Grade 3 Math Colorado standards Standards

Geometry

Measurement & Data

Operations & Algebraic Thinking

Number & Operations—Fractions

Number & Operations in Base Ten

Standards for Mathematical Practice

Reason with shapes and their attributes.

Geometry: Reason with shapes and their attributes.

Explain 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.

Identify examples of shapes that share some attributes (e.g., squares and rectangles have four sides) but do not share other attributes (e.g., squares have four equal sides but rectangles don’t necessarily have four equal sides).

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

Recognize that shapes can be partitioned into equal areas.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Measurement & Data: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

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.

Tell time to the nearest half hour on analog and digital clocks.

Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (This excludes compound units such as cm3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Identify appropriate tools for measuring liquid volumes, like measuring cups and spoons, and for measuring masses, such as scales and balances.

Represent and interpret data.

Measurement & Data: Represent and interpret data.

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.

Use a scaled picture graph and a scaled bar graph to answer “how many” or “how many more/less” questions.

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

Generate measurement data by measuring lengths using rulers, yardsticks, meter sticks, and measuring tapes marked with units and half-units.

Match the measurement data to a given line plot, where the horizontal scale is marked off in whole-number and half-number units.

Use concepts of area and relate area to multiplication and to addition.

Measurement & Data: Geometric measurement: Use concepts of area and relate area to multiplication and to addition.

Recognize area as an attribute of plane figures and understand concepts of area measurement.

Recognize area as an attribute of plane figures and associate unit square grids with measuring area.

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.

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

Measure areas by counting unit squares (square cm, square in) marked on a figure to measure.

Use concepts of area and relate area to the operations of multiplication and addition.

Use concepts of area and relate area to the operations of multiplication and addition.

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.

the area of a rectangle by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

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.

The area of the rectangle should not exceed 12 square units.

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. Use area models to represent the distributive property in mathematical reasoning.

Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Measurement & Data: Geometric measurement: Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

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.

Solve real-world and mathematical problems involving perimeters of squares, rectangles, and triangles, including finding the perimeter given the side lengths.

Use place value understanding and properties of operations to perform multi-digit arithmetic. A range of algorithms may be used.

Number & Operations in Base Ten: Use place value understanding and properties of operations to perform multi-digit arithmetic. A range of algorithms may be used.

Use place value understanding to round whole numbers to the nearest 10 or 100.

Use place value understanding to round whole numbers 1-50 to the nearest 10.

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Add and subtract within 50 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

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.

Multiply one-digit whole numbers by 10 to produce products in the range 10-100 (e.g., 4 x 10, 10 x 10) using strategies based on place value and properties of operations.

Develop understanding of fractions as numbers.

Number & Operations—Fractions: Develop understanding of fractions as numbers.

Describe a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Describe a fraction 1 as the quantity formed by 1 part when a whole is 𝑏𝑏 partitioned into b parts.

Limit b to be 2, 3, or 4 parts.

Describe a fraction as a number on the number line; represent fractions on a number line diagram.

Describe a fraction as a number on the number line.

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.

Represent 1 , 1 , 2 , 1 , and 3 on the number line.

Represent a fraction a/b on a number line diagram by marking off a lengths 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.

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Explain equivalence of 1 . and 2 . using a number line as well as part/whole 2 4 models.

Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Represent and solve problems involving multiplication and division.

Operations & Algebraic Thinking: Represent and solve problems involving multiplication and division.

Interpret products of whole numbers, e.g., interpret 5×7 as the total number of objects in 5 groups of 7 objects each.

Interpret products of whole numbers, e.g., interpret 2 x 4 as the total number of objects in 2 groups of 4 objects each. Limit the whole numbers to numbers less than or equal to 5.

Interpret whole-number quotients of whole numbers, e.g., interpret 56÷8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56÷8.

Interpret whole-number quotients of whole numbers, (e.g., interpret 10 divided by 2 as the number of objects in each share when 10 objects are partitioned equally into 2 groups, or as a number of shares when 10 objects are partitioned into equal shares of 2 objects each).

Limit dividends to numbers less than or equal to 12 and divisors less than or equal to 6.

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Use multiplication and division within 12 to solve problems in situations involving equal groups, arrays, and measurement quantities (e.g., by using objects, drawings, and other written ways to represent the problem).

Use repeated addition as a multiplication strategy and repeated subtraction as a division strategy.

Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Determine the unknown whole number in a multiplication or division equation given a rectangular array with either an unknown number of rows or columns or an unknown total.

Limit the product to 12 or fewer.

Apply properties of multiplication and the relationship between multiplication and division.

Operations & Algebraic Thinking: Apply properties of multiplication and the relationship between multiplication and division.

Apply properties of operations as strategies to multiply and divide.

Apply properties of operations as strategies to multiply and divide (students need not use formal terms for these properties).

Examples: If 3 x 2 = 6 is known, then 2 x 3 = 6 is also known (commutative property of multiplication). 2 x 3 x 1 can be found by 2 x 3 = 6, then 6 x 1 = 6, or by 3 x 1 = 3, then 2 x 3 =6 (associative property of multiplication).

Interpret division as an unknown-factor problem.

Interpret division as an unknown factor problem.

For example, find 12 divided by 3 by finding the number that makes 12 when multiplied by 3.

Multiply and divide within 100.

Operations & Algebraic Thinking: Multiply and divide within 100.

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.

Multiply and divide within 12, using strategies such as the relationship between multiplication and division (e.g., knowing that 2 x 6 = 12, one knows 12 divided by 2 is 6) or properties of operations).

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Operations & Algebraic Thinking: Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This evidence outcome is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order of operations when there are no parentheses to specify a particular order.)

Use addition and subtraction within 50 to solve one- and two-step word problems.

Use multiplication and subtraction within 12 to solve one-step word problems (this EEO includes problems involving whole number calculations).

Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.

Identify arithmetic patterns (including patterns in the addition table or multiplication table) equivalent to counting by 2s, 3s, 4s, 5s, and 10s (EE:3.A.D.9).

Algebra and Functions

Data, Statistics, and Probability

Geometry

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Number and Quantity