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Grade 2 Mathematics.

10textbooks

250lessons

106competencies

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The whole year, lesson by lesson.

Textbook 1Numbers to 200 and the First Hundred

4 chapters · 25 lessons

Chapter 1

Reviewing Tens and Ones to 100

Chapter 2

Building One Hundred

Chapter 3

Numbers from 101 to 150

Chapter 4

Numbers from 151 to 200

Textbook 2Numbers to 1,000 and Place Value

4 chapters · 25 lessons

Chapter 1

Counting by Hundreds to 1,000

Chapter 2

Hundreds, Tens, and Ones to 1,000

Chapter 3

Comparing and Ordering Three-Digit Numbers

Chapter 4

Skip-Counting and Estimating within 1,000

Textbook 3Addition with Regrouping

4 chapters · 25 lessons

Chapter 1

Adding Two-Digit Numbers without Regrouping

Chapter 2

Regrouping Ones into a Ten

Chapter 3

Adding Three-Digit Numbers

Chapter 4

Addition Situations and Strategy Choice

Textbook 4Subtraction with Regrouping

4 chapters · 25 lessons

Chapter 1

Subtracting Two-Digit Numbers without Regrouping

Chapter 2

Regrouping One Ten into Ten Ones

Chapter 3

Subtracting Three-Digit Numbers

Chapter 4

Subtraction Situations and Difference

Textbook 5Addition, Subtraction, Unknowns, and One-Step Problems

4 chapters · 25 lessons

Chapter 1

Missing Addends

Chapter 2

Missing Parts in Subtraction

Chapter 3

Choosing Addition or Subtraction

Chapter 4

Reasonableness, Estimation, and Error Analysis

Textbook 6Equal Groups, Repeated Addition, Arrays, and Multiplication

4 chapters · 25 lessons

Chapter 1

Equal Groups

Chapter 2

Repeated Addition and Multiplication Sentences

Chapter 3

Arrays and Skip-Counting

Chapter 4

Conceptual Multiplication Problems

Textbook 7Skip-Counting, Growing Patterns, and Missing Numbers

4 chapters · 25 lessons

Chapter 1

Skip-Counting Patterns

Chapter 2

Growing Visual Patterns

Chapter 3

Missing Numbers in Addition and Subtraction Equations

Chapter 4

Patterns and Unknowns in Everyday Situations

Textbook 8Shape Attributes, Equal Parts, and Symmetry

4 chapters · 25 lessons

Chapter 1

Attributes of Two-Dimensional Shapes

Chapter 2

Attributes of Three-Dimensional Shapes

Chapter 3

Equal Parts of Shapes

Chapter 4

Introductory Line Symmetry

Textbook 9Standard Length, Mass, Capacity, and Time

4 chapters · 25 lessons

Chapter 1

Measuring in Centimeters

Chapter 2

Measuring in Meters

Chapter 3

Introductory Mass and Capacity

Chapter 4

Time to Five Minutes and Daily Schedules

Textbook 10Bar Graphs, Pictographs, Money, Change, and Everyday Modeling

4 chapters · 25 lessons

Chapter 1

Collecting Data and Constructing Pictographs

Chapter 2

Bar Graphs and Data Questions

Chapter 3

Money Amounts, Simple Purchases, Change, and Saving Totals

Chapter 4

Grade 2 Everyday Mathematical Modeling

Every coin is a 15-minute lesson.

Explained simply, shown with pictures, then put to the test. Stars are chapter reviews. The trophy is the final review.

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Every competency, covered.

The 106 competencies set for Grade 2 Mathematics, and every one has lessons behind it.

Numbers to 200 and the First Hundred

22 competencies

Count forward and backward within 1,000 from a given number.
Read and write numerals from 0 to 1,000.
Match numerals, spoken number names, quantities, and place-value representations within 1,000.
Represent a three-digit number as hundreds, tens, and ones.
Explain the value of each digit in a three-digit number.
Compose and decompose three-digit numbers in standard and nonstandard ways.
Regroup ten ones as one ten and one ten as ten ones.
Regroup ten tens as one hundred and one hundred as ten tens.
Write a number in standard, expanded, word, and pictorial forms.
Compare three-digit numbers using place value.
Use greater-than, less-than, and equal-to symbols accurately.
Order three or more numbers within 1,000.
Identify numbers immediately before and after a given number.
Identify the nearest lower and higher multiple of ten or hundred in supported contexts.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Numbers to 1,000 and Place Value

26 competencies

Count forward and backward within 1,000 from a given number.
Read and write numerals from 0 to 1,000.
Match numerals, spoken number names, quantities, and place-value representations within 1,000.
Represent a three-digit number as hundreds, tens, and ones.
Explain the value of each digit in a three-digit number.
Compose and decompose three-digit numbers in standard and nonstandard ways.
Regroup ten ones as one ten and one ten as ten ones.
Regroup ten tens as one hundred and one hundred as ten tens.
Write a number in standard, expanded, word, and pictorial forms.
Compare three-digit numbers using place value.
Use greater-than, less-than, and equal-to symbols accurately.
Order three or more numbers within 1,000.
Identify numbers immediately before and after a given number.
Identify the nearest lower and higher multiple of ten or hundred in supported contexts.
Estimate a quantity or result using nearby tens or hundreds.
Extend number patterns based on adding or subtracting a fixed amount.
Skip-count forward and backward by 2s, 5s, 10s, and 100s in supported ranges.
Describe a pattern rule using words.
Identify and correct a term that does not follow a pattern rule.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Addition with Regrouping

25 competencies

Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Revise an incorrect model by changing the operation, quantities, labels, or representation.
Create a one-step everyday story matching a supplied number sentence.
Regroup ten ones as one ten and one ten as ten ones.
Regroup ten tens as one hundred and one hundred as ten tens.
Add two-digit numbers without regrouping.
Add two-digit numbers with regrouping from ones to tens.
Add three-digit numbers without regrouping.
Add three-digit numbers with regrouping across one place.
Explain regrouping in addition using place-value models.
Use addition to check subtraction and subtraction to check addition.
Select an efficient mental, pictorial, or written strategy for an addition or subtraction calculation.
Identify what is known, what is changing or being compared, and what must be found in a one-step problem.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Subtraction with Regrouping

25 competencies

Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Revise an incorrect model by changing the operation, quantities, labels, or representation.
Create a one-step everyday story matching a supplied number sentence.
Regroup ten ones as one ten and one ten as ten ones.
Regroup ten tens as one hundred and one hundred as ten tens.
Subtract two-digit numbers without regrouping.
Subtract two-digit numbers with regrouping from tens to ones.
Subtract three-digit numbers without regrouping.
Subtract three-digit numbers with regrouping across one place.
Explain regrouping in subtraction using place-value models.
Use addition to check subtraction and subtraction to check addition.
Select an efficient mental, pictorial, or written strategy for an addition or subtraction calculation.
Identify what is known, what is changing or being compared, and what must be found in a one-step problem.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Addition, Subtraction, Unknowns, and One-Step Problems

26 competencies

Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Revise an incorrect model by changing the operation, quantities, labels, or representation.
Create a one-step everyday story matching a supplied number sentence.
Identify the nearest lower and higher multiple of ten or hundred in supported contexts.
Estimate a quantity or result using nearby tens or hundreds.
Use addition to check subtraction and subtraction to check addition.
Select an efficient mental, pictorial, or written strategy for an addition or subtraction calculation.
Represent an unknown number with a box.
Find a missing addend in an addition equation.
Find a missing part in a subtraction equation using objects, drawings, or related facts.
Determine whether an equation with a missing box represents the modeled situation.
Explain equality as a relationship between two expressions or quantities with the same value.
Determine whether an addition or subtraction equation is true or false.
Identify what is known, what is changing or being compared, and what must be found in a one-step problem.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Equal Groups, Repeated Addition, Arrays, and Multiplication

24 competencies

Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Revise an incorrect model by changing the operation, quantities, labels, or representation.
Create a one-step everyday story matching a supplied number sentence.
Explain multiplication as combining equal-sized groups.
Explain multiplication as repeated addition.
Represent multiplication using objects, equal-group drawings, arrays, jumps, and a multiplication number sentence.
Determine the total in small equal-group situations without relying on memorized multiplication facts.
Connect skip-counting by 2s, 5s, and 10s to equal groups.
Explain that changing the order of equal-group factors may produce the same total in supported models without requiring formal property terminology.
Skip-count forward and backward by 2s, 5s, 10s, and 100s in supported ranges.
Describe a pattern rule using words.
Identify what is known, what is changing or being compared, and what must be found in a one-step problem.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Skip-Counting, Growing Patterns, and Missing Numbers

30 competencies

Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Revise an incorrect model by changing the operation, quantities, labels, or representation.
Create a one-step everyday story matching a supplied number sentence.
Count forward and backward within 1,000 from a given number.
Identify numbers immediately before and after a given number.
Identify the nearest lower and higher multiple of ten or hundred in supported contexts.
Estimate a quantity or result using nearby tens or hundreds.
Recognize, describe, extend, and create repeating patterns.
Recognize and extend growing visual patterns.
Extend number patterns based on adding or subtracting a fixed amount.
Skip-count forward and backward by 2s, 5s, 10s, and 100s in supported ranges.
Describe a pattern rule using words.
Identify and correct a term that does not follow a pattern rule.
Represent an unknown number with a box.
Find a missing addend in an addition equation.
Find a missing part in a subtraction equation using objects, drawings, or related facts.
Determine whether an equation with a missing box represents the modeled situation.
Explain equality as a relationship between two expressions or quantities with the same value.
Determine whether an addition or subtraction equation is true or false.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Shape Attributes, Equal Parts, and Symmetry

21 competencies

Describe two-dimensional shapes using sides and corners or vertices.
Recognize triangles, quadrilaterals, pentagons, hexagons, circles, and other familiar shapes in varied orientations.
Group two-dimensional shapes using one stated attribute.
Describe three-dimensional shapes using faces, edges, and vertices where appropriate.
Recognize cubes, rectangular prisms, spheres, cylinders, cones, and pyramids in varied orientations.
Match faces of three-dimensional solids with familiar two-dimensional shapes.
Compose and decompose two-dimensional and three-dimensional shapes.
Partition a rectangle, square, circle, or other suitable shape into two equal shares.
Partition a suitable shape into three or four equal shares.
Use the words half, third, and fourth to describe one equal share without formal fraction arithmetic.
Explain that equal shares need not have identical orientation but must have equal area.
Recognize and complete a simple line-symmetric figure.
Identify a possible line of symmetry by folding or visual matching.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Standard Length, Mass, Capacity, and Time

26 competencies

Select centimeters or meters as an appropriate unit for measuring length.
Measure object length accurately to the nearest whole centimeter.
Measure longer distances in whole meters.
Use a ruler or meter tool from the zero mark and read the correct endpoint.
Estimate length before measuring and compare the estimate with the result.
Compare and order measured lengths expressed in the same unit.
Solve one-step addition or subtraction problems involving lengths in the same unit.
Measure or compare mass using a scale and one stated metric unit.
Measure or compare capacity using marked containers and one stated metric unit.
Read analog and digital time to five-minute intervals.
Count minutes around an analog clock by fives.
Match common time expressions such as five past, quarter past, half past, quarter to, and five-minute digital forms where locally appropriate.
Place daily events in chronological order using clock times.
Solve direct one-step scheduling questions without formal elapsed-time algorithms.
Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Bar Graphs, Pictographs, Money, Change, and Everyday Modeling

46 competencies

Formulate a simple categorical data question.
Collect and record category data using tallies or a simple table.
Construct a pictograph using a one-symbol-per-item scale.
Construct a horizontal or vertical bar graph using a one-unit scale.
Include a title, category labels, and an accurately marked scale.
Interpret category totals from tables, pictographs, and bar graphs.
Compare categories using more, fewer, equal, most, least, and difference.
Use addition or subtraction to answer a one-step question about graph data.
Identify an error in a table, pictograph, or bar graph.
Explain whether a graph answers the original data question.
Recognize and state the values of common local or value-labeled coins and notes.
Count a small mixed collection of money.
Make a stated amount in more than one way.
Compare two money amounts.
Determine whether a small amount is sufficient to pay a stated price.
Calculate simple change using subtraction or counting on.
Add a small saved amount to an existing total.
Determine how much more is needed to reach a small stated savings amount without teaching saving behavior or financial judgment.
Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Revise an incorrect model by changing the operation, quantities, labels, or representation.
Create a one-step everyday story matching a supplied number sentence.
Add two-digit numbers without regrouping.
Add two-digit numbers with regrouping from ones to tens.
Add three-digit numbers without regrouping.
Add three-digit numbers with regrouping across one place.
Explain regrouping in addition using place-value models.
Subtract two-digit numbers without regrouping.
Subtract two-digit numbers with regrouping from tens to ones.
Subtract three-digit numbers without regrouping.
Subtract three-digit numbers with regrouping across one place.
Explain regrouping in subtraction using place-value models.
Use addition to check subtraction and subtraction to check addition.
Select an efficient mental, pictorial, or written strategy for an addition or subtraction calculation.
Identify what is known, what is changing or being compared, and what must be found in a one-step problem.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

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The whole year, lesson by lesson.

Textbook 1Numbers to 200 and the First Hundred

4 chapters · 25 lessons

Chapter 1

Reviewing Tens and Ones to 100

Chapter 2

Building One Hundred

Chapter 3

Numbers from 101 to 150

Chapter 4

Numbers from 151 to 200

Textbook 2Numbers to 1,000 and Place Value

4 chapters · 25 lessons

Chapter 1

Counting by Hundreds to 1,000

Chapter 2

Hundreds, Tens, and Ones to 1,000

Chapter 3

Comparing and Ordering Three-Digit Numbers

Chapter 4

Skip-Counting and Estimating within 1,000

Textbook 3Addition with Regrouping

4 chapters · 25 lessons

Chapter 1

Adding Two-Digit Numbers without Regrouping

Chapter 2

Regrouping Ones into a Ten

Chapter 3

Adding Three-Digit Numbers

Chapter 4

Addition Situations and Strategy Choice

Textbook 4Subtraction with Regrouping

4 chapters · 25 lessons

Chapter 1

Subtracting Two-Digit Numbers without Regrouping

Chapter 2

Regrouping One Ten into Ten Ones

Chapter 3

Subtracting Three-Digit Numbers

Chapter 4

Subtraction Situations and Difference

Textbook 5Addition, Subtraction, Unknowns, and One-Step Problems

4 chapters · 25 lessons

Chapter 1

Missing Addends

Chapter 2

Missing Parts in Subtraction

Chapter 3

Choosing Addition or Subtraction

Chapter 4

Reasonableness, Estimation, and Error Analysis

Textbook 6Equal Groups, Repeated Addition, Arrays, and Multiplication

4 chapters · 25 lessons

Chapter 1

Equal Groups

Chapter 2

Repeated Addition and Multiplication Sentences

Chapter 3

Arrays and Skip-Counting

Chapter 4

Conceptual Multiplication Problems

Textbook 7Skip-Counting, Growing Patterns, and Missing Numbers

4 chapters · 25 lessons

Chapter 1

Skip-Counting Patterns

Chapter 2

Growing Visual Patterns

Chapter 3

Missing Numbers in Addition and Subtraction Equations

Chapter 4

Patterns and Unknowns in Everyday Situations

Textbook 8Shape Attributes, Equal Parts, and Symmetry

4 chapters · 25 lessons

Chapter 1

Attributes of Two-Dimensional Shapes

Chapter 2

Attributes of Three-Dimensional Shapes

Chapter 3

Equal Parts of Shapes

Chapter 4

Introductory Line Symmetry

Textbook 9Standard Length, Mass, Capacity, and Time

4 chapters · 25 lessons

Chapter 1

Measuring in Centimeters

Chapter 2

Measuring in Meters

Chapter 3

Introductory Mass and Capacity

Chapter 4

Time to Five Minutes and Daily Schedules

Textbook 10Bar Graphs, Pictographs, Money, Change, and Everyday Modeling

4 chapters · 25 lessons

Chapter 1

Collecting Data and Constructing Pictographs

Chapter 2

Bar Graphs and Data Questions

Chapter 3

Money Amounts, Simple Purchases, Change, and Saving Totals

Chapter 4

Grade 2 Everyday Mathematical Modeling

Every competency, covered.

The 106 competencies set for Grade 2 Mathematics, and every one has lessons behind it.

Numbers to 200 and the First Hundred

22 competencies

Count forward and backward within 1,000 from a given number.
Read and write numerals from 0 to 1,000.
Match numerals, spoken number names, quantities, and place-value representations within 1,000.
Represent a three-digit number as hundreds, tens, and ones.
Explain the value of each digit in a three-digit number.
Compose and decompose three-digit numbers in standard and nonstandard ways.
Regroup ten ones as one ten and one ten as ten ones.
Regroup ten tens as one hundred and one hundred as ten tens.
Write a number in standard, expanded, word, and pictorial forms.
Compare three-digit numbers using place value.
Use greater-than, less-than, and equal-to symbols accurately.
Order three or more numbers within 1,000.
Identify numbers immediately before and after a given number.
Identify the nearest lower and higher multiple of ten or hundred in supported contexts.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Numbers to 1,000 and Place Value

26 competencies

Count forward and backward within 1,000 from a given number.
Read and write numerals from 0 to 1,000.
Match numerals, spoken number names, quantities, and place-value representations within 1,000.
Represent a three-digit number as hundreds, tens, and ones.
Explain the value of each digit in a three-digit number.
Compose and decompose three-digit numbers in standard and nonstandard ways.
Regroup ten ones as one ten and one ten as ten ones.
Regroup ten tens as one hundred and one hundred as ten tens.
Write a number in standard, expanded, word, and pictorial forms.
Compare three-digit numbers using place value.
Use greater-than, less-than, and equal-to symbols accurately.
Order three or more numbers within 1,000.
Identify numbers immediately before and after a given number.
Identify the nearest lower and higher multiple of ten or hundred in supported contexts.
Estimate a quantity or result using nearby tens or hundreds.
Extend number patterns based on adding or subtracting a fixed amount.
Skip-count forward and backward by 2s, 5s, 10s, and 100s in supported ranges.
Describe a pattern rule using words.
Identify and correct a term that does not follow a pattern rule.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Addition with Regrouping

25 competencies

Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Revise an incorrect model by changing the operation, quantities, labels, or representation.
Create a one-step everyday story matching a supplied number sentence.
Regroup ten ones as one ten and one ten as ten ones.
Regroup ten tens as one hundred and one hundred as ten tens.
Add two-digit numbers without regrouping.
Add two-digit numbers with regrouping from ones to tens.
Add three-digit numbers without regrouping.
Add three-digit numbers with regrouping across one place.
Explain regrouping in addition using place-value models.
Use addition to check subtraction and subtraction to check addition.
Select an efficient mental, pictorial, or written strategy for an addition or subtraction calculation.
Identify what is known, what is changing or being compared, and what must be found in a one-step problem.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Subtraction with Regrouping

25 competencies

Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Revise an incorrect model by changing the operation, quantities, labels, or representation.
Create a one-step everyday story matching a supplied number sentence.
Regroup ten ones as one ten and one ten as ten ones.
Regroup ten tens as one hundred and one hundred as ten tens.
Subtract two-digit numbers without regrouping.
Subtract two-digit numbers with regrouping from tens to ones.
Subtract three-digit numbers without regrouping.
Subtract three-digit numbers with regrouping across one place.
Explain regrouping in subtraction using place-value models.
Use addition to check subtraction and subtraction to check addition.
Select an efficient mental, pictorial, or written strategy for an addition or subtraction calculation.
Identify what is known, what is changing or being compared, and what must be found in a one-step problem.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Addition, Subtraction, Unknowns, and One-Step Problems

26 competencies

Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Revise an incorrect model by changing the operation, quantities, labels, or representation.
Create a one-step everyday story matching a supplied number sentence.
Identify the nearest lower and higher multiple of ten or hundred in supported contexts.
Estimate a quantity or result using nearby tens or hundreds.
Use addition to check subtraction and subtraction to check addition.
Select an efficient mental, pictorial, or written strategy for an addition or subtraction calculation.
Represent an unknown number with a box.
Find a missing addend in an addition equation.
Find a missing part in a subtraction equation using objects, drawings, or related facts.
Determine whether an equation with a missing box represents the modeled situation.
Explain equality as a relationship between two expressions or quantities with the same value.
Determine whether an addition or subtraction equation is true or false.
Identify what is known, what is changing or being compared, and what must be found in a one-step problem.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Equal Groups, Repeated Addition, Arrays, and Multiplication

24 competencies

Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Revise an incorrect model by changing the operation, quantities, labels, or representation.
Create a one-step everyday story matching a supplied number sentence.
Explain multiplication as combining equal-sized groups.
Explain multiplication as repeated addition.
Represent multiplication using objects, equal-group drawings, arrays, jumps, and a multiplication number sentence.
Determine the total in small equal-group situations without relying on memorized multiplication facts.
Connect skip-counting by 2s, 5s, and 10s to equal groups.
Explain that changing the order of equal-group factors may produce the same total in supported models without requiring formal property terminology.
Skip-count forward and backward by 2s, 5s, 10s, and 100s in supported ranges.
Describe a pattern rule using words.
Identify what is known, what is changing or being compared, and what must be found in a one-step problem.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Skip-Counting, Growing Patterns, and Missing Numbers

30 competencies

Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Revise an incorrect model by changing the operation, quantities, labels, or representation.
Create a one-step everyday story matching a supplied number sentence.
Count forward and backward within 1,000 from a given number.
Identify numbers immediately before and after a given number.
Identify the nearest lower and higher multiple of ten or hundred in supported contexts.
Estimate a quantity or result using nearby tens or hundreds.
Recognize, describe, extend, and create repeating patterns.
Recognize and extend growing visual patterns.
Extend number patterns based on adding or subtracting a fixed amount.
Skip-count forward and backward by 2s, 5s, 10s, and 100s in supported ranges.
Describe a pattern rule using words.
Identify and correct a term that does not follow a pattern rule.
Represent an unknown number with a box.
Find a missing addend in an addition equation.
Find a missing part in a subtraction equation using objects, drawings, or related facts.
Determine whether an equation with a missing box represents the modeled situation.
Explain equality as a relationship between two expressions or quantities with the same value.
Determine whether an addition or subtraction equation is true or false.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Shape Attributes, Equal Parts, and Symmetry

21 competencies

Describe two-dimensional shapes using sides and corners or vertices.
Recognize triangles, quadrilaterals, pentagons, hexagons, circles, and other familiar shapes in varied orientations.
Group two-dimensional shapes using one stated attribute.
Describe three-dimensional shapes using faces, edges, and vertices where appropriate.
Recognize cubes, rectangular prisms, spheres, cylinders, cones, and pyramids in varied orientations.
Match faces of three-dimensional solids with familiar two-dimensional shapes.
Compose and decompose two-dimensional and three-dimensional shapes.
Partition a rectangle, square, circle, or other suitable shape into two equal shares.
Partition a suitable shape into three or four equal shares.
Use the words half, third, and fourth to describe one equal share without formal fraction arithmetic.
Explain that equal shares need not have identical orientation but must have equal area.
Recognize and complete a simple line-symmetric figure.
Identify a possible line of symmetry by folding or visual matching.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Standard Length, Mass, Capacity, and Time

26 competencies

Select centimeters or meters as an appropriate unit for measuring length.
Measure object length accurately to the nearest whole centimeter.
Measure longer distances in whole meters.
Use a ruler or meter tool from the zero mark and read the correct endpoint.
Estimate length before measuring and compare the estimate with the result.
Compare and order measured lengths expressed in the same unit.
Solve one-step addition or subtraction problems involving lengths in the same unit.
Measure or compare mass using a scale and one stated metric unit.
Measure or compare capacity using marked containers and one stated metric unit.
Read analog and digital time to five-minute intervals.
Count minutes around an analog clock by fives.
Match common time expressions such as five past, quarter past, half past, quarter to, and five-minute digital forms where locally appropriate.
Place daily events in chronological order using clock times.
Solve direct one-step scheduling questions without formal elapsed-time algorithms.
Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.

Bar Graphs, Pictographs, Money, Change, and Everyday Modeling

46 competencies

Formulate a simple categorical data question.
Collect and record category data using tallies or a simple table.
Construct a pictograph using a one-symbol-per-item scale.
Construct a horizontal or vertical bar graph using a one-unit scale.
Include a title, category labels, and an accurately marked scale.
Interpret category totals from tables, pictographs, and bar graphs.
Compare categories using more, fewer, equal, most, least, and difference.
Use addition or subtraction to answer a one-step question about graph data.
Identify an error in a table, pictograph, or bar graph.
Explain whether a graph answers the original data question.
Recognize and state the values of common local or value-labeled coins and notes.
Count a small mixed collection of money.
Make a stated amount in more than one way.
Compare two money amounts.
Determine whether a small amount is sufficient to pay a stated price.
Calculate simple change using subtraction or counting on.
Add a small saved amount to an existing total.
Determine how much more is needed to reach a small stated savings amount without teaching saving behavior or financial judgment.
Identify the important quantities and relationships in an everyday one-step situation.
Represent an everyday situation with a drawing, model, or number sentence.
Use addition, subtraction, conceptual multiplication, measurement, time, data, geometry, or money to solve a one-step situation.
Interpret the mathematical result using the units and language of the original situation.
Check whether the number sentence and answer match the real situation.
Revise an incorrect model by changing the operation, quantities, labels, or representation.
Create a one-step everyday story matching a supplied number sentence.
Add two-digit numbers without regrouping.
Add two-digit numbers with regrouping from ones to tens.
Add three-digit numbers without regrouping.
Add three-digit numbers with regrouping across one place.
Explain regrouping in addition using place-value models.
Subtract two-digit numbers without regrouping.
Subtract two-digit numbers with regrouping from tens to ones.
Subtract three-digit numbers without regrouping.
Subtract three-digit numbers with regrouping across one place.
Explain regrouping in subtraction using place-value models.
Use addition to check subtraction and subtraction to check addition.
Select an efficient mental, pictorial, or written strategy for an addition or subtraction calculation.
Identify what is known, what is changing or being compared, and what must be found in a one-step problem.
Choose addition, subtraction, or conceptual multiplication for a one-step situation.
Represent a problem using objects, drawings, number bonds, bar-like models, number lines, arrays, equations, clocks, graphs, or measurement diagrams.
Explain why the selected operation or strategy matches the situation.
Estimate or predict whether an answer should be larger, smaller, or near a benchmark.
Check a result using a different representation or inverse relationship where available.
Determine whether an answer is reasonable in context.
Compare two valid solution strategies.
Identify and correct a counting, place-value, regrouping, graphing, or modeling error.