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 & See Illustrative Mathematics' guidance
Operations and Algebraic Thinking
OA.B Gains familiarity with factors and multiples
OA.B: Learning Goals and IM Assessments
Determine if a number is prime or composite.
Explain what it means to be a factor or a multiple of a whole number.
Relate the side lengths and area of a rectangle to factors and multiples
Apply multiplication fluency within 100 and the relationship between multiplication and division to find factor pairs and multiples.
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)
Five in a Row: Multiplication & Division (Stages 1, 2)
Find the Number (Stages 1, 2)
Can You Build It? (Stages 1, 2)
Capture Squares (Stage 7)
Number Line Scoot (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.4
Factors and multiples/prime and composite:
Numbers and Operations - Fractions
NF.A Extends understanding of fraction equivalence and ordering
NF.A: Learning Goals and IM Assessments
Make sense of fractions with denominators 2, 3, 4, 5, 6, 8, 10, and 12 through physical representations and diagrams.
Reason about the location of fractions on the number line.
Generate equivalent fractions with the following denominators: 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Use visual representations to reason about fraction equivalence, including using benchmarks such as 1/2 and 1.
Use visual representations or a numerical process to reason about fraction comparison.
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)
Get Your Numbers in Order (Stages 2, 3)
Mystery Number (Stages 3, 4)
How Close? (Stage 6)
Compare (Stages 3, 5)
Five in a Row: Multiplication & Division (Stages 1, 2, 3)
Number Line Scoot (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.
CAASPP Focused Interim Assessment Block: Grade 4 - Fraction Equivalence and Ordering
Interim Assessment Item Portal (pdf/print) or Test Administrator Interface (digital)
Numbers and Operations - Fractions
NF.B Builds fractions from unit fractions by applying/extending previous understandings of operations on whole numbers
NF.C Understands decimal notations for fractions, and compare decimal fractions
Measurement and Data
MD.B Represents and interprets data (involving line plots)
NF.B: Learning Goals and IM Assessments
Recognize that n*a/b=(n*a)/b.
Represent and explain that a fraction a/b is a multiple of 1/b, namely a*1/b.
Represent and solve problems involving multiplication of a fraction by a whole number.
Create and analyze line plots display measurement data in fractions of a unit (18,14,12).
Represent and solve problems that involve the addition and subtraction of fractions and mixed numbers, including measurements presented in line plots.
Use various strategies to add and subtract fractions and mixed numbers with like denominators.
Reason about equivalence to add tenths and hundredths.
Reason about equivalence to solve problems involving addition and subtraction of fractions and mixed numbers.
NF.C: Learning Goals and IM Assessments
Reason about equivalence to add tenths and hundredths.
Checkpoint: 4.3.C
MD.B: Learning Goals and IM Assessments
Create and analyze line plots that display measurement data in fractions of a unit (18,14,12).
Checkpoint 4.3.B
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)
Compare (Stages 3, 5, 6)
Jump the Line (Stage 2)
Rolling for Fractions (Stages 1, 2)
Estimate and Measure (Stage 3)
Target Measurement (Stages 2, 3)
Would You Rather (Stage 2)
Creating Line Plots (Stages 3, 4)
Number Line Scoot (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.
MD.B.4
NF.B.3
NF.B.4
NF.C.5
CAASPP Focused Interim Assessment Block: Grade 4 - Build Fractions from Unit Fractions
Interim Assessment Item Portal (pdf/print) or Test Administrator Interface (digital)
Numbers and Operations in Base Ten
NBT.A Generalizes place value understanding for multi-digit whole numbers
Numbers and Operations in Base Ten
NBT.B.4 Fluently* add and subtract multi-digit whole numbers using the standard algorithm.
Numbers and Operations - Fractions
NF.C Understands decimal notations for fractions, and compare decimal fractions
NBT.A: Learning Goals and IM Assessments
Read, represent, and describe the relative magnitude of multi-digit whole numbers up to 1 million.
Recognize that in a multi-digit whole number, the value of a digit in one place represents ten times what it represents in the place to its right.
Compare, order, and round multi-digit whole numbers within 1,000,000.
NBT.B.4: Learning Goals and IM Assessments
Add and subtract multi-digit whole numbers using the standard algorithm.
Checkpoint: 4.4.D
NF.C: Learning Goals and IM Assessments
Write tenths and hundredths in decimal notation.
Checkpoint: 4.4.A
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, adapt Unit 4.
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
Get Your Numbers in Order (Stage 4)
Greatest of Them All (Stages 2, 3)
Mystery Number (Stages 4, 5)
Tic Tac Round (Stage 1)
Number Puzzles: Addition & Subtraction (Stage 6)
Rolling for Fractions (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
NBT.A.3
NBT.B.4
Add multi-digit numbers using partial sums with decomposing one or both addends:
Subtract multi-digit numbers by decomposing the subtrahend and counting on or counting back:
Add and subtract multi-digit numbers by adjusting:
Add and subtract multi-digit numbers with the standard algorithm:
NF.C.6
Fraction, Decimal, and Percent (note: eliminate percent from prompts)
Fraction, Decimal, and Percent (note: eliminate percent from prompts)
NF.C.7
CAASPP Focused Interim Assessment Block: Grade 4 - Fractions and Decimal Notation
Interim Assessment Item Portal (pdf/print) or Test Administrator Interface (digital)
OR
CAASPP Focused Interim Assessment Block: Grade-4 Place Value and Multidigit Whole Numbers
Interim Assessment Item Portal (pdf/print) or Test Administrator Interface (digital)
Operations and Algebraic Thinking
OA.A Use the four operations with whole numbers to solve problems
Measurement and Data
MD.A Solves problems involving measurement and conversion of measurements
OA.A: Learning Goals and IM Assessments
Analyze, describe, and represent multiplicative comparison situations.
Solve one-step and two-step problems involving multiplicative comparison.
Checkpoint: 4.5.A,
Solve multi-step problems involving multiplicative comparison and measurement.
Checkpoint: 4.5.B
MD.A: Learning Goals and IM Assessments
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, adapt Unit 5.
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
How Close? (Stages 5, 6)
Compare (Stage 3)
Five in a Row: Multiplication & Division (Stage 2)
Rectangle Rumble (Stage 3)
Can You Draw It? (Stage 4)
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
OA.A.1
OA.A.2
Understand the difference between additive and multiplicative comparison, note: use as bridge between +/- from previous weeks to x/÷ in this and upcoming weeks):
Solve problems with multiplicative comparison:
Operations and Algebraic Thinking
OA.A Use the four operations with whole numbers to solve problems
Operations and Algebraic Thinking
OA.B Gains familiarity with factors and multiples
Operations and Algebraic Thinking
OA.C Generates and analyzes patterns
Numbers and Operations in Base Ten
NBT. B Uses place value understanding and properties of operations to perform multi-digit arithmetic
Measurement and Data
MD.A Solves problems involving measurement and conversion of measurements
OA.A: Learning Goals and IM Assessments
Multiply a whole number of up to four digits by a one-digit whole number, and 2 two-digit numbers using strategies based on place value and the properties of operations.
Divide numbers of up to four digits by one-digit divisors to find whole-number quotients and remainders, using strategies based on place value, properties of operations, and the relationship between multiplication and division.
Use the four operations to solve problems that involve multi-digit whole numbers and assess the reasonableness of answers.
OA.B: Learning Goals and IM Assessments
Divide numbers of up to four digits by one-digit divisors to find whole-number quotients and remainders, using strategies based on place value, properties of operations, and the relationship between multiplication and division.
Checkpoint: 4.6.C
OA.B: Learning Goals and IM Assessments
Generate a number or shape pattern that follows a given rule.
Identify apparent features of a number pattern that were not explicit in the rule itself.
NBT.B: Learning Goals and IM Assessments
Multiply a whole number of up to four digits by a one-digit whole number, and 2 two-digit numbers using strategies based on place value and the properties of operations.
Divide numbers of up to four digits by one-digit divisors to find whole-number quotients and remainders, using strategies based on place value, properties of operations, and the relationship between multiplication and division.
Use the four operations to solve problems that involve multi-digit whole numbers and assess the reasonableness of answers.
MD.A: Learning Goals and IM Assessments
Use the four operations to solve problems that involve multi-digit whole numbers and assess the reasonableness of answers.
Checkpoint: 4.6.D
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, adapt Unit 6.
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
Compare (Stages 3, 4, 7)
Five in a Row: Multiplication & Division (Stages 2, 3)
Number Puzzles: Multiplication & Division (Stage 1)
Rolling for Fractions (Stage 2)
Watch Your Remainder (Stage 1)
How Are They the Same? (Stage 4)
Can You Draw It? (Stage 4)
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.3
Represent and solve word problems that add/subtract multi-digit numbers:
Solve one-step multiplication/division problems with remainders; interpret remainders:
Multi-step word problems with addition/subtraction:
Multi-step word problems with all four operations and interpret remainders:
OA.B.5
NBT.B.5
Multiply 2-digit numbers by 1-digit numbers using representations and partial products:
NBT.B.6
MD.A.3
CAASPP Focused Interim Assessment Block: Grade 4 - Multidigit Arithmetic: Place Value and Operations
Interim Assessment Item Portal (pdf/print) or Test Administrator Interface (digital)
Or
CAASPP Focused Interim Assessment Block: Grade 4 - Four Operations: Interpret, Represent, and Solve
Interim Assessment Item Portal (pdf/print) or Test Administrator Interface (digital)
Measurement and Data
MD.C Geometric measurement: Understands concepts of angle and angle measurement
MD.C: Learning Goals and IM Assessments
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, adapt Unit 7.
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
Compare (Stages 5, 7)
Which One? (Stage 4)
Target Measurement (Stage 4)
Can You Draw It? (Stage 4)
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
MD.C.5
MD.C.6
MD.C.7
Geometry
G.A Draws and identifies lines and angles, and classifies shapes by properties of their lines and angles
G.A: Learning Goals and IM Assessments
Student can consistently draw and identify points, lines, line segments, rays, perpendicular lines, and parallel lines; draw and identify acute, obtuse, right, and straight angles; classify shapes by properties of their lines and angles; and recognize and draw lines of symmetry for two-dimensional figures.
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, adapt Unit 8.
Look for stages in bolded Red to target math fluency & number sense (good for Tier II Intervention)
Compare (Stages 5, 7)
Picture Books (Stage 3)
Which One? (Stages 4, 5)
How Are They the Same? (Stage 4)
Can You Draw It? (Stages 4, 5)
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.
Numbers and Operations - Fractions
NF.A Extends understanding of fraction equivalence and ordering
NF.B Builds fractions from unit fractions by applying/extending previous understandings of operations on whole numbers
NF.C Understands decimal notations for fractions, and compare decimal fractions
Numbers and Operations in Base Ten
NBT.B Uses place value understanding and properties of operations to perform multi-digit arithmetic
NBT.B.4 Fluently* add and subtract multi-digit whole numbers using the standard algorithm.
Operations and Algebraic Thinking
OA.A Use the four operations with whole numbers to solve problems
Learning Goals and IM Assessments
Student can solve problems involving fraction equivalence and operating with fractions.
Student can add, subtract, multiply, and divide multi-digit numbers using place value understanding.
Student can solve problems involving measurement comparison.
As Needed, Choose Any of the Centers from Previous Units
For Lesson 1, Lesson 2, and Lesson 3: Practice Problems (Unit 3 Section B)
For Lesson 4: Practice Problems (Unit 4 Section D)
For Lesson 5: Practice Problems (Unit 6 Section B)
For Lesson 6: Practice Problems (Unit 6 Section C)
For Lesson 7: Practice Problems (Unit 5 Section A) and Practice Problems (Unit 5 Section C)
For Lesson 8 and Lesson 9: Practice Problems (Unit 6 Section D)
For Lesson 1, Lesson 2, and Lesson 3, look to Unit 3 Section B: Addition and Subtraction of Fractions
For Lesson 4, look to Unit 4 Section D: Add and Subtract
For Lesson 5, look to Unit 6 Section B: Multi-digit Multiplication
For Lesson 6, look to Unit 6 Section C: Multi-digit Division
For Lesson 7, look to Unit 5 Section A: Multiplicative Comparison and Unit 5 Section C: Let’s Put it to Work
For Lesson 8 and Lesson 9, look to Unit 6 Section D: Let’s Put It to Work: Problem Solving with Large Numbers