers up to 1,000. They will be asked to consider which strategy is most efficient for each problem they encounter. Students relate 100 more, 100 less, 10 more, and 10 less to addition and subtraction. In Lesson 2, students add and subtract multiples of 100 by counting on by hundreds. Students continue to add and subtract multiples of 100 with the added complexity of some tens. Lesson 3 focuses on addition, while Lesson 4 emphasizes related strategies for subtraction. Students apply the use of number bonds to decompose larger numbers, just as they did with numbers within 100. The ease of subtracting a multiple of 100 is highlighted again, as students extend their work. This topic provides students the opportunity to solidify their new skills. They confront a variety of problems, solve them, and then share their solution strategies. Through spirited discussion, students critique the work of their peers while deepening their understanding of various strategies.
Lessons
Lesson 1: Relate 10/100 More and 10/00 Less to Addition and Subtraction.
Lesson 2: Add and Subtract Multiples of 100, Counting On to Subtract
Lesson 4: Subtract Multiples of 100 and Some Tens Within 1,000
Lesson 5: Associative Property to Make a Hundred In One Addend
Lesson 6: Associative Property: Subtract From Three-Digit Numbers, Verify With Addition
Lesson 7: Strategies For Varied Addition and Subtraction Problems Within 1,000
Topic F: Strategies for Composing Tens and Hundreds within 1000
Topic F: Strategies for Composing Tens and Hundreds within 1000
Standards
2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
Overview
Students employ concrete and pictorial representations of the vertical algorithm when they encounter addition problems for which they do not have an obvious simplifying strategy.
Lessons
Lesson 8: Relate Manipulative Representations to the Addition Algorithm
Lesson 9: Relate Manipulative Representations to the Addition Algorithm (Continued)
Lesson 10: Math Drawings Representing Additions and Relating Drawings to Addition Algorithm
Lesson 12: Choose and Explain Solution Strategies, Record With Written Method
Topic G: Strategies for Decomposing Tens and Hundreds within 1000
Topic G: Strategies for Decomposing Tens and Hundreds within 1000
Standards
2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
Overview
Students model decompositions with place value disks on their place value charts while simultaneously recording these changes in the vertical form. Students transition into creating math drawings, thus completing the move from concrete to pictorial representations. This topic also focuses on the special case of subtracting from multiples of 100 and numbers with zero in the tens place. Students work with three-digit subtraction problems, applying multiple strategies to solve. As students apply alternate methods, the emphasis is placed on students explaining and critiquing various strategies.
Lessons
Lesson 13: Relate Manipulative Representation to the Subtraction Algorithm
Lesson 14: Math Drawings Representing Subtraction With Up to Two Decompositions
Lesson 15: Math Drawings Representing Subtraction With Up to Two Decompositions (Continued)
Lesson 18: Alternate Methods for Subtracting From Multiples of 100
Module 5: Foundations of Multiplication and Division
Module 5: Foundations of Multiplication and Division
(13 hours)
(13 hours)
Standards
2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
Overview
Students develop place value strategies to fluently add and subtract within 100 and develop conceptual understanding of addition and subtraction of multi-digit numbers within 1000. Students continue renaming place value units.
This unit is a combination of SECOND GRADE units. Neither first or second graders are expected to master multiplication or division - nor should the symbols be introduced . First graders will benefit from this unit as repeated addition and subtraction. Second graders will benefit from the conceptual understanding of arrays and equal groups.
Unit Vocab
Array (an arrangement of objects in rows and columns)
Columns (the vertical groups in a rectangular array) Even number (a whole number whose last digit is 0, 2, 4, 6, or 8)
Odd number (any number that is not even)
Repeated addition (e.g., 2 + 2 + 2) Rows (the horizontal groups in a rectangular array)
Tessellation (tiling of a plane using one or more geometric shapes with no overlaps and no gaps)
Whole number (e.g., 0, 1, 2, 3…)
Topic A: Formation of Equal Groups
Topic A: Formation of Equal Groups
Standards
2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
Overview
Topic A covers the concrete level as students use objects to create equal groups, providing a foundation for the construction of arrays in Topic B.
Lessons
Lesson 2: Math Drawings Representing Equal Groups and Relating Repeated Addition
Lesson 3: Math Drawings Representing Equal Groups and Relating Repeated Addition (Continued)
Lesson 4: Represent Equal Groups and Relate to Repeated Addition
Topic B: Arrays and Equal Groups
Topic B: Arrays and Equal Groups
Standards
2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends
Overview
Topic B focuses on spatial relationships and structuring as students organize equal groups (from Topic A) into rectangular arrays. They build small arrays (up to 5 by 5) and use repeated addition of the number in each row or column (i.e., group) to find the total.
In Lesson 5, students compose arrays either one row or one column at a time and count to find the total using the scattered sets from Topic A. This is foundational to the spatial structuring students need to discern a row or column as a single entity, or unit, when working with tiled arrays without gaps and overlaps in Topic C. In Lesson 6, students decompose one array by both rows and columns. In Lesson 7, students move to the pictorial as they use math drawings to represent arrays and relate the drawings to repeated addition. In Lesson 8, students work with square tiles to create arrays with gaps, composing the arrays from parts to whole, either one row or one column at a time. In Lesson 9, students apply the work of Topic B to word problems involving repeated addition (shown below), interpreting array situations as either rows or columns and using the RDW process.
Lessons
Topic C: Rectangular Arrays as a Foundation for Multiplication and Division
Topic C: Rectangular Arrays as a Foundation for Multiplication and Division
Standards
2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
Overview
Topic C is designed to deepen students’ understanding of spatial structuring as they build and partition rectangles with rows and columns of same-size squares.
In Lessons 10 and 11, students compose a rectangle by making tile arrays with no gaps or overlaps. Lesson 12 introduces the added complexity of composing a rectangle by using math drawings. After students compose rectangles, they decompose, or partition, them using tiles in Lesson 13. In Lesson 14, students are encouraged to think flexibly as they use paper models to further develop their ability to visualize arrays. Lesson 15 moves toward more abstract reasoning as students use math drawings to partition rectangles. In Lesson 16, students practice spatial structuring skills by working with grids and diagram
Lessons
Lesson 10: Square Tiles to Compose a Rectangle, Relate to Array Model
Lesson 11: Square Tiles to Compose a Rectangle, Relate to Array Model (Continued)
Lesson 12: Use Math Drawings to Compose A Rectangle With Square Tiles
Lesson 14: Partition A Rectangle Into Same-Size Squares, Compose Arrays With Squares
Lesson 15: Partition A Rectangle With Square Tiles, Relate to Repeated Addition
Lesson 16: Use Grid Paper to Create Designs to Develop Spatial Structuring
Module 6: Time, Shapes, and Fractions as Equal Parts
Module 6: Time, Shapes, and Fractions as Equal Parts
(13 hours)
(13 hours)
Standards
2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. (Sizes are compared directly or visually, not compared by measuring.)
2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Overview
The final module of the year, students extend their understanding of part–whole relationships through the lens of geometry. As students compose and decompose shapes, they begin to develop an understanding of unit fractions as equal parts of a whole.
This unit is a combination of SECOND GRADE units. Neither first or second graders are expected to master multiplication or division - nor should the symbols be introduced . First graders will benefit from this unit as repeated addition and subtraction. Second graders will benefit from the conceptual understanding of arrays and equal groups.
Unit Vocab
a.m./p.m.
Analog clock Angle (e.g., a figure formed by the corner of a polygon)
Parallel (used to describe opposite sides of a parallelogram, e.g., “These sides are parallel because if they kept on going, they’d never intersect!”) Parallelogram (a quadrilateral with both pairs of opposite sides parallel)
Partition (used in reference to partitioning rectangles, e.g. "Let's partition this rectangle to make an array" or "Let's partition this tape to show the money that was spent and the money that was left. Which part will be longer?")
Pentagon (a two-dimensional figure enclosed by five straight sides and five angles)
Polygon (a closed figure with three or more straight sides, e.g., triangle, quadrilateral, pentagon, hexagon)
Quadrilateral (a four-sided polygon, e.g., square, rhombus, rectangle, parallelogram, trapezoid)
Quarter past, quarter to Right angle (e.g., a square corner)
Third of (shapes), thirds (three equal shares)
Whole (used in reference to fractions, e.g., 2 halves make 1 whole, and 3 thirds make 1 whole)
Topic A: Composite Shapes and Fractions Concepts
Topic A: Composite Shapes and Fractions Concepts
Standards
2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Overview
Students build and partition composite shapes, exploring fraction concepts as they identify the relationships between parts and wholes. Students see that the tangram puzzle is composed of many smaller two-dimensional shapes. Students interpret equal shares within composite shapes. In Lesson 8, students continue to use pattern blocks to build composite shapes from equal parts.
Lessons
Lesson 6: Combine Shapes to Create a Composite Shape and New Shapes
Lesson 7: Interpret Equal Shares In Composite Shapes As Halves, Thirds, Fourths
Lesson 8: Interpret Equal Shares In Composite Shapes As Halves, Thirds, Fourths (Continued)
Topic B: Halves, Thirds, and Fourths of Circles and Rectangles
Topic B: Halves, Thirds, and Fourths of Circles and Rectangles
Standards
2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Overview
This topic focuses on partitioning circles and rectangles into equal fractional parts. Students are first introduced to partitioning shapes into two equal shares, or halves, using both circles and rectangles. Lesson 10 continues the same process with fourths and thirds. Students build upon their new knowledge by assembling a whole out of fractional parts. Given a circle made of two parts, students will see that the whole circle is composed of 2 halves. Students learn that equal parts of a rectangle can have different shapes. This topic provides a foundation for the next topic applying what students have learned about fractional parts of a circle, particularly halves and quarters, to telling time on an analog clock.
Lessons
Topic C: Application of Fractions to Tell Time
Topic C: Application of Fractions to Tell Time
Standards
2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Overview
Students apply fraction and skip-counting skills to telling time. The topic starts in which students make paper clocks from templates. Students start to relate each of the 12 numbers on the clock face with intervals of 5 minutes with the complexity of a.m. and p.m. Students apply their subtraction skills to solve problems involving time intervals.
Lessons
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