Grade 3 · Mathematics
3.1A
Apply mathematics to real-world problems
Apply mathematics to problems arising in everyday life, society, and the workplace.
3.1B
Problem-solving model
Use a problem‑solving model to analyze information, plan, determine, and justify solutions; evaluate reasonableness.
3.1C
Select tools & techniques
Select appropriate tools and techniques (mental math, estimation, number sense) to solve problems.
3.1D
Communicate ideas
Communicate mathematical ideas using multiple representations.
3.1E
Use representations
Create and use representations to organize, record, and communicate ideas.
3.1F
Analyze relationships
Analyze mathematical relationships to connect and communicate ideas.
3.1G
Justify with precise language
Display, explain, and justify ideas using precise mathematical language.
3.2A
Compose/decompose to 100,000
Compose and decompose numbers up to 100,000 using objects, pictorial models, numbers, including expanded notation.
3.2B
Base-10 relationships
Describe base‑10 place value relationships through the hundred thousands place.
3.2C
Number line & rounding
Represent a number between benchmark multiples (10, 100, 1,000, 10,000) on a number line and use to describe relative size and round whole numbers.
3.2D
Compare & order to 100,000
Compare and order whole numbers up to 100,000; use >, <, =.
3.3A
Represent fractions
Represent fractions 0 < a/b ≤ 1 (denominators 2,3,4,6,8) using concrete and pictorial models, including strip diagrams and number lines.
3.3B
Point to fraction
Determine the corresponding fraction for a given point on a number line (denominators 2,3,4,6,8).
3.3C
Unit fraction meaning
Explain the meaning of unit fraction 1/b as one part of a whole partitioned into b equal parts.
3.3D
Compose/decompose fractions
Compose and decompose a/b as a sum of unit fractions 1/b.
3.3E
Partitioning situations
Solve problems by partitioning objects/sets into fractional parts (denominators 2,3,4,6,8).
3.3F
Equivalent fractions models
Represent equivalent fractions (denominators 2,3,4,6,8) with objects and models, including number lines.
3.3G
Equivalence definition
Explain equivalence via same point on a number line or same portion of same‑size whole (area model).
3.3H
Compare fractions
Compare two fractions with same numerator or denominator using reasoning; justify with symbols, words, objects, or models.
3.4A
Add/subtract within 1,000
Solve one‑ and two‑step problems with addition/subtraction within 1,000 using place value and properties; demonstrate fluency.
3.4B
Estimate sums/differences
Round to nearest 10 or 100 or use compatible numbers to estimate.
3.4C
Value of coins & bills
Determine the value of a collection of coins and bills.
3.4D
Equal groups/arrays
Determine total objects when groups are combined or arranged in arrays up to 10×10.
3.4E
Represent multiplication
Represent multiplication facts with repeated addition, equal groups, arrays, area models, number line jumps, skip counting.
3.4F
Recall multiplication/division facts
Recall facts to multiply up to 10×10 with automaticity and recall corresponding division facts.
3.4G
Multiply 2-digit by 1-digit
Use strategies and algorithms, including the standard algorithm, to multiply a two‑digit number by a one‑digit number.
3.4H
Equal shares/partitioning
Determine the number in each group when partitioning or sharing equally.
3.4I
Even & odd
Determine if a number is even or odd using divisibility rules.
3.4J
Quotients & relationships
Determine a quotient using the relationship between multiplication and division.
3.4K
Solve mult/div problems
Solve one‑ and two‑step problems involving multiplication and division within 100 using models, properties, or fact recall.
3.5A
Add/subtract models & equations
Represent one‑ and two‑step problems involving addition/subtraction to 1,000 using models, number lines, and equations.
3.5B
Mult/div models & equations
Represent and solve one‑ and two‑step multiplication/division problems within 100 using arrays, strip diagrams, and equations.
3.5C
Multiplicative comparison
Describe a multiplication expression as a comparison (e.g., 3×24 is 3 times as much as 24).
3.5D
Unknowns in equations
Determine the unknown whole number in multiplication or division equations (missing factor or product).
3.5E
Tables & verbal descriptions
Represent real‑world relationships using number pairs in a table and verbal descriptions.
3.6A
Classify 2D/3D figures
Classify and sort 2D and 3D figures (cones, cylinders, spheres, triangular/rectangular prisms, cubes) using formal geometric language.
3.6B
Quadrilaterals
Use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as quadrilaterals; draw examples outside subcategories.
3.6C
Area of rectangles
Determine the area of rectangles with whole‑number side lengths using multiplication (rows × unit squares per row).
3.6D
Area of composite rectangles
Decompose composite figures formed by rectangles to determine total area using the additive property of area.
3.6E
Equal shares as unit fractions
Decompose two congruent figures into equal‑area parts and express each part as a unit fraction of the whole.
3.7A
Fractions on number lines
Represent halves, fourths, and eighths as distances from zero on a number line.
3.7B
Perimeter
Determine the perimeter of a polygon or a missing side given the perimeter and other side lengths.
3.7C
Add/subtract time intervals
Solve problems involving addition and subtraction of time intervals in minutes using models/tools.
3.7D
Choose measurement type
Determine when to use liquid volume (capacity) or weight measurements.
3.7E
Measure capacity/weight
Determine liquid volume (capacity) or weight using appropriate units and tools.
3.8A
Summarize data
Summarize a multicategry data set using a frequency table, dot plot, pictograph, or bar graph with scaled intervals.
3.8B
Solve problems with data
Solve one‑ and two‑step problems using categorical data represented with a table, dot plot, pictograph, or bar graph with scaled intervals.
3.9A
Human capital & income
Explain the connection between human capital/labor and income.
3.9B
Scarcity & cost
Describe how availability or scarcity of resources impacts cost.
3.9C
Spending decisions
Identify costs and benefits of planned and unplanned spending decisions.
3.9D
Credit & interest
Explain that credit is borrowed money that must be paid back, usually with interest.
3.9E
Savings plans
List reasons to save and explain benefits of a savings plan, including for college.
3.9F
Money decisions
Identify decisions involving income, spending, saving, credit, and charitable giving.