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Grade 3 Math

32 curriculum outcomes with explicit teaching progressions

Select a record to inspect its progression

Operations Algebraic Thinking · 3.OA.A.1

Interpret products of whole numbers

Independently interpret a product of whole numbers, such as interpreting 5 × 7 as the total number of objects in 5 groups of 7 objects each, and describe a context in which a total can be expressed as such a product. across representations and contexts.

Component progression

  1. 1I can distinguish equal-group situations from situations in which groups contain different quantities, and identify the number of groups and the number of objects in each group.
  2. 2I can interpret a multiplication expression a × b as a groups of b objects each and connect each factor to the quantities in the situation.
  3. 3I can represent an equal-groups situation with a multiplication equation and explain how the equation matches the context.
Operations Algebraic Thinking · 3.OA.A.2

Interpret whole-number quotients

Independently interpret a whole-number quotient of whole numbers, such as interpreting 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as the number of shares when 56 objects are partitioned into equal shares of 8 objects each, and describe a context in which a number of shares or a number of groups can be expressed as such a quotient. across representations and contexts.

Component progression

  1. 1I can interpret division in a partitive context by sharing a total quantity equally among a known number of groups and determining the size of each group.
  2. 2I can interpret division in a quotitive (measurement) context by partitioning a total into groups of a known size and determining the number of groups.
  3. 3I can interpret a division expression a ÷ b in context, explaining whether the divisor represents the number of groups or the size of each group, and represent sharing and measurement division situations with equations.
Operations Algebraic Thinking · 3.OA.A.3

Solve multiplication and division word problems within 100

Independently use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, using drawings and equations with a symbol for the unknown number to represent the problem. across representations and contexts.

Component progression

  1. 1I can identify the multiplicative structure of a contextual problem and distinguish multiplication situations from division situations without relying only on keywords.
  2. 2I can solve multiplication and division word problems within 100 involving equal groups, rectangular arrays, and measurement quantities.
  3. 3I can represent a multiplication or division word problem with a drawing and an equation using a symbol for the unknown, and justify how the representation and solution match the situation.
Operations Algebraic Thinking · 3.OA.A.4

Determine an unknown number in a multiplication or division equation

Independently determine the unknown whole number in a multiplication or division equation relating three whole numbers, such as determining the unknown number that makes 8 × ? = 48, 5 = ⬜ ÷ 3, or 6 × 6 = ? true. across representations and contexts.

Component progression

  1. 1I can recognize an unknown factor, dividend, or divisor in a multiplication or division equation and distinguish it from the known quantities.
  2. 2I can determine an unknown whole number in a multiplication or division equation using equal-group, array, or related visual reasoning.
  3. 3I can determine an unknown whole number in a multiplication or division equation by reasoning about the inverse relationship between multiplication and division, and justify the result.
Operations Algebraic Thinking · 3.OA.B.5

Apply properties of operations as multiplication and division strategies

Independently apply properties of operations as strategies to multiply and divide, including the commutative property (if 6 × 4 = 24 is known, then 4 × 6 = 24 is also known), the associative property (3 × 5 × 2 can be found by (3 × 5) × 2 = 15 × 2 = 30, or by 3 × (5 × 2) = 3 × 10 = 30), and the distributive property (knowing 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56). across representations and contexts.

Component progression

  1. 1I can use equal groups and arrays to recognize that reversing two factors or regrouping three factors does not change the product, and use this to transform an unfamiliar fact into a related known fact.
  2. 2I can decompose a rectangular array or equal-groups model into two parts, write an equation such as 7 × 8 = (5 × 8) + (2 × 8), and explain the correspondence between the model and equation.
  3. 3I can choose among commutative, associative, and distributive reasoning to multiply or divide efficiently, and explain why the chosen strategy preserves the value of the original expression.
Operations Algebraic Thinking · 3.OA.B.6

Understand division as an unknown-factor problem

Independently understand division as an unknown-factor problem, such as finding 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. across representations and contexts.

Component progression

  1. 1I can use equal groups and arrays to connect a multiplication equation and a division equation that involve the same three quantities.
  2. 2I can interpret a ÷ b = ? as the unknown-factor question b × ? = a and explain the relationship using quantities, models, and equations.
  3. 3I can determine quotients within 100 by reasoning from a related, known multiplication fact.
Operations Algebraic Thinking · 3.OA.C.7

Fluently multiply and divide within 100

Independently fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations; by the end of grade 3, know from memory all products of two one-digit numbers. across representations and contexts.

Component progression

  1. 1I can develop accurate and increasingly efficient recall of multiplication facts involving 0, 1, 2, 5, and 10 using conceptual patterns rather than isolated memorization.
  2. 2I can derive multiplication and division facts within 100 from known facts using commutative, associative, distributive, and unknown-factor strategies.
  3. 3I can demonstrate accurate and increasingly efficient multiplication and division within 100 across the grade 3 fact range, including recall from memory of all products of two one-digit numbers.
Operations Algebraic Thinking · 3.OA.D.8

Solve two-step word problems and assess reasonableness

Independently solve two-step word problems using the four operations, represent these problems using equations with a letter standing for the unknown quantity, and assess the reasonableness of answers using mental computation and estimation strategies including rounding; limited to problems posed with whole numbers and having whole-number answers. across representations and contexts.

Component progression

  1. 1I can analyze a two-step word problem using the four operations, identify how the result of one step is used in the next, and represent the problem with one or more equations using a letter for the unknown quantity.
  2. 2I can solve a two-step word problem using the four operations, performing operations in the conventional order when no parentheses specify otherwise.
  3. 3I can assess the reasonableness of an answer to a two-step problem using mental computation, estimation, and rounding.
Operations Algebraic Thinking · 3.OA.D.9

Identify and explain arithmetic patterns

Independently identify arithmetic patterns, including patterns in the addition table or multiplication table, and explain them using properties of operations, such as observing that 4 times a number is always even and explaining why 4 times a number can be decomposed into two equal addends. across representations and contexts.

Component progression

  1. 1I can identify arithmetic patterns in addition and multiplication tables, including patterns generated by repeated operations.
  2. 2I can describe the numerical relationship that generates an observed arithmetic pattern and use the rule to predict additional values.
  3. 3I can explain why an observed arithmetic pattern occurs using properties of operations and relationships among factors, addends, and products.
Number Operations Base Ten · 3.NBT.A.1

Round whole numbers to the nearest ten or hundred

Independently use place value understanding to round whole numbers to the nearest 10 or 100. across representations and contexts.

Component progression

  1. 1I can use place value to locate a whole number between two benchmark tens or hundreds on a number line.
  2. 2I can round a whole number to the nearest ten using place-value reasoning and distance from multiples of ten.
  3. 3I can round a whole number to the nearest hundred using place-value reasoning and distance from multiples of one hundred.
Number Operations Base Ten · 3.NBT.A.2

Fluently add and subtract within 1,000

Independently fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. across representations and contexts.

Component progression

  1. 1I can add whole numbers within 1,000 by composing hundreds, tens, and ones, and explain the place-value reasoning.
  2. 2I can subtract whole numbers within 1,000 by decomposing hundreds, tens, and ones, and explain the place-value reasoning.
  3. 3I can solve contextual addition and subtraction problems within 1,000 and use rounding or estimation to verify that the result is reasonable.
Number Operations Base Ten · 3.NBT.A.3

Multiply one-digit numbers by multiples of ten

Independently multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60), using strategies based on place value and properties of operations. across representations and contexts.

Component progression

  1. 1I can interpret a multiple of 10 from 10 through 90 as a number of groups of ten and connect that structure to place value.
  2. 2I can multiply a one-digit whole number by a multiple of 10 from 10 through 90 using place-value and properties-of-operations reasoning.
  3. 3I can explain and model a product of a one-digit number and a multiple of 10 using equal groups, place value, and properties of operations.
Number Operations Fractions · 3.NF.A.1

Understand a fraction as a quantity formed by parts of a whole

Independently understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts, and understand a fraction a/b as the quantity formed by a parts of size 1/b, limited to fractions with denominators 2, 3, 4, 6, and 8. across representations and contexts.

Component progression

  1. 1I can distinguish equal partitions of a whole from unequal partitions, and understand 1/b as one part of a whole partitioned into b equal parts.
  2. 2I can understand a fraction a/b as a copies of the unit fraction 1/b, interpreting the numerator as the count of unit-fraction parts and the denominator as the size of the equal partition.
  3. 3I can represent fractions with denominators 2, 3, 4, 6, or 8 accurately using area models with equal-sized wholes and equal partitions.
Number Operations Fractions · 3.NF.A.2a

Represent a unit fraction on a number line

Independently represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts; recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. across representations and contexts.

Component progression

  1. 1I can understand the interval from 0 to 1 on a number line as one whole.
  2. 2I can partition the interval from 0 to 1 into b equal intervals to represent fractional units of size 1/b.
  3. 3I can locate a unit fraction 1/b on a number line by measuring one unit-fraction length from zero.
Number Operations Fractions · 3.NF.A.2b

Represent a non-unit fraction on a number line

Independently represent a fraction a/b on a number line diagram by marking off a lengths of 1/b from 0; recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. across representations and contexts.

Component progression

  1. 1I can mark off a lengths of size 1/b from zero on a number line partitioned into unit fractions.
  2. 2I can locate a given fraction a/b on a number line by iterating the unit fraction 1/b a times from zero.
  3. 3I can identify the fraction a/b represented by a marked point on a number line, given the partitioning of the whole.
Number Operations Fractions · 3.NF.A.3a

Understand fraction equivalence

Independently understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line, limited to denominators 2, 3, 4, 6, and 8. across representations and contexts.

Component progression

  1. 1I can recognize that two fractions are equivalent when equal-sized area models of each show the same amount shaded.
  2. 2I can recognize that two fractions are equivalent when they mark the same point on a number line.
  3. 3I can explain what it means for two fractions to be equivalent: the same size, or the same point on a number line.
Number Operations Fractions · 3.NF.A.3b

Recognize and generate simple equivalent fractions

Independently recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3, and explain why the fractions are equivalent, e.g., by using a visual fraction model. across representations and contexts.

Component progression

  1. 1I can recognize when two given fractions, such as 1/2 and 2/4, name the same amount across visual and numerical representations.
  2. 2I can generate a fraction equivalent to a given fraction, such as finding a fraction equal to 4/6, using reasoning from a model.
  3. 3I can justify why two fractions are equivalent using a visual fraction model, a number line, or reasoning about equal-sized parts.
Number Operations Fractions · 3.NF.A.3c

Express whole numbers as fractions

Independently express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers, e.g., express 3 in the form 3 = 3/1, recognize that 6/1 = 6, and locate 4/4 and 1 at the same point of a number line diagram. across representations and contexts.

Component progression

  1. 1I can express a whole number as a fraction with denominator 1, such as writing 3 = 3/1.
  2. 2I can recognize a fraction equivalent to a whole number, such as recognizing that 6/1 = 6.
  3. 3I can locate a whole number and an equivalent fraction, such as 4/4 and 1, at the same point on a number line diagram.
Number Operations Fractions · 3.NF.A.3d

Compare fractions with the same numerator or denominator

Independently compare two fractions with the same numerator or the same denominator by reasoning about their size, recognizing that comparisons are valid only when the two fractions refer to the same whole, and record the results of comparisons with the symbols >, =, or <, justifying the conclusions, e.g., by using a visual fraction model. across representations and contexts.

Component progression

  1. 1I can compare fractions with the same denominator by reasoning about the number of equal-sized parts.
  2. 2I can compare fractions with the same numerator by reasoning about the relative size of the unit fractions.
  3. 3I can record a fraction comparison using >, =, or <, justify it with a visual model, and recognize the comparison is valid only when both fractions refer to the same whole.
Measurement Data · 3.MD.A.1

Tell time to the minute and solve time-interval problems

Independently tell and write time to the nearest minute and measure time intervals in minutes; solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. across representations and contexts.

Component progression

  1. 1I can read analog and digital clocks and write time to the nearest minute.
  2. 2I can determine elapsed time in minutes within an hour using a clock, number line, or additive reasoning.
  3. 3I can solve word problems involving addition and subtraction of time intervals in minutes, including problems with an unknown start or end time, by representing the problem on a number line diagram.
Measurement Data · 3.MD.A.2

Measure, estimate, and solve problems with liquid volume and mass

Independently measure and estimate liquid volumes and masses of objects using standard units of grams, kilograms, and liters, and add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes given in the same units, e.g., by using drawings such as a beaker with a measurement scale, excluding multiplicative comparison problems and compound units. across representations and contexts.

Component progression

  1. 1I can measure and estimate liquid volumes using liters, and select reasonable estimates for familiar contexts.
  2. 2I can measure and estimate masses using grams and kilograms, and select reasonable units and estimates.
  3. 3I can add, subtract, multiply, or divide to solve a one-step word problem involving masses or liquid volumes given in the same units.
Measurement Data · 3.MD.B.3

Draw and use scaled picture and bar graphs

Independently draw a scaled picture graph and a scaled bar graph to represent a data set with several categories, and solve one- and two-step how-many-more and how-many-less problems using information presented in scaled bar graphs, e.g., a bar graph in which each square might represent 5 pets. across representations and contexts.

Component progression

  1. 1I can draw a scaled picture graph to represent a data set with several categories, and interpret scales greater than one to determine the values represented.
  2. 2I can draw a scaled bar graph to represent a data set with several categories, and interpret it by using axis labels, intervals, and scale to determine category values.
  3. 3I can solve one- and two-step how-many-more, how-many-fewer, and total problems using information presented in scaled picture and bar graphs.
Measurement Data · 3.MD.B.4

Measure lengths and display fractional measurement data

Independently generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch, and show the data by making a line plot, where the horizontal scale is marked off in appropriate units: whole numbers, halves, or quarters. across representations and contexts.

Component progression

  1. 1I can measure lengths to the nearest half or quarter inch using a ruler marked with halves and fourths.
  2. 2I can make a line plot to display measurement data, with the horizontal scale marked off in whole numbers, halves, or quarters as appropriate.
  3. 3I can interpret and compare values and frequencies shown on a line plot containing whole, half, and quarter-unit measurement data.
Measurement Data · 3.MD.C.5

Understand concepts of area measurement

Independently recognize area as an attribute of plane figures and understand concepts of area measurement: a square with side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area; a plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. across representations and contexts.

Component progression

  1. 1I can understand a square with side length 1 unit as a unit square that has one square unit of area.
  2. 2I can recognize that a plane figure covered without gaps or overlaps by n unit squares has an area of n square units.
  3. 3I can measure and express the area of a plane figure using standard and improvised square units.
Measurement Data · 3.MD.C.6

Measure area by counting unit squares

Independently measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). across representations and contexts.

Component progression

  1. 1I can tile a plane figure with unit squares without gaps or overlaps in preparation for measuring its area.
  2. 2I can count unit squares to measure the area of a plane figure in square centimeters, square meters, square inches, or square feet.
  3. 3I can measure the area of a plane figure using an improvised (non-standard) square unit by counting how many fit.
Measurement Data · 3.MD.C.7a

Relate tiled rectangle area to multiplication

Independently find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. across representations and contexts.

Component progression

  1. 1I can tile a rectangle with unit squares and count the number of rows and the number of unit squares in each row.
  2. 2I can show that the total number of unit squares found by tiling a rectangle equals the product of its side lengths.
  3. 3I can explain why multiplying a rectangle's side lengths gives the same area as counting the tiles that cover it.
Measurement Data · 3.MD.C.7b

Use the area formula for rectangles

Independently multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. across representations and contexts.

Component progression

  1. 1I can multiply whole-number side lengths to find a rectangle's area, expressing the result in square units.
  2. 2I can solve real-world and mathematical problems by finding the area of a rectangle from its side lengths.
  3. 3I can represent a whole-number product as the area of a rectangle with corresponding whole-number side lengths.
Measurement Data · 3.MD.C.7c

Use area models to represent the distributive property

Independently use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c, and use area models to represent the distributive property in mathematical reasoning. across representations and contexts.

Component progression

  1. 1I can use tiling to decompose a rectangle with side length b + c into two smaller rectangles with side lengths b and c.
  2. 2I can show, using the decomposed tiling, that the total area of a rectangle with side lengths a and b + c equals a × b plus a × c.
  3. 3I can use a decomposed area model to represent and apply the distributive property in solving a multiplication problem.
Measurement Data · 3.MD.C.7d

Find the area of rectilinear figures

Independently recognize area as additive; find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems. across representations and contexts.

Component progression

  1. 1I can recognize that the area of a figure made of non-overlapping parts equals the sum of the areas of those parts.
  2. 2I can decompose a rectilinear figure into non-overlapping rectangles.
  3. 3I can find the area of a rectilinear figure by adding the areas of its decomposed rectangles, and apply this technique to solve real-world problems.
Measurement Data · 3.MD.D.8

Solve problems involving perimeter

Independently solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. across representations and contexts.

Component progression

  1. 1I can interpret perimeter as the total length around a polygon and distinguish perimeter from area.
  2. 2I can find the perimeter of a polygon by adding its side lengths, including finding an unknown side length when the perimeter and remaining sides are known.
  3. 3I can investigate and compare rectangles with the same perimeter and different areas, or the same area and different perimeters, and explain why the two measures are independent.
Geometry · 3.G.A.1

Reason about categories of quadrilaterals

Independently understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals); recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. across representations and contexts.

Component progression

  1. 1I can describe and compare quadrilaterals using attributes such as number of sides, parallel sides, equal side lengths, and angle structure.
  2. 2I can classify rhombuses, rectangles, squares, and other quadrilaterals by their shared attributes and justify category membership.
  3. 3I can explain how shared attributes define a larger category such as quadrilaterals, and draw a quadrilateral that does not belong to the rhombus, rectangle, or square subcategories.
Geometry · 3.G.A.2

Partition shapes into equal-area parts and name unit fractions

Independently partition shapes into parts with equal areas, and express the area of each part as a unit fraction of the whole; for example, partition a shape into 4 parts with equal area and describe the area of each part as 1/4 of the area of the shape. across representations and contexts.

Component progression

  1. 1I can partition a plane figure into two, three, four, six, or eight parts with equal areas.
  2. 2I can express the area of one equal part of a partitioned shape as a unit fraction of the whole, such as 1/4 for a shape partitioned into 4 equal-area parts.
  3. 3I can describe a collection of several equal-area parts of a partitioned shape as a non-unit fraction of the whole area.
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