Read the stories of the mathematics of each course of IM K–5 Math, detailed by authors of the curriculum. These stories convey the coherent structure of grade-level content, how concepts are developed for students, and the deliberate choice of tools and representations used in each grade, from kindergarten through grade 5.
Why these? Student Achievement Partners' instructional considerations
Operations and Algebraic Thinking
OA.A Represents and solves problems involving addition and subtraction (within 100)
OA.B.2 Fluently* add and subtract within 20 using mental strategies
OA.B.2 Know from memory all sums of two one-digit numbers
Measurement and Data
MD.D Represents and interprets data
*Computing Fluently: Student flexibly, efficiently, and accurately computes using 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).
OA.A: Learning Goals and IM Assessments
Build toward fluency with adding within 100. Build toward fluency with subtracting within 20.
Checkpoint 2.1.A, 2.1 End of Unit
Solve one- and two-step problems using addition and subtraction within 20.
Checkpoint 2.1.B, 2.1 End of Unit
Represent and solve Compare problems with unknowns in all positions within 100.
Checkpoint 2.1.C; 2.1 End of Unit
OA.B.2: Learning Goals and IM Assessments
Build toward fluency with adding within 100. Build toward fluency with subtracting within 20.
Checkpoint 2.1.A, 2.1 End of Unit
Solve one- and two-step problems using addition and subtraction within 20.
Checkpoint 2.1.B, 2.1 End of Unit
MD.D: Learning Goals and IM Assessments
Interpret picture and bar graphs. Represent data using picture and bar graphs.
Checkpoint 2.1.B, 2.1 End of Unit
Make sense of and interpret tape diagrams.
Checkpoint 2.1.C; 2.1 End of Unit
Represent numerical data on a line plot.
Checkpoint 2.3.C
Do so by giving your students the Unit 1 Pre-unit problems
Did the Pre-unit problems reveal a need to address unfinished learning? If yes, adapt Unit 1.
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
What's Behind my Back? (Stages 2, 3)
Shake and Spill (Stage 5)
How Close? (Stages 1, 2, 3)
Number Puzzles: Addition and Subtraction (Stages 1, 2)
Sort and Display (Stages 1, 2)
Counting Collections (Stage 3)
These resource sheets adapted from Howard County Public Schools and commoncoresheets.com can be used for independent practice or homework. They are intended to reinforce procedures and concepts.
They should not be used as a source of direct instruction or whole-group practice.
OA.B.2
MD.D.10
Operations and Algebraic Thinking
OA.A Represents and solves problems involving addition and subtraction (within 100)
Numbers and Operations in Base Ten
NBT.B Uses place value understanding and properties of operations to add and subtract
NBT.B.5 Fluently* add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.
*Computing Fluently: Student flexibly, efficiently, and accurately computes using strategies based on place value, properties of operations, and the relationship between addition and subtraction. Some examples include: Place value understand for computing 48 + 37: “l Adding by place value: 40 + 30 = 70, 8 + 7 = 15, and 70 + 15 = 85”; Composing and decomposing (making a “friendly” number) for computing 48 + 37: 48 + 2 = 50, 37 – 2 = 35, and 50 + 35 = 85; Relationship strategy for computing 81 – 37: “l added up (from smaller number to larger number): 37 + 3 = 40, 40 + 40 = 80, 80 + 1 = 81, and 3 + 40 + 1 = 44”
OA.A: Learning Goals and IM Assessments
Represent and solve one- and two-step problems involving addition and subtraction within 100, including different problem types with unknowns in all positions.
Checkpoint 2.2.C; 2.2 End of Unit
NBT.B: Learning Goals and IM Assessments
Add and subtract within 100 using strategies based on place value and the relationship between addition and subtraction. Problems in this section are limited to the problems like 65 – 23, where decomposing a ten is not required.
Checkpoint 2.2.A; 2.2 End of Unit
Subtract within 100 using strategies based on place value, including decomposing a ten, and the properties of operations.
Checkpoint 2.2.B; 2.2 End of Unit
Represent and solve one- and two-step problems involving addition and subtraction within 100, including different problem types with unknowns in all positions.
Checkpoint 2.2.C; 2.2 End of Unit
NBT.B.5: Learning Goals and IM Assessments
Do so by giving your students the Unit 2 Pre-unit problems
Did the Pre-unit problems reveal a need to address unfinished learning? If yes, adapt Unit 2.
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
Math Stories (Stages 4, 5)
Capture Squares (Stages 1, 2, 3, 4)
Target Numbers (Stages 4, 5)
Five in a Row: Addition and Subtraction (Stages 5, 6)
These resource sheets adapted from Howard County Public Schools and commoncoresheets.com can be used for independent practice or homework. They are intended to reinforce procedures and concepts.
They should not be used as a source of direct instruction or whole-group practice.
OA.A.1
Solve one-step result unknown word problems:
Solve one-step change unknown word problems:
NBT.B.5
Operations and Algebraic Thinking
OA.A Represents and solves problems involving addition and subtraction (within 100)
Numbers and Operations in Base Ten
NBT.A Understand place value
NBT.B Uses place value understanding and properties of operations to add and subtract
NBT.B.5 Fluently* add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.
Measurement and Data
MD.A Measures and estimates length in standard units
MD.B Relates addition and subtraction to length
*Computing Fluently: Student flexibly, efficiently, and accurately computes using strategies based on place value, properties of operations, and the relationship between addition and subtraction. Some examples include: Place value understand for computing 48 + 37: “l Adding by place value: 40 + 30 = 70, 8 + 7 = 15, and 70 + 15 = 85”; Composing and decomposing (making a “friendly” number) for computing 48 + 37: 48 + 2 = 50, 37 – 2 = 35, and 50 + 35 = 85; Relationship strategy for computing 81 – 37: “l added up (from smaller number to larger number): 37 + 3 = 40, 40 + 40 = 80, 80 + 1 = 81, and 3 + 40 + 1 = 44”
OA.A: Learning Goals and IM Assessments
Represent and solve one-step story problems within 100.
Checkpoint 2.3.A, 2.3.B; 2.3 End of Unit
NBT.A: Learning Goals and IM Assessments
NBT.B: Learning Goals and IM Assessments
Represent and solve one-step story problems within 100.
Checkpoint 2.3.A
Represent and solve one- and two-step story problems within 100.
Checkpoint 2.3.B
MD.A Measures and estimates length in standard units
Measure length in centimeters and meters.
Checkpoint 2.3.A, 2.3 End of Unit
Measure length in feet and inches.
Checkpoint 2.3.B, 2.3 End of Unit
Represent numerical data on a line plot.
Checkpoint 2.3.C; 2.3 End of Unit
MD.B Relates addition and subtraction to length
Represent and solve one-step story problems within 100.
Checkpoint 2.3.A, 2.3.B, 2.3 End of Unit
Do so by giving your students the Unit 3 Pre-unit problems
Did the Pre-unit problems reveal a need to address unfinished learning? If yes, adapt Unit 3.
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
Math Stories (Stage 5)
Capture Squares (Stage 4)
Target Numbers (Stage 5)
Five in a Row: Addition and Subtraction (Stage 6)
Number Puzzles: Addition and Subtraction (Stages 2, 3, 4)
Estimate and Measure (Stages 1, 2)
Target Measurements (Stage 1)
Creating Line Plots (Stage 1)
These resource sheets adapted from Howard County Public Schools and commoncoresheets.com can be used for independent practice or homework. They are intended to reinforce procedures and concepts.
They should not be used as a source of direct instruction or whole-group practice.
MD.A.1
MD.A.2
MD.A.3
MD.A.4
MD.B.5
MD.D.9
NBT.B.5
Operations and Algebraic Thinking
OA.A Represents and solves problems involving addition and subtraction (within 100)
OA.B.2 Fluently* Add and Subtract within 20 using mental strategies
OA.B.2 Know from memory all sums of two one-digit numbers
Numbers and Operations in Base Ten
NBT.B Uses place value understanding and properties of operations to add and subtract
*Computing Fluently: Student flexibly, efficiently, and accurately computes using 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).
OA.A: Learning Goals and IM Assessments
Represent sums and differences on a number line.
Checkpoint 2.4.B; 2.4 End of Unit
By the end of Trimester 2, Grade 2 student knows from memory foundational addition fact sets: +/- 0, 1, 2; Doubles; Combos of 10; 10 + __.
To continue fully developing mastery of addition facts by the end of Trimester 3, Grade 2 student uses reasoning strategies and the foundational addition fact sets listed above to derive unknown facts. For example, Near Doubles (e.g., 7+8 is 15 because I know 7+7 is 14 and this is 7+8 is 1 more); Making 10 (e.g., 9+4 is 13 because I took 1 from the 4 to make a 10) Pretending-a-10 (e.g., 9+4 → I’ll pretend the 9 is a 10 because I know 10+4 is 14, so 9+4 is 13)
NBT.B: Learning Goals and IM Assessments
Represent sums and differences on a number line.
Checkpoint 2.4.B; 2.4 End of Unit
Do so by giving your students the Unit 4 Pre-unit problems
Did the Pre-unit problems reveal a need to address unfinished learning?
If yes, continue targeted Centers and Practice Problems from Grade 2 Unit 3 because Grade 2 Unit 4 builds exclusively from Grade 2 Unit 3 (see K-5 Dependency Chart)
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
Number Line Scoot (Stage 1)
Capture Squares (Stages 3, 4)
How Close? (Stage 3)
Five in a Row: Addition and Subtraction (Stage 6)
Number Puzzles: Addition and Subtraction (Stage 4)
Jump the Line (Stage 1)
These resource sheets adapted from Howard County Public Schools and commoncoresheets.com can be used for independent practice or homework. They are intended to reinforce procedures and concepts.
They should not be used as a source of direct instruction or whole-group practice.
MD.B.6
NBT.B.5
Numbers and Operations in Base Ten
NBT.A Understand place value
Measurement and Data
MD.B Relates addition and subtraction to length
NBT.A: Learning Goals and IM Assessments
Read, write, and represent three-digit numbers using base-ten numerals and expanded form. Use place value understanding to compose and decompose three-digit numbers.
Checkpoint 2.5.A; 2.5 End of Unit
Compare and order three-digit numbers using place value understanding and the relative position of numbers on a number line.
Checkpoint 2.5.B; 2.5 End of Unit
MD.B: Learning Goals and IM Assessments
Represent whole numbers up to 1,000 as lengths from 0 on a number line.
Checkpoint 2.5.B
Do so by giving your students the Unit 5 Pre-unit problems
Did the Pre-unit problems reveal a need to address unfinished learning?
If yes, continue targeted Centers and Practice Problems from Grade 2 Unit 4, because Grade 2 Unit 5 builds from Grade 2 Units 2, 3, 4.
If additional support is needed, do Centers and Practice Problems from Grade 1 Unit 4 (see K-5 Dependency Chart)
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
Get Your Numbers in Order (Stages 1, 2)
Greatest of them All (Stages 1, 2)
Mystery Number (Stages 1, 2)
Number Puzzles: Addition and Subtraction (Stages 2, 3, 4)
Jump the Line (Stage 1)
These resource sheets adapted from Howard County Public Schools and commoncoresheets.com can be used for independent practice or homework. They are intended to reinforce procedures and concepts.
They should not be used as a source of direct instruction or whole-group practice.
NBT.A.1
NBT.A.2
Skip count by 5s, 10s, 100s starting at any number:
Skip count by 2s, 5s, 10s, and 100s:
NBT.A.3
NBT.A.4
Operations and Algebraic Thinking
OA.A Represents and solves problems involving addition and subtraction (within 100)
Numbers and Operations in Base Ten
NBT.B: Uses place value understanding and properties of operations to add and subtract
Measurement and Data
MD.C Work with time and money
Geometry
G.A Reason with shapes and their attributes
Examples of shapes: triangles, quadrilaterals, pentagons, hexagons, cubes
Examples of attributes: number of angles, number of faces, number of sides
OA.A: Learning Goals and IM Assessments
Use addition and subtraction within 100 to solve one- and two-step word problems.
Checkpoint 2.6.D; 2.6 End of Unit
NBT.B: Learning Goals and IM Assessments
Use addition and subtraction within 100 to solve one- and two-step word problems.
Checkpoint 2.6.D
MD.C: Learning Goals and IM Assessments
Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
Checkpoint 2.6.C; 2.6 End of Unit
Find the value of a group of bills and coins.
Checkpoint 2.6.D; 2.6 End of Unit
G.A: Learning Goals and IM Assessments
Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.
Checkpoint 2.6.A, 2.6 End of Unit
Partition rectangles and circles into halves, thirds, and fourths and name the pieces. Recognize 2 halves, 3 thirds, and 4 fourths as one whole. Understand that equal pieces do not need to be the same shape.
Checkpoint 2.6.B, 2.6 End of Unit
Do so by giving your students the Unit 6 Pre-unit problems
Did the Pre-unit problems reveal a need to address unfinished learning?
If yes, continue targeted Centers and Practice Problems from Grade 2 Unit 2 because Grade 2 Unit 6 builds from Grade 2 Unit 2.
If additional support is needed, do Centers and Practice Problems from Grade 1 Unit 7 and Kindergarten Unit 3 (see K-5 Dependency Chart)
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
Capture Squares (Stages 3, 4)
Number Puzzles: Addition and Subtraction (Stages 2, 3, 4)
Which One? (Stages 2, 3)
Picture Books (Stage 3)
How are They the Same? (Stage 2)
Can You Draw it? (Stages 1, 2)
Would You Rather? (Stage 1)
These resource sheets adapted from Howard County Public Schools and commoncoresheets.com can be used for independent practice or homework. They are intended to reinforce procedures and concepts.
They should not be used as a source of direct instruction or whole-group practice.
G.A.1
G.A.3
MD.C.7
MD.C.8
NBT.B.6
Numbers and Operations in Base Ten
NBT.B Uses place value understanding and properties of operations to add and subtract
NBT.B: Learning Goals and IM Assessments
Student can consistently use multiple strategies to efficiently and accurately add up to 4 two-digit numbers and and add and subtract with and without regrouping within 1,000.
Do so by giving your students the Unit 7 Pre-unit problems
Did the Pre-unit problems reveal a need to address unfinished learning?
If yes, continue targeted Centers and Practice Problems from Grade 2 Unit 5 because Grade 2 Unit 7 builds from Grade 2 Unit 5 (see K-5 Dependency Chart).
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
Get Your Numbers in Order (Stage 2)
Greatest of them All (Stage 2)
Number Line Scoot (Stage 1)
Mystery Number (Stage 2)
Target Numbers (Stages 5, 6, 7)
How Close? (Stages 3, 4)
Five in a Row: Addition and Subtraction (Stages 6, 7, 8)
Number Puzzles: Addition and Subtraction (Stage 4)
Jump the Line (Stage 1)
These resource sheets adapted from Howard County Public Schools and commoncoresheets.com can be used for independent practice or homework. They are intended to reinforce procedures and concepts.
They should not be used as a source of direct instruction or whole-group practice.
Operations and Algebraic Thinking
OA.B.2 Fluently* Add and Subtract within 20 using mental strategies
OA.C Work with equal groups of objects to gain foundations for multiplication.
OA.B.2: Learning Goals and IM Assessments
With consistency, student fluently adds and subtracts within 20 with flexibility, accuracy, and efficiency:
Student flexibly uses strategies* (e.g., counting on, making ten, decomposing a number into a ten, relating addition to subtraction, using already known addition facts) to add and subtract within 20.
With flexible strategy use, student accurately and efficiently computes within 20.
Checkpoints 2.8.A, 2.8.B; 2.8 End of Unit; Grade 2 End of Course Assessment
OA.C: Learning Goals and IM Assessments
Student can consistently determine whether a group of objects (up to 20) has an odd or even number of members and create a visual representation to model repeated addition (with up to 5 rows and columns).
Do so by giving your students the Unit 8 Pre-unit problems
Did the Pre-unit problems reveal a need to address unfinished learning?
If yes, continue targeted Centers and Practice Problems from Grade 2 Unit 6 because Grade 2 Unit 8 builds from Grade 2 Unit 6 (see K-5 Dependency Chart).
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
Write Numbers (Stage 4)
Target Numbers (Stages 6, 7)
How Close? (Stage 4)
Five in a Row: Addition and Subtraction (Stages 7, 8)
These resource sheets adapted from Howard County Public Schools and commoncoresheets.com can be used for independent practice or homework. They are intended to reinforce procedures and concepts.
They should not be used as a source of direct instruction or whole-group practice.
G.A.2
OA.B.2
OA.C.3
OA.C.4
Learning Goals and IM Assessments
Fluently add and subtract within 20.
Add and subtract within 1,000 using strategies based on place value and the properties of operations.
Fluently add and subtract within 100.
Represent and solve one- and two-step story problems within 100.
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
Target Numbers (Stages 4, 5, 6)
Five in a Row: Addition and Subtraction (Stage 6)
For Lesson 1 and Lesson 2: Practice Problems (Unit 1 Section A)
For Lesson 3: Practice Problems (Unit 3 Section A)
For Lesson 4: Practice Problems (Unit 3 Section C)
For Lesson 5 and Lesson 6: Practice Problems (Unit 5 Section A)
For Lesson 7 and Lesson 8: Practice Problems (Unit 7 Section B); Practice Problems (Unit 7 Section C)
For Lesson 10: Practice Problems (Unit 1 Section B)
For Lesson 11: Practice Problems (Unit 1 Section C)
Lesson 12, and Lesson 13: Practice Problems (Unit 2 Section C)
For Lesson 1 and Lesson 2, look to Unit 1 Section A: Add and Subtract Within 20
For Lesson 3 and Lesson 4, look to Unit 3 Section A: Metric Measurement
For Lesson 4, look to Unit 3 Section C: Line Plots
For Lesson 5 and Lesson 6, look to Unit 5 Section A: The Value of Three Digits
For Lesson 7 and Lesson 8, look to Unit 7 Section B: Add within 1,000 using Place Value Strategies; Unit 7 Section C: Subtract within 1,000 using Place Value Strategies
For Lesson 5 and Lesson 6, look to Unit 5 Section A: The Value of Three Digits
For Lesson 7 and Lesson 8, look to Unit 7 Section B: Add within 1,000 using Place Value Strategies; Unit 7 Section C: Subtract within 1,000 using Place Value Strategies