Grade 4 Math Colorado standards Standards

Geometry

Measurement & Data

Operations & Algebraic Thinking

Number & Operations—Fractions

Number & Operations in Base Ten

Standards for Mathematical Practice

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Geometry: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Identify points, lines, line segments, intersecting lines, and parallel lines in two-dimensional figures.

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Identify and sort two-dimensional figures based on the presence or absence of parallel lines and/or right angles.

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts.

Identify line-symmetric figures and indicate lines of symmetry by drawing or folding.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Measurement & Data: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.

Within a single system of measurement, identify the smaller measurement unit (e.g., an inch is smaller than a foot, a minute is shorter than an hour).

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Tell time using a digital clock.

Tell time to the nearest quarter hour using an analog clock.

Measure mass or volume using standard tools.

Use standard measurements to compare lengths of objects.

Identify coins (penny, nickel, dime, quarter) and their values.

Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.

Apply repeated addition or multiplication to find area of rectangles up to at least 25 square units in real-world and mathematical problems for which unit squares are given or defined.

For example, find the area of the floor of a room that has been drawn on graph paper.

Represent and interpret data.

Measurement & Data: Represent and interpret data.

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

Make a line plot displaying a data set of measurements in whole units

Solve problems involving addition and subtraction by using information presented in line plots.

Understand concepts of angle and measure angles.

Measurement & Data: Geometric measurement: Understand concepts of angle and measure angles.

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

Recognize angles as geometric shapes that are formed whenever two rays share a common endpoint (EE.4.MD.C.5.b).

An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles.

An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Identify right angles.

Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Compare angles, using >, =, and < symbols to record the results of comparisons.

Example, given obviously obtuse angle A and obviously obtuse angle B, A > B.

Generalize place value understanding for multi-digit whole numbers.

Number & Operations in Base Ten: Generalize place value understanding for multi-digit whole numbers.

Explain that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

Recognize that in a two-digit whole number, a digit in the tens place represents ten times what it represents in the place to its right.

For example, in the number 55 the five in the tens place (50) is ten times the value of the five in the ones place (5).

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Indicate an understanding of two-digit whole numbers using base-ten numerals, number names, and expanded form

Compare two two-digit whole numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of the comparisons

Use place value understanding to round multi-digit whole numbers to any place.

Use place value understanding to round whole numbers 1-100 to the nearest 10.

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Number & Operations in Base Ten: Use place value understanding and properties of operations to perform multi-digit arithmetic.

Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Add and subtract within 100 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Multiply one-digit whole numbers using models and illustrations using equations, rectangular arrays, and/or area models.

Products should include values up to at least 25.

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Find whole-number quotients with dividends up to at least 25 and one-digit divisors, using strategies based on the concept of division using fair and equal shares.

Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Extend understanding of fraction equivalence and ordering.

Number & Operations—Fractions: Extend understanding of fraction equivalence and ordering.

Explain why a fraction a/b is equivalent to a fraction n×a/n×b by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Explain why fraction 𝑎𝑎 is equivalent to a fraction 𝑛𝑛×𝑎𝑎 by using visual fraction 𝑏𝑏 𝑛𝑛×𝑏𝑏 models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size.

Equivalent fractions should include 1 = 2 and 1 = 2 . 2 4 3 6

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Differentiate between whole and half.

Build fractions from unit fractions.

Number & Operations—Fractions: Build fractions from unit fractions.

Understand a fraction a/b with a>1 as a sum of fractions 1/b.

Understand the following additive fraction relationships: 2 as a sum or 1 and 2 2 1 ; 2 as a sum of 1 and 1 ; 3 as a sum of 1 , 1 , and 1 ; 2 as a sum of 1 and 1 ; 3 as a 2 3 3 3 3 3 3 3 4 4 4 4 sum of 1 , 1 , and 1 ; and 4 as a sum of 1 , 1 , 1 , and 1 .

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Compose and decompose visual fraction models to illustrate these relationships.

Decompose a fraction into a sum of fractions with like denominators in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

Solve word problems involving addition and subtraction of these fractions by using visual fraction models to represent the problem.

Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Apply and extend previous understandings of multiplication to understand the following multiplicative relationships involving fractions and whole numbers: 1 x 2, 1 x 2, and 1 x 3. 1 x 2, 1 x 3, and 1 x 4.

Understand a fraction a/b as a multiple of 1/b.

Compose and decompose visual fraction models to illustrate these relationships.

Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

Solve word problems involving multiplication of these fractions by using visual fraction models to represent the problem. For example, if two people equally share 2 of a pizza, how much of the pizza will each 3 person get?

Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

Use decimal notation for fractions, and compare decimal fractions.

Number & Operations—Fractions: Use decimal notation for fractions, and compare decimal fractions.

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.)

Add two fractions with denominators of 10. For example, 2 + 4 = 6 . 10 10 10

Use decimal notation for fractions with denominators 10 or 100.

Represent a fraction <1 with a denominator of 10 as a decimal number. For example, 2 = 0.2. Locate 0.2 on a number line diagram.

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

Compare two visual representations of decimals to tenths by reasoning about their size.

Recognize that comparisons are valid only when the two decimals refer to the same whole.

Use the four operations with whole numbers to solve problems.

Operations & Algebraic Thinking: Use the four operations with whole numbers to solve problems.

Interpret a multiplication equation as a comparison, e.g., interpret 35=5×7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Interpret a multiplication equation (with a product up to at least 15) as a comparison, e.g., interpret 12 = 3 x 4 as a statement that 12 is 3 times as many and 4 and 4 times as many as 3.

Match verbal statements of multiplicative comparisons to multiplication equations and models.

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Multiply or divide to solve one-step word problems involving multiplicative comparison for products up to at least 25.

Examples: If it takes you 3 minutes to drink your milk and takes your friend 2 times as long, how long does it take your friend to drink their milk?

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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.

Solve one- and two-step addition and subtraction problems within 100 with whole numbers and having whole-number answers.

Solve one-step multiplication and division problems within 25 with whole numbers and having whole number answers.

Gain familiarity with factors and multiples.

Operations & Algebraic Thinking: Gain familiarity with factors and multiples.

Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Find all factor pairs for a whole number in the range 1-12. Recognize that a whole number is a multiple of each of its factors.

Determine whether a number in the range 1-12 is a multiple of a given one-digit number.

Generate and analyze patterns.

Operations & Algebraic Thinking: Generate and analyze patterns.

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

Use an arithmetic pattern to predict what terms are next in the sequence.

For example, in the pattern 4, 8, 12, 16, generate the next terns 20 and 24.

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